35 



AV.W y 

 AV.V.' ' 



5th. The three equations of motion of a rigid body about its 

 centre of gravity are included in the equation 



— (^Du. — Sm\=^I)u.\JSm; (1.) 



dt\ dt J 



u being the symbol of the position of any particle hm of the body, 

 and U the symbol of the accelerating force acting on §m. 



6th. If w be assumed to represent the expression a^a + w^-f w 3 y, 

 where w,, co 2 , cw 3 are the angular velocities of the planes oiyz, zx, 

 xxj about the axes of x, y, z respectively, then the symbol of the 

 velocity of §m is Dw.u ; from which follow immediately the three 

 well-known equations, 



dx dv dz 



— =zw.-,z — wy, —=iv=,x — cv,z, — = w,y — w x. 

 dt " ^ dt dt y 2 



The symbol u> 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 



-^■{Aw 1 a + Bw2j3-f Cw 3 y}:=2:DM.U&ra, 



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 1 a + Bw 2 j8 + Co;37 , \ = ^.'Dtt'.(Aar'a + By'j8 + C«V)- 



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



equation becomes 



dvj Zm' . , . , wri , N 

 -^- = -7-*(Aw'-y)(D«'.y); 



C— A 

 y being the polar axis, and X= 



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



|.=gMW.r)(W.r); 



which equation gives immediately all the well-known expressions 

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



the velocity of the noi-th 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- 



