24 6 
PROFESSOR, CLERK MAXWELL OX STRESSES IX RARIFIED 
3RV^|=p(RS) i ^(-2« 3 +a^+«y=).(48) 
Similarly, by putting Q=(u-\-£) (y-\-rjf, we obtain the approximate equation 
Wp0 a £=p(B.e)j^-S^+af) .(49) 
and in the same way we find 
’R s pd-=p{B t e)^(a s +a^-Saf) . (50) 
ClJb O jjb 
(12.) Approximate Values of Terms of Three Dimensions. 
From equations (48), (49), and (50), we find 
9 f v ±\‘ d A 
2 p\6) da? 
a/3 2 = 
O 
ay ' nz — 
•W-Y—" 
2 p \ 6 ) dx 
From which by substitution we obtain 
03 __ 9 dfV\kW 
p 2 i\ejdf 
g 9 fl/lifdd 
y = ~2 p\e) Jz' 
ary—/3~y = 
3 p/RAde 
2 p\o) dy 
3 /ARAd# 
(51) 
The value of a/3y is of a smaller order of magnitude, and we do not require it in 
this investigation. 
(13.) Equation of Temperature. 
Adding the three equations of the form (44), and omitting terms containing small 
quantities of two dimensions, and also products of differential coefficients such as 
da dd „ , 
— we find 
dx dx 
be 
bt 
5 fi 
cP6 cff (ffh 2 6 bp 
2 p\dx* + df+dzf-T~ 3 P bt' 
(52) 
The first term of the second member represents the rate of increase of temperature 
due to conduction of heat, as in Fourier’s Theory, and the second term represents the 
increase of temperature due to increase of density. We must remember that the gas 
here considered is one for which the ratio of the specific heats is 1 - G6. 
