THere are diverse Motions of the Moon, being 15 in number; accounted by Ricciolus, in his Al­magesto Novo Astronomiae▪ lib. 4. cap. 18.

But here I intend to treat of those Motions that are most usefull for Seamen and Mariners, according as their daily practise doth require.

South and North Moon, maketh a full-Sea, at Buchan­ness, and all along the South-side of the Murray-F [...]rth, (viz) Cromarty, Millorchy, Inverness, Findorne, Spey: also Ba [...]ff, Peterhead, Isle of Wight, at Deal, at Beachy, and before the Race of Blanquet, in the Condado, at Dover-Peer, and before Dunkirk, at Emden, before the Elve, be­fore the Eyder, and before Enchusen, on the Coast of Flan­ders, in the Road of Gibralter, at Graveling and before Gher­brough, before the Hever, before Horn, and at Hampton-Key, at Jutland-Islands, Kentish Knock, at Liegh, and at Newport half Tyde, at Portsmouth half Tyde, at Qu [...]brough, in the Sleeve, between Vshant and Silly, at the Shooe, at the Spits, at South-Hampton, and all along the Swin, before Vr [...]ck

S. by W. or, N. by E. Moon, at New-burgh, ABERDEEN, Stonhyve, Redbane, at Blacktail, and thwart of Beachy in the Offing, in the Camber of Rie, at Flushing within the Maes, and at Maldon, at the West end of the Nower, at Roches­ter, within Terveer, at Winchelsey.

[Page 30] S. S. W. or, N. N. E. Moon, at Montrose, the out end of Tay, St. Andrews, Cryle, E [...]ster, and all a­long the Coast of Fiffe to Brunt-Island, at Army, at Black-ness in Bluet, at Bell-Isle, at Baraik [...], with­out Calice, at Corpus-Christi point, before Camfer, and at Camfor, at Edam, before the Fen in the Channel, before Gourie, and at Graves-end, under Holy-Island, and at Horn, before the Maes, at Ramkins, before Terveer, before the River of Thames, and at Tinmouth, at the Weilings, and from the West end of the Weight, before Yarmouth, on the Coast of Zealand, at Fern-head.

S. W. by S. or, N. E. by N. Moon, at LIETH in the Firth, Dundee, Brunt-Island, Holy-Island, Lucas, without Bluet, at Denby, without Fountnay, at Lisbon, before the Weilings.

S. W. or, N. E. Moon, at Ennerkything, Queens-fer­rie, St. Margarets-hoop, Borrowstonness, Lyme-Kills, and all above Inchgarvie, except Stirling-Bridge, at LONDON, and before Newcastle, at Amsterdam, and Armentiers, the River of Bourdeaux, the South Coast of Britaign, the Coast of Biscay, at Bockness, between Calice and Dover, before Conquet, and at the North-Cape, at Dort, without the Banks of Flanders. at Groy, at Gascoign, and the Coast of Gallicia, before Hartlepool, on the West Coast of Ireland, Killiars, and before the River of Nantz, at Orkness, at the Penns, Porthus, and Picton; at Roterdam, in Robin-Hoods Bay, and from the Race to the Pole-head, upon the Coast of Spain, and in Shotland, before the Tees, and be­fore the Bay of Tinmouth, at Vse, and in the Zierick-Sea.

S. W. by W. or, N. E. by E. Moon, from Buchan­ness, and all alongst the Coast without, above the May, or Highland in the South-Firth, and from Flambrough-head, to Birdlington-Bay without, Ostond, at Brest before the Bass, the River of Bourdeaux within the Haven, and at Berwick, at Huntclif-foot, at the Maes, and before St. [Page 31] Mathews Point, on the Coast of Portugall, at Roven, and before Rochel, at Silly, and in the Sound, at Staples, between Vshant and the Main.

W. S. W. or, E. N. E. Moon, A little off the Shore before Humber, between Bridlington and Lower-ness, at Lands-end of Golph, from Ostend to St. Ca­tharines, at Aberwark, in the Bree-sound, Bloy, Baltimore, at Cork, at Calice, and in the Creek, at Dungarvan, at Flambrough, and Bridlington, at Kingsale, in Mousehole, at Mathews, and within Mounts Bay, at the Clefts of the Texel, in the Vourd, at the Bay within Vshant, in the Sea of Wales, and Severn, at Yough-Hall, before Scarbrough, at Seven-Isles, without the Haven in the Broad Sound, at Lawrens, in Cork-Haven.

