( 243 ) 



d.v d?/ de 



p,, = i ((S^ J^ ,p^) — S^, _ ^^, 



y),., =r - (^, ^£, + .!>., JS, ) 

 ;>,, = - (tr., (v, J^ .0,, .p, ). 



Ill oi'der lo iiitroduco the forces which uct oii llic meiliuni eiieruv 



we will Iraiistbrni the righthaiul nieiiihei' of equation (1) in such 



'ó 

 a wav that the diftercutial i(uolient witii uo longer occurs in it, 



<l' d d Ö d 



l»ul a (lifierential (luotient with — = -—-(- n), • \i\, -I- iiv — 



This can he done as follows. We put 



1 ^ 



— *cr = o'li" 



Then equation (Jj can be written: 

 d{Qi^,AV) d\<>'w,AV) 

 ^ dt ^ d't 



, d'AV f ö^'iD^. ö^'iü^ ö(>'a>. 



d't \ d.r ' '' dl/ ' ■ d: 



If we now ))ut : 



2x^ @/ 



P XX = (> U\, 



c' q' C^ W 



p'xz 



and y> — y>' i=: / (i. e. />j.i — p'^.^.z^tj.^. etc), and we add zl I' AV /vO 

 to l)0tli members of the equation, then we get : 



dt ^ d't 



d! LV 



As however = L I Dir \\\ the last two terms cancel each 



d't 



other. So we get an equation the left hand member of which may 



be interpreted to represent tiie force which is exerted b} l he tensions 



t on the volume element A I'', whereas the righthand member represents 



the increase of the momentum of the 'masses oLV and oLV. 



