(/70

the former Series exhibitlng the Sine by the Arch, by Division it is ersie cconclude, that the Natura! Tangent to the Arch A is A -t* A 3 ■+ " A *

—• A 7 -+■ A ?, (3c. and the Natura! Secant to the fame Arch i -+

3*5 2SZ;

— A 1 -1- — A 4 -t- --- A 6 ■+ A 8 , Öc. and from the Aritbtnctick. of

Infinites, the Numbcr of these Sccants being the Arch A, it follows that the

Summ Total of all the Infinite Secants on that Arch is A -+ -4- A 5 -4* —- A 5

6 24

-4- ——- A 7 +■ A 9, tßc. the which by what foregoes, 'is the Lcga-

ritbm Tangent of Napicr's Form, for the Arch of 45 ’° -V* A, as before.

And Collecting the Infinite Summ of all the Natura! Tangents on the faidArch A, there will arise v A A 4* — A 4 -i- — A 6 ■+■ A 8 ■+■

12 4 f 2520

, A I0 , iyc. which will be found to be the Logaritkm of the Secant ofthe tarne Arch A.

XXXIX. The Height of the Pole, and the Suns Declination being known,I^uoVef rif" a ^ ar S e P'UZ-Dial, truly wrought, having a Box with a Compals or necdlecoJsjfs It Se *; fixt to its Meridian below, may go as near as any other Instrument, to stiew

tjt.the Variation of the Necdle at Lea. For, when it is set to the just Hour

*' I4 ' f ' * 35 ' arid Minute of the Day, the Meridian of it stands just in its due place ;

and lo shews how far the Necdle Varies from it, as exactly as the largenefcof the Card will permit.

But becausc these Dials are so rarely Just, &c. though they may be ufedand taken notice of, yet they are not to be relied on. The thing therefore isto be performed, as followeth:

Find out the Sun’s Ajimuthal Distance from the Meridian forne hours be-fore or aster noon, and then its Magnetica! A^imuth, or Distance from theMeridian pointed at by the Necdle, and the Difterence of these two Di-stances, is the Variation of the Ncedle.

To find the Sun’s true Atimutb, or by how many Degrees, (3c. of theHori/,on, it is distant from the Meridian: It’s Declination, it’s Altitude,and the Eievation of the Pole, must all three be known ; and thence thetrue Anmuth may be eafily Calculatcd. The true Anmuth of the Sun beingthus found, and the Magnctical Anmuth of it aecordiirg to your Nee die,being obierved, Substract the lesser Number from the greater, and the.Remainder is the Variation of the Needle. If the Magnetica! Anmuth beless than the other, then the Variation is towards the tarne fide of the"Meridian, w'nere theSun is; if greater, on the other.