W. by S. or, E. by N. Moon, at Ar [...]roth, at Caldy, and in the Bay of Canarvan, at the Fourn, in Foy, at Fal­mouth, at Garnsey▪ at Humber, in all the Havens on the South Coast of Ireland, thwart of Londey, and before Line, in Malford, at Moonless, at St. Maloes, at New-Castle, in Plimouth, and before St. Pauls, in Ramsey, at the mouth of Severn, between Silly and the Lizard, at the Spurn, in Wales, at Merles, and all along the Coast of Bristol.

E. or W. Moon, at Abermorick, and Antwerp, before Bremen, and at Blackney, in the Channel before Bourdeaux, and at Bristol, at Concallo, at Dartmouth, before Hambrough, at Hull, at the Holms, and before Humbers mouth, at Lin half [...]yde, at Londey, at St Pauls in the Haven, without Silly, in the Channel, and at Salcomb, in Torbay, and before the Tessell, without Vshant, at Wells, at Weighmouth, and at Waterford, and St. Davids-head.

E. by S▪ or, W. by N. Moon, at Bristol-Key, between Foy and Falmouth▪ in the Channel, and at Foulness, at Lime, before St. Nicolas, before Podessinsk, in Russia, at [Page 32] Sedmouth, and at the Start, at Weighmouth-Key.

E. S, E. or, W. N. W. Moon, at Bridgwater, at Cape Cleer, before the Coast of Friezland, and the Fly, at Kilduyn, at the Lizard by the Land, between Musehole and Falmouth, and in Milford Haven, thwart of Plimouth, Off the Start in the Channel, in the Road of the Texel, at the Ness by Wieringben, and at Winterton, at Exwater, at Lands-end.

S. E. by E. or, N. W. by W. Moon, between Bea­chy and the Isle of Wight without the Caskets in the Channel, at Dublin, without the Fly, at Lambey, in St. Magnes Sound, at Machnells Castle, at the Needles, at Isle of Wight, thwart of the Isle of Wight in the Channel, all within the Isle of Wight, between the Isle of Wight and Beachy by the Shore, at Yarmouth, at Peter-Port, at Harflew, at the Hague.

S. E. or, N. W. Moon, at Penthland-Firth, at Kirk­wa, at Elwick, at the Mull-head, at Catness, at Orkney, the Bass-Island, at Dumbar, at Kildren, at the Isle of Man, between Garnsey and the Caskets, before Cromer, before the Casket, and Garnsey, at Seven-Clifts, before the Eas­tern and Western Emes, and at Egmont, at Frieze, and Fair-Isles, between Garnsey and Caskets, at Harlem, and at Homehead, at Kildive, at the Race of Portland, within the Seyn, before Schelbagh, and at Seven Cliffs, at the East end of the Weight, and on Wieringen-Flats, at Pool, at Farro-head in the Channel, between Farro head, and the Mull of Kintire

S. E. by S. or, N W. by N. Moon, at Alborough, at the Caskets, and at Chamberness, at Dungeness, and Dun­nose, thwart of Garnsey in the Channel, at Leystaff, and thwart of it without the Banks, at Orford-ness, at Sho­ram, at Tergow, at Deep.

S. S. E. or, N. N. W. Moon, Bulleyn deep, at Cows, in the Foss of Caen, in Calice Road, and in Chamberness-Road, [Page 33] at Dover, and in the Downs, in the Freith, and at the South-Foreland, at St. Helens, at Harwich, and with­out the Banks of Harwich, in Leystaff Road, and at Long­sand-head, all the Coast of Normandy, and Picardy, at Or­fordness without the Banks, and between Orford and Or­well-Waves, at Seyn-head, in Yarmouth Road, and in Yar­mouth-Haven, at Brassie-Sound, at St. Iohns-Deluce, at Ca [...]e­stoun, and at Scra [...]sler.

S. by E. or, N. by W. Moon, before the Haven of Caven, in the Chamber, between Cripple Sand and the Creyl, and at Culshot, in Fair-Isle Roads, and at the North-Fore­land, in the Chamber, and Gore [...]end, at Harwich within, before Margate, between the Naze and Warhead of Lo­wer, at Orfordness within the Sands, at Rye, and into Thames-Roads, at Calshot.

