118 Prof. H. Lamb on the Uniform 



latter is regarded as moving through a liquid at rest at in- 

 finity) which ultimately varies inversely as the distance, 

 instead o£ as the square of the distance. 



It remains to estimate the degree of approximation which 

 the preceding results afford in various parts of the field. 

 For this we have recourse, again, to a comparison of the 

 ''constraining'"' forces, which would be necessary to make 

 the solution exact, with the viscous forces. The former are 

 still given by the formulae (2), provided u has its altered 

 meaning. 



At distant points, well outside the wake, the terms in (24) 

 which depend on %may be neglected, and we have, ultimately, 



3 x 3 y 3 z rvr . 



a =2 Va V v =2 m r*' w =2 va r z ' ' ' l ' 



Also, from (30), 



f=0, n =~-Uka^e- k{r - x \ ?=-|uA'a^^ r - r) . (33) 



Hence 



V ^ T-2 2' Sy ~ —k(r-x) v ^ T*2 "^V ~W~^ 





the resultant of which Is 



R=JuV^- i( '- J, 1 (35) 



in a direction at right angles to the radius vector. The 

 viscous forces may be found from (21) and (25). If we 

 retain only the terms which are most important when r is 

 larse, we find 



__ 2 iifi z ( r ~ tV ) -Jc(r-x) /ns\ 



\^j l w——vk z \J j— e • (36) 



It follows from (18) that the ratio of the forces is of the 

 order (ljkr) . (a/r). The approximation in this part of the 

 field is therefore amply sufficient. 



