of the Motion of Heat. 505 



the symbols L, M, N being defined as follows : — 



L=p{(5F+?+r)^+(?+5^ + ^)^+(r+^+5^)5}. (21) 

 +(P+«^+P)(p«^+P?|j+P«§i) 



n= (5f+ ? + fl (A ( ^ } + Jt (w y 2) + |_ (pW} ) 



+(?+?+5?j(^(^T 2 )+| / (M 2 )+^( P n)- • (23) 



We easily find, to a first approximation, L = 0, and 



M-KF+^+R«i (24) 



N=| (?+?+ r*)(^f + ^ + ^); • (25) 

 thus equation (20) becomes 



pi-SV+f+W) 



dt 



= - W+?+W-¥HP+^+t 2 )(^ + ^+ ^r) (26) 



To the left-hand side let us add 



calling 



ip(fMV + CT=A, (28) 



we obtain 



= -K? 2 +?+1 2 )^-|(f +V + f 2 )(^f + ^ + ^) (29) 

 If we make Sp^p^ + nf + g 2 ) and introduce Lord Rayleigh's 



