621 



We thus find for the numerical value of the work of the friction 

 per second : 



7t 



sill d dO^ 



3gt; 

 2^a 



1 + '-^ 



si7i I'J 



= I 2jra* sin* >'J 



9gV 

 4^ 



( 



1 + 



3jy 



dd = 



= 6ji Lv^a — 



(. 

 ^a 



1 + 





When to this term the heat calculated from the dissipation-function 

 is added, the force, necessary to entertain the motion, and theiefore 

 also the friction in question, is just increased bj the missing term. 



With the aid of this last foruiiila for the resistance we find for 

 the mean deviation of the particles: 



RT 1 



1 + - 



1 4- 



^ 3. That, when the above mentioned work of the resistance is 

 taken into consideration, the dissipation function can give the resistance 

 to which the particle is submitted, ma}' be made evident in the 

 following way. 



. We think the incompressible tluid enclosed by a surface .S', 

 jmrt of which is formed by the surface of a body of arbitrary form, 

 which moves through the fluid. Now we consider the kinetic energy 



T=^ I I I (jq' d.i' dy dz (the molar energy only, not the heat) and 



deduce from the equation of motion an energy equation which 

 indicates how the kinetic energy changes with the time. We then 

 find ') : 



dT rrr . . ^ rr 



= I I j ^( Am4~ ^ " f ^'^^) dti dy dz — 4 II Q9^ (^" + "*" i '"'') ^^ "H 



dt 



-f 



JJ(.v,.- 



\ \\v^Z,u^dS 



- j I F dx dj 



iy dz 



(I) 



Here A', F, /^ represent the components of the external force acting 

 on the fluid, pro nnit of mass, A',, F,, Z^ the pressure components 



') See Basset 11 I.e. p. 252 and Helmholtz "Wissenschaftl. Abhandlungen" 

 Lpzg. 1882 p. 225. 



