﻿450 Mr. G. B. Jeffery on the 



We have 



div. v = -y ~- (A) + — ^^ ^ (r sin 0) + — *-2 ^r 

 r* o** r sin 00 v r sin o<£ 



and 3) __ d d w d w Jd 



t~~Wt + U Tr + r S3 r sin §0' 



and the equations of motion are * 





r » p or L3 o?' 



i 





2u 2 cot 





"^ - 2 - ^ 



2)r ^w 



w? 2 cot -p, 



— = -Pfl - 



2)£ ' r 



?' y 



2 'dv 

 ' r 2 00 r 2 sin 6 B0 



1 a/' . r 1 o 



p %+>[It*^^ 



i? 2 cos# 3w? 2 Bin 



~" r 2 sin 2 0~ 7 2 sn?0" cty + ? PJ 



®* r r v pr sin 0o<j) [_ 3r sin op ^ ' 



™ _ w 2 Bit 2 cosfl di?! 



V W r 2 sin 2 6 + r 2 sin (j> + r 2 sin 2 d</> J * 



§ 2. Transformation of the Stresses. 



If ws denotes the component in the direction n of the 

 stress across a surface whose normal is in the direction s 

 and if the Cartesian components of velocity are u', i/, iv f , we 

 have 



A' X- 



2 



where 8 = div. v and A, = — f^yit. 



These are identical with the usual expressions for an 

 elastic solid except for the term/), which indicates a pressure 

 equal in all directions. The components of stress in an 

 elastic solid were transformed to curvilinear coordinates by 

 Lame, and we can at once obtain the corresponding formulae 

 for a viscous fluid by inserting the uniform pressure p. 



* Cf. Basset, p. 246, where a slight misprint occurs in the third 

 equation. 



