NEWTON S PRINCIPLE. 365 



with observation in regard to the time, it does not 

 explain the minuter variations of the time, and totally 

 fails to account for the successive diminutions of the arcs 

 of vibration. 



It becomes necessary to consider the effect of the internal 

 friction of the fluid. This has been accomplished by 

 Professor Stokes. The equations, however, in this case 

 become so complicated, that it requires a very long 

 analysis to obtain the motion even of so simple a body as 

 a sphere. We shall therefore merely state the results 

 arrived at. The sphere is suspended by a fine wire, the 

 length of which is much greater than the radius of the 

 sphere. The resistance both to the sphere and the cylin 

 drical wire have to be discussed. The motions are con 

 sidered very small, so that by some obvious reductions the 

 problem is reduced to the two following. 



The centre of a sphere performs small periodic oscil 

 lations along a right line in a boundless fluid, the sphere 

 itself having a motion of translation only. Find the motion 

 of the fluid. 



An infinite cylinder performs small oscillations in a fluid 

 in a straight line perpendicular to its axis. To find the 

 motion of the fluid. 



Let be the abscissa of the centre of the sphere at any 

 time L Let T be the time of one of its small oscillations 

 from rest to rest, a its radius, m its mass. Let mf be the 

 mass of the fluid displaced, p its density, and ^ some con 

 stant depending on the internal friction of the fluid. Then 

 put 



1 JL &amp;gt;= 



2 + 4va * ~~4 va V va 

 Then the resistance on the sphere is 