I charge the Printer with severall Errors in his Almanack, set forth and printed by him for the Year 1683. And first, concerning the Eclipse which did fall out upon the 17 day of Ianuar in the afternoon, wherein he is deficient in giving the Digits Eclipsed; as also, in reference to the tyme of the E­clipse duration.

Courteous Reader, I confess, being about my serious Imployments in the Printing Press, I could not have leasure to Calculate that Eclipse, but made use of several E­phimerides; as Vincent Wing, and Samuel Morland, &c. And Argolus doth assert the Digits Eclipsed to be 10 and more, Iohn Gadbury 9: Paterson 8 dig. 13 min. as for the time, Iohn Gadbury sayeth, the middle will be at 3 hou. afternoon, the end at 4 hou. 3 min, or after the going down of the Sun: for in the Latitude of 57 degrees 10 minuts, being for Aber­deen, the Sun seteth being in the 8 degree of Aquarius, at 3 hou. 57 min. but Paterson sayeth 10 min. before 4 hou. at Aberdeen, which is near half an hour; (a Prodigie which was never seen, the Sun to set at 3 hou. 30 min. at Aberdeen!) but by reason of the refraction, the Sun may appear or show himself above the Horizon, when he is not, If so the pa­rall [...]x be lesser then the refraction; and so I may truely and warrantably say, the Sun doth set at Aberdeen, the 17 day of Januar, at 4 hou. 18 min. afternoon. But granting I be [Page 38] redundant in some Minuts, but not so grosly, and as to say, not so deficient as he is, in saying the Sun being in the 8 de­gree of Aquarius, seteth at 3 hou. 30 min. but in trueth, at 3 hou. 57 min. But what doth this concern me? My An­tagonist cannot say, there is any wrong done to the Vulgar, or Horascopographier. But, as for that Eclipse which by an Telescope of 6 foot long, I did observe at the seting of the Sun, and did not find above two digits of the Suns body ob­scured, with no apparent darkness, or shaddow of change by that Eclipse: it was (as we all say,) to West-ward Inha­bitants. But lastly, I shall lay down some certain things to be observed in going about this Eclipse, and some things I shall demand of this Mathematician, in which I hope he will satisfie me, except he be, Mathematicus nomine tenus, (as I suppose) for I shall be as Laconick as I can, in­tending not to trouble the Reader with frivolous Expres­sions. First, supposing the middle tyme of the Eclipse to be at 3 a clock in the afternoon, according to Iohn Gadbury. First, Granting the true places of the Luminaries, with the Mo [...]ns-Latitude, either by Calculation or Ephimerides. Se­condly, I find the right ascention of the Sun in 8 degrees of Aquarius to be 310 degrees, added to 45 degrees or 3 hours, giveth 23 hou. 42 min. which sheweth the 25 degree of Pisces to be on the Meridian or Medium Coeli; and the Ascendent 28 deg. 28 min. of Cancer: and consequently, the Nonagisimo degree falleth in 28 deg. 28 min. of Aries, being East ward of the Meridian 33 deg. 28 min. Thirdly, The Declination of the 25 deg. of Pisces, added to 57 deg. 10 min. giveth 59 deg. 9. min, the Arch of the Meridian between the 25 degree of Pisces and the Zenith. Fourthly, The Angle of the Ecliptick with the Meridian, being 66 deg. 33 min. giveth the Arch between the Nonagesim and the Zenith, by saying as R: Sine 59 deg. 9 min [...]: Sine 66 deg. 33 min: Sine of 51 deg. 48 min. Fifthly, Having the true [Page 39] Latitude of the Moon, with the Parallax of Altitude, and having found the Parallacticall Angle, that is to say, the Angle made by the Ecliptick, and Vertical drawn through the Center of the Moon to be 52 deg. 11 min. Sixthly, The Altitude of the Sun being at 3 hours in the afternoon, in the Latitude of 57 deg. 10 min. is 5 deg, 41 min. These being premised, I desire to know of James Paterson, the Parallax of Altitude, Longitud, right Ascention and Decli­nation: whereby we may know the tyme of the visible Conjunction, the beginning of the Ecl [...]pse, the middle, and end end; with the Digits Eclipsed: whither above or un­der the Center of the Sun. There are here required the resolution of severall Triangles, wherein, ex tribus datis quartus requiritur, either by Calculation, or Projection.

Also he errs again in his Tyde-Table at Lieth, as if the Moon were not able to rule the Tyde here as at Aberdeen.

