THE Variation of the Needle or Cumpas, is properly the ark of the Horizō contained betwéen the true meridiā of any place and the mag­neticall meridian of the same, and is denominated to bee Esterly or Westerly, accordyng to the posi­tion of the magneticall meridian to the Estwards or Westwards of the true meridian: And may be accompted either from the North parte, or the South parte thereof, but vppon opposit points it hath contrary denominations.

The magneticall meridian is to bee vnderstood a greate circle passyng by the Zenith and the Pole of the Magnes, deui­dyng the Horizon into two equall parts crossyng the same at opposit points: which intersections or crossynges, are shewed by the Needle or wiers of the Cumpas touched with the Ma­gnes or the Lodestone.

The Azimuth of the Sun is a great circle, passyng by the Zenith and the true place of the Sun: crossyng the Horizon at right Angles in opposit poincts, and diuidyng the same into two equall parts. And it is said to be giuen when the distance thereof from the true meridian is knowne.

The Azimuths of the Sun vpon equall eleuations in for­noone and afternoone, haue equall distances from the true meridian, so that the middle poinct of the whole difference of any two Azimuths obserued vppon equall eleuations in for­noone and afternoone, is the true meridian.

[Page]This difference of Azimuths is found vppon the Instru­ment of Uariation, by addyng together the Uariations of the Sunnes shadowe at equall eleuations in fornoone and after­noone. The half whereof is the distance of the Azimuths from the true Meridian: the whiche compared with either of the same variations of the Sunnes shadowe, the difference shalbe the variation of the Needle from the true meridian.

Or els subtracting the lesser variation of the Sunnes sha­dowe, from the greater (at equall eleuations) the halfe of the remayner shall be the true variation of the Needle from the meridian.

But the Azimuth of the Sunne beyng otherwise giuen, and the variation of the shadowe likewise giuen, the difference betweene them is the variation of the Needle.

The Variation of the Sunnes shadowe I call, the Hori­zontall distance betweene the Azimuth of the Sunne and the magneticall circle, whiche are represented in the Instrument by the shadowe of the line and the Needle.

FIrst you must place the Instrument vp­pon some Stoole, or other thyng that is flat, so as it may stande leuell, and the Plummet in the Standerd which is pla­ced at the North ende of the fixed Flye, may fall perpendicularly with the line in the same Standerd.

You must haue regard that in remouing the Instrument to the Sunne as he goeth about, it may alwaies stande leuell as aforesaied.

You are then to consider, that the [...]tring that recheth from the South part of the Instrumēt, to the top of the Standerd, is the chiefest string to giue the Sunnes shadow, which must be so directed by turnyng the Instruments South side to the Sunne wards, that the shadowe of the same may fall directly longst vpon the line of South and North in the fixed Flye, for it ought not to crosse or decline from the same line in any part, but if it do, you must seeke to reforme it by setting the Stan­derd more vpright, or remouyng it at the South end.

Then must you also see, that the string that is fastned to the hoope of Brasse that enuironeth the fixed Flye, maie be so placed, that it agree iustly with the shadow of the former line, and the line of South and North in the fixed Flye, in such sort that both the shadowes maie be as it were hidden in the saied line of the Flye: which you maie doe aptly, by turnyng the said hoope, and remouyng the same line at either side of it, as you shall see cause.

The Instrument beyng duly placed in forme aforesaid, it differeth nothyng from the Cumpas of Uariation, but onely in this poinct, that whereas the Flye of the Cumpas of Ua­riation, is so turned by vertue of the Magneticall wiers, that [Page] the North poinct thereof doeth shew the Pole of the Magnes or line of Uariation: In this Instrument, the North poinct of the Needle doeth supply that, whiche the North poinct of the Cumpas should doe. And the North poinct of the Flye which is fixed in the bottome of the Instrument, doth alwaies aun­swere to the shadowe that the Sunne giueth.

WHen you would obserue the variation in any place, you must begin in y^e fornoone, the sooner, the better, and the more effec­tuall maie your obseruatiōs be, do thus.

Take your Astrolabe and obserue du­ly the height of the Sūne, for yourmore ease it shall bee best for you to note the same, when it agreeth to be iust vppon a degree, without any consideration of minuts or fractions, and at the instant of the same height, turne your Instrument to the Sunne, so as the shadowe of the lines maie fall iustly vppon the line of South and North in the fixed Flye.

Then, when the Needle doeth stande, looke directly ouer the North poinct of the Needle, what degree and fraction, if there be any, doth aunswere vnto the same in the fixed Flye, that is to saie, how many degrees it is from the North of the fixed Flye, which you shall note diligently, and may saie, that so many degrees &c. is the variation of the Sunnes shadowe from the North, as the North poinct of the Flye is from the North poinct of the Needle, either Eastwardes or West­wardes as you shall finde the same. Thus maie you obserue diuers tymes, vpon seuerall degrees of the Sunnes eleuati­on. And like as you doe in the fornoone, so must you also ob­serue [Page] the Sunnes eleuation in the afternoone, vpon the same degree of height, and with the same side of the Astrolabe and Index turned towards the Sunne, as it was in the fornoone, (for auoydyng of error that maie bee in the Instrument) no­tyng at euery height what you finde the variation. And when the Sunne commeth to the meridian, it shall be good that you exactly obserue his eleuation vpon the same, for knowyng the true Latitude of the place: all whiche you shall set downe in forme followyng.

