217] 
475 
217. 
A MEMOIR ON THE PROBLEM OF THE ROTATION OF A 
SOLID BODY. 
[From the Memoirs of the Royal Astronomical Society, vol. xxix. (1861), pp. 307—342. 
Read May 11, I860.] 
The present memoir was written for the sake of the further elaboration of the 
analytical theory of the Rotation of a Solid Body, upon principles similar to those 
of my “ Memoir on the Problem of Disturbed Elliptic Motion,” Mem. R. Ast. Soc. 
vol. xxvii. pp. 1—29 (1858) [212] ; the like elements are adopted, and the course of 
the investigation corresponds precisely to that of the memoir just referred to. The 
formulae for the variations of the elements in the two problems (the motion being 
in each case referred to a fixed plane of reference and origin of angles therein) are 
found to be (as it is known they should be) identical in form ; an investigation, in 
the present memoir, of the transformation of the system to the case of a variable 
plane of reference and departure-point as an origin of angles in such plane, would 
have been a mere repetition of that contained in the former memoir, and it was 
therefore unnecessary to give it. A point in the present memoir to which attention 
may be called is the definition of the angle g (varying uniformly with the time, 
but used as an element) which corresponds to the mean anomaly in elliptic motion. 
Besides the ultimate system of formulæ for the variations of the elements in terms 
of the differential coefficients of the Disturbing Function with respect to the elements, 
it appears to me that the intermediate formulæ for the variations in terms of the 
differential coefficients with respect to the coordinates (which are in the ordinary 
investigation altogether passed over) are not without interest, and that it is possible 
that they might be employed with advantage in the integration of the equations of 
motion for the purposes of physical astronomy. 
60—2