AFTER all the Application of ſo many Men in all Times and Countries to Agriculture, one would ſcarce have thought there was yet left ſo notable and ſo very obvious an Improvement of it as that I am a going to propoſe.Idea of ſloping Walls for Fruit. It conſiſts in building Walls for Fruits, Grapes &c, not in a perpendicular Situation, as is commonly done, but ſo ſloping, thô otherwiſe ſtraight and plane, as to receive the Beams of the Sun, not only for a longer time, but alſo with a much fuller and better Expoſition.

It will appear that this way of building Fruit-Walls will be very advantagious, if we compare perpendicular Walls in ſeveral Countries and Expoſitions with one another, and with ſloping Walls: examining withal ſome of their moſt conſiderable Proprieties.

South-Walls are commonly reckoned to be the beſt for Fruits.Defects of perpendicular South-walls. But in theſe Climates, and much more in hotter Countries, when the Days are ſomething long, and the Heat of the Summer is in its greateſt ſtrength, it is late before the Sun ſhines upon them, and the Sun leaves them as early in the Afternoon. When it is about Mid-day the Sun is ſo high, that it ſhines but faintly and very ſloping upon them; which makes the Heat to be much the leſs; both becauſe a ſmall quantity of Rays falls then upon theſe Walls; and becauſe that very quantity acts with a kind of glancing; and not with full force. Before or after Noon the Rays come yet upon our ordinary South-walls with more obliquity.Perpendicular South-walls, Eaſt-walls, and Weſt-walls compared together.

In the North part of France Eaſt Walls are looked upon as almoſt of the ſame goodneſs for Fruit as South-walls: which proceeds more from the Defect I have noted in South-walls, than from any particular Excellency in thoſe facing the Eaſt. And accordingly South-walls are here, and in all other cold Climates, much the beſt of the two. Weſt-walls in France, as well as here, are but indifferent, thô they have the like Expoſition to the Sun as Eaſt-walls. I take the reaſon of this difference between Eaſt-walls and Weſt-walls to be partly becauſe in the Morning the Air is purer, and that the Sun ſhines oftener and ſtronger than in the Afternoon; and meets with the Dew while it is yet freſh upon Plants, whoſe motion it revives after a long reſt, and as it were a refreſhing Sleep. But the chief cauſe of it muſt be attributed to the coldneſs of the Air in the Morning, that checks the Vegetation, till the preſence of the Sun revives it; which it dos much ſooner and much more effectually on the Eaſt-wall than on the Weſterly. In the Afternoon the Heat of the Air is great every where; and Heat alone, without any Sun-ſhine, is able to make Plants vegetate, thô not ſo perfectly. Which, if it were not ſufficiently known, might be eaſily evinced from what is obſerved in Summer in the Fields, when the Sun happens not to be ſeen for ſome Weeks together. I ſaid that the Sun ſhines ſtronger in the Morning than in the Afternoon, thô it be hotter in the Afternoon than in the Morning. But this is not becauſe the Sun in the Afternoon ſhines with more force; but becauſe it continues to act upon an Air already warmed with the impreſſion of the Morning Sun. In order to be ſatisfied in it, one may, when the Days are long, compare nicely the Effects of a burning Speculum at 5, 6 and 7 a Clock in the Morning, with its Effects at 7, 6 and 5 in the Afternoon. For the like reaſon it is much warmer a Month or two after than a Month or two before the Summer Solſtice; thô we cannot but ſuppoſe the Sun to ſhine ſenſibly with the ſame force at equal diſtances from the Tropick.

Conceive a perpendicular Wall with Trees againſt it.Perpendicular Walls compared with Sloping Walls. It is evident that it is expoſed only to one half of the viſible Sky. And the point to which it is directly expoſed falls upon the Horizon. To which point ſhould we ſuppoſe the Sun to be ſomething near, one half of the time it would be under the Horizon, and the other half it would ſhine but weakly thrô ſo great a depth of Air.

But if we ſuppoſe the ſaid Wall remaining on the ſame place to be inclined, with the Trees againſt it, ſo as to become elevated only 45 Degrees upon the Horizon, and to have the Trees on its upper ſide; the Wall in that ſituation will be expoſed to three quarters of the viſible Sky: and the point to which it is directly expoſed will be 45 Degrees high. To all the Neigbourhood of which place if the Sun happens to come, it muſt needs act from thence upon the Wall with a conſiderable force. And ſo far the advantage of ſloping Walls is already plain and obvious, without any Calculation.

Now if we proceed farther, and bring the matter to a Calculation, according to ſome Principles, which ſhall be explained in a proper place, and which moſt Mathematicians will admit of; we ſhall not only ſay that there is a great advantage in ſloping Walls; but we may alſo ſhew in Numbers, ſometimes exactly, ſometimes by a near Computation, the Increaſe of Heat we ſhall have, by uſing them rather than perpendicular Walls.

Thus,The ſame done in a particular Example for the Equinox; for Inſtance, if in the Latitude of 52½ Degrees, which is more Northerly by one Degree than London, a South-wall, very ſmooth and even, be ſo leaning as to have its Plane paſſing thrô the Pole of the World; which ſloping for many Fruits is not altogether the beſt that might be aſſigned; the Action of the Sun upon it in an Equinoctial Day will be to the Action of the Sun in the ſame Day upon an ordinary upright South-wall (ſuppoſing it alſo to be ſmooth and even) as 100 to 63. And theſe Numbers we can eaſily continue with exactneſs to many more places at pleaſure. So then here the Heat of the Sun is increaſed ſomething more than in the proportion of 3 to 2 (not to ſay of 11 to 7) above what it is in the perpendicular Wall; which is very conſiderable. But that Increaſe will be yet greater and greater, as the Sun comes to have a greater Northerly Declination.

For in the Summer Solſtice the Action of the Sun,and for the Summer Solſtice. upon that even and ſmooth ſloping Wall, will be increaſed ſo as to be upon one account more than 3½ times greater than the Action upon the perpendicular Wall. Beſides another very conſiderable addition of Heat, which would make that Action from 3½ to become 4½ times greater, were it not that ſomething is to be ſubſtracted from this laſt number, upon the account of the Light of the Sun not coming ſo freely thrô a greater depth of Air: which Correction has no place in the Equinoctial Day. However we may ſuppoſe the Heat, in the Summer Solſtice, to be about fourfold what it would have been upon the perpendicular Wall.

This Increaſe of Heat is ſo extraordinary,The reſult of which ſhews the great advantage of Sloping Walls. and for above two Months the Sun keeps ſo very near the Tropick, viz. within a diſtance from it of 3½ Degrees, that ſeeing what our South-walls are already able to do, I do not doubt but ſuch a Wall as this would make Grapes, and Figs, and other Fruits equal here in goodneſs to thoſe of ſome much hotter Climates.

Yet I confeſs this improvement for Fruit-Walls is not like to be ſo uſeful here as in France, What Countries they are beſt for. or thoſe other Countries where they enjoy the ſight of the Sun oftener than we uſe to do; a due regard being had every where to the natural productions of the place.A good Culture is neceſſary for them to have their full effect. Nor do I look for any excellent effect from it, unleſs the Trees or Grapes be raiſed from the beſt Kinds, and the Soil be good and deep, and the Trees and Vines be governed and cultivated by a skilful Artiſt. It is too common here to leave theſe Plants to themſelves, and in a manner without any Culture. Whereas, beſides the neceſſary care of Pruning them duly, they do not think it too much, even in Latitudes where they have not the ſame occaſion for thoſe foreign helps, to dig very frequently about them, or to do it at leaſt four or five times in a Year.

Leſt thoſe that deſire good Fruits, and are no proper Judges in an Inquiry that depends ſo much on Geometry, ſhould look upon what I have ſaid as a bare Speculation, I will make them acquainted with the following Story. By which it will appear, that as we have already our Reflexions and Calculations of our ſide, ſo we are not altogether deſtitute of Experience.

Having explained to a Perſon of Quality the preſent Invention of Sloping Walls,An Inſtance from Experience of the uſefulneſs of Sloping Walls. I received for anſwer, that upon a Sloping Wall, which I ſaw ſince, and I will deſcribe by and by, there grew ſome Years ago Grapes equal in Goodneſs to thoſe that grow in France. This Wall was nothing but a facing of Bricks laid flat (and by conſequence only two or three Inches thick) upon a natural ſlope of Earth, about ſeven or eight Foot high. It was of very many Years ſtanding, yet extreamly ſound and intire; except in ſome few places, where the Brick it ſelf was mouldered away. It had been made only becauſe (being very near and directly oppoſite to the Houſe) it was thought to be handſomer than the naked Earth. It made an Angle of about 60 Degrees with the Horizon; and was expoſed not directly to the South, but ſeveral Degrees Weſtward. The Soil is not extraordinary. The Houſe was but low, but it muſt needs ſhade that place a great part of the Day. There has been added ſince ſome pretty high Buildings to both ends of the Houſe, which Buildings by their ſhade have intirely ſpoiled the ſaid Vine, ſo that it has been pulled up. I felt the Bricks of that Slope one Day, when the Sun ſhone almoſt perpendicularly upon them, and they were exceeding hot. But thoſe Noble Perſons, to whom the Houſe belonged, thought the goodneſs of the Grapes might ariſe from the Soil; and forgetting the Expoſition, they never tryed to recover their loſs by another Sloping Wall, for which the Ground would have afforded them abundance of convenient places.

And thus we have not only a notable Experience for us;How Sloping Walls may be built with little charge: but we ſee alſo how eaſily and how cheap our Sloping Walls may be built, without any danger of their tumbling down, as our Garden-walls are apt to do. But this being a very material Point, and conſidering that moſt People may think it either very chargeable, or very impracticable, to build a Sloping Wall, let us a little inlarge upon it.

I conceive then that the facing the Slope of Terraſſe Walks, either with a Brick-wall, ſuch as I juſt now deſcribed, or elſe with a Wall twice, or at moſt three or four times as thick is the beſt, eaſieſt, and handſomeſt way of building our Inclining Walls. Whoſe name ought not therefore to miſlead one ſo far, as to make him think, that we would propoſe the building of a thick Wall ſloping and incompaſſed on both ſides with Air. The thicker Walls are propereſt when they are leſs ſloping: for ſo their ſtrength may better ſerve to keep the Terraſſes from breaking out. It is not required we ſhould lay the flat ſides of the Bricks perpendicularly to the plane of our Wall: but it will be more proper to lay them parallel to it: So that each Bed or Floor of Bricks, of which our Wall is compoſed, may be only two or three Inches thick. And thus the Joynts of the Bricks may be ſo diſpoſed as to leave no room for Plants or Inſects to come out of the Ground.

After having explained a better way,And how far the Roofs of Houſes might ſerve inſtead of Sloping Walls. 'tis hardly worth our while to obſerve that the Roofs of long and low Buildings in the Country, and even the Roofs of Houſes in great Towns, might alſo conveniently be made to ſerve for Sloping Walls; eſpecially if ſome regard were had to it in building. So, for inſtance, in the Country the Roof of a long Building might on one ſide be brought as low as the very Ground. And thus Trees and Vines, eſpecially the laſt, might be made to grow againſt the Roof, without ſpending their very ſtrength in growing up to an immoderate height. In Cities, where they uſe ſometimes to make one Roof to ſerve many Houſes of one ſide the Street, one might, between the Garret Windows, cut out in the Roof a rectangular Space, of the ſame height and breadth with the Space the Windows take up; and from within one might ſlide up to that Space a ſquare Box full of Earth, of a fit Figure and bigneſs to ſtand handſomly between the Windows. This Box being ſupported at ſome height from the Floor, one need not fear any inconveniency from the Water's dropping out: which, in caſe it ſhould do, might be received in ſome Veſſels. It is ſo eaſie to prevent the Rain from running in, between the Roof and the Box, that it is to no purpoſe to inlarge upon it. Out of theſe Boxes one might raiſe ſome excellent Trees and Vines, and ſpread them upon ſome Frames diſpoſed againſt the Roof. And this, beſides the more ſubſtantial Advantage of yielding a conſiderable quantity of Fruit, would alſo prove a delightful Ornament to that part of our Buildings, which ſeems to want it moſt. However at London the Smoak of Sea-coal is much to be feared; ſince it both takes off the ſtrength of the Sun, and dos ſettle upon Trees, where its great acrimony muſt needs be unnatural and pernicious. But I muſt give over and leave the Application of this Doctrine to every body's Induſtry.

I need not mention that, in the making our Bricks, ſome holes may be made in them to receive Pegs of Wood to ſerve as neceſſity ſhall require: unleſs you chuſe rather to uſe thoſe Frames the French call des Eſpaliers; which indeed ſeem to be much better.The Advantage of their having no Foundation. But it is worth obſerving, that ſuch Walls as theſe, having no Foundation, leave in the Earth more room for the Roots of our Trees; and are cheaper built and leſs apt to fall. If they be not made both exceeding heavy and little ſloping, I do not think that they will compreſs ſo much the Ground under them as to obſtruct the growing and ſpreading of the Roots. And thus much is ſufficient as to the manner of building our Walls.

Let us now ſee, as far as we can, how we may chuſe, in any Latitude, the propereſt Elevation for our South Wall, and for the Fruit we deſign to raiſe.

In order then to determine what Slope is beſt to give,Rule for determining the quantity of the Inclination of Sloping South-Walls. in cold and temperate Countries, to our South-wall, I look for the Sun's Meridian Altitude at leaſt ten Days, or a Fortnight, or three Weeks, &c. before the latter half of the Fruit of the Kind I deſign to have uſes to be ripe: and then I make the Complement of that Altitude, to 90 Degrees, the meaſure of the Elevation of the Wall above the Horizon. However I would not be tyed by this Rule, but that I might alter, upon the leaſt conſideration, the ſloping of the Wall by ſeveral Degrees; eſpecially if one be afraid of taking in too much Heat. And if the Sun's Declination, belonging to the Meridian Altitude found by the Rule aforeſaid, ſhould be otherwiſe, I commonly reduce it ſo (in our Northern Climates) as to make it fall in the Space, which is from the Equator to the Parallel that goes thrô the 16th or 20th Degree of North Latitude. The longer the Fruit is a growing ripe, and alſo the more diſtance of time there is between the firſt and the laſt ripe Fruit of the ſame Tree, the more Days would I allow backwards in the finding the Sun's Meridian. Altitude, and Declination: Indeavouring by this to make, for the moſt part, the ſtrongeſt Heat of all to fall ſomething before the middle of the ripening time. For the Degree of Heat, that ariſes barely from the Expoſition, is during many Days ſenſibly the ſame, and as it were at a ſtay, when it is at the greateſt. And we muſt, for the moſt part, indeavour that, when our Tree makes an end of yielding its Fruit, eſpecially if this be about the latter end of the Year, the Sun may already, by changing its Declination, have been withdrawing it ſelf ſome 5, or 10, or 15 Degrees from the Line perpendicular to our inclined Plane. Thus all the while the Fruit is growing ripe it will injoy the greateſt Heat.

But let us inquire more particularly after the Limits of the Elevations of South-walls: ſo that we may reſolve to keep them, in each Climate, within the two Extreams we ſhall find.

I ſhould not eaſily chuſe to make any where, except perhaps in extraordinary high Grounds, the South-wall more ſloping than an Elevation of about 30 or 40 Degrees upon the Horizon would make it to be. For, thô a great obliquity of the Wall would not hinder. Vegetation, but rather, for ought I know, forward it; yet, our experience in this kind being ſo very narrow I cannot know otherwiſe, than by gueſs, how the Elevations of only 10 or 20 Degrees upon the Horizon would agree with Plants. However ſuch ſmall Elevations are not fit for South-walls, in theſe Countries.Of Sloping-Walls in very hot Countries. But, if there were any uſe for our South-walls in the Torrid Zone, as there may poſſibly be for thoſe Fruits, which, being peculiar to that Climate, require alſo a great deal of Sunſhine to bring them to perfection, eſpecially in the higher Situations, upon ſome Hills or ſome Mountains, I ſhould even there chuſe not to give theſe Walls leſs than 40, or 45 Degrees Elevation: which ſloping would perhaps give but too much Heat. For there is ſome reaſon to doubt whether it would not ſcorch any Plant whatſoever, that is ſet, in theſe hot Countries, againſt a Wall very much inclined. So I ſhould leave the moſt ſloping South-walls for the Climates that have about 40, or 45 Degrees Latitude: and not uſe them there neither, but upon Mountains, or for the Plants of hotter Countries. In Iſeland, which is placed under the Polar Circle, the inclined South-walls muſt make an Angle of more than 46 Degrees, and leſs than 66½ Degrees with the Horizon. Generally, in all the temperate Zone, I ſhould limit the Elevation of the South-wall between 30 and 66 Degrees. Theſe ſeveral Conſiderations muſt be duly weighed together, as well as the tenderneſs of your Plants, in order to chuſe a properer Elevation. But a ſmall errour in this is not of great conſequence, if you intend to raiſe all the Heat poſſible. For you can indeed erre conſiderably but one way, to wit,A Table giving the Limits of the Elevation of South Walls in Temperate Countreys. in procuring too much Heat. If you do not fear to exceed in this, you may follow the Numbers of this Table; where the firſt Column gives the Latitude or Elevation of the Pole; Latitude. Deg. Greateſt Elevation of the South Wall. Deg. Leaſt Elevation of the South Wall. Deg. Leaſt Elevation corrected. Deg. Middle Elevation. Deg. 40 40 20 30 35 50 50 30 35 42½ 60 60 40 40 50 70 70 50 50 60 I II III IV V The ſecond Column gives the greateſt, and the third Column the leaſt Elevation of the South Wall upon the Horizon. The fourth Column gives the ſame leaſt Elevation, with ſome Corrections, that are not made in order to increaſe the Heat, but, at the expenſe of ſome Heat, to give (in ſmaller Latitudes) more Elevation to the Wall. The fifth Column gives only the middle Numbers between thoſe of the ſecond and fourth; never differing from them one way or another more than 10 Degrees. The Table was made from this Rule, That the Elevation of the South Wall, in temperate Countries, ought, in order to make the moſt of the Sun's Heat, neither to be more than the Height of the Pole, nor leſs than the Height of the Pole wanting 20 Degrees.

