Equations of Motion. 



9 



But if r is constant, the rate of linear displacement alon^ r 

 at this surface is „ 



The total retardation at surface rdO dz is 



J/Jl!L^2i\rdO dz. 



We have seen before that in order that the form of the ele- 

 ment may be maintained there must be a rate of displacement 

 at rdO dz of 



II. 



r 

 This gives a rate of intlow at dr dz of 



2« 



which, added to the rate of inflow due to change of velocity 

 of I'l' along rdO, gives a total rate of . 



Jr 2n 

 df) r ' 

 In the direction of z the rate is 



dr^ 

 dz 

 The rates for the direction of z are the same as in rectangular 

 co-ordinates. 



Collecting these results, we have the following rates of 

 displacement: 



(1) h- normal to rdO dz, 



(If r 



ci. '{ (2) — — 2r normal to r/r dz, 

 rde 



(3) — normal to rdO dr. 



dz 



c dr 



(1) /• (- 2 r normal to rdO dz, 



dr 



dr 2 It 



h. ' (2) 1 normal to dr dz, 



do r 



(3) r 



r/r 

 dz 



normal to rdO dr 



