15. On a New Theorem in Elasticity. 
By M. N. Sana. M.Sc., Lecturer, Mathematical Physics, 
University College of Science, Calcutta. 
1. The Equations of motion of an elastic system are ! 
pv =pY +——+—-+—— - (1). 
p= pee eae 
pw=pZ + pling dy 2 ie f 
‘ Multiplying the equations by w, v and w, and adding, we 
ave, 
+ asad we 1 F(w)- ae 
tive 
=p(Xu + ¥o+2u)+u (32 hin Ft. 
0 Oy Oz. 
Or, OF. Ol, 0Z, 9%, foes (2). 
Me ae ta Gs) (e Wy 
s Now multiplying by (dz . dy . dz . dt), and integrating we 
ve 
9 
a. 
* since MY. ene xz *) andy (| ata 
Oy Ox 
x x) @ 
(x.2+%,%5 cay” 
t= 
rH casts) aan \\\ raw 
Mee s 
t=r 
-\\\{ p(Xu+ Yv+ Zw) dt. do 
s=0 
i} Love’s Elasticity, page 88. 