IN the former declaration, the onely way to try the variation, is by comparyng of the seuerall correspondent obseruations of the Sunnes eleuation in the fornoone, with those of the afternoone, so that if the Sunne should bee obscured, or by any o­ther occasion like obseruation can not be made in the afternoone, then the former rule giueth not the desired purpose. Therefore I thought good to shewe, how by any one obseruation in the fore or afternoone, the eleuation of the Pole and place of the Sunne giuen, you maie knowe the true meridian and the variation of the Needle from the same in any place, whiche thing maie be done and aptly demonstra­ted vpon the Globe, but moste exactly calculated by the Table of Sines.

To finde out the variation vpon the Globe, you must first set your Globe to stande dewly accordyng to the eleuation of the Pole at the place proposed. Then seeke in the Ephemeri­des for the true place of the Sunne that daie, and note it with some small prick in the ecliptik of the Globe. And placyng the Quadrant of Altitude or moueable verticall, at the verticall poinct or Zenith, take the eleuation of the Sunne obserued by the Astrolabe or other Instrument at the tyme proposed, and [Page] note it iustly vppon the same quadrant of altitude. Then turne your Globe and quadrant towardes that part of the Horizon that the Sunne was in at the tyme of the obseruation, till the pricke you made for the place of the Sunne in the ecliptik, concur and agree iustly with the eleuation marked in the said quadrant of altitude. So shall you see the quadrant shewe you vpon the Horizon, the Azimuth and distance of the Sunne from the true meridian of that place, whiche you shall com­pare with the variation obserued vppon the Instrument at that instant of the Sunnes eleuation, And if they agree and concur iust, then shall you bee in the true and common meri­dian, whiche sheweth the Pole of the worlde and Pole of the Magnes or Lodestone: But if thei differ, you shal subtract the lesser from the greater, the remayner sheweth the variation. And if the variation vpon the Instrument be greater then the true distance of the Azimuth from the meridian founde vppon the Globe, the same surplus is to be accompted for variation, vpon the contrary side of the meridian: if it bee lesse, it is to bee accompted on the same side of the meridian that the variation is taken, whether it bee in the fornoone or afternoone. This precept needeth no further demonstration, then the Instru­ment it self, the Globe I meane.

But for example of the worke, I take the first obseruati­on, in the former Chapter sperified, made at Lymehouse the sixteenth of October 1580. in the fornoone, which is 17. d. ele­uation, and variation 52. d. 35′. from North to West.

First I set my Globe at 51. d. 32′. for the eleuation of the Pole. Secondly I take the place of the Sunne 2. d. 55′.m. and note it vpon the Ecliptick. Thirdly I note vpō the quadrant of altitude, the eleuation of the Sunne 17. d. This done, I moue the quadrant of altitude towardes the East of the Ho­rizon, and turne the Globe till the prick in the Eclipticke for the place of the Sunne, doe agree iustly, with the eleuation noted vppon the quadrant of altitude, and finde the true Azi­muth shewed by the said quadrant vpon the Horizon to be ne­rest, about 41. ⅔ from the meridian. And conferryng the same [Page] with the variation founde vppon the Instrument 52. d. 35′. I find the difference 11. d. 15′. And because the obseruation is no­ted to be in the fornoone frō the North to the West, or South to the East, and the variation vppon the Instrument greater then the Azimuth founde on the Globe, I accompt the same from the North to the East, or from the South to the West. So I conclude the variation at Lymehouse to be about 11. ¼. from North to East, or South to West.

THE summe of the worke, is to finde the ark of the Horizon, betweene the meridian and the Azimuth of the Sunne at the time of the obseruation, whiche beyng compared with the variation founde in the Instrument, the difference is the variation of the Needle. For attaynyng of the same arke. First it is necessarie to haue the arke of the Equinoctiall betweene the Sunne at the tyme of the obseruation, and the meridian, which ark is thus found.

Multiply the sine of the Sunnes meridian altitude for the daie proposed, by the whole sine, the product diuide by the sine of the eleuation of the Equinoctiall (or the complement of the Latitude) the quotient is the versed sine or shaft of the semidi­urnall arke, whiche you shall note for the first nomber.

Then againe multiplie the sine of the Sunnes eleuation at the tyme of the obseruation, by the whole sine, and the pro­duce diuide by the sine of the eleuation of the Equinoctiall, the quotient subtract from the nomber you first noted, the rest is the versed sine of the arke of the distance betwéene the Sunne and the meridian in the parallell that it is in for the tyme pro­posed, [Page] in suche partes as the Semidiameter of the Equinoc­tiall is the whole sine: but it is necessarie before you applie it a­ny furder, to reduce it into suche parts as the Semidiameter of the parellell is the whole sine, whiche you maie doe thus: Multiplie this remayner by the whole sine, the product diuide by the sine of the complement of the declination (which is the Semidiamiter of the parallell) the quotient is the versed sine in his proportionall parts.

