On Forced Precession fyc. of a Rotating El lipsoidal Shell. 545 



that Professor H. A. Lorentz (Koninkligke Akademie van 

 Wetenschappen te Amsterdam, April 6, 1898) has shown that 

 the charge on the ions whose motion causes those lines in the 

 spectrum which are affected by the Zeeman effect is of the 

 same order as the charge on a hydrogen ion in electrolysis. 



I wish to thank my assistant Mr. E. Everett for the help 

 he has given in these investigations. 



LVIII. On the Forced Precession and Nutations of a Rotating 

 Ellipsoidal Shell containing Liquid. By Prof. W. McF. 

 Orr, M.A.. Royal College of Science, Dublin* . 



1. rilHE object of the following analysis is mainly to deter- 

 jl mine the difference between the precession and 

 nutation of a spinning body like the earth subject to external 

 couples such as those which act on the earth on the hypotheses 

 that it is perfectly rigid and that it is a shell filled with liquid. 

 The liquid is supposed to be homogeneous, incompressible, 

 and frictionless, the shell to be rigid, and the inner and outer 

 surfaces to be surfaces of revo^tion about a common axis. 

 Owing to these suppositions the bearing of the results obtained 

 on the question of the internal liquidity or solidity of the 

 earth is probably remote. Results for the problem to be 

 discussed here have been stated long ago by Lord Kelvin f, 

 but without any indication of the analysis by which he obtained 

 them. It will appear that while the results here obtained for 

 the precession and the nineteen-yearly nutation agree closely 

 with Lord Kelvin's, those for the halt-yearly and the fort- 

 nightly nutations differ. 



2. The method employed in specifying the motion of the 

 shell and contents is due to GreenhilJ %, and has been already 

 applied to the discussion of the free oscillations of such a 

 system by Hougvb § in illustration of the free nutations of the 

 earth. 



We refer to axes fixed with respect to the shell, the axes of 

 x,y being at right angles in the plane of the equator, and the 

 axis of z being the polar axis. Let the motion of the shell 

 and its contents at any instant be the same as if at that instant 

 the whole system were instantaneously set rotating like a 

 rigid body with velocities f, rj, f, and immediately afterwards 



* Communicated by the Author. 



t British Association Report, 1876, Math. Papers, vol. iii. p. 320, and 

 Popular Lectures and Addresses, vol. ii. pp. 244 et seq. 



X Proc. Camb. Phil. Soc. vol. iv. 



§ "On the Oscillations of a Rotating Ellipsoidal Shell containing 

 Li4uid," Phil. Trans. Roy. Soc. 1895, A. Part I. 



