1 36 Cambridge Philosophical Society. 



velocity of ^m is Dcu.w ; from which follow immediately the three 

 well-known equations, 



dx dy dz _ 



The symbol w represents in direction the axis of instantaneous 

 rotation, and in magnitude the angular velocity about that axis. 

 7th. The equation (1.) maybe reduced to the form 



-^ { A w la + BwzjS + C Way } = SDm .U Jot, 



which includes Euler's three equations of motion about a fixed point. 

 8th. If the forces U, U', U", &c. arise from the attraction of a 

 distant body, the symbol of whose position is u' , this equation may 

 be further reduced to the form 



^ / Aw.a+BwajS-i- Cwgy") = ^' DM'.(Aa?'a+By/3 + CzV)- 



9th. In the case of the earth attracted by the sun or moon, this 

 equation becomes 



y being the polar axis, and A= . 



10th. The mean daily motion of y is given by the equation 



5 = ^X(A«'.7)(D«'.y); 

 dt nr^ 



which equation gives immediately all the well-known expressions 

 for solar and lunar precession and nutation, for -5- is the symbol of 



the velocity of the north pole, representing that velocity both in 

 magnitude and direction. 



Supplement to a Memoir on some cases of Fluid Motion. By G. 

 G. Stokes, M.A., Fellow of Pembroke College, Cambridge. 



In a former paper the author had given the mathematical calcula- 

 tion of an instance of fluid motion, which seemed to offer an accurate 

 means of comparing theory and observation in a class of motions, in 

 which, so far as the author is aware, they had not been hitherto com- 

 pared. The instance referred to is that in which a vessel or box of 

 the form of a rectangular parallelepiped is filled with fluid, closed, 

 and made to perform small oscillations. It appears from theory that 

 the effect of the inertia of the fluid is the same as that of a solid 

 having the same mass, centre of gravity and principal axes, as the 

 solidified fluid, but different principal moments of inertia. In this 

 supplement the author gave a series for the calculation of the prin- 

 cipal moments, which is more rapidly convergent than one which he 

 had previously given. It is remarkable that these series, though 

 numerically equal, appear under very diflferent forms, the wthterm of 



