Bi9 



8 J /nm ' I J • 1 



^a^'iv — kv\\/ (wlieii at the same time m is iiegleoted with 



respect lo J/). He now equalizes tins value to llie value ^n%akv 

 derived from pheuomeiiological considerations, and lluis finds an 

 equation from vvliicli k can be calculated. 



In my opinion, liowBNer, there are several objections to this way 

 of calculation. The assnmptions on which the deductions of the two 

 expressions are based are not the same; the results refer theiefore 

 to different cases and need not be ecpial. In his kinetic con'ijidera- 

 tions CrNNiNGHAM supposed namely, that the colliding molecules 

 possess Maxweli/s partition of velocities, viz. in the gas or the fluid 

 there is no internal friction (this depends on the deviations from 

 Maxweli/s pai'tition), while moreover colliding molecules exei-t only 

 normal forces on the particles viz. there is no external friction. 



In the case of Stokes' formula on the contrary there is an inter- 

 nal friction and the fluid exerts also lateral forces on the body. 

 In my opinion it is therefore impossible by equalization of the two 

 results to obtain a relation which has any significance. Moreover 

 there is still the inner contradiction in the kinetic deduction between 

 a uniform transformation of velocity kv and the assumption of a 

 purely elastic collision. For this reason no great importance may 



( ^V' 



be ascribed to the tinal result: If = Bvgn'?;! 1 -|- 1,63 — I • 



Instead of assuming a uniform motion of the fluid with the sphere 

 to an amount kv it might be preferable to suppose the normal velocity 

 of the fluid to be equal to that of the pai'ticle, the tangential one 

 being different and a friction existing proportional to the relative 

 tangential velocity. 



The resistance of a sphere under this assumption has been calcu- 

 lated by Lamb and by Basset ')• The first of these uses in his 

 deduction the dissipation function (with the aid of the property : in 

 a fluid the energy transformed into heat = the work of the forces 

 necessary to entertain the motion) ; the other one follows a direct method 

 by calculating the pressure at the surface. The two results however 



I _^ 4 -^ + 6 T- 

 do not agree exactly. Lamb finds: TJ =i^n^av 



(-1)' 



1) See: Horace Lamb "A Treatise on the Math. Theory of the Motion of 

 Fluids". Gambr. 1879 p. 230 ilnot reprinted in the later issues) and A. B. Basset, 

 •A Treatise on Hydrodynamics" Gambr. 1888 II p. 270. 