As for the flowings at Lieth, which he carps at, they are not set down by my self, at upon my own account, but in so far, as they have been approved of, by ancient Seamen, Masters and Coasters; asserting that at Lieth, a S. W. by S. Moon maketh at nearest a full-Sea. This being a generall Observation, therefore doth admit of some particulars; as the Wind blowing at such and such an Art, causeth the flowings to varie, sometymes an half point, and sometymes more, in setting the flowings high, and other times low: yea, the Seasons of the year, sometimes doth alter and change the streams, as about Lambas, the streams then are higher, then at certain other tymes, and consequently the generall Role doth not hold altogether certain at all times; but doth sometime varie. It is holden as a generall Rule by most of Seamen, that 3 quarters of an hour doth answere to a point of the Compass, the reason fo this is, (as they say,) because a quarter of the [Page 40] Horizon, answereth to a quarter of the Equinoctiall, and consequently, 8 Points to 6 hours: so that they would have the Equinoctiall equally divyded, as they do the Points of the Compass. I confess, into a Parallell Sphear, it will hold true, but not into an Oblique Sphere: As admit, in the Latitude of 56 degrees, S. W. by S. being 3 Points, or 33 deg. 45 min. or 2 hou. 15 min. I find in the Equinoctiall 29 deg. to which in time answereth to 1 hou. 56 min. of difference, being 19 min. in tyme. And this found out by a Sphericall right Angled Triangle, by saying, as R: S: Lat:: Tang. Arch of the Horizon: Tang. of the Equi­noctiall Arch. The neglect of this is an Error, although not admitted by many Seamen; but constantly asserting that 45 min. in tyme doth answere to a point of the Compass. James Paterson, in his Corrected Tyde-Table, doth make Lieth to differ from other Tables, sometimes a whole hour, sometimes less; and in some agreeing, (to the great detri­ment and h [...]zard of Ships seeking Lieth Harbour.) not determinating the true place of the Moon, which maketh a full Sea at Lieth; for if he shall have his recourse to the Theorie of the Moon, except only the middle Motion, he shall involve himself into such a Laborinth, out of which he shall never be able to extricate himself. Therefore by all that I have said, I see no ground for his Corrected Tyde-Table: And no marvell, he not being bred a Seaman, nei­ [...]her educate in Letters or Learning, as I am informed, and [...]et calls himself, Mathematicus; O horrid Impudence! [...]ut being a while in Ireland, and having gotten some smat­ [...]erings in the Mathematicks, cometh to Edinburgh, and [...]ayeth himself forth for Mathematicus: if it be other­wise then is related, certainly he will shew himself in giving a solution to these five following Problems, not [...]y Assertion, but by Mathematicall Demonstration, I call them [...]irocinia Nautica.

[Page 41]PROBLEM I.

There are two Islands in the parallell of 40 degrees, dis­tant from each other 70 Leagues, a Ship sailing from the Westermost Island, between the N, and E. doth meet with a Ship that had sailed from the Eastermost, between the N. and W. and they are both in the Latitude of 41 degrees 30 minuts, and these two Ships have sailed 100 Leagues, I demand by what Courses these two Ships have sailed? and how many Leagues in every particular Course?

PROBLEM II.

There are 3 Islands, A, B, C, the Island A, and B, in the parallell of 40 degrees, and are distant from each o­ther 30 Leagues, the third Island C, distant from A, 45 Leagues, and bearing of A, North-West: a Ship steering her Course East-South-East from C, so long, till she com­eth to the parallell of 40 degrees. I demand how far she hath sailed from the Island C, before she bring the two Islands A, and B, sub maximo Angulo, or greatest Angle?

PROBLEM III.

A Ship in the Latitude of 40 degrees, is bound West-ward, and being at A, she setteth an Island B, bearing of her South, and keeping her Course West, being at C, she setteth the same Island bearing of her South by East, 5 de­grees Easterly. Again, being at D, South-South East 4 de­grees Easterly. Lastly, being at E, she setteth the same to bear of her South-East by East 6 deg, 15 min. Easterly: and hath sailed between D, and E, 2, 9 Leaug, more then between C, and D. I demand how far B was distant from A, when bearing Southerly.

PROBLEM IV.

A Ship in the Latitude of 40 degrees, saileth so long be­tween the North and East, till she altereth her Longitude 10 degrees, and hath departed from her first Meridian, 96 Leagus, 2 Myles: I demand how far she hath sailed? and by what Course?

[Page 42]PROBLEM V.

