their calculations do not always give the perihelion distance of a comet or its periodic time of revolution round the Sun; but limit themselves to announcing the angle of the eccentricity (φ), the mean daily motion (μ), and the logarithm of the semi-axis major or mean distance (a); leaving the student to find out for himself the perihelion distance (q) and the period.
EXAMPLE.
| Given, in the case of Holmes's Comet in 1906— | ||
| ||
| ||
|
To find the Perihelion Distance (q).
(i.) Look out in a Book of Tables the Natural Sine of 24° 20' 26".
(ii.) Subtract this from Unity (1⋅0).
(iii.) Find the logarithm of the result.
(iv.) Add this to the logarithm of a.
(v.) And this will give the logarithm of q.
Example.
| (i a.) | Nat. Sine of 24° 20' 26" = 0⋅4121594. | ||||
| (ii a.) | 1⋅0 − 0⋅4121594 = 0⋅5878406. | ||||
| (iii a.) | Logarithm of 0⋅5878406 is 9⋅7692595. | ||||
| (iv a.) | Add | Log. a | = | 0⋅557427 | |
| Log. (1-e) | = | 9⋅769260 | |||
| Log. (q) | 0⋅326687 | ||||
| ∴ q = 2⋅1217. | |||||
To find the Periodic Time in Years.
(i.) Calculate number of seconds of arc in 360°.
(ii.) Find logarithm of that number of seconds.