This versed sine thus reduced and subtracted from the whole sine, leaueth the second right sine, which you shall seeke in the Table of sines, and thereby findyng his arke, you shall subtract the same from the quadrant or 90. d. the remayner is the arke of the forsaid parellell of the Sunne, which is answe­rable or correspondent in degrees and minuts, to the arke of the Equinoctiall that you seeke. The reason of the precept is this.

As the right sine of the eleuation of the E­quinoctiall, is in proportion to the right sine of the meridian altitude of the Sūne or any Starre: so is the whole sine, to the versed sine of the Se­midiurnall arke. And againe, as the right sine of the meridian altitude, is to the right sine of the e­leuation of the Sunne or Starre at the tyme of the obseruation: So is the versed sine of the Se­midiurnall arke of the same, to the excesse or dif­ference betweene the same versed sine and the versed sine of the distance from the meridian.

For the better vnderstandyng of the premisses, I haue set downe this figure following, and wishe the Reader to con­sider of the same with the 4. Pro. of the 6. of Euclide.

FOR the accomplishyng of this proposi­tion, you are to imagine a sphericall triā ­gle vppon the superficies of the Globe, whose sides must be. First the portion or arke of the meridian betweene your Ze­nith and the Pole, whiche is the comple­ment of the latitude. The second the ark of the verticall circle contayned betweene your Zenith and the Sunne, which is the complement of the Sunnes eleuation at the tyme of the obseruation. The third side is an arke of the circle of declination comprehended betweene the Sunne and the eleuated Pole, this arke is found by addyng, or subtrac­tyng, the declination of the Sunne, to or from, the quadrant or 90. d. whiche must be done with this consideration, that if you be on the same side of the Equinoctiall that the Sunne is, you are to subtract the declination from the quadrant. If on the o­ther side, to add it to the same, so haue you the three sides of the sphericall triangle giuen. Then the substance of the work con­sisteth in findyng the quātitie of the angle of the same triangle at the Zenith, for the complement thereof to the Semicircle or two right angles, is the Horizontall distance of the Sunnes Azimuth from the meridian, which beyng compared with the variation of the Sunnes shadowe vppon the Instrument, gi­ueth the thyng required.

WHereas in the three last Chapters, the groundes of the calculations consist in the eleuation of the Pole to be giuen, which thyng to knowe is no lesse diffi­cuit, [Page] then the cheef matter that is by them required. For the common precepts, whiche as yet haue cheefly been giuen for the findyng thereof, depende onely vppon the obseruation of the meridian altitude of the Sunne or Starres, or els vppon certaine false and grosse rules of the guardes and Pole starre. Therefore I haue thought good, that as I haue shewed the waie to know the variatiō vpon any one obseruation, either in forenoone or afternoone, the latitude of the place presupposed: so likewise, vpon twoo obseruations by the Sunne, either in forenoone or afternoone, to sette doune the waie and maner how to finde the eleuation of the Pole, situation of the meridi­an, and variation of the Needle in any place by the Globe.

But this you must alwaies regard, that your two obserua­tions maie haue conuenient distance of tyme betweene them, the greater the better: So as the higher eleuation bee not ta­ken nere the meridian, the lower eleuation the nerer it is ta­ken to the Azimuth of East or West, or to the Horizon, the better, with which eleuations, you are to note the difference of the Sunnes Azimuths or variations founde by the shadowe vppon the Instrument exactly, for without that, the eleuations onely are in vaine.

First it is requisit, that your Globe be so fitted, that the meridian circle and the Horizon doe crosse eche other at right angles, and diuide them selues equally into Semicircles. And also that the quadrant of altitude (or moueable verticall) bee placed duly vpon the meridian circle at the Zenith, so as being turned circularly, it may touche the Horizon equally in euery part. These thinges beyng duly considered, there needeth not any further regard to bee had for placyng of the Globe, onely this you may respect in settyng the Pole at aduentures aboue the Horizon betweene it and the Zenith, that the meridian cir­cle may cut the Horizon in iust degrees, so may your quadrāt of altitude be placed at your Zenith iustly vpon a degree also.

Then must you fasten your Globe to the Horizon, so as it may remaine immoueable, but in fastnyng the same you must regard that you force it not from one side of the Horizon to an [Page] other, but that it rest equidistāt in the same. And hauyng your Globe thus disposed, it is ready for you to apply your obserua­tions vpon, which you shall thus doe.

