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Prof. M. P. Eudski on 



and writing again for # , y , z 0i a?, ?/, z, we have the equa- 

 tions : — 



The precise integration of these equations is impossible, 

 but we may avail ourselves of the circumstance that in the 

 present problem the quantities 



d% dv d£ 

 dt' dt' dt 

 are quite insignificant in comparison to other terms. We 

 put 



dj[ = dy = dZ _ 

 dt dt dt 



we remark further that the terms 



-^£ + -'S' ands!mikr ' 



being the components of a rotation superimposed on the 

 strain, shall give no deformation of the body, and reduce 

 the equations to the form : 



P [ ~~ x te 9 + r *) +ypq + zpr]=X, 



But if a, by c are the direction cosines of the axis R, then 



p = a(o, 

 q = bo>, 

 c=reo, 



where <o is the angular velocity about the axis R, which in 

 the present problem is evidently constant. Further, the 

 forces X contain the attraction of the particles and the com- 

 ponents of elastic forces. So we may write our equations in 

 the form 



._ dhdV^d$ n 



- , dS dV d6 A 

 n ^ + m dy + lt + Ty = °> 



n ^ +m dz + ^ + I = °' 



(i.; 



