Hendricks, Joel E.

The Analyst

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1880 Excerpt: ...Schefler, Prof. J., .. 173 Infinite Series 191 Schneider, Prof. Elias, .. 173.Tudson, Prof. C. H 105 Seitz, Prof. E. B... 98 Kirkwood, Prof. Daniel, ... 1 Stone, Prof. Ormond, .. 98 Kummell, Charles H..93 The Moons of Mars and the Nebular Law of Facility of Error in two Hypothesis, ... 56 Dimensions, ... 3, 41, 73 I The Great Wheat Fields, . 168 Marcy, W. L 63 j The Bitungential, ...171 'Muir, Thomas, A. M., ... 169 j West, Judge W. H., . 176 Mathiot, Octavian L., ... 124; Wood, Prof. De Volson, .. 10 Mechanics by Quaternions, 17, 49 Woodward, R. S... 164 I THE ANALYST. Vol. VIII. January, 1881. No. 1. ON THE LIMIT OF PLANETAR Y STABILITY. BY PROFESSOR DANIEL KIRKWOOD. Laplace, in his Systeme du Monde, pointed out the limit at which, according to his estimate, the moon's attraction could have retained an elastic atmosphere. The question of a satellite's stability was also considered by the late Professor Vaughan, of Cincinnati. I have seen no attempt, however, to obtain for the different members of our system any definite numerical results. In the present paper it is proposed to find the approximate limits of stability in the cases of the eight major planets and certain of the satellites, on the hypothesis that their primitive condition was either liquid or gaseous. Let M = the mass of the larger or central body, m = that of the dependent planet or satellite, x = the distance from the centre of the former to the limit of stability of the latter, a = the distance between their centres; then, since the disturbing or separating force of the larger upon the smaller mass is the difference between the attraction of the former on the nearest point of the surface of the latter and that on its centre of gravity, we have M M m.... x a--xf ( )l or, putting a = 1 and red