of the Motion of Heat. 503 



Similarly equation (11) of the former paper becomes here 



,£<?+ ?+ ^ +2,f ||+2^| +2^|f =0. (6) 



From (5), (6), and from (8) in the former paper we obtain 



P j t Hv? + v> + w*) + u(3f + ?4- f ) } + 6p!?u ^ + 2p^u ^ + 2 P fu |^ 



+ (3?/2 + „2 + ^2 + 3 |2 + ~2 + p) |_ ( p |2) + 2wv ^_ (p^) + 2WMJ |- (p J*) 



= 2pw ^- + (3w 2 + v 2 + W* + 3£ 2 + rf + f9) P X + 2?/t?p Y 4- 2uwpZ, . (7) 

 whence, comparing with (4), 



- *£ + 1- (pf(f+^+H)- (3p+ ?+ ?)|- (^) 



If the disturbance is not a very violent one, the first, the 

 fourth, and the fifth member on the left-hand side may be 

 omitted. Hence 



» 3 ,.» 



an equation which (under somewhat particular assumptions) 

 was given by Maxwell. Let us write 



D,=f (f + ^ + H-f . (3r + 7? T +^) ; . . (10) 

 equation (9) becomes 



ff=5W+^^?+ffl. • (ID 



Now this equation would lead at once to results contrary to 

 experience, as shown by Maxwell, unless D^ = ; accordingly 

 the first term on the right-hand side may be dropped. And 

 if | 2 , rj 2 , and ? 2 can be replaced each with sufficient approxi- 

 mation by Kf^ + ^ + f*)? we sna H nave 



^=t^p<F+y+a . .. . (12) 



an approximate equation which is of secondary importance 

 only in the subsequent calculation. 



3. Let us now proceed to prove our principal equation. 