So then the ſecond and fourth Column may pretty well ſerve, eſpecially in great Latitudes, for Limits of the Elevations of our warmeſt South Walls.It is difficult to determine thoſe Limits in very hot Countries. But the Elevations, for hotteſt Countries, cannot be ſo well determined, till Experience has taught what may and what may not be done there. In thoſe hot Climates the Rule I gave juſt now is of little or no uſe. For it ſuppoſes that Fruits are ripe by the end of October, or long before. But in the Torrid Zone we may have Fruits all the Year round. In great Latitudes the Sun in Autumn and Winter ſhines ſeldom, and always thrô a great depth of Air; which inclines one to neglect that inſignificant Sun-ſhine, and to make the moſt of the Sun-ſhine in the Spring and Summer; by keeping the South Walls, as our Rule does, rather more ſloping than they needed have been otherwiſe. But pretty near the Equator the Sun comes every Day to a conſiderable Height. And that invites one not to neglect the Sun-ſhine ſo much during Autumn and Winter, and by conſequence to make there the Walls rather leſs ſloping. Which the ſcorching Heat requiring alſo, all theſe Reaſons ſeem to prove that the South Walls muſt again grow rather more upright, as one comes nearer the Equator. For let it ever be remembred to conſider whether the Climate, the height of the Situation, the Soil, the Expoſition, the Nature of your Plants, and the Seaſon of their growing be ſuch as to permit you to give your Sloping Walls the moſt Heat you can procure.

As to the Uſe of the Table,The Uſe of the Table. the Fruits that ripen in Autumn, and very late in the Year, require the greateſt Elevations; thoſe that ripen in June, or July the leaſt. Such as grow ripe in May will have almoſt the leaſt Elevations: and ſuch as grow ripe in April, Auguſt, and September, require ſome middling ones. But if any Fruit, ſuch as Peaſe &c, are to grow ripe in March, they require again the greateſt Elevations. Now all this is ſaid upon ſuppoſition that you are in no fear of procuring too much Heat. And this is what we can at preſent determine about the Limits of the Elevations of South Walls.

Before we proceed farther,Vines are commonly planted upon a riſing Ground well expoſed. ſhould not we relate, as an Experiment favouring our Inclined Walls, that where Vines do grow in the open Air, they chuſe to Plant them not upon a flat, but upon a riſing Ground, expoſed to the Eaſt, or South-Eaſt, or South? Which ſloping of the Ground, conſonant to the Theory I have been propoſing, is found by Experience to be of an extraordinary Advantage. And to this muſt alſo be referred what Monſieur La Quintinye has writ concerning the Expoſition and Declivity of the Ground for great Gardens. But, if after all there ſhould be left ſome Scruples in the Reader's Mind, let him either examine the Demonſtrations I ſhall give in this Diſcourſe, or cauſe ſome proper Judge to tell him how far he may rely upon them.

Having then no reaſon to think, but that our Theory will be found agreeable to Nature, we may ſee farther how it can be brought to an extended and eaſie Practice.

If any body therefore is deſirous, particularly in a Country not expoſed to ſome returns of Froſt in the Spring,A Hill well expoſed cut into Terraſſes with Sloping Walls for Fruit. and to blaſting Winds, to raiſe a pretty deal of good Fruit, either for his own uſe or for the Market, I would adviſe him, both as the beſt and the leaſt chargeable, to chuſe, in a very good Soil, eſpecially in the ſide of a narrow Vale, a convenient Hill or Riſing, with a pretty ſtrong Aſcent, and expoſed to the South South Eaſt, or to the South and by Eaſt, or to the South, or to the South and by Weſt, or at leaſt not far from theſe Expoſitions: and to diſpoſe his Ground by Terraſſes, one above another, ſo that, in the Latitude of London, the ſloping of the Terraſſes be elevated upon the Horizon, for the South Wall, neither leſs than 36, nor more than 52 Degrees.Fig. I. See the Figure I, where the Section of thoſe Terraſſes is repreſented, in two ſeveral Places, to the Eye. And here you may take notice that, if the Ground be not very ſteep, the leſs the Sloping Wall is elevated upon the Horizon, the leſs Room, all things being alike, each Terraſſe will take, and the leſs charge will be required. In the making of theſe Terraſſes a ſufficient quantity of the good Earth muſt be carefully gathered along the Ridge of each Walk, there to receive and nouriſh the Roots of our Trees. Neither is it neceſſary to be very curious in keeping your Terraſſes, or Sloping Grounds, ſtraight and parallel. But you may follow the winding of the Hill, provided it keeps within the extent of good Expoſitions: and take every where ſo much breadth as dos moſt conveniently give your Terraſſes the Height you require. Thus the Expence will not be conſiderable; and even the plain Countrey Man may not think it above his power; eſpecially if he dos his Work by parts, and in ſeveral Years. And I am much miſtaken, if even thoſe irregular Terraſſes do not prove very pleaſant and entertaining to the Eye.Something like this done in China, but for another reaſon. A late ingenious Account of China, tells us how agreeable the proſpects of their Hills are, which the Country Men divide into ſeveral Levels, parted by a Sloping Ground between. All this trouble is taken, in that induſtrious Country, in order to keep the Rain from running off their Fields. But here we ſhall have probably more occaſion to think how we may not be troubled with too much Water; and how that of the upper Terraſſes may be prevented from falling into the lower ones: which being always eaſie to be done, and the Remedy depending, in a great meaſure, upon the Extent of the Ground, I muſt here forbear any farther Diſcourſe.

Thus have I brought our Theory to ſome conſiſtence, and ſhewn how it might eaſily be reduced to Practice.Fig. I. But while the firſt Figure is under our Eyes,A conſiderable Declivity to the South in a large Garden may be turned to much advantage. I cannot but obſerve, that inſtead of looking with others upon a great Declivity towards the South as a conſiderable inconveniency in the Ground for a great Garden, I ſhould rather admire it, for the multitude of Sloping Walls, well expoſed, it would afford from place to place; beſides the pleaſantneſs of many Walls breaſt high, and of a good proſpect abroad. And as to the ſhade for Walks, one might have it at the top of all from ſome rows of Trees.

I will here add ſome Reflexions, I chuſe among a great many, by which we may farther compare Inclined Walls with perpendicular ones. For I ſhould ſwell this to an unreaſonable Bulk, ſhould I ſpeak of all the Calculations I have made relating to this matter.A perpendicular Wall in no Countrey ſo hot as a Sloping Wall proper to the Place and Expoſition. I ſhall only then obſerve that, from the Equator to the very Pole, that is in the whole Terreſtrial Globe, I find not one Place, and not one Expoſition whatſoever, in which a perpendicular Wall is ſo hot as a Wall ſloping to a proper Degree for the Expoſition.The North Expoſition is made tolerable by a Sloping Wall. And, whereas the North Expoſition is utterly naught, in our ordinary manner of building perpendicular Walls, if in the Latitude of 51½ Degrees a North Wall be elevated only 38½ Degrees upon the Horizon, it will injoy the Sun, thô much ſloping, for every Minute it can ſhine in the whole half Year, from the Spring Equinox to the Autumn Equinox. But during the two Months and three Days about the Summer Solſtice it will injoy the Sun with an Elevation, or Inclination, ever greater than of 20 Degrees: which gives more than the ninth part of the full Action of the Sun. And for ought I ſee that may be near as much as our ordinary South Walls do then receive. This might ſerve for the Summer Fruits that are ripe about the end of July, and for raiſing of Peaſe, &c. For thô one would not chuſe to build ſuch a Wall without ſome neceſſity, or ſome other conſiderable advantage, yet having it at hand one would not leave it without uſe. The North Expoſition dos mend very faſt as the Countrey lies more Southerly: And above all others it dos require, in temperate Countries on this ſide the Equator, Walls with a very ſmall Elevation, ſuch as 25, or 30, or 35 Degrees. So then we find that even the very worſt of perpendicular Walls may become tolerably good, if they be made ſloping.

It will appear, by the ſequel of this Diſcourſe, how many Advantages, beſides the bare Increaſe of Heat, do follow our building of Sloping Walls: But one of them lies already too obvious not to be ſpoken of here.

I ſay then that this Contrivance ſeems to be of an extraordinary conſequence, Ʋſe of Sloping Walls for having Fruits, Melons &c, early and thoroughly ripe. for the raiſing of all ſorts of Fruits ſomething earlier than we uſe to have them, and for their perfect ripening: And that it may prevent ſome of thoſe, that are fond of Fruits, from falling into the Diſeaſes that uſually follow the eating Fruit not thoroughly ripe. I expect from theſe Walls ſuch Melons, and Figs, and Grapes, as, I think, have never been ſeen in this Country. I forbear ſpeaking of other Fruits; but ſhall only ſay that, if we had once ſome excellent Kinds of Trees raiſed by this Method, we might not need to ſend for new Graffs again to France. And if, the Summer being extraordinary wet and cloudy, our Sloping South Wall ſhould bring forth but indifferent Fruits, yet even then thoſe Fruits will be more tolerable than ſuch as we gather from our ordinary Walls. But all this will become more evident, when the Principles I build upon ſhall be laid down.

There is yet ſomething I have to ſay, both in reference to the propereſt matter to build our Walls withal, and to ſome other circumſtances in the manner of building.

As to the propereſt Matter for our Walls,Walls of Bricks are beſt in England. I think Brick to be much better, in this Countrey, than Stone: becauſe they grow hotter, and keep much longer the Heat. By which means they do ſtill warm the Plants a good while after the Sun is hid under a Cloud, and, in a manner, loſt to other Walls. I know nothing▪ that is more convenient than they are, or of a better Shape for our purpoſe. The biggeſt and thickeſt Bricks will be beſt: And I ſhould chuſe, as I ſaid before, to diſpoſe them ſo that they might appear by their broadeſt ſides. Thus the Wall will be cheaper, the Bricks will be apt to grow warmer, and, their Interſtices being fewer and leſs deep, there will be leſs room to take care of againſt Inſects finding a ſhelter there.Of Walls of Slate, or of any dark coloured Stone, whether natural or painted. Walls of Slate, or of any dark coloured Stone, whether natural or painted, will alſo be very good. For theſe Colours imbibe the Light, or Heat, much more than Colours that are whiter.

Our Walls ought not to have any Building raiſed from the top of them;Sloping Walls not to be clogged with any Shade, except perhaps in Winter, or when the Sun is very low. nor any other Shade caſt upon them in Vegetating time, by the Interpoſition of any thing ſtanding, on either ſide of them, between them and the Sun. But if they be deprived of the ſight of the Sun, while it is only within a few Degrees from the Horizon, the loſs is not conſiderable, and abundantly made up, if, at the ſame time, they be ſecured from Winds.

The Foundation,Sloping Walls may aſcend obliquely upon a Hill; and the uſe of making them ſo. or rather Bottom of Sloping Walls needs not be horizontal; but it may aſcend obliquely upon a Hill by ſome Degrees. Which is of ſome conveniency for the running off of the Water, and for the chuſing a South Expoſition upon a Hill that looks to the South-Eaſt, or South-Weſt, or to any other point, either between, or, at leaſt, not much above 45 Degrees diſtance from theſe places. For the moſt part of the Spring and Summer ſuch a Wall will injoy as much Sun, as if the Foundation had been horizontal; but the Ground at the Foot of it will injoy leſs. And this is what I had further to mention as to the way of building our Sloping Walls.

I have ſeen,Many Slopes in ſeveral Gardens are ready made, and fit for Sloping Walls. in many Gardens, and other places, ſome Slopes of Earth ready made, and fit every way for Trees to grow againſt them, if they had been but faced with Bricks. But they lay neglected, perhaps becauſe the good Uſe that might be made of them was unknown.

If any were apt yet to think that there can be no great difference between two South Walls,The goodneſs of a Wall proved owing in a great meaſure to the Expoſition. of which the one receives the Light of the Sun much fuller and longer than the other; let them conſider that, upon the very ſame Soil, the South-ſide of a Wall is as good for Fruit as the North-ſide is bad. That the Eaſt-ſide of another Wall is very good, at leaſt in France, and the Weſt-ſide but indifferent. Which diverſity can certainly be attributed to nothing but the Expoſition; and makes it more than probable that by ſo much as this is mended, by ſo much Fruits ought to be more perfect.

I have given to this Theory ſome of the Commendations it juſtly deſerves,The Author's Deſign in commending this Theory. knowing how hard a matter it is to perſuade People to go out of their ordinary way: And I wiſh I may have ſaid enough to bring it into common Practice. I hope this is not out of any vain Oſtentation, ſince I chuſe to publiſh here what I know to be much inferiour to ſome Meditations of another Kind, I have had theſe many Years by me. And thus much I beg leave to ſay; leſt a thing that might be uſeful ſhould be neglected and thrown by, before it be underſtood.

If the vegetation of Plants did only depend upon the Sun-ſhine coming freely to them, there would be but little occaſion left for any farther Improvement.The Advantage for Vegetation of a cloſe and warm Air; and of ſmall and narrow Gardens. But it is well known that a warm and pretty cloſe Air, well ſheltered from Winds, thô not ſo much expoſed to the Sun, in a word, ſuch an Air as is found in the Gardens at Paris, and other great Cities where they do not burn Sea Coal, dos often bring forth better Fruit than will be found in other places, in the Neighbourhood, thô better expoſed. However, at the ſame time that we get wholly the advantage of Sloping Walls, we may alſo keep all others, and ſecure thoſe Walls from cold and dangerous Winds. This makes me recommend Gardens of but an indifferent bigneſs, with high Walls to them: being willing to purchaſe a cloſe Air with ſome little loſs of Sunſhine. But if the Gardens be very narrow, as I ſhould for the moſt part chuſe, the Walls may be leſs high. The breadth of your Gardens ought not be the ſame in all Expoſitions. And it is of great conſequence that the length of very narrow Gardens be from Eaſt to Weſt, and not from North to South. In diſpoſing thus the length of the Garden, the Wall may be from 8 or 10, to 15 Foot, or a little more, in the Slope: the breadth of the Garden, or Earth, between the Walls, from 11 or 12, to 50 or 100 Foot: and the length as great as you pleaſe. But the ſmalleſt Breadths are beſt: And thoſe, as I ſaid, do not ſo much require high Walls: and by conſequence will not be ſo chargeable. In Gardens that run from North to South, a very ſmall Breadth will be as prejudicial as it is good in Gardens that run from Eaſt to Weſt. For it is eaſie to ſee that, in theſe laſt, the Shade of the long Walls upon each other is but little, in vegetating time; and falls either upon the ſhorteſt Days, or upon ſuch Moments as the Sun is but low and weak. But, in Gardens that run from North to South, and are of the ſame breadth with the former, the Shade is more conſiderable. And I find that ſuch Gardens, having an Eaſt Wall and a Weſt Wall, each with an Elevation of 30 Degrees, and each of 7 Foot in perpendicular Height, muſt be 68 Foot wide, from Wall to Wall, if you will that neither Wall ſhould take from the other the ſight of the Sun, but when it is leſs than 5 Degrees high.

Leſt any one ſhould wonder at this extraordinary narrowneſs, which dos often turn what we called a Garden into a narrow Walk, I will ſhew that I do not chuſe it without ſecuring that great advantage of a warm and cloſe Air: In order to which I give here the Section of a Walk, or narrow Garden for Trees, whoſe length runs Eaſt and Weſt.Fig. II, III. Let the South Wall AB have a proper Elevation for your Climate,How to make ſome Terraſſes running from Eaſt to Weſt, ſo that the Air between be extreamly warm; and for the Fruits you deſign to have; ſuppoſe at London an Elevation of 45 Degrees. That Elevation is good for thoſe Trees, whoſe lateſt Fruits are ripe near the 20th of September, when the Sun is about 3 or 4 Degrees South Declination: at which time the Sun is already withdrawn about 10 Degrees from the perpendicular to the Wall AB. Let the perpendicular Height BC of your Wall be for Inſtance, of 7 or 10 Foot; which will give 9⌊9, or 14⌊1 Foot in the Slope AB, and 7 or 10 Foot in the horizontal Line AC. Let the Line AD be in the Plane of the Equator: and it will make here at London an Angle of 38½ Degrees with the horizontal Line AE. Make the Breadth of your Walk the narroweſt you can. Allow, for Inſtance, four Foot to the Ground that is to receive the Trees, and to be now and then cultivated: three Foot to the Walk or Path; which ought, of right, to be dug up every Winter: four Foot more to another Line of cultivated Ground. So you will have 11 Foot for the whole Breadth of your Walk AE. Draw from the top B of your Sloping Wall an horizontal Line BDG. Draw alſo the Sloping Line EG, repreſenting your North Wall, and make it, if you pleaſe, parallel to the Plane of the Equator; or rather, if you think fit, make it yet more inclined to the Horizon, I mean more approaching to it, by ſome 10 Degrees. Make the tops of your Terraſſes GH, BI, of what Breadth you pleaſe; ſuppoſe of 1, 2, or 3 Foot. But they muſt be broader if you intend them for Walks. Draw the new Slopes HK, IL, either parallel to BA, GE, or elſe with what alteration you think convenient. And ſo you have two Terraſſes; to which you may, upon the ſame Level, and at convenient Diſtances, add as many more as you pleaſe. Now it is evident that the Heat of the Sun, being at the ſame time reflected, in the Spring and Summer, by both the Walls, will warm extreamly the Air ABGE; and, in all probability, give a much cloſer Heat than is in great Cities: eſpecially if, to break the Winds, you have, from diſtance to diſtance, another Teraſſe running from North to South,and that they be not expoſed to Winds. between thoſe I have deſcribed. Theſe Terraſſes have a double advantage againſt Winds, in that they receive them more ſloping, and alſo reflect them upwards: So that the firſt Terraſſes are a pretty good Shelter to defend the following ones. If the Ground be falling or hanging towards the South, the top GH might be kept lower than the top BI; or the contrary done if the falling be to the North and but little. For I would chuſe, except in hot Countries, to avoid any other North Expoſition.

In caſe you ſhould deſire to make your Walls higher, you might, for inſtance, increaſe by a quarter the Lines in each of the Figures; or elſe increaſe them in any other ſuch proportion; and keep the ſame Inclinations as before. So you might make AB of 13⌊2 Foot, and AE of 14⌊7 Foot; or elſe AB of 18⌊8 Foot, and AE of 14⌊7 or 20 Foot. Only the cultivated Ground needs not exceed 5 or 6 Foot; and the Path may be accordingly increaſed as it lights.

On the other hand,Terraſſes to be made higher when they are far aſunder. in caſe your Walk be made a pretty deal wider, it would, at the ſame time, be proper that your Sloping Walls ſhould be made higher, thô in a leſs proportion than the Walk is increaſed. And this is in order to procure more cloſeneſs to your Air, and to have both more Sun-ſhine and a better Shelter againſt Winds. So, for inſtance, if you make your Walk four times as broad as it was ſuppoſed in the ſecond and third Figures, and your Wall higher only in the proportion of 4 to 3 than it was already, the Foot of your Wall would not, after that change, loſe half the Sun-ſhine it ſhould have loſt before. And the Sun, of which it would be deprived, being ever very low and oblique, it would yet amount to much leſs as to the loſs of Heat: Eſpecially almoſt all that loſs falling upon the ſhorteſt Days, and coming to nothing near the Equinox.