First, take your highest eleuation, and note it vpon your quadrant of altitude, and place the ende of the saied quadrant vpon the Horizon at 10. 15. or 20. d. frō the meridian circle, (but the nerer you set the same to the meridian, the more con­ueniently, without impechement, will your triall bee made.) Then giue a pricke vpon the Globe in the Azimuth, that the quadrant sheweth at the degree of the eleuation, noted vpon the quadrant, then againe note the lesser eleuation vpon the quadrant of altitude, and remoue the same vpon the Horizon (from that place where it was first fixed, towardes the Azi­muth of East or West, whiche shalbe nerest the same) so ma­ny degrees as you finde the difference of Azimuthes betwene the twoo eleuations by the shadowe of the Sunne, vpon the instrument of Variation, and staiyng your quadrant of alti­tude vpon that poinct of the Hozizon: note also your lesser e­leuation in the same Azimuth vpon your Globe. This doen you must haue a paire of Calliper compasses, suche as maie conueniently reche to 113. d. ½. of the Equinoctiall of your Globe, (whiche is a quadrant, and the greatest declination of the Sunne) then you must consider whiche of the Poles of the worlde is eleuated aboue your Horizon, and whether your de­clination bee towardes, or from that Pole, that is to saie, whe­ther the Sunne be betweene the eleuated Pole and the Equi­noctiall, or the Equinoctiall betweene the Sunne and the Pole. If the Sunne bee betweene the Pole and the Equi­noctiall, then are you to subtracte the declination from 90. d. If the Equinoctiall bee betweene the Sunne and the Pole, you must adde the declination to 90. d. And take the same re­mainyng or collected number of degrees &c. with your com­passes vpon the Equinoctiall. And sett the one ende of your compasse at the pricke made vpon your Globe, for the highest obseruation, and with the other ende describe an arke or peece of a circle, vpon the same side of the meridian that your pricke [Page] is on, from the meridian to the Horizon. Then againe with your compasse vnaltered, settyng the one foote in the pricke for the lowest obseruation, describe an other peece of a like circle crossyng the former. The poinct of the intersection, or crossyng of these twoo circles, is the eleuated Pole, to the whiche if you remoue the quadrant of altitude, you shall finde what the eleuation thereof is. And the poincte that the same quadrant sheweth vpon the Horizon, is the intersection of the meridian and the Horizon, the Horizontall distance betweene this intersection, and the Azimuth of the lesser obseruation, subtracted from the semicircle, or 180. d. leueth the Horizon­tall distaunce of the same Azimuth from the true meridian. So haue you the eleuation of the Pole, and situation of the meridian.

Now if you compare the Horizontall distance of the A­zimuth of the Sunne, from the meridian at the tyme of the obseruation, with the variation by the Sunnes shadow found vpon the instrument, at the tyme of the same obseruation, and takyng the one out of the other, the remainer shalbe the true variation, whiche you are to accompte, as in the latter ende of the third Chapter is shewed. So haue you giuen the eleuation of the Pole, the meridian, and Variation of the Née­dle, the thynges proposed to be shewed.

FIrst it is to bee vnderstoode, that by ex­perience of trauellers, it is founde and confirmed, that the meridian common to the Pole of the worlde, and the Pole of the Magnes, (that is to saie, where the Compasse, or Needle touched with the Magnes, sheweth the Pole of the worlde directly,) passeth at the Ilandes of the Açores, or nere there a­boute, but I finde by greate probabilitie, that it is somewhat to the Eastwardes of those Ilandes, and not to the West­wardes. From whiche meridian I accompt the beginnyng of longitudes, and finde our meridian of London, to bee from the same 23. d. ½. our latitude as before saied 51. d. 32′. and the Veriation of the Compasse or Needle 11. d. ¼. from the North to the Eastwardes. Now vpon these groundes▪ I find by calculation, the Pole of the Magnes, or the intersection of the twoo Magneticall meridians, vpon the superficies of the earth, to bee from the Pole artike 25. d. 44′. and in longitude 180. d. that is to saie. 25. d. 44′. in the former common meri­dian, on the other side of the Pole.

It maie bee happely that some of you will bee desirous to knowe the maner how this Magneticall Pole is founde out, that you maie apply the same to like purpose hereafter. Ther­fore I thought good to sette doune an example of the former calculation.

HAuyng shewed in the former Chapter, vpon the groundes therein specified, the place of the Pole of the Magnes, vppon the superificies of the earth: there resteth now to bee declared, of the poincte Re­spectiue, where it should be, by the newe propertie founde of the declinyng of the Needle, at this place for London 71. d. 50′.

First it is to bee considered, that as the Magneticall me­ridians doe crosse them selues at their Pole, before specified: so doe their plaines likewise crosse in a right line, passyng by the saied Pole, and the centre of the earth. Then producyng a straight line, in the Magneticall plaine of London, declinyng from the plaine of the Horizon 71. d. 50′. where the same doth crosse with the former common section of the twoo plaines, there by reason should the poinct Respectiue dee. Whiche in­tersection I finde to bee from the centre of the earth 1085. [Page] miles (after the rate of 60. to a degree in the Equator, and 3436 4 / 11. for the Scinidiameter of the earth) and the distance of the same from the axis of the world 471. miles.

IN all sea chartes generally, whiche are made without consideratiō of the variation, are com­mitted great errours and confusion. For, either the partes in them contained, are framed to a­gree in their latitudes by the skale thereof, and so wrested from the true courses that one place beareth from an other by the Cumpas, or els in setting the parts to agree in their due courses, thei haue placed them in false latitudes, or a­bridged, or ouer stretched the true distances betweene them.