Mr. Norwood, in his application of Sphericall Trigono­metrie, to the third kynd of sailing, by the Arch of a great Circle, which is demonstrated by him, and others, to be the best way of sailing. (Consideratis Considerandis) There­fore, supposing two Places or Islands, lying in the parallell of 60 degrees, distant from each other 20 degrees in Longi­tude; and there are two Ships, the one sailing in the pa­rallel, the other upon the Arch of a great Circle: I de­mand whither or no, he that saileth upon the Arch of a great Circle, doth make a major, or, minor ratio, to the great Circle, then he that sailoth upon the Arch of the Parallell, doth to the Parallell in which he saileth?

In all these five Problems, I have given Letters Alpha­beticall, by which any Mathematician may forme Triangles at pleasure, secundum data & requisita: And this much as to this purpose in the Art Nauticall; and so I proceed to another head.

I have in the said Almanack for the Year 1683, described an Instrument, called the Lyne of Chorde, with a Scale of inch, and half inch, divyded in 8 equall parts, the former, serving for measuring of all right lyned Angles, the latter, for measuring the length, breadth, and thickness on Pa­per; and may serve for Foots, Ells, Falls, R [...]ods, Myles, or Leagues: all which the Printer hath not in his Prog­nostication.

I confess I have not the Lyne of Chords, or equall par [...]s mentioned in my Almanack, wha [...]thee, cannot a right lyned Angle, be measured by a line of Sines, or Tan­gents, as well as by a lyne of Chords? especially by a line of Sines, seeing Sines are halfs of Choras▪ so that what i [...] per­formed by the whole, may be performed by the half: & contra. As for your lyne of Chords, with your use ye make of them; if there be no more, * Cabin-boy can say al [...] much [Page 43] as you can say, without any detriment to the Mathematicall-Science. What do ye say, as not being acquaint (as I sup­pose) with the Orthographicall Projection, wherein the Ob­ject, either Sphere or Glob is supposed to be projected in plano, at an infinite or indeterminate distance from the eye; from whence cometh or ariseth Ptolimie his Analemma, wherein the Solisticiall Colure being seen directly, is circu­larly projected. The other five, to wit, the Horizon, Equi­noctial, and Ecliptick; with the hour of Sex, and Prime Azi­muth o [...] East and West, being seen perpendicularly, are pro­jected in straight Lines: the Eye being in the intersection of all those Circles in principio Arietis. The other Circles that are seen Obliquly, are projected Eliptically, the parallels to these five mentioned are projected in straight lyns, accor­ding to the nature of their Primativs. These being premised the Primatives are divyded accordingly, by Sines, and so are contracted; the nearer they aproach the Solisticial Co­lure. From hence I say, that all the Problems performed by Ptolemie his Analemma, may be performed by a Lyne of Chords: yea, all the Problems performed by the Sines in the Scamans Callender, may be performed by the Lyne of Chords. Lastly, I say, that a Lyne of Chords of four inches Radius, will performe a Problem, either Astronomicall or Geographi­call, better then a Globe of two foot Radius. And in so far, I have exalted your Line of Chords, in that wherein ye was deficient.