But thoſe extraordinary Banks would perhaps be more chargeable,Roofs may be uſed inſtead of Terraſſes. as they would alſo be more laſting, than two bare Roofs, like thoſe of Houſes, and ſupporting, inſtead of Tiles, a Brick Wall. Which Roofs would alſo yield under them a Space that might be turned to ſome uſe. The greater thoſe Banks or Roofs are, the greater is the quantity of Rain brought to the Foot of them; and the cloſer and ſtronger is the Heat. Unleſs, for the conveniency of a Garden between,Of Plants of hotter Countries. you ſhould remove them farther aſunder. Such a Walk as I have deſcribed would alſo be good for raiſing in it thoſe rare foreign and Medicinal Plants, that require more Heat than the Climate dos give.Of Orange Trees. And I don't doubt but Orange Trees may grow there in the nature of Standards, provided, in Winter, the place be ſecured from Cold: which is not impracticable. However we have what we aimed at, the cloſeneſs of Air, and Walls pretty well ſecured againſt dangerous Winds.

I cannot here diſſemble ſome faults of our Sloping Walls.Of ſome Objections againſt Sloping Walls. For, as they have ſeveral very great advantages, ſo on the other hand there is in them ſome inconveniencies, which I could heartily wiſh were otherwiſe. However theſe laſt are not at all able to ballance the former; as will eaſily appear to any one that reads impartially this whole Diſcourſe.

Let me firſt mention one very conſiderable Objection,Sloping South Walls expoſed to the miſchiefs of latter Froſts, unleſs prevented. againſt our Sloping South Walls, in thoſe cold Countries, where the paſſage, from cold to fair Weather, is not, as in Denmark, quick and certain; but the Air is ſubject, as here, to ſome returns of Froſt, after it has been fair for a good while. And that is, that the Heat of theſe Walls will probably make the Bloſſoms of ſome Trees to come out too ſoon, and expoſe them to an evident danger of being ſpoiled by the latter Froſts. To this Objection I have little to ſay, but that it dos already grant a great deal in favour of our Walls: and that we may take our chance, as others do; there being but a few Days more of danger, for our South Walls, than for thoſe of other people; whoſe Bloſſoms are like enough to be ſpoiled when ours are. Let us alſo remember that, in thoſe Climates, a kindly and natural forwardneſs, together with a perfect maturity, owing not to our artificial Fires, but to the light of the Sun, is hardly to be had, but at the rate of running that hazard. Let us then, as I ſaid, try our Fortune; and in the mean while uſe,Of Remedies againſt an early Vegetation and Winds. if we think fit, all the Remedies Agriculture dos afford, to keep back this early Vegetation, and to prevent the miſchiefs of Froſt: for which I refer you to the proper Authors. See La Quintinye. However here is an eaſie Remedy we may uſe, not only againſt this too great forwardneſs, but alſo againſt Winds.

Suppoſe we make but few parallel Terraſſes, all of them running from Eaſt to Weſt, for inſtance, but two, or four, &c. Let, in the II Figure, AB repreſent the South Wall of the Northermoſt Terraſſe,Fig. II. and EG the North Wall of the Southermoſt Terraſſe. Prolong upwards, indefinitly, the Lines AB, EG, in M and N; and prolong alſo the Horizontal Line EA Northwards in O, and Southwards in P. You may fill all the Angle MAO with Trees, and very tall and thick Hedges &c, without any injury to the South Wall AB, and the Angle NEP, without any injury to the North Wall GE. And yet both the Walls AB and EG will, for ſix Months together, enjoy the Sun-ſhine, for twelve Hours or more. Now this Remedy is better againſt Winds, and againſt the forwardneſs of bloſſoming, than againſt the forwardneſs of Fruits; and, by conſequence, is ſo much more to be valued. Thus ſeveral Ridings might be made in a large Foreſt; provided the Ground were not already worn out; or that it were put in heart again.

Another Objection againſt our Sloping Walls,Sloping Walls are expoſed to one ſort of white Froſts. is, that in the Spring, in ſome cold Mornings, the Dew may ſometimes fall, in great plenty, upon the Bloſſoms, and there freeze, as it falls; which might endanger them, and blaſt all our hopes. I confeſs, I do not know how far this miſchief is to be feared. But this I may ſay, that, in the coldeſt part of the Spring, the Sun ſhines upon our Terraſſes, from the time it begins to be ſome few degrees high; and, by conſequence, ſoon after the Dew is fallen. So that there will be no time, at leaſt in fair Weather, without which we have commonly no Dews, for much harm to be done: Eſpecially the Vapours, or Steams, that ariſe from the Ground, being more like to diſperſe in the Air, than to condenſe againſt our Trees; as I ſhall explain hereafter. However this inconveniency being already too much felt in ordinary Gardens, the Remedies againſt it are found, and well known; at leaſt by ſuch as raiſe ſome early and tender Plants, at the latter end of Winter.

Our Walls are alſo more expoſed to Storms,They are much expoſed to Hail. and Hail, than ordinary Walls. Yet this ought not to deter us. For we ſhall not have this accident every Year, at ſuch times, when we may fear it. And, if we ſhould have it, yet it is to be ſuppoſed that many of our Fruits will eſcape being ſpoiled. Neither is it impoſſible to cover ſuch Trees, as are moſt precious, when there is any proſpect of a Storm.

I expect ſome will object alſo,Of the Trees growing obliquely to the Ground. that, the natural poſture of Trees being to grow upright, their leaning againſt a Bank will be like to diſagree with their Vegetation. But this Objection has not that ſtrength in it, which is in the former; and might well have paſſed under ſilence. For it is a common thing, in our Gardens, to force Trees into a Figure not at all natural to them. And even Trees, that grow in the open Air, have ſome of their Branches bending downwards; and moſt of them in a manner parallel to the Horizon. It was ordered wiſely, for the beauty and ſtability of Trees, but not for their fruitfulneſs, that they ſhould naturally grow upright. Now theſe firſt conſiderations ceaſing, in an Inclined Wall, I do not doubt but that, as to the production of Fruit, Vegetation will have there its ordinary courſe.Of the dampneſs that may be objected againſt Sloping Walls.

It has been twice objected to me that the dampneſs of the Ground would probably ſpoil the Fruits growing againſt our Sloping Walls. Which makes me take notice of this Objection, for otherwiſe I ſhould have neglected to give it an anſwer. I ſay then that either this inconvenience is not at all to be feared; or, if it be, that the Remedies are obvious and eaſie. I do not fear it in ſuch Terraſſes as thoſe of the II, III, and XIth Figures; eſpecially when they are well expoſed. For I cannot ſee what mighty ſtore of Dampneſs can come, or be kept there; ſince water naturally runs off of ſuch heaps. But as to the lower Terraſſes of the firſt Figure, if one or two beds of Bricks be not enough, at leaſt three or four ſuch Beds, and what elſe one pleaſes underneath, will be ſufficient to make the Wall remain dry at the outſide. Moreover it is not neceſſary that the Fruit ſhould touch the very Wall. But in caſe it ſhould grow too cloſe againſt it, a thin Slate, or a ſmall Ring, of any proper matter and ſhape, will eaſily keep it from the Terraſſe. After all I think Experience, to which I muſt appeal, will add no ſtrength to this Objection.

Some have urged,Of their being expoſed to Mice and Ants, &c. againſt our Walls, that our Fruit will be eaten up by Mice, or by Ants, &c. Thô I might ſay that all other Trees are expoſed to this very miſchief; for 'tis known that thoſe Mice and Ants can eaſily creep upon them, yet to this, and all other Objections, I will give but one general Anſwer.Of all other Objections againſt them. I ask whether the inconvenience that is objected be real, neceſſary, general, and unavoidable? or elſe whether it be not, in a great meaſure, imaginary? I ask whether there be no Remedy left againſt it to our Care and Induſtry? I ask, when all is granted to the Objection that can be given it, whether there will be nothing at all left for us, but Trees without Fruit? 'Tis true that I ought by ſo much more to fear the reſort of Inſects to our Fruits, as they are like to prove more excellent than others are. But it is well for us that the firſt Inventers and Improvers of Arts have not at all been moved by ſuch Objections as theſe. Are they greater than ſuch as may be made againſt a Countrey-man, who would ſow his Grounds? How is he ſecured againſt the vexations of troubleſom Neighbours, againſt the Invaſions of an Enemy, the miſchiefs of Civil Wars, the unfaithfulneſs of Servants? How can he depend upon fair and ſeaſonable Weather; without too much Drought or Rain, without Hail and Storms and ſtrong Winds? May not his Seed be eaten up in the Fields; may not his increaſe be ſtolen away from him; or deſtroyed by numberleſs ſorts of Inſects? What ſhall I ſay of the miſchiefs of Fire? What of Taxes and Tithes? What of the price of Rents and Leaſes? What of ſelling one's increaſe to ſuch as will not, or cannot, pay their Debts? What of all other fears and troubles that may come upon this poor Countrey-man? Yet for all this our Fields are ploughed, we are nouriſhed, and our Barns are filled with Grain. Such is the Profuſion, with which God Almighty provides for us, that, after all deductions made, we have enough to bleſs his Munificence, and to live with plenty.

Now having, in ſome meaſure, ſatisfied the curioſity and impatience of the Reader, I may proeeed to ſhew how I calculate the proportion of Heat, I gave before, between a Perpendicular and a Sloping South Wall; and treat at large of the Principles and Method, upon which thoſe, and the like Calculations, are grounded: endeavouring to make our Doctrine as general and as exact as the Nature of the Subject will bear.

I begin with Calculating,Calculation ſhewing for an Example the proportion of Heat at the Solſtice, in the Latitude of 52½ upon a perpendicular Wall, and a ſloping ſmooth South Wall, paſſing thrô the Pole. for the Parallel that lies one Degree North of London, the proportion between the Actions of the Sun, in the Summer Solſtice, upon a Perpendicular, and upon an Inclined ſmooth Wall, with an Elevation of 52¼ Degrees; which is an Inclination very good there, for the Fruits that are ripe in the Month of October, or the latter end of September. For other Fruits that Elevation is rather of the greateſt.

The Circle PTEP deſcribed from the Center C repreſents the Celeſtial Sphere.Fig. IV. CH is the Horizon;The Ground and Method of this Calculation. P the Pole; CE the Equator; IT a Parallel to the Equator, as ſuppoſe here the Tropick of Cancer. CIP is the Plane of the Inclined Wall Ci; CM the Plane of the perpendicular Wall Cm. Upon the Circumference of the Parallel TI I ſuppoſe a right Cylindrical Surface elevated and prolonged of each ſide as far as is neceſſary: Which I do in order to find upon it the proportion of the Sun's Heat.

Now it is eaſily known that the Quantity of Rays, falling from the Sun upon any Plane, is as the Sine of the Sun's Altitude on that Plane.

And that the Force of each Ray, coming from the Sun upon a Plane, is alſo as the Sine of the Sun's Altitude on that Plane.

From whence it follows that the whole Action of the Rays, upon a Plane, is as the Square of the Sine of the Sun's Altitude on the Plane, and the time that Action laſts, joyntly: neglecting the Effects of the Atmoſphere.

Let now the whole perpendicular Force of the Sun, upon a Plane directly expoſed to it, be expreſſed by the Radius CE, which is Unity divided into 10000 parts. The Force of the Sun at the Meridian in T upon the Wall Ci, will be as the Square of the Sine TI; that is, ſuppoſing ſtill CE for Unity, as the Line TV equal to 8410 parts; which I take upon the Cylindrical Surface Northward. Now from the Vertex I, upon the Axis IP, I draw thrô the Point V the Parabola INV. And the Lines or Ordinates as TV, MN &c, drawn parallel to the Axis IP, from any Point as T or M in the Line IT, till they meet the Parabola IV, expreſs by their Lengths TV, MN the Action of the Sun in the Tropick, in T or M &c, upon the Sloping Wall Ci. The Sum of all thoſe Lines till Noon is the Cylindrical Surface ITVI, which gives the whole Heat of the Morning Sun upon the Sloping Wall Ci, ſecluding, as before, the Effects of the Atmoſphere.

Now from the Point T drawing a Parallel to the Horizon, till it meets with the Line CmM, make the Line TL oppoſite to TV equal to the Square of that Parallel; ſuppoſing ſtill Unity to be expreſſed by CE. And in our Example you will find TL equal to 2350 parts. Draw the Parabola ML, of which M is the Vertex, MT the Tangent at the Vertex, and L a Point thrô which that Parabola paſſes. The Ordinates, ſuch as TL, will give, for every correſpondent point of the Circle TM, the Action of the Sun upon the perpendicular Wall Cm. And the Cylindrical Surface MTLM will give the whole Heat of the morning Sun, upon that perpendicular Wall, excepting only the Effects of the Atmoſphere.

Make the Point M the Vertex of another Parabola, of which MT is the Tangent at the Vertex, and V a point thrô which the ſaid Parabola paſſes. It is evident that the Cylindrical Spaces MTV, MTL are to one another as TV to TL, that is as 8410 to 2350, or as 3⌊58 to 1. And that proportion obtaining for every Point in the Arc MT, it is clear the Heats ariſing from thence keep that very proportion upon the Walls; notwithſtanding any variety you may ſuppoſe in the Thickneſs and Effects of the Air, thrô which the Light is to come from different Altitudes.

But there is yet all the Heat expreſſed by the Cylindrical Surface MVI to be accounted for.

The Proportion between the Arcs TM, TI will be found, by the help of their Verſed Sines, to be as 100 to 127⌊6. And the Proportion between the very ſmall Arcs tm, ti will be found as 100 to 122½: which depends upon the Proportion of the Line TM to TI being as tm is to ti. And if upon TV you take the Point τ, which is three times farther from v than from T, and thrô that Point you conceive the Circle τμι parallel to TMI, and meeting the two Parabolas in μ and ι, you will find the Proportion, between the Arcs τμ and τι, as 100 to 124½.

So then one cannot err ſenſibly with ſuppoſing the whole Cylindrical Space MTVM to the Cylindrical Space ITVI as 100 to 125, or thereabouts; that is as 8410 to 10512; which ſtands for the Cylindrical Space ITV, ſuppoſing the Cylindrical Space MTL, MTV to be 2350 and 8410. And the Number 10512 being divided by 2350, you find the Cylindrical Space MTL to the Cylindrical Space ITV as 1 to 4⌊47. But this Number is to be ſomething diminiſht, becauſe of the different Transparency of the Air for different Altitudes. IMN is very conſiderably leſs than the 1/27 of the Cylindrical Space ITV: and it is upon IMN, and the neighbouring parts, that the greateſt Diminution of the Heat of the Sun dos fall. From whence it appears that the ſaid Diminution cannot be very great: Eſpecially, in our preſent Inquiry, not the whole Diminution of the Sun's Heat being to be accounted for; but the Diminution or Difference only from what the Heat of the Sun is, when as high as in T.

However the Number 3⌊58 being certainly too ſmall,The Reſult of it. and the Number 4⌊47 certainly too great, to expreſs the whole Heat upon the Sloping Wall, it cannot but be pretty near 4 times as great as the Heat upon the perpendicular Wall: the middle Number between thoſe being 4⌊02.

This Method, which is clear and eaſie, is ſufficiently exact for our purpoſe: and it can be eaſily transfered to other Latitudes, and to the Caſes where the Wall is more or leſs ſloping: not to mention thoſe where the Wall has indifferently any other Expoſition.

Thus if we leave the Latitude of 52½ Degrees,Other Examples to the ſame purpoſe for the Latitudes of 51½; which is about the middle of England and Holland, and make the like Calculations for the Latitude of London, LT will become 2204; TV will remain 8410. The Space MTL will be to the Space MTV as 2204 to 8410; or as 1 to 3⌊82. The Arc τμ will be 47° 38′. τι is of 60 Degrees, as it was before. Now as 47° 38′ to 60°, ſo is 8410 to 10593, which comes for the Space ITV. And dividing 10595 by 2204 the Quotient is 4⌊81; which is too great to expreſs the Heat upon the Sloping Wall, as 3⌊82 is too little. The middle Number is 4⌊31, which was only 4⌊02 before. So here the Diſproportion is conſiderably greater, between the Heat for the Sloping and the perpendicular Wall. On the Equinoctial Day the Heats are as 1000 to 614.

In the Latitude of 45 Degrees TL becomes 1344,and 45 Degrees. which gives MTL to MTV as 1 to 6⌊26. So the Heat is already 6¼ times greater for the Sloping than the Perpendicular Wall: beſides the Addition of Heat MVI, which is very conſiderable. For the whole Space ITV is about 8½ times bigger than MTL. The Middle between thoſe two Numbers is 7⅜. On the Equinoctial Day the Heat is exactly doubled. The immediate Action of the Sun upon the Walls, without any regard to the Heat reflected from the Ground, or occaſioned by the Warmth of the Air, dos not become equal for both the Perpendicular and Sloping Wall,Sloping Walls are more neceſſary in colder Countries; but the Increaſe of Heat they give is greater in warmer Climates. till the Sun has got a conſiderable South Latitude.

By this it appears that our Walls are not only good for the Climates of cold Countries, but that they will have the greateſt Effect farther from the Poles. In England and Holland, and all the North, they are almoſt neceſſary; becauſe without them Fruits can hardly be very good. In France &c, they cannot fail of producing moſt excellent Fruits, of the Kinds that require a great deal of Heat, they being able there to outdo ſo much ordinary South Walls; than which confeſſedly there is among perpendicular Walls no hotter Expoſition.

Hitherto I have not compared Sloping and Perpendicular South Walls to the beſt Advantage of the former.Sloping South Wall paſſing thrò the Pole leſs hot, in the Solſtice, than the South Wall paſſing thrô the lower point of the Polar Circle. For in our firſt Latitude of 52½ if the Sloping Wall was at Noon expoſed directly to the Sun in the Tropick, there would already be above 4¼ times the Heat from the Compariſon of the two oppoſite Parabolas. Beſides that Addition I have ſo often mentioned, which would make the Heat about 6⅙. times greater, were it not for the Interpoſition of the Atmoſphere. The middle Number is 5⅕ or thereabouts. In the Equinox the Proportion of Heats would be found as 1000 to 748. So then a little loſs of Heat near the Equinox is here very largely made up about the Solſtice. And this may invite (inſtead of giving to the South Walls the ſame Elevation, as the Pole has above the Horizon) to give them rather a ſmaller Elevation by 15 or 20 Degrees.

