6 PROCEEDINGS OP THE AMERICAN ACADEMY. 



/ f / "A (^) • n^ • '^^ ■'■ J ^^^1 since this result is iudependeut of the form 



of S and of the volume of the space euclosed by it, at every point within 

 the solid 



90 h,.h,.h,\9(/]) 9(;'y) 9(,^)l .7. 



5^ _ /<s . h, . kj I 9 f^ 9/(0) \ 



^^ 5^ _ //g . hr, . h^ f 9 fjtj_ 9F(0) 



9t xpiO) y9^\hr,lH' 9 



9_(k'k 9m\ 9(K^i 5m\\ (H) 



9v\/is/ii- 9ri J^9i\hiK- 9^ J)' ^'' 



/Ji_ 



9t xp{b) \9^\Ihhi' 9$ 



LfA. l^M\+ 3 ( h^ 9_F(0)\'^ 

 9v\hsf'i' 3-n )^9C\l'iK' H JI' 



three different forms of the equation of continuity. 

 In Cartesian co-ordinates, this eciuation becomes 



96 _ 1 (9 fK\9JW\,5 f>^m\ 9 f/^/(6)\^ 

 ^-^(e)\9x\ 9x )'^9y\ 9y ) ^ 9 z\ 9z Jj 



^ v^i^C^). (10) 



-^(6) 



+-(^'(*)-ii)}- ^"> 



9 



1 



If the flow of heat within a solid is steady, -^ vanishes at every point, 

 q is a solenoidal vector, and the equation of continuity in terms of Cartesian 

 co-ordinates becomes 



Or 



