from a Vibrating Body to a surrounding Gas. 419 



We have from (21) 



from which the complete integral of (15) for n = l may be got 

 from that for n = 0. In the form (17) of the integral the parts 

 arising from differentiation of the parts containing e~'""' ande* mr 

 respectively will contain those same exponentials; and therefore 

 the complete integral of (15) for n = l, subject to the condition 

 that the part containing e imr shall disappear, will be got by dif- 

 ferentiating the complete integral for >i = subject to that same 

 condition. The form of the integral in the shape of a descending 

 series is given at once by (17). Hence we get by differentiating 

 (26) and (27), and at the same time changing the arbitrary con- 

 stant by writing BjWT" 1 for B, 



mnr m 

 "02 - + 1>T 



...} 



mrr™ 



2*71 



m 5 r 



-B.^+log^l 



2-,t-,6 3 



4 2 .6 



...} Urn 



-1.1.3.5 



—1.1.8 s . 



P9) 



1.2. 3{$mr) 3 



To determine the arbitrary constants B, and B, the first be- 

 longing to the actual motion, the second to the motion which 

 would take place if the fluid were confined by an infinite number 



of planes passing 

 for r = c, 



th 



roue 



h the 



must have, as before, 



whence 

 B * 



o-j 



+ 



dr ~ 



2 2 . 4* 



Ui 



d fi _ TT 



7+ Ioj 



m~e- 

 -2" 



2 2 .4 



+ 



••) 



m*c* m*c 4 



~9~~ °1~" 02~? ^2 + 



(30) 



2 s . 4, 



!> 2 . 4*. 6 



*»- 



7T 



T (mc) + i gfnimc), suppose : 



g E 2 