If you deſire a more accurate Method of comparing the Sun's Heat upon two different Walls,A more accurate Method of comparing the Sun's Heat upon two plane Walls in any Situation. This Method depends upon the Quadrature and Center of Gravity of the Line of Sines and its Segments: but with neglecting the Effects of the Air, you will have it in the Solution of the following Probleme; which depends upon the Quadrature and the Center of Gravity of the Line of Sines.

The Latitude being given, for Inſtance that of London, to find for a given Day, ſuppoſe that of the Summer Solſtice, the Heat of the Sun upon any Plane Wall whatſoever; ſuppoſe a Sloping Wall that lies, for Inſtance, North-Eaſt and North-Weſt, and has an Elevation of 48 Degrees upon the Horizon, going obliquely from the North-Eaſt Point towards he North. The great variety of Caſes, into which this Problem may be branched, obliges me thus to fix my Diſcourſe, by applying it, in a great meaſure, to a particular Example.

Conceive,Fig. V 〈 in non-Latin alphabet 〉 . in the fifth Figure, the Sphere POBD αβGAP, projected about the Center C, for an Eye placed at an infinite Diſtance, in the common Section of the Planes of the Sloping Wall, and of the Equator, or its Parallels. Let ακCNKA be the Plane of the Sloping Wall; βXCEξB the Plane of the Equator; P the Pole of the World; DEZKHζκD the Horizon; OTZNζG the Tropick or Parallel; N the common Section of its Plane, with the Plane of the Wall, whether this Section fall within or without the Sphere; Z, ζ the two Interſections of the Tropick or Parallel with the Horizon, if they meet each other. In the Triangle CKE the ſide EK being given, as here of 45 Degrees, and the Angle E being of 38½, and the Angle K of 48 Degrees, you will eaſily find the ſide EC and the Angle C. Take upon the Equator CX equal to the Complement of CE; and thrô the Point X conceive the Meridian XHPTξX. In the Rectangular Triangle EBD find BD; and ſo draw thrô the Point E the Horizon DEZKHζκD, cutting, as I ſaid, if it lights ſo, the Tropick or Parallel OG in the Points Z, ζ; and draw the Indefinite Lines ZY, ζυ perpendicular to OG. Take the Radius of the Sphere for Unity; and make OV, perpendicular to OG, equal to the Square of the Sine of the Arc OA. From the Point N as Vertex draw thrô the Point V the Parabola NYV υ, making NO to be a Tangent at the Vertex. Transfer as much of the Cylindrical Surface NVNON into the ſixth Figure,Fig. VI. (where it is opened, and the Parallel or Tropick becomes a ſtraight Line) as there is of it that is ſeen from the Wall. And thus having drawn from the Points Z, ζ duly transfered, if they be ſeen by the Sloping Wall, the Ordinates ZY. ζυ, the Space between them ZYVNZ, after it is increaſed in the proportion of the Circumference or Radius of the Tropick or Parallel to the Circumference or Radius of the Equator, will give you the meaſure of the Heat upon the Sloping Wall. But this is with neglecting the Effects of the Atmoſphere. Now that Space, or a Solid proportional to it, is found by having the Quadrature and Center of Gravity of the Line of Sines, and of its Segments; all which are already known. The Truth of this Aſſertion is obvious without any farther Demonſtration of it; and will appear to agree with the following Conſtruction, which alſo dos ſolve the Problem.

To the Circle ONG,Fig. V. Fig. V. conceive the correſpondent Line of Sines AOYBZGA Fig.Fig. VII. VII. In which the Axis AB is equal to the Semi circumference, and the other Axis OG is equal to the Diameter of the Parallel or Tropick. Thrô the Point N duly transfered upon OG, to wit, with making GN, GN equal in both Figures, draw the Parallel NNN to the Axis AB, till it meets in N, N with the Curve AOB continued for that purpoſe as far as is neceſſary. And having alſo duly trasfered the Point Z, by taking the Line NZ equal to the Arc NZ, and having drawn ZY perpendicular to NNN, and meeting with the Line of Sines AOB in Y, upon NNZ as the Edge, and ZYOANZ as Baſis, erect a Semi-quadrantal Ungula; and find its Solidity or bigneſs, by thoſe Rules Dr. Wallis has publiſht in his Mechanicks; where he has given the Quadrature and the Center of Gravity of the Line of Sines and its Segments. Then depreſs that Ungula, or make it ſmaller, in the Proportion of the Square of NO to the Square of the Sine of the Arc OA. When the Solid of this new Ungula is found, correct it again, increaſing it in the Proportion of the Circumference or Radius of the Tropick or Parallel to the Circumference or Radius of the Equator. The new reſulting Solid will be proportional to the Heat of the Sun upon the Sloping Wall, if we neglect the Effects of the Air.

After the ſame way might be found the Solid expreſſing the Heat MTMLM of the IV.Fig. IV. Figure, upon a perpendicular South Wall; for the Solution is general.and is general:

But if the Cylindrical Surface MTMLM be alſo duly transfered into the VI.and in ſome few Caſes Fig. VI. Figure, as you ſee it done;capable of a very eaſie Approximation; and upon the Baſis MTM, when it falls intire between the Points N, N, you draw the Curve Line MAM, whoſe Ordinates upon MM are every where proportional to the correſpondent Ordinates of the Curve MLM, and whoſe ſwelling comes juſt to touch the Curve NVN, the Heats expreſſed by the Surfaces MLMM,notwithſtanding the Effects of the Air. MAMM will be as TL to TA, notwithſtanding the Effects of the Air. Which conſideration may be of ſome Uſe, where the begneſs of the remaining part is but ſmall, and to be gueſſed at, as we did heretofore, by ſome eaſie Approximation. But this by the by.

This Solution gives,A Corollary for finding the Heat of the Sun upon a Plane, parallel to the Horizon. as a Corollary, the Method of meaſuring the Heat of the Sun upon the Horizon, any Day in the Year, for any propoſed Climate; thô it remains yet to account for the Diminution of Heat ariſing from the Atmoſphere.

I do not expect that the whole crowd of Geometers will ſee that our Conſtructions carry with themſelves the Strength and Evidence of a Demonſtration. But this Diſcourſe being intended to be, in a great meaſure, popular, I am loth to fill it with a long Digreſſion, only to make our Proofs evident to a greater number of Mathematicians. Let it be enough that ſome of them may perceive that we have advanced here nothing but what is exactly true.A Table ſhewing the Sun's Heat upon a Plane for each Degree of the Sun's Elevation upon it.

Having calculated a Table of the Sun's Heat upon a Plane, for each Degree of the Sun's Elevation upon the ſaid Plane, I thought it might be acceptable to ſome if I tranſcribed it here. In this Table the Heats to an Elevation and to its Complement make always the ſame Sum: Which depends upon the Squares of the Sides being, in a Rectangular Triangle, equal to the Square of the Hypotenuſe.

The Sun's Elevation upon a Plane. The Sun's Heat upon the Plane. The Sun's Elevation upon a Plane. The Sun's Heat upon the Plane. The Sun's Elevation upon a Plane. The Sun's Heat upon the Plane. Deg. Parts. Deg. Parts. Deg. Parts. 1 3 31 2653 61 7650 2 12 32 2808 62 7796 3 27 33 2966 63 7939 4 49 34 3127 64 8078 5 76 35 3290 65 8214 6 109 36 3455 66 8346 7 149 37 3622 67 8473 8 194 38 3790 68 8597 9 245 39 3960 69 8716 10 302 40 4132 70 8830 11 364 41 4304 71 8940 12 432 42 4477 72 9045 13 506 43 4651 73 9145 14 585 44 4825 74 9240 15 670 45 5000 75 9330 16 760 46 5175 76 9415 17 855 47 5349 77 9494 18 955 48 5523 78 9568 19 1060 49 5696 79 9636 20 1170 50 5868 80 9698 21 1284 51 6040 81 9755 22 1403 52 6210 82 9806 23 1527 53 6378 83 9851 24 1654 54 6545 84 9891 25 1786 45 6710 85 9924 26 1922 56 6873 86 9951 27 2061 57 7034 87 9973 28 2204 58 7192 88 9988 29 2350 59 7347 89 9997 30 2500 60 7500 90 10000 Degrees. Squares of their Sines Degrees. Squares of their Sines. Degrees. Squares of their Sines.

If the Sun's Altitude be given,The Ʋſe of the Table. and you expoſe to its Rays a Plane, with more or leſs Obliquity; the Sun's Heat upon it will be, in any Obliquity, as the Table ſhews. But if the Sun's Altitude be ſuppoſed to change, the Effects of the Atmoſphere ought alſo to come under conſideration. I need not ſay that I make no allowance for the Sun's apparent Diameter being of a pretty great bigneſs, and not inſenſible like the Stars.

As to the Diminution of the Sun's Heat,The Diminution of Heat occaſioned by the Air is conſiderable; occaſion'd by the Interpoſition of a greater or leſs depth of Air, it is certainly very great. We cannot bear the Sight of the Sun when it is ſomething high; much leſs if it was in the very Zenith. But it is no hard matter to bear it, when the Sun is within three or four Degrees of the Horizon. It is not eaſie to find by bare Study the Laws of that Diminution;but hardly to be found by Meditation; and why. not only becauſe of the different Denſity and continual Refraction of the Air, at ſeveral Heights from the Center of the Earth; but eſpecially becauſe of that wonderful Propriety of Light, that makes it go thrô, and among Terreſtrial Bodies, under a certain and determinate Degree of ſmallneſs, depending upon their Denſity,A Method for finding it by ſome Experiments with a burning Speeulum. without being affected at all in its Paſſage. However I ſee how that Diminution might be found, by ſome Experiments made with a large burning Speculum conſtantly turned to the Sun for a whole Summer-Day, and with a Thermometer kept by it always at the ſame degree of Heat.

The middle of the Speculum muſt be ſhaded by a round Plate, ſupported exactly over againſt it. In the Shade of this Plate, and not far from the Focus of the Speculum, the Thermometer, which ought to be but ſmall, muſt be duly faſtened. The Speculum ought to have a graduated Circle about it. And by the different opening of an Arched Ruler, that is to move about the Center of the Speculum, and to be every where pretty near its Surface, it ought to have an Opaque Vail ſpread, more or leſs, before it: So that a greater or ſmaller Sectour be uncovered, according as the ſtrength of the Sun's Heat requires. That Heat will be reciprocal to the Arc or Sectour uncovered. So then keeping, in one of the longeſt Days, a Table of the Quantity of this Arc, for the ſeveral Minutes, or other Intervals of Time, of which the Day is compoſed, one may eaſily gather the Proportion of the Sun's Heat it-ſelf, ſuch as is tranſmitted thrô the Atmoſphere.

A Table giving the Length of a Beam of Light in the Air, ſuppoſing the Height of the Atmoſphere given, &c. The following Table, which is very ſhort and eaſie to make, or, inſtead of it, ſome other Table made upon the like Principles, might help us alſo to gueſs a little, in ſo dark an Inquiry. This Table gives, upon ſome Suppoſitions, the Length of the Way of the Sun-Beams thrô the Air, to every apparent Altitude of the Sun.

Apparent Altitude of the Sun. Length of the Way of the Sun-Beams thrô the Air. Deg. Min Parts. 0. 0 20. 0. 18 19. 0. 37 18. 0. 57 17. 1. 18 16. 1. 41 15. 2. 6 14. 2. 33½ 13. 3. 4 12. 3. 39 11. 4. 19 10. 5. 6 9. 6. 3 8. 7. 13 7. 8. 45 6. 10. 51 5. 13. 55 4 19. 4 3 29. 45 2 31. 31 1⌊9 33. 32 1⌊8 35. 51 1⌊7 38. 30 1⌊6 31. 39 1⌊5 45. 26 1⌊4 50. 9 1⌊3 56. 21 1⌊2 65. 19 1⌊1 90. 0 1.

Let 2r be the Diameter of the Earth, equal, for inſtance, to 400 Parts: a the Perpendicular Height of the Air that is able to obſtruct ſenſibly the Light of the Sun: this I ſuppoſe, for an Example, equal to 1 Part. Let the Indeterminate q be the Length of the Way of the Sun-Beams thrô that Air: s the Sine of the Sun's Apparent Altitude to the Radius r: and neglect the Effects of Refraction. In theſe Suppoſitions you will find 〈 math 〉 . Which Equation is the Ground, upon which the Table was calculated. And if you give any other Value to the Quantity a, you will eaſily make ſuch another Table, at your pleaſure, by the help of the ſame Equation.

If we ſuppoſe the Air every where of an Uniform Denſity; and its Perpendicular Height given; which will be eaſily determined in that Suppoſition: and the whole Refraction of the Rays of Light to be, at their coming into the Atmoſphere: and that the ſame Quantity of Light penetrates into the Air, whether it comes with more, or with leſs Obliquity; it will be eaſie to make a Table ſhewing the loſs of Light occaſioned by the Air, for any given Apparent Altitude of the Sun. And this may, perhaps, ſerve well enough for Uſe.

From Experience find the Proportion of Light, ſuppoſe as a to b, for any two Apparent Altitudes of the Sun; ſuppoſe 62 and 30 Degrees. Let the Length of the Rays in the Air for thoſe Apparent Altitudes be as n to m. Draw,Fig. VIII. in the eighth Figure, the Aſſymptote OAB, of an Indefinite Length. Take in it OB equal to m; OA equal to n; and AB will be equal to m—n. Draw to the Aſſymptote the perpendicular. Lines AD, BC, equal reſpectively to a and b. Thrô the Points C and D draw the Logarithmic Line FCDQ: and draw the Ordinate OQ. If▪ you ſuppoſe OQ for the whole Light, that enters the Atmoſphere; and, upon the Aſſymptote, you take, from the Point O, the Line OE equal to the Length of the Rays of Light in the Air; the correſpondent Ordinate EF will give the Quantity of Light remaining, after the Paſſage thrô ſo much Air, as the Length of the Rays dos expoſe: And a Table of its Diminution will eaſily be calculated. The Ground, I proceed upon, is that if two Solid Rays of Light paſs, thrô a given Thickneſs of Air equally denſe, they will loſe of their Quantity, or Strength, in the ſame Proportion, as they have to one another. By the like Method you may find how much more Light there is, at any time, near the Surface of a Calm Water, than in any given Depth. And this is what we had to ſay of the Diminution of Heat, occaſioned by the Rays of Light croſſing the Atmoſphere. Let us now take our leave of theſe Mathematical Speculations, and go on to conſider what Advantage we can make of Movable Walls.

As there are ſome Countries, or ſome ſorts of Fruits, for which the beſt is not always the hotteſt Expoſition; ſo there are ſome other Countries, or ſome other ſorts of Fruits, for which we cannot well procure too much Heat. But it will be a hard matter to outdo much the South Walls of our ſecond, or third, or eleventh Figure; of which laſt I ſhall ſpeak hereafter; unleſs it be perhaps by a Movable Wall.Of Movable Walls, in order to receive the Light of the Sun almoſt perpendicularly for the whole Day. I ſhall not mention here the placing ſome Earth, and having a Sloping Wall built, all along in a kind of Boat; or otherwiſe built, in any other ſort of floating Veſſel; as ſuppoſe a round one. Thô with the turning of the Veſſel, ſo as to follow the Sun, and making it, and the Wall at the ſame time, lean more or leſs, one might be ſure to injoy almoſt all the Sun's Heat.Deſcription of an Engine for that purpoſe. I will only deſcribe a kind of movable Box, which having an Inclined Brick Wall faſtened to it, will, without any Water, which both is difficult to procure, and rots Veſſels too eaſily, have the ſame advantage of being conſtantly turned towards the Sun; and may, in Winter time, be laid up in an Orange Houſe. Fig. IX. X. In the IX and X Figures AB is a ſtrong Poſt faſtened upright in the Ground; whoſe upper end B is ſhaped into an Hemiſphere, or rather into a Part of a Sphere, yet ſomething bigger. Upon B there reſts a ſtrong piece of Oak, CC; in the middle of which there is a concave Place, ſo made as to fit the Figure of B, and to leave the liberty of turning and inclining the Box ſeveral Degrees to and fro. The concave Surface will be great enough, if it contains the half of the Surface of an Hemiſphere. D is the Box it ſelf; which is ſomewhat long, and ſo ſhaped that the Sun may ſhine pretty fully upon the foreſide of it. To the two ſides of the Box, and to the Piece CC, are faſtened two inclined Pieces of Timber EF, EF, almoſt parallel to one another; and upon theſe, cloſe by the Box, another pretty long horizontal Piece of Timber GG. The remaining Pieces GF, GF; GF, GF; FF; EG, EG; EE, are ſo diſpoſed as to give much Strength to the whole Frame. Upon the Part GFFG I place a Floor of Boards, and the Piece GG jets out ſome two or four Inches, from that Floor. I uſe both the Piece GG, and the Floor of Boards, for the Foundation of my inclined Brick Wall; to which I give a thickneſs equal to once or twice the thickneſs of a Brick, according to the Weight as I deſire it ſhould have. Under the Box are yet two ſtrong parallel Pieces of Timber HH, running on each ſide cloſe by the Poſt AB; and made firm together, at both their Ends, by two croſs Pieces. From the back End of HH there riſes ſeveral Pieces HK, HI; which being faſtened to the Pieces EF, ſome near the Middle, ſome at or near the upper End of the Floor or Frame, help to bear it up. In the Pieces HH there might be ſome holes, at proper diſtances from each other, for two Iron Pegs, one of each ſide the Poſt AB, to keep, at your pleaſure, the whole Box in a proper Elevation. But this might be done more conveniently with Cords. For from the Ends E, E; F, F; G, G; H, H, you might have ſome Cords faſtened to ſome pretty great Weights of Metal or Stone, or elſe to ſome Buckles, to keep the whole Engine firm in any poſition. In the making of it it muſt be ſo proportioned, in all its Parts, that the Center of Gravity may fall under B, but withal near it. And ſo it will be proper that the Floor be not exactly flat, but convex. The Addition of ſome movable Weight like P might alſo help to alter the Center of Gravity, and to manage the Engine more eaſily. And it is to be obſerved, that the farther • C is from the Box, the wider you may make it at bottom. Such an Engine as this will eaſily be defended from Ants and other creeping Inſects. About the Floor GFFG one might have a kind of plain Border, with an Inclination to the Floor, of about 45 Degrees every where: which Border, by its Reflexion, would much increaſe the Heat, and make it cloſer; giving beſides ſome Shelter from Winds: And upon it one might ſpread a Net, to keep off the Birds and Flys.

