623 



As the normal forces at the surface are perpendicular to the 

 relative velocity they do not contribute to the last integral ; this 

 term represents therefore the work of the friction. The result is 

 thus: the vv^ork done per unit of time by liie external forces that 

 act on the body is equal to the heat generated in the fluid increased 

 by the absolute value of the work of the external friction '). 



Taking now as the body a sphere with the velocity v, whicii is 

 kept in a state of uniform motion by a force K in the centre, the 

 work per unit of time is Kv. This K being equal to the resistance 

 W that has to be overcome, it is also equal to 



Wv= I I I F cLv dy dz -\- the work done by the friction along the 

 surface. From this formula we can calculate W. 



1) "Absolute" value, as X^ and u,- referring both to the fluid are oppositely 

 directed, so that finally the form becomes positive. The result says therefore only : 

 external work = total generaled heat. It must be remarked, that Rayleygh, who 

 first introduced the dissipation function, did not mean the above mentioned F. but 

 the total generated heat. (Proc. Lond. Math. Soc. 1878 p. 363). 