[Page]In the Marine plattes made for Newfoundlande, the course sette downe from Silly to Cape Raso is due Wiste, whiche is founde to bee so by our common sailyng Cumpasse, whose wiers are sette at ½. a poinct from North to East, not­withstandyng Silly beyng in latitude 50. d. little more. Cape Raso in Newfoundland is founde to bee but in 46. d. ⅓, which is 3. d. ⅔. lesse then the latitude of Silly.

To make a shewe of reformation of this error, (caused by the Variation and settyng of the wiers in the Cumpasse) or to giue a light of that difference in latitude, thei haue placed in the plat against that coaste, a newe skale of latitude, some vp­pon the line of South and North, and some other haue placed the same vpon the line of North Northeast, & South South-Weste, (because that poincte of the Cumpasse sheweth the Pole nerest in that place) and haue furnished the degrées ther­of, agreeably to the latitude of Cape Raso: and by that mea­nes haue had a double skale of latitude, one for the Easter co­stes, the other for that Weste. But how farre the same hath been from reformyng the error, or giuyng any helpe to Na­uigation, you maie easely iudge.

Others to auoide that error of the difference in latitude in that voyage and course, haue vsed Cumpasses whose wiers haue been sette directly vnder the North poincte, and thereby saityng Weste from Silly, haue fallen to the Northwardes of Cape Raso about 50. leagues, and in latitude nere 49. d.

Some other haue vsed in the same voiage to place a blank Flye vpon their sailyng Cumpasse, whiche thei haue remoo­ued from tyme to tyme, as thei haue iudged the variation hath altered, by whiche waie, albeeit thei maie seeme to keepe them selues neerer the parallell, yet the same in Nauigation worketh the greatest confusion of all other, and therefore is to bee vtterly abolished.

In our voiages from hence Eastwardes to S. Nicolas in Russia, and to the Narue in Liuonia &c. the Marine plattes of the coastes are described by our common sailyng Cumpas, with consideration of the variations at diuers places, where­by [Page] the true meridians reformedly set doune, declining from y^e parallell meridians of the plat, doe necessarily widen. North­wardes, and straighten to the Southwardes, contrary to the true forme and nature of meridians. And yet notwithstan­dyng, that is the best meanes hetherto knowen, to reforme in plat, the errors that els would growe, by the strange variati­ons that waie.

And albeeit these plattes serue verie well for those Naui­gations, yet by meanes of the variations considered, the sorme of those coastes is so distorted from the right shape it should beare, beyng truely described vpon the Globe or otherwise in plaine, accordyng to the true latitude and longitude: That whereas the Narue (beyng in latitude 59. d. ¼. and in longi­tude from the meridian of London 26. d. 10′.) should be from S. Nicolas 9. d. 40′. in longitude to the Westwardes (S. Nico­las beyng in latitude 64. d. 35′. and in longitude from London 35. d. 50′.) In the sailyng plat it is brought to bee in the meri­dian of Colmogorod, (whiche is in latitude 64. d. 20′. and in longitude from London 37. d. 45′.) whiche is 1. d. 55′. to the Eastwardes of the meridian of S. Nicolas.

In the Mediterranean Sea, and in the coastes thereof, where, in great reason should be the perfectest descriptions of the world, for that in those parts haue béen the seates & abodes of the moste famous and learned men in all ages, we see not­withstandyng in the Marine plattes of those partes, grosse errors committed, through want of knowledge of the varia­tion and the vse thereof, in whiche thei haue not accompted of 3. 4. or 5. degrees error in the latitude of places.

But those defectes of the latitudes, haue been verie well reformed, by the famous and learned Gerardus Mercator (whom I honour and esteeme as the cheef Cosmographer of the world) in his vniuersal Mapp, which though he haue made with sailyng lines, and dedicated to the vse of Seamen, yet for want of consideration of the Variation, and partly by angmē ­tyng his degrees of latitude towardes the Poles, the same is more fitte for suche to beholde, as studie in Cosmographie, by [Page] readyng aucthours vpon the lande, then to bee vsed in Naui­gation at the sea.

There is also in the same Vniuersall Mappe, and likewise in all other moderne Mappes of the North partes of Europe, a greate fault, by placyng twoo Wardhouses distant one from the other aboue 20. d. in longitude, whereas indeede thei are but one thyng, and no suche distance betweene them. This er­ror hath growen by taking Wardhouse, and the Sea coastes, from thence to S. Nicolas, Vaigats and the Ob &c. out of the Mappe of Anthony Ienkinsons trauaile to Boghar and Per­sia. In the whiche I placed that border of the Sea coaste, and for some causes went no further in that descriptiō then Ward­house, whiche is in latitude 70. d. ⅓. and in longitude from London 29. d. Wherfore to accomplishe the whole border of that coaste, he was forced to seeke some other description to ioine with it, & tooke as appeareth the Mappe of Olaus Mag­nus of the North countries, wherin he found likewise Ward­house, but falsly placed, in latitude about 19. d. too muche, and in longitude as muche too little, the which, although he might take to bee the same specified in Maister Ienkinsons Mappe, yet he was constrained to separate thē the saied distance of 20. d. in lōgitude (or to leaue there so much superfluous roome) o­therwise he should haue thrust the South partes of those coū ­tries togethers, and confounded the whole description.