If, by an eaſie change, you ſhould deſire to have two Boxes and two Trees, in one ſingle Engine, the Boxes being ſomething diſtant from each other, there would be room for the Poſt AB between them; and you might make them as broad as you would at Bottom; and fix the bearing Place much lower, if you thought it convenient ſo. Inſtead of Bricks the Floor might perhaps be covered with Lead, either painted dark or black, or not painted at all. But I am apt to think it would give, in ſome Climates not far from this, and at ſome Seaſons in the Year, too great a Heat for Vines, and ſuch other tender Trees.

One advantage of Movable Walls is that they may,Advantage of movable Walls againſt ſtorms and winds. at any time, be turned from Storms, and from cold or blaſting Winds; and take in as much, or as little, of the Sun-ſhine, as one pleaſes. They might beſides, when the Sun is ſtrong, and the Fruit grown large, be ſometimes preſented ſide ways to the Sun, that it may ſhine fully upon the Sides of the Fruits; and give them alſo that fine Colour which becomes the whole Fruit ſo well. But after all theſe Walls may better ſerve the turn of ſome Curious Body,Their Ʋſe for early Fruits. than the Publick. They will be good particularly for Melons, Vines, Figs &c, and for raiſing early moſt ſorts of Fruits.

As to our former Sloping Walls,Of the Rain falling upon Sloping Walls. it remains yet to order them ſo that we may not be troubled with the Rain, they are apt to bring in abundance to the Root of our Trees. But this certainly can be no fault in a dry Seaſon, or light Ground, or Eaſterly Wall, or hot Countrey; eſpecially conſidering the great force of the Sun upon our Terraſſes, which will quickly dry the Ground. In other places, beſides what may be done, by receiving and turning off the Rain, the Walk might be made as you ſee in the XIth Figure;Fig. XI. where it is pretty deep in the middle of it. is the Slope of the South Wall;Terraſſes ſo ſhaped as to give ſome more Advantages in reference to Rain and Heat. AM the Cultivated Ground, ſome three, four, or five Foot broad: MN another thin Sloping Wall, parallel to BA, and ſome three or four Foot high: NO the Walk, or Path; which may be five or ſix Foot broad, and paved, if you think fit. OP, PE, EG are the correſpondent Sloping North Walls and Cultivated Ground. The great Depth of NO will keep the Grounds AMN, EPO pretty dry: and the Path NO may be made falling, in order to bring the Water to ſome Drains, where it may be loſt. In an extraordinary wet Weather, one might uſe ſome ſlight Boards, like QR, and place them ſo, near the Foot of the Sloping Wall, that they might receive the Rain at their upper end, in order to convey it to the bottom NO. For this purpoſe it is proper that there be a very ſmall jetting out in the Wall, to which the Boards may be cloſely applyed. Or rather one might, at firſt, fix in the Wall a long and narrow piece of beaten Lead, which neceſſarily receiving the Rain, would eaſily bring it to the upper Surface of the Boards, or to ſome Gutters placed along the Wall, which would be much convenienter than the Boards; and would eaſily convey the Water to ſome other Gutters that ſhould make it fall upon the Bottom NO. The Slope MN, receiving ſo directly the Sun-ſhine upon it, will help very much to heat the Ground NMA; and by conſequence will, in ſome meaſure, forward Vegetation. The Bottom NO, which is to ſerve for a Path or Walk, muſt be raiſing near the middle in a round Figure, to keep it dry there. The two Terraſſes being farther from one another, than in the ſecond or third Figure, the Heat will accordingly be leſs cloſe.

Now we have begun to propoſe, for our Terraſſes, a Shape ſomething different from that excellent one, in the ſecond and third Figure; we may farther obſerve that there would perhaps be ſome ſmall Advantage to ſhape our cultivated Ground ſo as to have it better expoſed to the Sun, and grow warmer. We might, for Inſtance, let the Section of our Walk, in the eleventh Figure, be according to the Lines BRMNOTEG; and order matters ſo, as not to be troubled with the Rain, eſpecially in the Ridge E. And by theſe means we ſhould alſo get a Sloping Wall OT, of a tolerable bigneſs, and very well ſheltered, but ill placed, and of an indifferent Expoſition.

You may remember how, ſpeaking to the firſt Figure, I did chuſe, in the ſide of a narrow Vale, a pretty ſteep Hill well expoſed; which I did ſhape into ſeveral Terraſſes, one above another.Idea of a paved ſloping Ground upon a Hill, to be uſed inſtead of Terraſſes with Sloping Walls. I don't know but that, keeping to the like Idea, it may ſucceed pretty well, eſpecially about 45 Degrees Latitude, to chuſe that Hill very ſteep, to take it almoſt as Nature dos give it us, and to pave it all over with Brick laid flat, except ſome Holes of an Oval Figure, about ſix or ſeven Foot long, and about four Foot broad. Theſe Holes are each to receive at the Top of them a Tree, whoſe Branches muſt be made to ſpread upon the paving of Bricks. The greateſt Diameter of the Ovals ought to be horizontal. They muſt be diſpoſed with as much regularity as poſſible. They will look handſomer, and will be more equally divided, and lie more convenient for the ſpreading of the Tree, and to receive all the Rain, if they be Checker-wiſe; as you ſee them in the twelth Figure. Fig. XII. But they will lie ſomething more conveniently to turn off the Rain, if they be above one another. However it ſeems there is no great danger to be feared, from too much Rain, in a Hill ſo well expoſed to the Sun; and where an extraordinary quantity of Rain will not fail to find its way down, or will ever be eaſily turned off. The uncovered Earth muſt be dug as often, as it is convenient. The Bricks will grow very hot, by the Sun ſhining ſo fully upon them:It will prevent the diſſipation of the Spirits of the Earth. And, for ought I know, they may hinder the too great and uſeleſs Diſſipation of the Spirits of the Earth, that ſecret and precious Fire of Nature, not only by preventing the growth of Graſs, but alſo by intercepting their way, and making them come out, in greater abundance, at the place where the Trees and their Roots are. The good Earth muſt have been gathered to a ſufficient Depth about the Ovals. It is eaſie to order it ſo that either all the Rain ſhall run into the Ovals, or moſt of it run down at the ſides of them, according as your Climate or the Seaſon requires. As to the Charge, both in Bricks and Mortar and Day-labour, it will come, for each Tree, to much leſs than half the correſpondent Charge, in building of a perpendicular Wall; thô we ſhould ſuppoſe this to have Trees on both ſides.

Since I began this Treatiſe,What the Author finds ſaid by others, particularly by Monſieur la Quintinie, that may have ſome relation to Sloping Walls. I have often inquired whether our Sloping Walls had been uſed any where: And particularly I have indeavoured to find, in Monſieur la Quintinye's Book, what he ſays that may relate to this matter. It is very plain that they are in no common uſe, if uſed at all, in theſe Northern Climates, where they are moſt wanted. And probably they have have had no occaſion to think of them in hotter Climates, where, for the moſt part, Heat is as much feared, as here it is deſired. But I would fain have known whether ever they had been deſignedly built, on purpoſe to injoy the Sun longer, and to increaſe its Heat.

Monſieur la Quintinye ſpeaksTom. 1. p. 20. Edition of Amſterdam, 1692. of ſome Sloping Grounds, which he calls des Ados. Theſe, he ſays, are an Earth raiſed up, with a Slope, along a well expoſed Wall, in order to ſow upon it,An Account of what Monſieur la Quintinye calls des Ados. in Winter time and in the Spring, ſome Plants, that are deſigned to be more forward, than in the open Ground. So Peaſe and Beans are ſown, and Artichokes, Vines, Rasberries &c, are planted upon an Ados; the Reflexion of the Sun, probably from the Wall above, and from the Ground before, heating theſe Slopes, as if they were real Walls. What I find ſaid of them, in the reſt of the Work, is much to the ſame purpoſe.

By this contrivance, the Origine of which I do not at preſent inquire into, one dos conſiderably increaſe the Heat, at all times in the Year; and I do not ſee that one can out-do it much in Winter or Autumn. But, in the Spring and Summer, the Wall hides the Sun from the Slope for ſome time; which perhaps the Reflexion from the ſaid Wall is not a ſufficient recompence for. To which muſt be added, that the Heat is perhaps better, being divided to a greater part of the Day, than crowded together about Noon. However by this Diſpoſition of the Wall the Heat is made cloſer.

In another Place Pag. 92. And of his Slopes of Earth expoſed to the South or Eaſt, and purpoſely made for Fruit. he dos mend the hanging of the Ground, in a large Garden, but without admiring at all the Remedy, by dividing it into ſeveral Parts, of different heights, and making each of them level, and parting them, either by ſome little Walls, or only by ſome Slopes of Earth cloſely beaten together. And being ſatisfied, as he has it ſomewhere elſe, that there is no place, in a Garden, but what may be of ſome uſe; he ſays, That theſe little Walls may ſerve for ſeveral things he mentions: and that the little Slopes will not be uſeleſs neither; but on the contrary, when they are expoſed to the South or Eaſt, they may either be uſed to raiſe at firſt ſome early Plants, for the Spring; as Winter Lettuce, Peaſe, Beans, Strawberries, Artichokes and after the Spring they may ſerve to raiſe ſome Seeds of Purſlain, Baſil &c: or elſe, if there be a great quantity of thoſe Slopes well expoſed, a part of them may be imployed for good and all to bring forth good Grapes and other Fruits; as it has been done in the King of France's Fruit or Kitchen Garden, in certain Slopes purpoſely made for that uſe.

I gueſs,Reflexion upon this Contrivance; by theſe Paſſages, that the worthy Author, who is ever very particular and full in what he writes, thô he ſays no more in this matter, uſed theſe Slopes no otherwiſe than as Grounds, and as they do chuſe ſome Hills well expoſed for their Vines,which is here compared with Sloping Walls. or even for their Gardens. But thô this be ſomething a-kin to the main Idea I follow, in this Diſcourſe, and a Confirmation of it, yet I believe there remain ſome conſiderable differences, between what Monſieur La Quintinye has writ, and what I propoſe. The Gardens of his making may juſtifie whether or no he had left any room for our Meditations. Which would indeed be only a fuller Explication of his Thoughts, if he had covered his Slopes with Bricks or Stones; and had made his Trees to grow againſt them obliquely to the Ground; and had uſed them in any Expoſition rather than perpendicular Walls; and had made them ſometimes more, ſometimes leſs Sloping; and had defended them, as I do, againſt Winds; and had likewiſe procured the cloſeneſs of Air, with no loſs of either Sun or Rain, for the ſix or ſeven hotteſt Months, from Equinox to Equinox: Not to mention ſome other Improvements you will find in this Treatiſe. However thoſe Ados of Earth have a peculiar advantage for all Herbs; and particularly for thoſe early Plants, that are to be gathered in February, March, or April.

To this I might add the Account Monſieur La Quintinye gives of Square or Rectangular Gardens;Part 1. where he explains how the Sun never ſhines upon more than two Walls at once;pag. 205. and in ſome Moments upon one only; without ever ſhining upon two oppoſite Walls together.Our Gardens, thô ſquare, may at once injoy the Sun upon their four Walls. But near the Summer Solſtice one might ſee, for a good while together about Noon, the Sun to ſhine at once pretty full upon the four Walls of a Rectangular Garden built after our way: and ſeldom, in the reſt of the Day, to ſhine upon leſs than three Walls, except the Sun be very low.

There is in Monſieur La Quintinye's Book a Ground Plat of the Kitchen Garden,In Monſieur La Quintinei's Ground Plat of the French King's Garden no footſtep found of Sloping Walls. or Fruit Garden, of Verſailles. Thô there be in that Garden a high and very long Terraſſe, with Trees on both ſides againſt it, yet the Ground Plat ſhews that the Walls of it are perpendicular. So this Terraſſe having at once the diſadvantages of being more chargeable, and leſs ſolid or laſting, and worſe for Vegetation than a Terraſſe with Sloping Walls would be, I cannot but conclude alſo from thence that Monſieur La Quintinye knew no other Walls than perpendicular ones. As to the Beauty,To what degree they may be unpleaſant to the Eye. I acknowledge indeed our Sloping Walls not to be altogether ſo handſome as the others are: And yet I do not doubt but the Eye will ſoon be accuſtomed to them; eſpecially when it may look upon them more as Terraſſes, than as Walls; ſo that their leaning may not ſeem to threaten a fall.

In the Engliſh Tranſlation of Monſieur La Quintinye, Objection from Monſieur la Quintinye's Engliſh Translation ſolved. I find a place, that ſeems peremptorily to condemn our Sloping Walls. It is near the end of the fifth Chapter of the third Part of the firſt Volume. There you may read, By all I have newly ſaid, about the Height of Walls, it appears that I have little value for thoſe leaning Walls, to pretend to make them Fruit Walls for Pears, Peaches, Apricocks but they may ſerve for ſomething elſe. And in the Margin you find alſo writ, Leaning Walls not proper. But the Senſe, in the French Original, is that ſuch Walls as are only breaſt high (des Murs d'appui) are not good for Fruit. Neither was the Author ſpeaking of Sloping Walls before, but of the Height of perpendicular Walls.

I have alſo heard of a large round Pit,Account of an Amphitheater with Sloping Walls. like an Amphitheater, built here in England with Sloping Walls all about it. The Ground in the middle was, as they ſaid, ſeveral Yards Diameter, perhaps about 50 or 100 or more. And upon all that Ground there grew Vines, both ſheltered from Winds, and cheriſhed with a cloſer Heat, than they could have in the open Air.

A Perſon of Quality has tryed about,And of ſome Melons, and other Fruits, heated with Convex Glaſſes. 53 Degrees Latitude, in the preſent Year 1697, to increaſe the Sun's Heat upon his Melons, by ſome pretty large Convex Glaſſes. Theſe being placed, between the Sun and the Melons, did gather the Rays in a pretty ſmall Focus each. And we have been told, to our admiration, that the Melons thus helpt have been tolerably good, and much better than others that did grow in the Neighbourhood, which were generally bad ones. As if it were enough to heat any one part of the Fruit, to make the Effects of it to ſpread over the whole. But I hear alſo that the like Tryals having been made upon ſeveral Fruits, in other places, have had no other ſucceſs than the giving them ſome unkindly precocity, leaving withal to them a harſh and unpleaſant taſte.

In ſome places,The fault of Vines that are commonly made to grow againſt a Roof, or the Coping of a Wall. they make a Vine to grow as high as the Roof of ſome ordinary Building; and there to ſpread its Branches over the whole Roof. In other places, they make the Vines to grow firſt as high as the top of a Garden Wall; and there to part into two Branches, running on each ſide, for 25 or 30 Foot together, upon the ſmall Coping of Bricks, they do ſometimes end their Garden Walls withal. Thô I have been told that, with the firſt of theſe two ways, they have had ſome good Grapes in England; yet I find, in both of them, this capital fault, that the Roots having work enough to feed ſo long a Stock, and to garniſh ſuch a large extent with Leaves, and a thouſand other little uſeleſs Shoots, there can remain no ſtrength in the Sap, for the production of Grapes; unleſs perhaps they be ſome few and ill favoured ones.

All theſe and the like Trials were indeavours towards what is here more fully ſtated:Judgement of thoſe and all other ſuch Trials, in order to make the moſt of the Sun's Heat. for I do not doubt but a great deal more beſides has been attempted, in many places, in order to make the moſt of the Sun's Heat. Whether I have done any thing more towards it than others, let either Experience juſtifie, or thoſe determine, that are able to underſtand the Mathematical part of this Diſcourſe. But after all I acknowledge readily that our Invention required but an ordinary Capacity, to light upon it; and even but an indifferent Skill in Geometry, to examine and eſtabliſh it upon its true Principles.

I muſt here repeat again and again,Caution againſt too much Heat Sloping Walls are like to procure. that I have, in this Diſcourſe, indeavoured to increaſe the Sun's Heat to an extraordinary degree: and this, I hope, I have found how to do effectually. But it is eaſie in hot Climates, and in ſome light and dry Grounds, and in the governing of tender Plants, to err by an exceſs of Heat. If any body ſhould fall into that Errour, it muſt be by his own fault. He may take as much and as little, as he pleaſes, of that degree of Heat, which is to be had by our Sloping Walls. Thô accommodating my ſelf to the Climate of England, where too much Heat is hardly to be feared, I may perhaps have ſometimes ſpoke, as if one were always to take the moſt. However a pretty good Remedy, againſt too much Heat, is to keep conſtantly the Ground ſufficiently watered: So that the Trees being conveniently full of moiſture, their Fruits may be ſo much the farther from being ſcorched and dryed up. And here I may obſerve by the by, that if our Terraſſes be ſo broad as to have, at the top of them, a little Rivulet, or Aqueduct, it will be very eaſie from thence to water them on both ſides. But this is perhaps above the Circumſtances of an ordinary Gentleman's Eſtate. The ſame conveniency for watering would be found, in the ſteep Hill of the twelfth Figure, Fig. XII. provided there were ſome Water at hand, above the uppermoſt Ovals.

If you have a Sloping Wall ready built,Frames called Eſpaliers by the French recommended, to take off ſome of the Sun's Heat, and to give more liberty to Trees. and you are unwilling to have all the Heat it dos give, you may keep your Trees upon ſome Frames or Eſpaliers, at ſome little diſtance from the Wall, as half a Foot, or a Foot, or a Foot and a half, more or leſs, as you intend to take off more or leſs of the Sun's Heat. Thoſe Frames, thô not much uſed in England, are yet better than the bare Wall, becauſe they leave more room and liberty to Trees.

Perhaps you may deſire to have ſome Method,A Method for chuſing the Elevation of a Sloping Wall, in any Expoſition whatſoever. for the chuſing of the Elevations of your Walls, when they have any other Expoſition than to the South, or to the North. I do for this make uſe, in our Climates, of the following Conſtruction; which I do not give as a Geometrical one, but only as a Mechanical Approximation, for the Solution of a Problem perhaps too hard, to be ſolved, in its full Extent, with any great exactneſs.

An Expoſition being given, in a given Climate, it is eaſily underſtood, by what I ſaid before, that all Fruits do not require the Sloping Wall ſhould have the ſame Elevation: but that ſome Fruits will have it great, ſome little: and that among theſe Elevations there is two Extreams, to wit, the higheſt Elevation and the loweſt, that ſtand, as it were, for Limits of the reſt. I call the higheſt Elevation, the Sloping Wall can have, in the given Expoſition, ſimply the greateſt or higheſt Elevation; and its proper Wall the higheſt Wall. And I call the loweſt Elevation, the ſame Wall can have, in the ſame Expoſition, the ſmalleſt or leaſt Elevation; and its proper Wall the loweſt Wall.

