226 Prof. D. N. Mallik on the 



3. Further, the equation of small motion in an elastic 

 medium (n, <r) is 



( - K+ ^T*- 2n XTy~Tz) = ai • ■ ■ (6) 



where k is the modulus of compression, and A, the cubical 

 dilatation. 



If A = 0, wo have, putting <o z = 2irh, f=a, and - = c 2 , 



which is the same equation as is derivable from the theorem 



~ fala + mb + nc)d& = \(Xdx+Ydy + Zdz), 



or the line-integral of E.M.F. is equal to the rate of decrease 

 of lines of force embraced by a circuit (Maxwell, vol. ii., 

 end of chapter viii., note), and necessarily involves the 

 supposition that 



!«+...+... =o. 



4. JSTow applying the condition &f(T— W)dt=0 from (1) 

 and (2), we get 



Wx = C 2 yVr, (8) 



where c is the velocity of propagation. Thus, we derive at 

 once 



f = c 2 v 2 /' an( i two similar equations, 

 in a medium defined by 



"dw "dy "dz 



5. If, however, the medium contains electrons, we must 

 take 



0% oy 02 



where p is the volume density of electricity of polarization or 

 charge of electrons ; and moreover, if 



t-l*y = ^ U ^ • • • • (10) 

 so that the total current is taken to consist of polarization 