As for measuring right Lyned Angles by a Lyne of Tangents, I hold it a more ready way, then by a Lyne of Chords; for in the one a Compass is requyred, for drawing an Arch from the Angular Point, but in the other, no Compass or Arch is requyred; save onely the Radius, and therefore, a Tangent Lyne is more usefull then a Lyne of Chords. This Tangent Lyne is wonderfull usefull in the Steriographicall Projection, which supposeth the Object, be it Sphere or Glob, contiguous [Page 44] with the Organ or Eye. But it may be said, that visibile po­situm supra visorum non facit visionem. I answere, it is true in opacuous, thick, and dark Bodies, but not in Diaphanus and Transparent Objects. This Projection is of greater use and concernment then the Orthographicall, because in the Orthographicall, the divisions of the Radius from the Center, doth shorten and become lesser and lesser towards the Pe­ripherie, according to the nature of Sines: but in the Sterio­graphicall, they increase from the Center towards the Pe­ripherie, according to the nature of Tangents; so that the increment of the one, doth supply the decrement of the o­ther: in this projection Circles directly or obliquely seen, are projected in Circles, but perpendicularly in straight Lines. I could inlarge and delate my self in this purpose, but fear­ing my enlargement should seem tedious to the Reader, I shall at present produce some Instruments, framed by this Projection, and where the Organ is placed. And first, Iohn Stoph [...]erus his Astrolob, where the Organ is placed at the Intersection of Aries and Libra; so that the aforenamed five great Circles, are projected in straight Lines, and the rest Circularly. Iohn Blackgrave, his Mathematical Jewel, yea, the Vniversal Mapps divyded into two Hemispheres, where Meridians and Parallels, are circularly projected; the Equator in a straight Line, but the Ecliptick in a Curve Line: I admire to see the same, as having no ground for that pro­jection; I pray you Mathematicus, let me know if there be any ground for the same? nam cupio docere vel doceri. I desire to know of you, if a Sphericall Triangle, such as for­merly I have described, i [...] in the Solistitial Colure the same, or any other Oblique Angled Sphericall Triangle be decirci­nated, peradventure without any terme given? if the quan­tity or measure of the sides and Angles may be had? I doubt not, but as Mathematicus ye can performe the same; if otherwise, send to Aberdeen, and you shall have the so­lution [Page 45] from me. And this much for the Steriographical Projectiion, the Organ placed at the intersection of Aries and Libra. The second position, is at the Poles of the Equinox, and from thence ariseth Stofler his Astrolob; from whence Mr. Gunters Quadrant is taken: this Astrolob hath the Equinoctiall directly seen, with all the Parallels, the Meridians Perpendicularly, and are projected in straight-Lines; the rest of the Circles Obliquly, and projected in Circles. The last is, when the Organ or Eye, is placed in the Zenith according to Clayius his Astrolob, or according to Mr. Gunters Fundamentall Diagram for plain dyaling; in which he doth project 10 great Circles, each of them having two Surfaces▪ except only the Horizon; so there doth arise 19 Faces, upon which plain Dyalls may be de­scribed, the Horizon, with all the Almicanters, are pro­jected circularly from the primative, the Az [...]muthes in streight Lines, the rest Circularly; all which is perform­ed Practically by Mr Gunter his last Edition: look Gunter Lib: 2. Cap: 3. Sect. 1. 2. 3. But if ye desire a com­pleat Demonstration of Mr. Gunter his Practise, consult Aguilonius in the 6 book of his Opticks. I doubt not but what is said, will put you to a studere, but stud [...]isse had been more proper for a Mathematician. There is another projection called Scenographical, keeping a middle between the former two, in debita distantia: but because it consists in shortning and lengthning of Objects, as they are divers­ly seen, being more proppe [...] for Painters and Limners then for Seamen, to speak further I desist. Onely observe, that all Sphericall Trigonometrie by calculation doth depend upon the projections: consult Theodosius de Sphericis.

As for your inch, and half inch, the one divyded into 16 equall parts, the other into eight; it had been better, and more like an Artist, to have divyded each of them▪ Diagonally in 100 parts, both for Navigation and Survey­ing: [Page 46] for Navigation by dividing the Meridian Line accor­ding to Mercator his projection, according to degrees of increasing Latitude: and in Surveying, as afterward in the next shall be made manifest.

I have severall Measures, for length, bread [...] and thickness, beginning from Barley Corn in reference to an inch, from thence to 12 inches making a foot, and 5 foot to a pace, and 1000 paces to a myle, and so foreward; as you may see into my Almanack, all which ye have not at all expres­sea into your Almanack.

