THE EARTH'S MOTION OF ROTATION.

Cambridge:

PRINTED BY C. J. CLAY, M.A.

AT THE UNIVERSITY PRESS.

OF ROTATION

INCLUDING THE THEORY OF

PRECESSION AND
AND NUTATION.

BY

C. H. H. CHEYNE, M.A.

ST JOHN'S COLLEGE, CAMBRIDGE,

SECOND MATHEMATICAL MASTER IN WESTMINSTER SCHOOL,
AUTHOR OF "AN ELEMENTARY TREATISE ON THE PLANETARY THEORY."

2

PREFACE.

IN offering to the student a treatment of the Problem of the Earth's rotation somewhat different from that which has been usually given in elementary text-books, a few words of explanation are necessary.

The FIRST PART consists of an application of the method of the variation of elements to the general problem of rotation. That the formulæ for calculating these elements are identical in the motions both of translation and rotation, appeared so remarkable, that it might be well to present the latter in a form easily accessible. As far as I am aware, an elementary investigation of these formulæ has not yet been given in attempting to supply this, I have adopted a method somewhat similar to that which I have given for the corresponding equations of the motion of translation, in an Elementary Treatise on the Planetary Theory. The striking analogy, thus developed, between the solutions of problems, in appearance so dissimilar, may, I hope, lead to a more complete study of Lagrange's beautiful theory of the variation of arbitrary constants.

In the SECOND PART the general rotation-formulæ are applied to the particular case of the Earth. These formulæ