And albeeit he had had the entire sailyng plat, that wee vse for those partes, yet if he had not knowen the secret effect of the Variation in the makyng thereof, he might haue fallen in­to the like absurditie or worse. But of those coastes and of the inwarde partes of the countries Russia, Muscouia &c. I haue made a perfect plat and description, by myne owne experience in sundrie voiages and trauailes, bothe by Sea and Lande to and fro in those partes, whiche I gaue to her Maiestie, in Anno 1578.

Besides these and like imperfections proceadyng of the Variation, there is yet an other inconuenience, whiche often­tymes encreaseth the former errours, and that is, the diuers [Page] placyng of the wiers fixed to the Flie of the Cumpasse.

This varietie ofsettyng the wiers, hath caused greate cō ­fusion in Nauigation, and in other accomptes of Sea causes, for when it is saied, that from suche a headlande, to suche a place is suche a course, or at suche a place the Moone vppon suche a poincte of the Compasse maketh the full Sea, it is re­quisite to bee demaunded, by what Cumpasse the obseruation was made, whereas if the wiers had not been altered from the North poinct of the Flie, (whiche I wishe had neuer been any where) these doubtes had been auoided.

It behoueth therefore all men that will make Hydrogra­phicall discriptions for the vse of saylyng, to haue speciall re­garde of the Cumpas by which their obseruations are made, and if they collect notes made by sundry Cumpasses of diners setts, they ought to reduce all the varieties vnto some one cer­taine, and to giue notice of the same, in their platt: And not to make a confused mingle mangle by ioyning together all vari­eties of obseruations, notes and reportes, as the Portingales and Spaniards haue done, in compoundyng these North parts of the worlde, with their owne discoueries, without considera­tion of the diuers sorts of the seuerall cumpasses by which thei were made.

Also it importeth all Maisters, Pilots and others by what name so euer that shall giue directions in Nauigatiō, to looke circumspectly to the settyng of the wiers of the Cumpas by whiche they shall sayle, that the same Cumpas be correspon­dent, to the lines of the Sea Card that they shall vse: that is to say, that it be of the same set for the Uariation, that the Cum­pas was of, by which the Carde was made.

And seyng wee haue in this our Countrey acquainted our selues commonly in our obseruations and Nauigations, with the Cumpas, whose wiers are set at ½. a poinct from North to East, I meane in the discriptions that I shall make, to ap­ply the same agreable to the said Cumpas, and would vse the like without alteration (and also the straight lines in Sea Cardes) if I should sayle rounde about the world to make the [Page] description thereof, but alwaies with regarde of the seuerall variations of euery place where the same should be observed.

AMongst the rules and Instruments for Nauigation, all suche are vaine and to small purpose, wherein the true meridian is presupposed to be giuen▪ by the magne­ticall Needle, without due consideration of the variation for that they are all groū ­ded vppon false suppositions▪ Hereby it commeth to passe that one Michiel Coigner of Antwerp in his New instruction (as he termeth it) of the most excellent and necessary poincts of Nauigation, wherein he sheweth the makyng and vse of a Nauticall Hemisphere, which he prefer­reth before all other Sea Instruments, is very childishly a­bused. For where as he pretendeth by it, to giue the eleuation of the Pole and the houre and instant of the tyme of the day, by any one obseruation in any place, besides that it is of all other that hitherto haue been vsed at Sea, the most tedious and vn­fit for that purpose, it is also by reason of the variation not con­sidered, [...]iere false and erronious. For, the true meridian which is the grounde of his purpose, is as farre to seeke as the thyng he promiseth to giue by the same. The like may be said of al other Instruments made vpon the same ground whether they serue for the Sea or Land.

The same Author in the 4. Chapter of his booke, entreting of saylyng vpon the poincts of the Cumpas, saieth, that in sai­ling South or North, he shall passe by the Poles of the world, and keepe vnder one meridian, till he come to the place from whence he first departed. And vppon the poincts of East and West out of the Equinoctiall, he shall saile vnder a parallell, till he returne to the place from whence he went. But in say­lyng [Page] vppon the poinct of Northeast, he shall describe a spirall line inclyning by little and little to wardes the Pole, as in his demonstration thereof in the same Chapter appeareth. But for want of due consideration of the variation, his rules, rea­sons and demonstrations, and suche others hitherto giuen for like purposes, are friuolous and false.

For if he direct his saylyng by the Cumpas (as of necessi­tie he must, beyng the onely Instrument for that purpose) it is manifest, that whether he sayle North or South, East or West, or by what other poinct so euer, the Cumpas not re­spectyng alwaies the Pole of the world, as he supposeth, but some other poinct or poincts distant from the same, shall leade hym accordyngly, whereby he shall neither keepe vnder one meridian, nor vnder one parallell of latitude, neither make such a spirall line to the Pole of the world, as he demōstrateth. His fault in settyng downe those rules is so muche the grea­ter, in that he acknowledgeth in the Chapter next before the variation at Antwerp, to bee about 9. d. from North to East accordyng to Mercators position, of the Magneticall Pole, which he also confirmeth by his owne experience.