I do confess, I have not expressed any Mea­sures into my Almanack, neither is it requyred I should do so, being different because of their Objects: for the Al­manak is in reference to Celestiall things, and the other to Terrestriall. But let us proceed to the purpose, wherein he [...]ayeth 5 foot make [...]h a pace, and therefore I desire to know of him, if paces in all Nations and Countries be equal, or un­equal; equal (I say) they cannot be, because the foots [...] diverse Nations are unequall; for the longer the foot be, [...]r shorter; the fewer or more [...]oots goeth to a pace: and herefore the paces are [...]nequal, and if paces, then myles; [...]nd if myles, then no certain [...]ie can be had for the mea­ [...]re of a degree upon the Arch of a great Circle; which is [...]bsurd, and not consistent with reason. But now, let us [...]ome to find the method and way, how the Ancient and Modern Geographers, did find out certain measures upon [...]arth, in reference to the Heavens. I will begin first, [...]ith the Egyptian Geographers, as Eratosthenes, who lived [...]6 Years before CHRIST; and Ptolomie who lived [...]o Year after CHRIST: They having chosen two places [...]ing under or near the same Meridian, differing onely observation, at 2 or 3 degrees in Latitude, which after­ [...]ards by a customary and standerd Measure of that King­ [...]me of Egypt, they did find five foot to go to a pace, [Page 47] and 1000 paces to a myle. But the Learned Mr. Norwood did of late into his Book, called the Seamans Practice, fol­lowing the Ancient Geographers, in their practice, in mea­suring▪ between York and London, find a degree upon the Meridian, to contain 367200 foot English; and a myle 6120, so that an Aegyptian pace containeth 6, 15 En­glish, and an Aegyptian foot 14, 75 English inches at near­est. But passi [...]g the fraction we take in numero ro [...]undo, 6 foot to the English pace, and consequently, 6000 foot to a myle in English measure. Now let us c [...]mpare Scots with English, and first, ye say that 37 English inches ac­cording to your standerd at Edinburgh giveth an Ell; Then a Fall, o [...] Pole being 6 Ell, giveth 2 [...]2 Inches, 222 by 4, the length of a Chain, the product is 888: which being multiplyed by 80, giveth 71040: and divyded by 12, the quotient is 5920 Foots short of 6000, by 80 Foot. Again, 42 Scots Inches in an Ell, as of the old standerd, that is, 3 Foot and a half; the Pole or Fall being 21 Foot, the Chain 84 Foot, multiplied by 80, giveth 6720 Foot, for the length of a Scots Myle; which being reduced to an English Myle, say as 10: 9 : : 6720: 6048 English, so that here the difference is onely 48 Foot, whereby the Scots Myle exceeds the English: and no wonder, because 6000 doth admit a Fraction, which will be near equi­valent to 48 Foot: and therefore, Mr Norwood's Practise doth altogether agree with a Scots Myle. But it may be said, or inquyred of me, the reason why I say, as 10: 9 : : 6720: 6048. I answere, because if an English Inch be di­vyded in 10 parts, 9 of these doth answere to a Scots Inch: Therefore, being to reduce English to Scots measure, say as 9: 10; but Scots to English, say as 10: 9. These be­ing premised, I would advyse Surveyers here, as in England [...] to divide their 4 Pole Chain into a 100 parts, which we call Links; and there will answere 10 Inch to a Link, this Chain [Page 48] so divyded, is very profitable for Surveying of Grounds, or Plating; and giving the Area, as ye say, 4 Pole in Latitude, and 10 in Longitude, giveth 160 square Poles for the Area: so also 1 Chain or 100 Links in breadth, multiplied by 10 Chains or 1000 Links in length, giveth for the Area 10 square Chains, or 100000 square Links; 75000 Links, 3 Rood, 50000 Links, 2 Rood; 25000 Links, 1 Rood: or 40 Pole, 625 Links square for a Pole. This I have premised for the benefit of Surveyers, they making use of the Diagonall-Scale, of Inch, and half Inch, or of any other Measure, Di­agonally divided.

Also in my Advertisement, being the last in my Almanack, such as desire Mathematicall-Arts or Instru­ments thereto belonging, especially a Spirall-Lyne, which I have so framed, that you may work more Arithmetick in one houre, then any other in two dayes with the pen.

Ye s [...]y ye have framed a Spiral-Line, so as the same had never been framed before; I had a true re­lation, from one that was a teacher of Mathematicks at London 40 years agoe, who told me, that one Mr. Brown a Carpenter, who lived at London, in the Minaries, near Tower-hill, was the first that did frame 3 Spiral-Lines upon a Circular Instrument, for Artificial-Numbers, Sines and Ta [...] ­gents; having two Brass Indices or Legs, fixed upon the Center, and opening in manner of a Sector, so that, when 3 Terms were given to find a fourth, the one Leg was placed to the first Terme, and the other to the second; then turning the Legs upon the Center, (not being alte­red or changed) the first to the third Terme, the second shall give the fourth requyred: whither the work be in Trigonometrie, Plain, or Spherical; or in Arithmetick sim­ply. This Instrument can be had at London, being more serviceable then his, which is only for Arithmetick He sayeth, [...]hat by this Instrument, they may work more Arithmetick [Page 49] in one houre, then any other in two days with the Pen▪ But I say, (in Arithmetical-Problems,) with the Pen shall work more in one hour, then he and his Spiral Line shall do n 10 dayes.‘—MART. Carpere vel noli nostra, vel ede tua.’