Let HA be the Horizon, Fig. XIII. AOP the Meridian; AO an Arc equal to the Elevation you chuſe to give to your Sloping Wall, when it looks to the North: AP the Height of the Pole. And you may find thus the greateſt Elevation of your Declining Wall; whether it declines to the Eaſt, or to the Weſt. Draw the Line PO, whoſe middle is D; and determine how much more you would take, for the greateſt Elevation of your Eaſt Wall, than for the greateſt Elevation of your Weſt Wall. For I do chuſe to give the Eaſt Wall a greater Elevation, that it may injoy the Morning Sun more fully: and to the Weſt Wall a ſmaller Elevation; that the Sun may come the ſooner to ſhine upon it. Suppoſe, for inſtance, you chuſe 5 Degrees, or 10 Degrees, for the difference of Elevations, between the higheſt Eaſt Wall, and the higheſt Weſt Wall. Place thoſe 10 Degrees, for inſtance, in the middle of the Arc PO, from S to T; and let S be higher than T. And draw the Lines DS, DT. Make the little Circle PDO to ſerve as a Compaſs; where the Point O will anſwer to the North Expoſition, and the Point P to the South Expoſition. Let your propoſed Expoſitions look, for inſtance, towards the 60th Degree, taken on both ſides the North: and upon the Circle ODP take OE equal to 60 Degrees. The Lines E σ, E τ, parallel to DS, DT, will give, upon the Arc AP, the greateſt Elevations A σ, A τ, for the two Walls: to wit, A σ for the Wall that looks 60 Degrees Eaſt-ward, from the North Point of the Horizon; and A τ for the Wall that looks 60 Degrees Weſtward, from the ſame Point.

The ſmalleſt Elevations, belonging to the ſame Expoſitions, will be found with taking AQ equal to the ſmalleſt Elevation of the South Wall, and proceeding, with the little Circle OQ, as was done, with the little Circle OP. Now the Point Q cannot be lower than the Point O. For whatever be the leaſt Elevation you can give to the South Wall, the North Wall requires either the ſame, or a lower: and never the ſame, but when it ſeems inconvenient, for Vegetation, to give a lower.

If the Point Q happens to be very near the Point O, as ſuppoſe within 5 Degrees from it; you may, upon the little Circle OQ, take O • of 60 Degrees, as before; and draw to OQ the perpendicular eh, meeting with the Arc AP in h; and ſo you will have the Arc Ah, for the leaſt Elevation. And, if you think fit, you may add to and ſubſtract a little from it, at your pleaſure; if you intend to give more Elevation to the Eaſt Wall, than to the Weſterly. But let it be ſo that you may ſtill remain, between the Limits O, Q. However much Niceneſs, in ſo wide a Conſtruction, is probably ſuperfluous.

The Heat remains ſenſibly the ſame,The Heat ſenſibly the ſame, upon a South or upon a North Sloping Wall, thô a little declining from the true North or South. for the South Wall, and for the North Wall too, if, keeping their Elevation each, they are made to decline ſome few Degrees, from the North or from the South. This is partly plain, becauſe the Heat, upon a Wall, whoſe Elevation is given, is a Maximum, when the Expoſition is to the South, and a Minimum, when it is to the North. And, this not being a ſufficient Proof, it is alſo further evident, by ſome Calculations, which I forbear to inſert here.

For thô a Maximum, A ſingular ſort of Maximums and Minimums, very different from thoſe that are commonly conſidered. or a Minimum, dos not, for the moſt part, alter its bigneſs ſenſibly, when the Elements, from which it reſults, are but a little changed; yet it happens ſometimes, as in the Points of Retrogreſſion of Curves, that a Maximum, or a Minimum will alter very much, upon the leaſt change in its Elements; as ſuppoſe in the Abſciſſe. And not only a Maximum, or Minimum, may be found, where the Fluxions of the Abſciſſe and Ordinate are either of them infinitely greater than the other; but where thoſe very Fluxions have any determinate and finite Proportion among themſelves.The ſame, in ſome meaſure, already obſerved by others. But a part of this has already been obſerved by others.

This Equality of Heat is the Ground of the Conſtruction I have given,The Ground of the foregoing Method. for determining the Elevation of declining Walls. For it follows eaſily from it, that the Elevation of the South Wall will remain ſenſibly the ſame, thô it declines, ſome few Degrees, from the true South; and that the Elevation of the North Wall will alſo remain ſenſibly the ſame, thô it ſhould decline, ſome few Degrees, from the true North.

But Experience will be,Experience muſt alſo be conſulted. in all Climates, the propereſt way to determine, for each Fruit, and each Expoſition and Situation, and each ſort of Materials, our Walls may be made withal, the Elevation that ſhould be given to Sloping Walls.

We muſt now compare,Of Walls that are not ſmooth. as well as we can, a ſmooth and plane Wall, with a rough irregular Wall, and with ſome other Walls, that are not plane.

In this Theory I have ſuppoſed hitherto the Walls to be very ſmooth and plane. And in that Suppoſition the Heat is as the Square of the Sine of the Sun's Elevation, upon the Plane of the Wall.There can be no ſuch thing as a Wall giving the Heat proportional to the Sine of the Sun's. Elevation upon it. But, if it was poſſible to have a Wall, of an uniform and determinate roughneſs every where, that could perpetually fold its rough Surface into larger and ſtraight priſmatical Furrows, ſo as to have always one ſide of the Furrows parallel to the Rays of Light, and the other ſide perpendicular to them, the Heat would then be, and only then, as the Sine of the Sun's Elevation upon the Wall. Which muſt be ſo underſtood, as not to exclude a Wall, whoſe roughneſs vaniſhes into an exact Plane. I am apt to think that our ordinary Walls, thô very rough and uneven, come nearer the firſt Suppoſition,But if there was, the [Fig. IV.] Method of calculating the Heat upon it would be eaſie. than the ſecond. But, if the ſecond was to take place, TV, TL muſt, in the fourth Figure, be made equal to the Sines of their proper Arcs TP, TZ: And the Parabolas MV, ML, IV, muſt be turned into ſtraight Lines,And Sloping Walls would be yet very advantagious, even in that ſuppoſition; thô leſs than before. and the reſt of the Calculation muſt be altered accordingly. The reſult of which would be a much ſmaller diſproportion of Heat than before, between the Sloping and the perpendicular Wall. But, notwithſtanding this, there would be yet left a very conſiderable Increaſe of Heat for Sloping Walls; which would give a ſufficient incouragement for the building of them: As will ſoon appear to you, by an eaſie Calculation, too obvious after all I have ſaid, for me to explain it any farther.Of a Wall giving a mean proportional. However it is not poſſible that the Heat ſhould follow this Proportion. If the Heat was ſuppoſed as S½,Heat, between ſuch a Wall as this and a Plane Wall. which is the mean proportional, between the Heats in the two former Suppoſitions, taking S for the Sine of the Sun's Elevation upon the Wall; then, TV, TL being duly determined, the Parabolas would be turned into Parabolas of another Kind, where the Cube of the Ordinate would be as the Square of the Abſciſſe. And the Calculations woud be made after a Method like that I followed before. And the reſult would come much nearer my firſt Suppoſition: thô it would perhaps yet fall ſhort of the true Increaſe of Heat, upon the Wall.A ſmooth Wall compared with a rough Wall.

A ſmooth South Wall ſeems to receive more Heat in all, than a rough irregular Wall. But the rough Wall receives more Heat, while the Sun ſhines very obliquely upon it, than a ſmooth South Wall would do: And it receives leſs Heat than the ſmooth Wall, when the Sun ſhines near full upon both. For my part I think the ſmooth Wall to be preferable; not only becauſe it ſeems to have more Heat in all, and looks much neater, but becauſe it gives no ſhelter to Inſects.How to make a Brick Wall ſmooth. The very ſloping of a Brick Wall will give an advantage for the poliſhing or making of it ſmooth, by the drawing to and fro of a rough and hard Stone ſufficiently plane upon it, the Stone being large and ſuſpended from above, to ſome convenient place for that purpoſe. But we have one ſort of very large and thin Bricks, whoſe Figure is an exact Square, already poliſhed to our Hands.

Neither ſhould I be very fond of a Sloping South Wall, with ſome ſmooth ſemi-cylindrical Furrows upon it,Of a Sloping Wall with Semicylindrical Furrows upon it. running from top to bottom, in all the Wall; as in Architecture ſome Pilaſters are often made; the flat part between the Furrows being alſo very ſmooth; unleſs the Furrows were very ſmall indeed; which would bring the Wall ſo much the nearer a Plane. Any other Furrows would prove too convenient a Neſt for Inſects.Theſe Furrows compared with a Plane Wall of the ſame breadth with them. I have calculated, more out of Curioſity, than for any real Uſe, the Proportion of Heat, for an Equinoctial Day, upon ſuch a Furrow, and upon the Plane Wall, or Faſcia, that could fill it up to the very Axis; ſuppoſing the Atmoſphere not to act upon the Rays of Light, and the Elevation of the Walls to be the ſame, with that of the Pole; and theſe Walls to be turned directly to the South. And I have alſo calculated the Heat, that the like Faſcia would receive, if it was turned directly to the Sun, for the whole Day.

In the ſeventh Figure, Fig. VII. where C is the Center of the Lines of Sines OA, AG, make up the Rectangles OCAD and GCAE; and upon the Axis AC conceive the Solid formed by the Revolution of the Space OAGO, as well as the Cylinder formed by the Revolution of the Space DEGOD. The Heat of the Sun, upon the Faſcia always perpendicular to its Rays, will be, at the Days end, as the Moment or Weight of the Cylinder ODEG, in reference to the Line OD; ſuppoſe as the Number 9870. And the Heat upon the Cylindrical Surface, will be as the Moment of the Solid OAG, in reference to the Line DE, that is as 2723. And the Heat upon the inclined Faſcia, will be as the Moment of the Solid OAG, in reference to the Line OD; that is as 2467.

But the inclined Faſcia, or the Plane Wall, receives, in proportion to its Surface, much more Heat than the Semi-cylindrical Cavity; as appears both by the very Numbers I have juſt now given; and by taking upon the Semi-cylindrical Surface a ſmall Space, equal to the like Space upon the inclined Plane Wall. For the Space, taken in the Cylindrical Surface, will be ſeen by the Sun, only for ſix Hours: And the moſt it can receive of the Sun's Heat dos but equal the Heat, that the Space taken in the Plane Wall dos receive, from Nine in the Morning to Three in the Afternoon. The Wall with the Cylindrical Furrows has ſome Advantage, in that the Solid, between the Furrows, not being thick, it may be heated from ſide to ſide, and in that the Reflexion of the Sun-Beams makes the Heat ſomething cloſer. But the advantage will be greater if the Furrows be very cloſe, and very ſmall, as ſuppoſe ſix or ten or more in an Inch: In which caſe they ſeem to be even preferable to a Plane Wall, thô the difference between them can be but little.

The whole direct or unreflected Heat, Fig. XIV. upon a Semicylindrical Space ADB,Meaſure of the Heat upon a Semicylindrical Space. is as the Sectour DAB, the Line DA being directed to the Sun, and the perpendicular Heat being expreſſed by a Height equal to the Radius of the Cylinder.

From whence it follows that the Heat, upon the Plane AB, is equal to the Heat, or Action of the Rays of Light, upon the Cylindrical Space ADB, when the Angle DAB is of 59 Degrees 4 Minutes, and about 50 Seconds. And ſo we leave off conſidering of Walls that are not Plane.

I have,An Account of a Table giving, from 40 to 67 Degrees Latitude, the Proportion of the Sun's Heat, in the Solſtice, upon a perpendicular and a Sloping South Wall. for the Reader's ſatisfaction, calculated, according to the Principles that have been laid down, the following Table, which gives for all Countries, from 40 to 67 Degrees Latitude, the proportion of Heat, in the Summer Solſtice, upon a Perpendicular South Wall, and a Sloping Wall paſſing thrô the Pole of the World. This Space dos comprehend almoſt all Europe. The Uſe of Sloping Walls, in very hot Countries, in ſuch ſituations as being high, are naturally temperate or cold. But, in the South parts of it, I ſhould not much care for our Sloping South Walls, unleſs it were for ſome Plants of the hotteſt Countries, or in a place naturally temperate or cold, upon the ſide of ſome little Vale duly choſen in a high Hill or Mountain. And thus thoſe many Habitations, which, being placed very high, are, in all times of the Year, much colder than the neighbouring Plains, and unfit upon that account, even in hot Countries, for the production of good Fruits, may hereafter injoy that bleſſing. And this ſo much the more, that the Heat of the South Wall may, perhaps without danger, be extremely increaſed there. So, for inſtance, in the middle of Spain, which is a Mountainous Kingdom, the Heat may be made, in the Solſtice, ten or fifteen times greater, upon our Wall, than upon a perpendicular South-Wall. And this, or rather a part of it, will give a very good help againſt the coldneſs of a Situation, proceeding from its Height.

Suppoſe that, in the fourth Figure, the Point τ is, as before, three times nearer to T than to V: and that the Cylindrical Surface TMV is to the Cylindrical Surface TIV as the Arc τμ to the Arc τι: You will find the Proportion, between the Cylindrical Surfaces TML, TMV, TIV, to be,The Table it ſelf, and its Explication. at the Solſtice, as in the following Table. The firſt Column gives the Elevation of the Pole in Degrees from 40 to 67. The fourth Column gives the Heat TIV, upon a ſmooth South Wall, ſo much inclined to the Horizon as to paſs thrô the Pole of the World; and it makes it always equal to 1000.

HP TML TMV TIV MN TML TMV TIV M. N. 40 65 677 1000 838 100 1043 1540 1291 41 74 690 1000 845 100 930 1348 1139 42 84 702 1000 851 100 835 1189 1012 43 95 714 1000 857 100 755 1057 906 44 106 725 1000 863 100 686 946 816 45 118 736 1000 868 100 626 851 738 46 130 746 1000 873 100 574 770 672 47 143 756 1000 878 100 529 700 614 48 157 765 1000 883 100 489 639 564 49 171 774 1000 887 100 454 586 520 50 185 783 1000 891 100 422 540 481 51 201 791 1000 896 100 394 499 447 52 216 799 1000 900 100 369 462 416 53 233 807 1000 903 100 347 430 388 54 249 814 1000 907 100 327 401 364 55 267 821 1000 911 100 308 375 342 56 284 829 1000 914 100 291 352 321 57 303 835 1000 918 100 276 33O 303 58 321 842 1000 921 100 262 311 287 59 340 848 1000 924 100 249 294 272 60 360 855 1000 927 100 238 278 258 61 379 861 1000 930 100 227 264 245 62 399 867 1000 933 100 217 250 234 63 420 873 1000 936 100 208 238 223 64 441 878 1000 939 100 199 227 213 65 462 884 1000 942 100 191 217 204 66 483 890 1000 945 100 184 207 196 67 504 895 1000 947 100 177 198 188 I II III IV V VI VII VIII IX

And indeed that Heat would be always the ſame, if it was not for the different Effects of the Atmoſphere, in ſeveral Climates, and for the various communication of Heat from the Ground to the Air, and ſo to the Sloping Wall. The ſecond Column gives, in the ſame proportion, the Heat TML, upon a ſmooth perpendicular South Wall: And the third Column gives that part TMV, of the total Heat TIV, upon the Sloping Wall, that is not affected by the Air. The fifth Column gives the middle Numbers between thoſe of the third and fourth. The three following Columns give the ſame Heats, and with the ſame Proportions; but the Heat, upon the South Wall, is always expreſt by 100. The ninth Column gives the middle Numbers, between thoſe of the ſeventh and eighth. The real direct or unreflected Heats, upon the Sloping Wall, being determined, by the Atmoſphere, to ſome Number between TMV and TIV, they cannot be very far from the Strength expreſt in the fifth and ninth Column.

The Uſe of the Table is as follows.The Ʋſe of the Table. Suppoſe I would know what might be at Paris, Example for Paris. in the Solſtice, the Proportion of Heat, between a perpendicular plane South Wall, and a Sloping plane South Wall, paſſing thrô the Pole of the World. I take the Height of the Pole at Paris, which is 49 Degrees 50 Minutes. And over againſt this Number I find TML, TMV, TIV muſt be 183, 781 and 1000. Or elſe that they muſt be 100, 427 and 548. I will uſe theſe laſt Numbers, as being more convenient. I conclude therefore that, the Heat, upon the perpendicular South Wall, being ſuppoſed of 100 Parts, the Heat, upon the Sloping Wall, is already, upon a conſideration, which is not at all ſubject to the Effects of the Atmoſphere, of 427 Parts. Beſides an additional Heat of 121 Parts, that would raiſe it to 548 Parts, were it not that from this Number, 121, ſomething is to be ſubſtracted, becauſe of the Effects of the Air. The laſt Column gives the middle Number 487; which we may ſuppoſe is not far from the real Heat upon the Sloping Wall.Of South Walls that are more inclined, to the Horizon, than the Wall that paſſes thrô the Pole of the World. And this is about 4⅚ times greater than the Heat upon the perpendicular Wall.

But if we go about to calculate the Heat, upon the Sloping South Wall, that paſſes thrô the loweſt Point of the Polar Circle, we ſhall find the Increaſe of Heat, upon it, to be yet much greater.Perpendicular and Sloping South Walls may be well compared together in the ſame, but not in different Climates.

And in general a Sloping South Wall, elevated at Paris, upon the Horizon, by ſo much as is the Height of the Pole, wanting the whole Diſtance between the two Tropicks, being much hotter in the Solſtice, than the Sloping South Wall, that paſſes thrô the Pole: it follows that any South Wall whatſoever, whoſe Elevation, upon the Horizon, is there between 2 Degrees 50 Minutes, and 49 Degrees 50 Minutes, muſt be hotter alſo.

This comparing together of perpendicular and Sloping South Walls proceeds well enough, for the ſame Climate, whether it be often cloudy or often fair: provided the Clouds do not uſe to come more at ſome certain hours of the Day than at others: ſuppoſe more about Noon than in the Morning. But we cannot, from the Table, determine ſafely the Proportion of Heat, between the perpendicular and Sloping South Walls of ſeveral Countries; the Interpoſition of the Air, and eſpecially the difference of Weathers being almoſt an inſuperable Obſtruction againſt it.

In the Tract of this Diſcourſe,Of ſome other Advantages of Sloping Walls: I have, in ſeveral places, ſhewn ſome of the Advantages we get by uſing Sloping inſtead of perpendicular Walls. I will now run over ſome other Advantages, that are yet untouched, or elſe not fully treated of.

Our Sloping Walls injoy much more the benefit of the Dew and Rain's falling,In reference to Dew and Rain; eſpecially as to the Eaſt Wall. than other Walls can do. And the Eaſt Sloping Wall will not have, as the perpendicular, that great fault of keeping the Rain from its Trees. The conſequence of this will eaſily be perceived, by thoſe that complain ſo much of the Drought incident to their Eaſt Walls.