But it seemeth he hath followed, that excellent Mathema­tician Petrus Nonius, especially concernyng the saylyng vp­pon the poincts of East and West. For he, in his first booke of the rules and Instruments of Nauigation, enforceth hym self to proue and demonstrate, that in saylyng East or West, out of the Equinoctiall, the course is performed by peeces of great circles, and yet describeth a parallell. But how that may stande with the principles of Geometry, I referre the iudge­ment to the expert Mathematicians, for it is like as a circle should be made of straight lines, which is impossible.

It appeareth in the discourse that he hath made of those matters, that he had not a right iudgement of the nature of the Cumpas in saylyng (admitting the same to shew the Pole without Variation) for if he had, he would neuer haue entred into suche a Labyrinth as he did. But he thought it a great ab­surditie that the Cumpas in euery Horizon should shewe the [Page] meridian and Poles of the world by the poincts of South and North, and by the poincts of East and West to shewe in the Horizon the verticall and Equinoctiall East and West (being a great circle) and yet in saylyng East or West, except in the Equinoctiall, it should performe but a parallell.

But it is to be vnderstood, that albeit the poincts, or ly­nes of the Cumpas doe alwaies in euery Horizon represent great circles in the Heauens, the points of South and North the meridian, and the poincts of East and West the verticall circle of East and West, eche crossyng other at right angles, and likewise of the other poincts. (The reason whereof is, be­cause the Cumpas lieth euery where leuell with the Horizon, so as a perpendicular line descendyng from the centre thereof at right angles with the plaine of the same, will alwaies fall vpon the centre of the earth, and consequently be the Semidi­ameter of a great circle.) So that where so euer the Cumpas be caried, these circles are supposed to be caried about with it, and the view of euery thyng in the Horizon represented by the poincts thereof, is likewise in great circles: Yet in saylyng by the Cumpas, the poincts of South and North onely, describe great circles generally, which are the meridians, & the points of East and West, describe a great circle in the Equinoctiall onely: in all other places out of the Equinoctiall, they describe but parallells. And the saylyng vppon any other poinct of the Cumpas, from any place, describeth a spirall line, according to the angle it maketh with the meridian. And hereby in saylyng vpō the poincts of East or West, out of the Equinoctiall, (the▪ North poinct alwaies respectyng the Pole) the course perfor­meth a parallell, accordyng to the distance of the centre of the Cumpas from the Pole. The maner thereof you may per­ceiue by fastnyng a small threed or Virginall wier at the Pole of a Globe, or centre of a circle, which shall represent a moue­able meridian to bee caried about the Globe or circle, and fixe vppon the same, a small Flye of a Cumpas, so as the line of South and North be answerable to the thréed or wier, and the North poinct thereby alwaies respect the North Pole: then [Page] in turnyng the threed about the Globe or circle, vpon the Pole or center, if the center of the Flye bee out of the Equinoctiall (between it and the Pole) albeit the points of East and West crossyng the same line and moneable meridian at right an­gles, doe shewe the verticall East and West vpon the Globe, which is a great circle, yet in cariyng the same Flye vpon the threed or moueable meridian, about the Pole or center, you shall by the center of the same Flye, describe but a parallell, ac­cordyng to the distance thereof from the Pole of the Globe, or center of y^e circle, not vnlike the circular motiō of a Horse dra­wyng in a mill, who though he looke forth straight in a right line, yet beyng fastned to the beame of the mill, is forced to make his course in a circle, whose Semidiameter is the lēgth of the beame contayned betweene the Horse, and the centre of the mill, or mispost.

And as in the Equinoctiall, the line of South and North in the Cumpas (by supposition representing the meridian) is parallell to the Axis of the earth (which is the common secti­on of all the meridian plaines) and the line of East and West crossyng the same Axis at right angles, representeth the ver­ticall East and West, which is the Equinoctiall, imaginyng to descende from the centre of the Cumpas a line, to fall per­pendicularly, and at right angles with the Axis of the worlde (whiche shall bee at the centre of the earth) and in saylyng East or West by the Cumpas, the imagined perpendicular line being caried about with the same (makyng alwaies right angles with the Axis) shal describe the plaine of the Equinoc­tiall equidistant from the Poles of the world, and at right an­gles with the Axis, and the poinct of the same line at the cen­tre of the Cumpas, the circumference of the Equinoctiall, vppon the superficies of the Sea: So beyng from the Equi­noctiall on either side, imaginyng the line of South, & North in your Cumpas to represent alwaies the Axis of the world, and to lye parallell with it, the line of East and West most crosse the same Axis alwaies, at right angles: and supposing a line to fall from the centre of your Cumpas to the Axis of [Page] the world, makyng right angles with the same Axis. In say­lyng East or West, that imagined line beeyng caried about with the Cumpas (alwaies at right angles with the Axis) shall describe the plaine of a parallell, equidistant to the plaine of the Equinoctiall, and the poinct thereof at the centre of the Cumpas, the circumference of the parallell vppon the super­ficies of the Sea: which parallell should be represented by the poincts of East and West of the Cumpas, if the line of South and North of the same-were parallell is the Axis of the earth, as was supposed: but it is not. And therfore as they decline one from the other, so doeth the verticall circle of East and West shewed by the Cumpas, decline from the parallel circle euery where.

