ARISING FROM INEQUALITIES OF TEMPERATURE. 



699 



which gives 



Since the combinations of a/Jy represent small numerical quantities, we 

 may at this stage of the calculation, when we are dealing with terms of the 

 third order, neglect terms involving them, except when they are multiplied 

 by the large coefficient pfp-. The equation may then be written approxi- 

 mately : 



fl .................. (48). 



Similarly, by putting Q = (u + ) (v + rff, we obtain the approximate equation 



r] ft R 1 IY) 



r>2 /) lx/l/ / T>/)\S jr / 3 oA32 t -.J\ />1Q\ 



/v pf -j = p (Jilv) \a. octp ~r ay ) ^4i/ j } 



djX D fJi 



and in the same way we find 



j n i ~* 



(50). 



(12) Approximate Values of Terms of Three Dimensions. 

 From equations (48), (49), and (50), we find 



e* \ f\ I T^ ) **/-* "/ 



2p\v / dx 

 From which by substitution we obtain 



9u./R\*dd , s 

 dy' 



2p\0/ dx 



.(51). 



The value of a/3y is of a smaller order of magnitude, and we do not 

 require it in this investigation. 



882 



