The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

SECT. IV. Shewing the Proportion between Per∣pendiculars and their Shades.

SEeing there is the same proportion between all Shades and their Perpendiculars; at least to sense, and seeing the seve∣ral Almucantars of the two great Luminaries are the chief Cause of the lengthning or shortning of them, I have here ad∣join'd a few by-Operations even in Altimetry it self, as belonging naturally to our Globe, since it not only shows us several ways of finding from time to time the said Almucantars, but gives us also at the same instant without trouble (as appears by the ensuing Operations) the above-mentioned Proportion, and consequently the height of all things Perpendicular to the Ho∣rizon.

OPERATION I. How to find the Proportion between the Perpendicular and its Shade.

COnsider the Northern or back part of the Globes Meridi∣an, which we will call hereafter the Quadrant of Propor∣tion, and which is not only devided like the Southern or fore-part into Degrees, but markt also (in relation to the affair in hand,) with several Figures, of which that next the Zenith is 17, and the remotest 188. And by the way you must take notice, that when you see a Cross behind any Figure, it signifies half an In∣teger more, so that 17 + is 17 Degrees and a half, 26 + is 26 and a half, &c. When you would therefore Operate, Turn the Southern or fore-part of the Meridian towards the Sun, 'till they be both in the same Plane, i. e. 'till the shade of the Pin in the Zenith falls directly upon the Quadrant of Proportion, and what Figure soever, (suppose 25) the shade of Extuberancy cuts, that will be the then Proportion between Perpendiculars and their Shades; for here you may take notice, that we ever suppose the Shade to be 100. Nay, if finding (by any of the former ways) the Sun's height to be (suppose) 14 Degrees, you rectify your Bead to 76 Degrees, or the Complement of it, you need only clap back your String, that is to say, draw it from the Zenith, over the Devisions of the afore-mention'd Quadrant, and then the Figures under the Bead (to wit 25) will shew you the required Proportion; In short, take but the Suns Height (any how) and reckon from the Zenith as many Degrees on your said Quadrant of Proportion, and the Fi∣gures at the end of your Account will give the Proportion sought for. Now if the Shade of Extuberancy, or the Bead marks not even Degrees for the Sun's Height, but (for Exam∣ples sake) 13.30′, and consequently falls between the Figures of 23 and 25 in the Quadrant of Proportion, you had best (to avoid all Calculation and Allowance) expect a Moment lon∣ger, for then the Sun's Height being even, and without Fra∣ction, you may operate as before.

OPERATION II. How to find the height of a Tower by the Globe.

THIS Operation appears at first Sight to be a Corollary of the former, for finding, as I showd you, that the Shade of Extuberancy falls in the Quadrant of Proportion, on the num∣ber (v. g▪) 25, and that the said▪ number represents a Perpen∣dicular, do but measure the shade of any Tower and you will soon have its height, seeing that as 100 is to 25 (i. e. as 100 is to the number found on the said Quadrant) so is the Shade of the Tower, (which being measur'd wee'l suppose 80 yards long) to a fourth number, viz. to 20 the required height.

OPERATION III. How by the help of your Globe to measure any Tower or height, and yet not▪ to seem to use any Instrument in the Operation.

THIS Operation may perchance a little surprise some, and yet it differs not in reality from the former; that showing you how to measure a height by your Globe upon the place, and this how to do it privately. To perform then the Operation, you must choose (when you are alone) any of the aforesaid Numbers, on the Quadrant of Proportion, as suppose 25, and seeing that belongs to the 14th. Degree from the Zenith, recti∣fy your Bead to the Complement, i. e. to the 76th from the Zenith in the said Quadrant; this being done move your String hanging on the Zenith's Pin, till your Bead touches the Parallel of the Day, which we now suppose to be the tenth of May, and the Hour-Circle, that meets with it there (to wit that of six in the morning, or six in the afternoon) tells you that at those hours, on that day of the Month, the perpendicular will be the fourth part of the Shade, i. e. as twenty five to an hun∣dred, so that having discours'd with some body of the possibili∣ty

of measuring heights without an Instrument, repair with him to any convenient place, about the foresaid times of the day, and when you find by your Watch that 'tis exactly six, do but measure the Shade and you will have the required height. And by the way take notice, that as it is in your power to choose what proportion you please, and the more odd and exotic it happens (if you can quickly reduce it) the better it is, for then People will not perchance so soon comprehend the Operation; I say, as you can choose your Proportion, so you may choose the Hour also, for if your Bead be rectify'd to the chosen Propor∣tion, according to the foregoing Example and Instructions, and brought to the hour pitcht upon (suppose 3 in the afternoon) the Parallel, (to wit, that of the fifth of February,) which meets with the the said Bead and Hour-Circle, tells you that then the Proportion will thus happen; nay, you may choose what day and hour you please, if you will be content with the casual Proportion or number which the Bead, when rectify'd (as we mentioned) falls upon.

