Ouranoskopia, or, The contemplation of the heavens, in a perpetual speculum, or general prognostication for ever wherein is succinctly demonstrated the names and natures of the signs, planets and aspects, terms of art, order of the spheres, the colours, magnitudes, motions, solid proportions and distances of the seven planets from the earth ... / by Iames Corss ...

CHAP. XXXI. Of the Planets Paralaxis Altitudinis, and how to calculate the same at all times.

I Promised in the 28 Chapter preceeding, to show you both a Demonstration of, and also by Examples how, to Calculate the Paralaxis Altitudinis of the Planets, for any time Assign'd: And I am now come to perform what I there promised, with as much brevity and facili∣ty as I can. — Which take as followeth.

In this Figure, Z, B, A, I, H, represents the Meridian, K, C, G, the Orbe of the Sun (or any other Planet) D, the Center of the Earth, E, F, the Superficies there∣of. Z, the Zenith. E, I, the Horizon, C, the place of the

Sun (or any other Planet) in his Orbe. The Line, D, C, B, represents the planets true place, from the Center of the Earth, in the Meridian at, B. The Line, E, C, A, his apparent place, as it appeareth from us at E. The Angle of the Paralax of Altitude, is, A, C, B, (which is equal to E, C, D.) The Angle, A, E, I, is the Angle of the apparent Altitude, of the Planet above the Hori∣zon (which in this Example we suppose to be 27 degr. 40 min.) whose Complement is, Z, E, A, (62 deg. 20 min.) —Here you may see that the apparent Altitude of the Planets, is lesse from the Superficies (or place of Observation at E,) then from the Center of the Earth; (at D,) from which place the Planet in his Orb appears higher in the Meridian at B, then he doth from E, in the Meridian at A, so that the Angle of the Planets Paralaxis Altitudinis, is nothing else but the difference between the true and apparent Altitude, in the Meridian or Circle of Altitude.

Here note, that the nearer a Planet is to the Horizon and Center of the Earth, the greater is the Paralax there∣of. And hence it is, that the Moon (because of her Vi∣cinity to the Earth) hath the greatest Paralax of all the other Planets. And that's a main reason why we have so few Solar Eclipses, and those few have so little ob∣scurity. Because frequently her Southern Paralax ex∣ceeds her Northern Latitude (the greatest Eclipses hap∣pening alwayes when they are equal, and least when her Latitude is South) &c. These things being premised, I come next to practice: And for Illustration, I shall add an Example of either of the Luminaries, for to find their Paralaxis Altitudinis at any time Assign'd.

First, an Example in the Sun.

Suppose the Altitude of the Sun to be (by observati∣on) 27 deg. 40 min. and his distance from the Earth (by calculation) 101798 parts: I demand how much will his Paralax of Altitude (then) be? — To resolve this (and all such like) Questions. I return to this annexed Diagram, for Demonstrations sake, where, In the Triangle, C, D, E, we have known, [1] E, C,

the distance of the Sun from the Earth 101798. [2] E, D, the Semidiamiter of the Earth 68, 1—2. [3] The Triangle, C, E, D, 117 d. 40 m. which bisected, gives 58 deg. 50 min. the half sum of the opposite Angles un∣known. Hence to find the Paralax of Altitude, A, C, B. Say by this Analagy.

As the sum, is to the difference, so is the Tangent of the half sum of the opposite Angles unknown, To the Tangent of an Arch: whose difference is the Paralaxis Altitudinis required.

[illustration] diagram demonstrating solving for the altitude of the sun

The Operation.

E, C.	101798,	0-0
E, D.	68,	1-2

				Logarithm.
Sum of E, C, and E, D.	101866,	1-2		5, 008244
Difference	101729,	1-2		5, 007658
So is the Tangent of			58 d. 50 m. 00 s.	10, 218369
				15, 226027
To the Tangent of			58. 47. 56.	10, 217783

Whose difference 2. 4. is the Angle, A, C, B, or the Suns Paralax of Altitude as was required.

The second Example is of the Moon.

Suppose the Altitude of the Moon were found (by Observation) to be (as before) 27 deg. 40 min. and her distance from the Earth (by Calculation) 3879. I de∣mand what, or how much will her Paralax of Altitude be at the time of the Observation?

In the Triangle C, D, E, the Line C, E, represents the distance of the Moon from the Earth 3879. the sid•• E, D, and Triangle C, D, E, being the same as before.

The Operation is as followeth.

E, C,	3879,	0-0
E, D,	68,	1-2
Sum of E, C, and E, D,	3957,	1-2		3,596322
Difference	3810,	1-2		3, 580982
So is the Tangent of			58 d. 50 m. 00 s.	10, 218369
				13, 799351
To the Tangent of			57. 55. 47.	10, 203029

Whose difference 54. 13. is the Angle A, C, B, or Paralaxis Altitudinis of the Moon at the time of the Observation, as was required.