It is a common fault,In reference to Froſt occaſioned by the Earths tranſpiring ſonte moiſture: in all perpendicular Walls, that the Ground being wet, and tranſpiring much humidity, this will ſtick upon the tender Bloſſoms, and in cold weather cover them with Froſt, and deſtroy them. If our Sloping Walls do not intirely prevent this, they cannot but do it at leaſt in a great meaſure: the very ſloping of the Tree turning it from thoſe Steams, and giving room for them to diſſipate themſelves in the Air.Or by the cold Vapours in the Air driving with the Wind, and ſticking upon Trees. In like manner our Terraſſes will have an advantage in reference to Froſt, occaſioned by the cold Vapours in the Air driving with the Wind and ſticking upon Trees. For one Terraſſe dos defend, in a great meaſure, the following Terraſſes againſt this Accident.

By our Theory the Extent of thoſe Places,The growing of Fruits extended to more Countries and Places. where ſeveral Fruits do grow, will be much inlarged. And not only two Zones of ſome Miles, or perhaps of ſome Degrees, round the whole Earth, one of each ſide the Equator, will be made able to produce, for inſtance, ſome good Grapes, whereas they afforded before only ſome bad or indifferent ones. But in Countries, where Vines do grow plentifully, if you mark upon the Hills, or Mountains, thoſe Limits, where Vines do begin to be but bad or indifferent, even againſt Walls built after the ordinary way; you may often take in yet a great deal more of Ground, with ſeveral Country Houſes and Towns in it, and have there ſome excellent Vines, by the help of Sloping Walls. What is here ſaid of Vines is, in like manner, eaſily underſtood of other Trees.

So then whereas every Climate in Europe begins to loſe ſome ſorts of Fruits, for want of Heat and Time to ripen them; we may every where open our Gardens to receive thoſe Fruits, which hitherto we have been unable to have, thô our near Neighbours Southwards did raiſe them, with no extraordinary trouble.

And not only the Places for the growing of Fruits are inlarged,And the time of their Ripeneſs, and uſe for Men, to more Days in the Year. but ſo are the Times alſo, in which we may injoy them. This advantage ariſing from our Walls giving probably their Fruits a Week, or perhaps a Fortnight, ſooner than we could have them otherwiſe.Ordinary Walls compared among themſelves, and with Sloping Walls, as to the forwardneſs of their Fruits. For ſince at Paris the Fruits of good Eſpaliers are ſomething ſooner ripe, than thoſe of Standard Trees; and theſe laſt are ſooner ripe, than thoſe of Dwarf Trees: And, among the Eſpaliers, thoſe of the South and of the Eaſt begin to give ſome ripe Fruits about eight or ten Days ſooner than thoſe of the Weſt, and about, at leaſt, fifteen or twenty Days ſooner than thoſe of the North; is it not eaſie, from thence, to conclude that our Sloping South Walls and Eaſt Walls will give their Fruits conſiderably ſooner, than ordinary Walls can do?

The Certainty of our latter Fruits coming to Ripeneſs is alſo much greater;The Certainty made greater of our latter Fruits coming to Perfection. ſince, by our having them early, we need not fear ſo much the beginnings of cold and wet Weather, that might hinder them from coming to Perfection.

Walls may not only be ſo expoſed,Slopes of Earth for ſmaller Plants. and ſo inclined, as to make ſeveral ſorts of Trees, growing againſt them, to bear early ſome excellent Fruits; but, according to the ſame Idea, the Ground it ſelf may be ſo ſhaped, into Slopes and Terraſſes, as to bring early ſome of the ſmalleſt ſorts of Plants, as Strawberries, Sallets &c. And as for ſuch Plants,Of the dividing a main Slope into many ſmall ones. as caſt a pretty deal of Shade, thô the ſame Sloping Ground might ſerve very well for them, yet one might alſo uſe, with ſome more advantage, a main Slope cut by Stories into ſeveral ſmall ones faced with Bricks, Fig. XV. as you ſee in the fifteenth Figure.

In the like manner we might eaſily ſo ſhape the large Furrows of our Fields,Of ſhaping the Level or ordinary Ground, into very large Furrows running Eaſt and Weſt, with a gentle Slope Southwards, and a ſteep one Northwards, or contrarywiſe; in order to increaſe or diminiſh a little the Sun's Heat. or the Surface of our other Grounds, as to have them expoſed to the Sun, with the ſame Obliquity, as the level Ground of any Country, not above 10 or 15 Degrees more to the South, or North, than we are our ſelves. For inſtance, in the Latitude of London, Fig. XVIII. the Ground will have the ſame Expoſition to the Sun, as the level Ground, in the Latitude of 45 Degrees, if going from South to North, you make, ſuppoſe for five Yards together, your Ground to riſe by an Angle of 6½ Degrees, in a Slope expoſed exactly to the South; and then you make your Ground to fall as much towards the North, by a Slope as ſteep as it can conveniently be, ſuppoſe of 35 or 40 Degrees: and then you begin again another long and gentle Slope towards the South, for five Yards together, to be followed as before, by a ſhort and ſteeper Slope towards the North; and ſo on. See the eighteenth Figure. Thô we do not, by this, give the ſame Weather, or Heat, to the Climate, nor the ſame Strength, or Weakneſs, to the Sun, as there is in a Country, where its Rays do not paſs thrô ſo much or ſo little Air; yet at firſt ſight it ſeems to be of ſome conſequence for Agriculture, both in cold and in hot Countries; and I could not forbear propoſing it to the conſideration of the Curious. If, in our Example, we do not get that degree of Heat, they have naturally in the Latitude of 45, ſuppoſing both Countries equally cloudy; yet, with the very Numbers I gave, we may poſſibly reach, upon our Ground, the Heat, which they have in 48 Degrees Latitude; and we may yet come nearer the Heat, which the Ground has in the Latitude of 45, if we make our Slope, that looks to the South, a little ſteeper; raiſing it, for inſtance, 10 or 12 Degrees above the Horizon. There is ſome Ground loſt here, thô not very much. As to the Trouble it is not greater than we ſee Countrey-men take, to make the Water to run off their Fields. And we have this conveniency, that we may give our Slopes only what Breadth we pleaſe; ſuppoſe as much as will reſult from the ſtrength of a Man to throw, with a Shovel, the Earth from him. But the broadeſt Slopes are beſt.

Thus we may help and increaſe a little,Application of this Practice to Ʋſe. by the ſhape of our Ground, the Heat of the Sun; or elſe we may abate a little from it. And by conſequence we may fit our Lands the better, to bear any Plants we have a mind to raiſe. This may ſerve to guide ſuch as would plant ſome Vines in their Country, whether it be naturally a little too hot or too cold. For it will either lead them, as daily Experience dos others, to chuſe a Ground fitly expoſed and inclined for their purpoſe: or elſe, if their Ground be not proper, it will let them ſee a poſſibility and a Method, with a little trouble, to make it ſo.

Every body knows what great difference of Heat and Vegetation there is,Of the difference of Heat, upon the North and South ſide of Mountains, Hills and Downs. in the ſame Climate, between the North and South ſide of great Mountains; and the like is, in ſome meaſure, obſerved, at much ſmaller diſtances, in our Hills. I remember that travelling once in England, in Summer, over ſome Downs, which had but an ordinary Declivity, one could plainly perceive, by turns that the Air became of a ſuddain much warmer, when the Declivity was towards the Sun; and colder, when it lay from it. Yet the Sun being high then did ſhine upon the whole Ground. In any Shade,The Heat of the Air in any place dos not very eaſily ſpread into the next Air. and even in our Woods, thô the communication be ſo open with the very next Air, warmed immediately by the Sun, and its Rays are let in at ſeveral places, yet the coolneſs is very ſenſible; the Heat ſpreading from the ambient Air, with leſs eaſe, than one is apt to think. Theſe conſiderations incline me to believe that, by this ſhaping the Ground, there may be ſomething done for the benefit of ſmaller Plants, eſpecially in a cloſe place, or calm weather, when the reflected Heat may not be blown away from the Ground that reflects it. For it ſeems each Surface of Ground makes then, cloſe about it, as it were a peculiar Climate.

And this is farther confirmed,Nor the reflected Heat ſpend it ſelf ſo faſt, but that it may be ſtrongly felt. by the common Experiment we have, how much hotter it is, in Summer, near a South Wall, or a row of Houſes, that look to the South, when the Sun ſhines full againſt them, than in any other place, where the Light of the Sun comes with the ſame Liberty. For it is plain the reflected Heat, being thus perpetually ſupplied from the Sun, dos not ſo much ſpend it ſelf, into the open Air, but that it may be ſtrongly felt, at ſome diſtance, all along the place that reflects it.

I cannot here but mention what I heard a learned Gentleman ſay, who has been in the Weſt-Indies. He aſſured that upon their Mountains, according as one goes up higher and higher, and the Heat dos become leſs, one finds, by degrees, very many of our European Plants naturally growing; the Mountains always giving them, in ſome peculiar places, as it were different Climates, fitted to their ſeveral Natures. So then, as the Diminution of Heat makes the Ground naturally to bring forth the Plants of colder Countries: ſo, on the other ſide, the Increaſe of Heat, which in a great meaſure lyes in our power, muſt needs fit our Grounds, and Gardens, for an eaſie and natural Production of the Plants of ſuch Countries, as are hotter, only to a certain degree, than ours.

The uſe of Sloping Grounds, for ſmaller Plants, is pretty well known already; eſpecially beyond Sea. And as for theſe Climates, not to mention what they call in French des Ados, An Account of a Slope where extraordinary Strawberries are ſaid to grow. I have heard that a Gentleman, who lives at Dublin, has in his Garden a pretty eaſie Slope well expoſed; which furniſhes him with Straw berries, long before they be ripe in other Gardens; and with ſuch Strawberries too, as have a colour, ſmell and taſte, to which the others are not to be compared.

It happens pretty often that the Sun dos ſhine only ſome part of the Day;Advantage of Sloping Walls, in ſuch Days as the Sun is ſeen for ſome Hours only. which makes, at ſuch times, perpendicular Walls, in the Spring and Summer, to be frequently altogether without it. But Sloping Walls, having before them a much greater part of the Sky, are ſo much the more likely to injoy the Sun, if it comes at all to be ſeen. This advantage, as well as that of injoying more fully the Sun, at any Moment it happens to ſhine, is ſo much the more to be valued, when the Climate is apt to be Cloudy, and ſubject to much Rain.

In pretty hot Countries,Advantage of inclining Sloping Walls more or leſs, according to the Climate, Situation and Expoſition. or in Climates, where their perpendicular South Walls are already as hot, as they deſire to have them, one may often, by inclining another Wall, to a proper quantity, make any Expoſition, from the North Eaſt Southwards to the North Weſt, to be equal in Heat to a perpendicular South Wall. The like may be ſaid of a perpendicular South Eaſt Wall, &c: If it be the beſt perpendicular Wall, in your Climate, you may make ſeveral other Expoſitions not to be inferiour to it, by inclining the Walls, as much as is neceſſary. And further, ſuppoſe Experience has taught, in your Country and Situation, the beſt Eaſt-South-Eaſt Wall, for inſtance, to be, for ſuch a kind of Fruits, that, which is elevated 75 Degrees upon the Horizon; you may give ſuch an Elevation to another Wall, in another given Expoſition, as will receive an equal Degree of Heat with the former.

Very few Grounds have ſo much good Earth,Advantage of Terraſſes with Sloping Walls, in reference to a ſufficient quantity of good Earth, which is eaſily procured. as is neceſſary for Fruit Gardens. The charge of bringing ſome, from another Place, is very great: And, unleſs one fetches it from far, there will probably be, too near the Garden and the Houſe, ſome large unſightly place left in a manner barren and deſolate. Neither is it practicable to take away the good Earth, from ſome Parts of your Garden, to bring it to ſome other Parts; except as far as your Alleys, and ſuch other Places, will give leave. But, in a Garden for Fruit, made as I ſhall preſently deſcribe, one may find, upon the Spot, ſo much good Earth, as will much more than double the natural Depth, there was of it before; thô you ſhould plant your Lines of Wall Trees, in the middle of a plat of good Ground, eight or nine Foot wide. And all this may be done, without altering at all the Beauty or Symmetry, of your Diſpoſition.

The ſixteenth Figure is the Ground Plat of a Garden for Trees, Fig. XVI. made up into Terraſſes. It is an exact Square of 470 Foot on each ſide:Deſcription of a Garden for Fruit, according to the preſent Theory. that Figure not being ſo offenſive, in our Diſpoſition, as it is in that which is common. If you would have a bigger Garden you may keep the ſame Breadth, and add two, or four, or ſix, or eight Terraſſes more &c, and order it ſo that the Door may ſtill remain in the middle. If you deſign to have a ſmaller Garden, you may make the Length of your Terraſſes leſs, by 50, or 100, or 150 Foot. And if you would have it ſmaller yet, you may, inſtead of ten Terraſſes,The Ʋſe of making the outſide Wall thicker at bottom than at top. make only eight, or ſix, &c. The outſide Wall is about 10 Foot high; and broader at bottom, than at top. The Breadth at bottom is 3 or 4 Foot. The Breadth at top might be made of 8 Inches; and it would be better yet, if the Wall ended there into a ſharp Edge. The ſides of the Wall are plane; and ſo they muſt needs be ſomewhat Sloping. Thô this may perhaps ſeem to be of little conſequence, yet I do not doubt but it will be a conſiderable advantage for this Wall, to injoy thus the Sun, near the Solſtice, for about half an hour, or an hour, longer of each ſide, than it could otherwiſe; and at the ſame time to injoy it more fully. To which advantage there muſt alſo be added that of a greater Solidity; which will make the Wall to be more laſting, and ſeldom to want any Reparations. On the inſide of this Wall is a Line of four or five Foot of cultivated Ground;A kind of Chanel, or Ditch, to keep the Garden from too much Water. then an Alley round the Garden, and a Chanel, or deep Trench, that may ſerve for a Drain to the Garden. I did ſuppoſe in the Figure that this Canal was faced on each ſide, with a competent perpendicular Brick Wall. But it ſhould always have ſome Water, whoſe Surface ought to be about three or four Foot lower than the Level of the little Walks. One or two of thoſe little Wind Mills, that turn alone towards the Wind, and are ſo common in the Fields in Holland, might ſerve to empty this Ditch, leſt it ſhould grow too full; and, if one would, they might alſo ſerve to diſtribute the Water of it to any other place, or to the Alleys, in order to water the Trees. Thoſe Wind Mills might be placed either within or without the Garden; as you think it moſt convenient. The Breadth of the Canal muſt be conſiderable, if you deſign it for ſtate and ornament; but it may be little, if you deſign it chiefly for uſe. Unleſs the neceſſity of having ſome Earth from thence, for the Terraſſes, makes you to chuſe a large Canal. Under the Middle of the Alleys, a croſs the whole Garden, ſhould be as it were a Common-ſhore, to receive all the ſuperfluous Water of the Alleys, and to carry it into the Ditch. And, if one ſuch Common-ſhore was not ſufficient, one might have two placed at equal diſtances, from the Middle of the Alleys; ſo as to leave between them about half the length of the Alleys, or very little more. After the Ditch comes a little Path, and a Line of cultivated Ground. Then the Slope of the main Terraſſe round the Garden. Then an Alley at the top of it. Then the inner Slope of the main Terraſſe. The reſt are the leſſer Terraſſes, with their reſpective Slopes on each ſide; their Thickneſſes at top; the cultivated Grounds at the foot of them, and the little Walks between. The Door, and Bridge, and main Staires, to get up the main Terraſſe, and leſſer Staires, to go down from it into the Alleys, are eaſily perceived in the Figure; whoſe particular meaſures are as follows hereafter.Meaſures of the Slopes, which are reſpectively made equal. But being made different they may be better fitted for ſeveral Fruits. Thô the Sloping, in all the little Terraſſes, have been made the ſame, and ſuch as are propereſt for latter Fruits, yet it would be more convenient to have them ſomething different. The perpendicular Height of the Terraſſes is 8 Foot. The Slopes that look to the South are elevated 51 Degrees 30 Minutes, above the Horizon. Thoſe that look to the Eaſt 45 Degrees. Thoſe that look to the Weſt 35 Degrees 22 Minutes. And thoſe that look to the North 28 Degrees 53 Minutes. The Height of the South Walls taken along the Slope is 10 Foot 2¾ Inches. That of the Eaſt Walls 11 Foot 3¾ Inches. That of the Weſt Walls 13 Foot 10 Inches. And that of the North Walls 16 Foot 6¾ Inches. The Baſes of the Slopes that look to the South, to the Eaſt, to the Weſt, and to the North have in Breath 6 Foot 4⅓ Inches, 8 Foot, 11 Foot 3¼ Inches, and 14 Foot 6 Inches. The Door is towards the Eaſt.

Expoſitions of the Walls. Height of the Walls in the Slope. Elevations of the Walls above the Horizon. Baſes of the Walls or their Talus. Perpendicular Height of the Walls.A Table ſhewing the Heights, Elevations and Baſes of the Walls.   Feet. Inches. Deg. Min. Feet. Inches. Feet. Inches. South. 10. 2¾ 51. 30 6. 4⅓ 8. 0 Eaſt. 11. 3 • 45. 0 8. 0 8. 0 Weſt. 13. 10 35. 22 11. 3¼ 8. 0 North. 16. 6¾ 28. 53 14. 6 8. 0

Here I bring into one Table the ſeveral Heights, Elevations and Baſes I ſaid did belong to our Sloping Walls.

I go on to give the Meaſures of two ſeveral Sections croſs our Garden.

But, with increaſing the Breadth of the Canal every where, by 15 Foot more, the whole Breadth and Length of the Garden would be 500 Foot each.

If the Garden be deſigned for Vines only,Of a Garden for Vines only. It requires but ſmall Terraſſes. the Terraſſes need not, I ſuppoſe, have more than 4 or 5, or at moſt 6 Foot, in the Slope that looks to the South; and accordingly they will be ſmaller, and nearer one another; and by conſequence they will be leſs chargeable; and the ſame Extent of Ground will yield more Fruit.

Suppoſing the Ground not to be of the very beſt ſort,Of the Number of ordinary Trees the Garden could hold: but of a middling kind, between that, and the ſort of Ground Monſieur La Quintinye calls indifferent; the Garden, whoſe Meaſures I have juſt now given, would hold almoſt 1600 ordinary Fruit Trees; taking in thoſe that may be placed againſt the outſide of the Wall, that goes round the Garden. This will appear upon examining the three following Tables, where I make yet no allowance for the Trees growing bigger, againſt our Walls, than againſt the ordinary ones.From whence is to be eſtimated the Number of its Fruits, But the Tables however will very well ſerve, to gueſs at the Quantity of Fruits, that will be produced. And this muſt be with allowing for each Tree according to the common rate of their Fruitfulneſs.