The angle of whiche declination, is alwaies equall to the latitude of the place, or distance of the parallell from the Equi­noctiall.

But as I haue already sufficiently declared, the Cumpas sheweth not alwaies the Pole of the worlde, but varieth from the same diuersly, and in sayling describeth circles accordyng­ly. Whiche thyng if Petrus Nonius and the rest that haue written of Nauigation, had ioyntly considered in the tracta­tion of their rules and Instruments, then might they haue been more auaileable to the vse of Nauigation, but they per­ceiuyng the difficultie of the thyng, and that if they had dealt therewith, it would haue vtterly ouerwhelmed their former plausible conceits, with Pedro de Medina (who as it appea­reth hauyng some small suspition of the matter, reasoneth ve­ry clerkly, that it is not necessary that such an absurdity as the Variation, should be admitted in such an excellent art as Na­uigation is) they haue all thought best to passe it ouer with si­lence. But I hope suche as intende hereafter to write of Na­uigation, will either frame their rules, precepts, and Instru­ments, with regarde of the Variation, as herein I haue she­wed, or els ease them selues of that trauaile, for as good none as vnprofitable.

VPon the Hypothesis of the Pole of the Magnes on the superficies of the earth, and the poinct Respectiue in the body thereof, accordyng to the former calcu­latiōs, might be inferred many pleasant conclusions, both for the longitude and latitude of places.

But touchyng the poinct Respectiue by the declinyng of the Needle, seeyng this is the first and onely experiment that hath been made of it, I can not inferr any furder matter ther­of, then that whiche I haue already set downe, vntill by obser­uations in other places, we finde how it will holde.

And as for the Variation, if it were generally regular and certaine, as in some part it seemeth to be: (that is to say, from hence West wardes to Meta Incognita, New foundland, Flo­rida, and that part of the coast of America) then might there be giuen by it generall rules most certaine and commodious for the vse of Nauigation.

And by the same Hypothesis of the Pole of the Magnes at 25. 44′. from the Pole of the world, the greatest variation of the Needle in the Equinoctiall, should be (at 90. d. of Longi­tude) 25. 44′. from North to East. And consequently the grea­test variation in the parallell of 70. d. should bee (at the longi­tude of 128. d. 51′.) from North to East 81. d. 14′. And in the meridian of 180. d. of longitude between the two Poles, (the Pole Artik I meane, and the supposed Pole of the Magnes,) there should the North poinct of the Needle or Cumpas re­specting his own Pole, shew the South, and the South point, the North Pole of the worlde.

But in my trauelles to the Northest parts, I haue found this position of the magneticall Pole clene reuersed: for where [Page] as the angle of Variation from hence Eastwardes in the pa­rallell of 70. d. should encrease and growe wider, till it came to 81. d. 14. from North to East as before. At the Iland Vaigats beyng in longitude from London 58. d. and in the same pa­rallell of 70. d. where, by the Hypothesis, the variation should be 49. d. 22′. from North to East, I finde the Needle to vary 7. d. from North to West. And the like effect I haue found by diuers obseruations in sundry other places of the East par­tes. Whiche obseruations with many more that I haue cau­sed to bee made, and dayly procure to be done in diuers other Countries, I reserue, with intent (if it bee possible) to finde some Hypothesis for the saluyng of this apparant confused ir­regularitie.

At Ratisbona or Regensburg in Bauaria, beyng in lati­tude 48. d. 52′. and in longitude 36. d. 20′. where, by the former position of the magneticall Pole at 25. d. 44′. the Variation should be 16. d. 44′. from North to East. Gerardus Mercator found the same to be onely 11.¾. as I gather by his placyng of the magneticall Pole at 16. d. 22′. from the Pole Artik vpon his obseruation made at that place: whiche confirmeth the re­trograde qualitie in the Variation from hence Eastwardes, as aforesaid.

Whiche straunge varietie, I haue here plainly proposed, to the ende that the learned sorte might consider thereof, and sharpnyng their wits, see what probable causes and grounds they can assigne for the same. For, consideryng it remayneth alwaies constant without alteration in euery seuerall place, there is hope it may be reduced into method and rule.

As for that Westwardes, because it carieth proportion, and hath some apparant regularitie, I will apply the same to the generall commoditie of all suche as shall trauaile that waies: which if I should here particularly decipher, it would require a volume, whereby (contrary to my first intent) I should farre exceede the bounds of an addition, I will there­fore abridge it to a Hydrographicall Plat, wherein all such er­rors and defects as haue been hither to vsed, shalbe reformed, [Page] which shall be easy for the meanest capacities to conceiue, and serue more effectually in vse, then if I should haue expressed the same by multitudes of rules in writyng. Therefore for this matter I referre you to the same, the whiche you shall looke for very shortly.