OPERATION IV. How to find the Hour by your Stick.

YOUR Stick being divided into ten equal parts, and each part by Pricks into as many equal Subdevisions, you must operate thus. Rectify your Bead (on the tenth v. g. of April) to the Sun's Meridian Altitude, and if you then move your String on the Pin of the Zenith, to the Quadrant of Proportion, the Bead will lye (for Example) on 87, so that having writ this on Paper with the figures of 12 above it, draw your String from the Zenith over the next Hour-Circle on which hand you please, I mean either over that of 11. or 1. and where your String cuts it on the said Parallel of the day, there place your Bead, and 'twill lye (v. g.) on 93 in the said Quardrant of Proportion; noting then 93 in your paper under the hours of 11. and 1. pro∣ceed then in this manner from Hour-Circle to Hour-Circle, 'till you come to 6, for after the Sun is within an hour of his Rising or Setting, you may easily guests what time of Day 'tis; besides shadows are then so long that they are troublesome to measure;

I say proceed in this manner to 6, and a Table like that in the Margin will show you the hour not only during that day, but du∣ring five or six successively; with∣out any considerable Errors, for you have nothing to do but to erect your Stick, as perpen∣dicularly as you can, and to measure its Shade with it, so that finding the length of the said Shade to be, suppose 200 i. e. twice as long as the Stick, your Paper will tell you, that when this proportion happens, 'tis either eight in the morning, or four in the afternoon.

OPERATION. V. How to to take an Angle in Altimetry by the Globe.

THIS Operation is to be perform'd like that of finding the height of the Sun and Moon when they shine not out, as I formerly show'd you; that is to say, you must place your Globe Horizontal, and having turned the Meridian towards▪ the Tower, move your Eye along the said Meridian, till the Extuberancy of the Globe permits you only to see the top of the Tower, and then bring but your String, (which we suppose you hold in both hands cross the Meridian) towards you, till it just takes away the sight of the said Top, and the Degree which your String then lies on, (counting from the Zenith) is that of the required Angle, to wit, of the Angle which is ordinarily taken by any Quadrant, Jacobs Staff, &c.

OPERATION VI. How to make and figure the Quadrant of Proportion, as also the Demonstration of the foregoing Operations.

IT appears plainly by the Scheme here before us, that the Shade (AB) being Radius, the Perpendicular (CB) is Tangent of (A v. g. 14.) the Degrees of the Suns height, as also that the Perpendicular (CB) being Radius, the Shade▪ (AB) is Tan∣gent

of the Complement of the said height; therefore if the Radius being 100, you mark from the Zenith to the Horizon each De∣gree of your Quadrant of Proportion with Figures according to the value of their respective Tangents, you must necessarily per∣form the late Operations, that give us the height of things, the hour of the Day, &c. For if your Bead be rectify'd (from the Horizon of your Globe) to (76) the Complement of the Suns height, it will be distant from the Zenith just as many Degrees as the Sun is high, to wit 14, and consequently being moved to the Quadrant of Proportion (which is figur'd we see, from the Zenith downwards) must lye there on 25, the Tangent of his said Height, therefore as the Radius 100 is to (25) this Tangent, so (80) the length of the Shade must be to the Perpendicular 20.

[illustration]

In the next Place if your Bead be rectify'd every hour to the Suns height, it must (when moved to the Quadrant) still lye on Tangent Complement of his said hourly height; Now the Shade being always as I told you the Tangent Complement of this height, the former little Tables must needs shew you the cor∣responding Hour, when we once know the value of the Shade, i. e. its proportion to the Stick. To conclude the Tangents of the first 10 Degrees are not exprest on the Quadrant▪ because when the Sun is no higher, we may easily guess at the hour, and besides (as we said) the Shade is then extremely long, and conse∣quently very troublesom to measure; nor need we go further than 62 Degrees, since his greatest Meridian Altitude exceeds not that value.

The End of the Fourth Section.

Notes

• A memoran∣dum.
• Sect. 1. Op. 2. p. 5.
• 	1.	2.	3.	4.	6.
  12.	11.	10.	9.	8.	7.	6.
  —	—	—	—	—	—	—
  87.	93.	110.	140.	200.	300.	625.
• Op. 2. Sect. 1. pag. 6.