Height of the Wall taken along the Slope.A Table ſhewing the Heights and Lengths and Expoſitions of the Walls. Length of the Wall. Expoſition of the Wall to the Heavens. The Walls ſpoken of in this Table. Feet. Inches. Feet. Inches.     10. 0 456. 0 Eaſt. Outſide of the Wall that goes round the Garden. 10. 0 468. 0 South. 10. 0 468. 0 Weſt. 10. 0 468. 0 North. 10. 0 458. 8 Eaſt. Inſide of the Wall that goes round the Garden. 10. 0 458. 8 South. 10. 0 446. 8 Weſt. 10. 0 458. 8 North. 11. 3¾ 347. 6 Eaſt. Outſide of the main Terraſſe round the Garden. 10. 2¾ 360. 4 South. 13. 10 359. 6 Weſt.   16. 6 360. 4 North.   11. 3¾ 27 Trees Eaſt. The Nine little Walls, at the Bottom of the Nine Alleys. 20. 2¾ and 9 Trees South and Weſt. The Nine Corners at the right hand, at the going into the Alleys. 13. 10 16. 6¾ and 9 Trees North and Weſt The Nine Corners at the left hand, at the going into the Alleys. 13. 10 16. 6¾ 297. 0 North. One of the North Walls of the little Alleys. 16. 6¾ 2376. 0 North. The remaining 8 North Walls. 10. 2¾ 297. 0 South. One of the South Walls of the little Alleys. 10. 2¾ 2376. 0 South. The remaining 8 South Walls.

This firſt Table allows twelve Foot to the Gate and Pillars; and makes the Length of a Sloping Wall middlemoſt, between its Length at Bottom, and its Length at Top. Only, as to the long Slopes of the little Alleys, obſerve that they are ſet down leſs by 8½ Foot, than what they really are at Bottom: So much being allowed, for the ſpreading of the Trees in the Corners.

The Reſult of the firſt Table is here ſet down in the ſecond. Eaſt.Short Table giving the Reſult of the former. South. South and Weſt. Weſt. North and Weſt. North. Length and Height of the Walls. Length and Height of the Walls. Length and Height of the Walls. Length and Height of the Walls. Length and Height of the Walls. Length and Height of the Walls. 914. 8 10. 0 926. 8. 10. 0 9 Trees. 10. 2 • ; 914. 8. 10. 0 9 Trees. 16. 6¾ 926. 8. 10. 0 247. 6. 11. 3¾ 3033. 4. 10. 2¾ and 359. 6 13. 10 and 3033. 4. 16. 6¾ 27 Trees 11. 3¾         13. 10         13. 10        

Monſieur La Quintinye divides our Wall Trees into two Claſſes:Some Suppoſitions taken from Monſieur La Quintinye: and, according to him, if the Ground be between very good and indifferent Soil, the Walls, whoſe Height is in the Table 10 Foot and 10 Foot 2¾ Inches, require the Trees of the firſt Claſs to be at eight Foot ſix Inches diſtance aſunder; and the Trees of the ſecond Claſs to be at ſeven Foot three Inches diſtance aſunder. The middle Number between thoſe is about 8 Foot. But the Walls, whoſe Height is in the Table 11 Foot 3 • ; Inches, and 13 Foot 10 Inches, and 16 Foot 6 • ; Inches, require to have their Trees alternately intermixt, with making them by turns a high one and a low one: and their Diſtances muſt be about five Foot three Inches, one with another.

According to theſe Determinations,By which a Table is made of the Number of ordinary Trees, the Garden would have. the laſt Table will give the following Numbers of ordinary Trees.

Eaſt. South. South and Weſt. Weſt. North and Weſt. North. Trees. Diſtance. Trees. Diſtance. Trees. Trees. Diſtance. Trees. Trees. Diſtance 114 8 116 8   114 8   116 8 66 5¼ 379 8 9 68 5¼ 9 577 5¼ 27 5¼                

The total Sum of Trees is 1595.3½ Vines to be ſubſtituted for one Tree. And for one Tree, that takes up 8 Foot Space, you may ſubſtitute, if you pleaſe, 3 • Vines. But if the Ground be very good the Number of Trees will be leſs.

So then our Garden might hold 1300 ordinary Trees,General Sum of ordinary Trees and Vines in the Garden. and 1000 ordinary Vines; or 1400 ordinary Trees, and 680 ordinary Vines. And from thence muſt be eſtimated the Number of its Fruits.

But it would be very unwiſe to make ſuch high Terraſſes,Of Terraſſes for Vines only. to ſerve for Vines only. For that Plant being of ſuch a Nature,Vines ought to be kept very low. as not to do well in theſe Countries, if it be ſuffered, as it is too often done, to ſpend its ſtrength in nouriſhing an overgrown Stock; we may follow their Directions, that adviſe us to keep it ſo low,La Quintinye. as to give, for inſtance, to Muſcat only the Height from three Foot to five. A Terraſſe for Vines would then be great enough, unleſs I miſtake in drawing this concluſion, if it was but half as high as thoſe I have deſcribed. Neither would it be neceſſary to allow more than half the Breadth, we did give to our Alleys, or very little beſides. And ſince this great narrowneſs might prove troubleſome, becauſe of the Rain, I would in building the Terraſſes ſpare, within, and at a good Depth under each of them, a little paved Ditch, to carry off the Rain at both Ends, and to keep the Alleys clear of too much Water. The ſame might alſo be conveniently done, in building any Terraſſes, thô never ſo big.

But,Of a large Terraſſe parted into two for Vines. if you think it too improper, to have in one Garden a mixture of large and ſmall Terraſſes, you might cut one great Terraſſe ſo, as to afford, in the middle of its Height, a Step for another row of Vines; as you ſee in the ſeventeenth Figure. Fig. XVII. I ſhould however, upon many other Accounts, and alſo for fear of the Vines of the lower part of the Terraſſe intangling with thoſe of the upper part, rather chuſe to have a whole Garden for Vines, excepting only the bad Walls in it: And ſuch might be, after ſome few changes, Fig. XVI. the ſixteenth Figure; if we ſuppoſe the outſide to be only of 240, or 300 Foot.

Now,The Garden will not hold ſo many Trees, as it would, if they were to keep within the ordinary Size. as I did already intimate once before, our Garden will probably not hold ſo many Trees, as are ſet down in the laſt Table. For there being more room with our Walls, than with the ordinary ones, for the ſpreading and growing of the Roots round about, they will make their Trees undoubtedly to grow bigger,The Trees in it will grow very large and why: and larger every way. The beſt Fault, in determining the Diſtances, between the Trees, is to make them too big at firſt;And muſt be far aſunder: for fear of the Confuſion, and want of Fruitfulneſs, that attends thoſe Diſtances, when they are made too ſmall. However in this we find a new advantage of our Gardens; ſince a ſmaller Number of Trees will garniſh the ſame Extent of Walls,Yet will not yield a leſs Crop of Fruits. and give no fewer Fruits, than a greater Number would have done; and will be withal more vigorous and laſting.They will be more laſting. But the Difficulty lies in gueſſing at the Diſtances we muſt chuſe.A gueſs at their Diſtances. For my part I would, for the firſt Tryal, if the Ground be good, not only make them as great, as the Diſtances, See La Quintinye Vol. II. p. 294. and Vol. l. p. 208. &c. Monſieur La Quintinye determines, for the very beſt ſort of Ground; but make them yet, by about one ſixth or one fifth part bigger. Neither would I begin to mix alternately big Trees and little Trees together; unleſs the Wall were, at leaſt, twelve Foot high.

We muſt take notice here that the Paris Foot,Proportion of the London Foot to that of Paris. uſed by Monſieur La Quintinye, and after him by me, is to that of London as 16 to 15. So that to the London Foot one muſt add ⅘ of an Inch, to make it a Paris Foot.

I have drawn,A Draught of the Garden in Perſpective. with a great deal of care, according to the Rules of Perſpective, in a large Print by it ſelf, the Elevation of the South-Weſt Corner of our Garden.Pag. 1. Any body may judge, by the effect of this Figure, particularly with hiding the lower part, whether Sloping Walls and Sloping Trees will be much offenſive to the Eye. For my part I think it may be a queſtion whether an ordinary Fruit-Garden, with perpendicular Walls, can ever be made to look ſo pleaſant, and ſo full of a regular and ſtately variety, as I find the Figure to be. That ſtatelineſs is altogether owing to thoſe great and maſſy Terraſſes, which, in our Draught, overrule, as it were, and maſter the whole; and have an effect like to that of very large Columns, in our Buildings. They have beſides, from ſo many Trees ſet againſt them, in a regular order, that Airineſs and Gayity, which ariſe in our Architecture, from abundance of proper Ornaments. The Canal is made broader than according to the meaſures of the Ground Plat. It will not only be nobler, if it be very broad; but, if you have no natural riſing, in the midſt of your Ground, it may yield alſo the Earth neceſſary for the Terraſſes, without ſinking the level of the Garden. The Figure will help to conceive how ſome Roofs might be uſed, inſtead of Terraſſes.

If the Garden be very large,Diviſion of a large Garden, by ſome Canals, into four or ſixteen little Gardens, or any other Number. and you are at a loſs where to have all the Earth, that would be required; even thô you ſhould pretty much increaſe the breadth of your Canal; keep the outermoſt ſquare Terraſſe untouched; and in the middle of your Ground Plat, draw, from ſide to ſide, a large Canal, like a Croſs, ending at the four ends perpendicularly againſt the main Terraſſe.This will yield the Earth neceſſary for the Terraſſes. This new Canal will give the Earth you want: And each of the four Diviſions of the Garden muſt be finiſhed by it ſelf, according to the Idea I have followed, in the ſixteenth Figure. Only the new Terraſſes, that go round the inner half of the four Diviſions of the Garden, and make up the Banks of the new Canal, ſhould not be ſo large, as the main Terraſſe.

After the ſame way, if the Extent of the Ground was extraordinary great, and there was yet ſome Earth wanting one might again, by four new Canals like a Croſs, ſubdivide each of the four laſt Diviſions: which would give ſixteen ſmall Gardens in all.And either give different Ponds for ſeveral ſorts of Fiſhes: Or elſe open the Way, by Boats, among the Gardens: If theſe Canals be deſigned for ſeveral Ponds, where you may keep different ſorts of Fiſhes, they need not have any communication one with another. But if you would have the liberty of going every where, with Boats, among the Gardens, it will be ſufficient, if all the Canals be opened, and continued into one another, along that Branch of the main Croſs, which the Bridge dos come up to: excepting only that part of the main Terraſſe, the Bridge ends againſt.Aud leave alſo a Foot Way into them all. Thus you might go, at your pleaſure, either with a Boat, or walking, to any one particular Garden. As the outer Terraſſes are made leſs and leſs, according as their Length decreaſes, ſo ſhould alſo the Canals be made leſs and leſs broad. Now, by ſuch Canals, your Garden might be divided, not only into four or ſixteen ſmaller Gardens, but into any other Number.

Thô ſuch large and magnificent Gardens can only be the Work of Princes,Any ordinary Gentleman may have a few Terraſſes, or Slopes, well expoſed. and other Great Men, or of powerful Societies; yet there is no ordinary Gentleman, that is able to have a Garden, but may, according to his ability, and the Directions I have given in other places of this Diſcourſe, have one or more Terraſſes, or Slopes, well expoſed, of what length he can afford: So that he may have, againſt them, a competent number of Vines, and other Trees. And whereas they ſay now, for inſtance, I have got fifty Yards of very good Wall; they may ſay hereafter, to a greater commendation of their Gardens, I have raiſed 30 or 40 Yards of a Sloping South Wall.

It may happen that,A Tryal of Sloping Walls not to be depended upon, unleſs made by a very good Artiſt. upon ſome Tryals made by an unskilful Artiſt, our Walls may ſeem not to be of any uſe, for the Production of good Fruits. But ordinary Agriculture dos not now thrive equally, in everybody's hands. And whilſt a diligent and underſtanding Country Man is largely repaid for his Care and Induſtry, the unskilful often ſees himſelf deceived in his hopes. There will ever be a juſt diſtinction, between thoſe that act by the certain Principles of an Art grounded upon Nature, and ſuch as act in a great meaſure by chance. The ſame Inſtruments, according to the ſeveral Applications that are made of them, being managed by two ſeveral Hands, produce often both what is deſervedly admired of one ſide, and what is as deſervedly deſpiſed on the other. In a word, I do not hope, by this Theory, to make all Gardeners equal among themſelves. But I give them, in all Countries, an eaſie,A good Culture more ſignificant than a good Expoſition. and natural, and very great Increaſe of the Sun's Heat; which may often aſſure them of an extraordinary Succeſs; thô without excluding the neceſſary Care and Skill, which after all is the moſt ſignificant Part.

If what I have been propoſing might,Sloping Walls very neceſſary, while our Summers continue to be ſo cold. at any time, have been acceptable and uſeful to Mankind, it muſt certainly be ſo now. Every body has been ſenſible, for theſe twelve or fifteen Years, of a very great, and, as ſome think, unaccountable Change in our Seaſons. Our Summers are much colder than they were; and 'tis but ſeldom they bring us any Thunder. Their Influence is felt in many of the Productions of the Earth; particularly in all ſorts of Fruits, that come late in the Year: for ſuch have no Heat to bring them to perfection. And the unſettledneſs of our Springs commonly deſtroys the very firſt hopes we have, at the bloſſoming of our Trees. The cauſe of this Change, in our Seaſons, is often the Subject of common Diſcourſe: And it is no wonder to ſee how wide and empty the gueſſes of moſt people are, upon that matter. This is certain, and was made out heretofore paſt diſpute,The cauſe of that change in our Seaſons referred to a Phenomenon like Smoak, that incompaſſes the Body of the Sun, and is ſeen to ſpread an exceeding great way from it. that from the Year 1683 downwards, and I ſay now even to the preſent time, the Sun has been in the very Middle, or Center, of a thin Miſt of a prodigious Extent; which, incompaſſing the whole Body of the Sun, ſpreads near the Plane of the Ecliptick, ſo as to reach almoſt the great Orb of the Earth; reſembling much, in its Figure, an ordinary Ocular Glaſs, or Lens, equally convex on both ſides. Its Thickneſs or Opacity (not where it is greateſt, but where we may begin to ſee it, when the Night is already become dark) is like that of the Tail of a Comet, or the Milky Way. But it is yet conſiderably greater, juſt in the Line that paſſes from the Earth thrô the Body of the Sun. Whoever has ſeen this Vail, that is ſpread between the Sun and us, will eaſily grant that it muſt needs take off ſome part of its Heat. There has not yet been found, at leaſt as far as I know, any other old Footſtep of this ſtrange Phenomenon, but that in 1660, Mr. J. Childrey, in his Britannia Baconica, has printed that he had obſerved it ſeveral Years together, and he deſired Aſtronomers to mind it. Thus much ſeems very poſſible, that it might be many Years unobſerved in the Sky, and perhaps have continued for ſome Ages, without being minded. But the very change in our Seaſons ſeems now to be a Proof, that it has either not been at all, in former times, unleſs we ſhould find in Hiſtory ſuch another Series of cold Summers, or at leaſt that it is has not been ſo thick, or has not laſted ſo long,The Origine of that Smoak. as at preſent. The true Syſtem of the World having at length been diſcovered, by the immortal Mr. Newton, we may perhaps gueſs more exactly, than heretofore, at the natural Cauſes of this Appearance. It ſeems then, at leaſt, the outſide of it, to ariſe from ſome Fumes, or Exhalations, which the Sun throws up, with an equal Strength, and the greateſt it can, all about its Body, perpendicularly to the ſeveral points of its Surface. And the Sun revolving at the ſame time, about its Axis, in ſome 25 Days, occaſions the ſpreading of that Smoak, near the Plane of the Sun's Equator, much farther than it dos towards the Poles. The Parts of Smoak, whoſe Swiftneſs is not ſo great, do not riſe ſo high; and perform all their Motions, within the Body of the Phenomenon; not being able ever to come near its Extremity. And, ſuppoſing ſeveral Degrees of Swiftneſs in thoſe Particles, the Phenomenon ought to grow much denſer, as one approaches the Sun: which our Obſervations alſo do confirm.How to determine the Figure of the Space it lies in.

From the Suppoſition that the Particles of Smoak, that fly out at the Sun's Equator, perpendicularly to its Surface, are able to riſe ſo far, as to reach, as by Obſervation they are ſeen to do, the Circumference of a Circle, that ſeems, at its Extremity, to be removed from the Sun by about 70 Degrees, I have calculated how high would riſe the Particles that ſhould, with the ſame perpendicular Velocity, fly out of the Poles of the Sun. And the Calculation gave me that Height, as agreed very well with the Breadth, the Phenomenon ſeems to have in all its Parts. It would have been eaſie, upon the ſame Grounds, to make the like Calculations, for ſo many points in the Section thrô the Axis, as would have made it ſufficiently known; and by conſequence have ſerved to eſtabliſh, or overthrow my Conjectures. But as yet I have neglected to do it. And this is no proper place to handle this Subject more exactly.

I ſhall only ſay that I look upon each Particle of Smoak, that riſes from the Sun, as having its Motion as free, as if it was a Planet: The ſame being obſerved alſo in the Smoak, that compoſes the Tayl of Comets. So then each of our Particles revolves in an Ellipſis, till being near the end of its Revolution it falls into the Sun again. The whole Body of the Phenomenon is thus perpetually ſupplyed afreſh, ſomewhat in the nature of thoſe Jets d'Eau, or Water Spouts, they call in French, des Gerbes. The extraordinary ſmall number of Spots, that appear for theſe many Years ſo ſeldom in the Sun, whereas in the firſt half of this Age they were ſo very numerous and ſo frequent, leads us to ſuſpect that the matter of thoſe Spots has, for ſeveral Years, been kept evaporated and diſperſed, in all the Space I have juſt now deſcribed.

For ought we know yet this Phenomenon may,It may grow thicker, and yet not be perceived to have changed, except perhaps by its Effects. at ſometimes, by the ſupervention of a thicker and heavier Smoak, grow denſer about the Sun, than at other times; thô the outſide of it ſpreads but to the ſame place, and ſeems not to increaſe in thickneſs. So that our Heat, in our Summers, may very much alter, without our being able to perceive any Change, in the outermoſt Part of the Phenomenon; which is the only Part viſible to us; unleſs the Sun ſhould be totally Eclipſed; and give us, in the middle of the Day, an Image of a dark Night.