PROPERTIES OF MATTER IN THE GASEOUS STATE. 
833 
Therefore 
or 
/ P u i c i" P ' x / /\ 
P =T+^T(“‘" a ) 
, pV C 2 2 — q 3 , A 
— C -— K —a ) 
^ = T “17 
/ OO / 
p c —p I c a —C 1 “c —a 
2? 
2 „ 2 / 
Co a 
(137) 
(138) 
Equation (138) holds whatever may be the value of - provided —— 1 is small, and it 
S 5 
^ q q C C _C • 
also holds when —— 1 is large, provided - 1 is small. When J is small and ' ^ ' is large 
s s s s 
c 1 may be neglected in comparison with c. 2 , and we have 
Pc p _ ] ^c Cl 
P 2 CL 
(139) 
Equation (139) is almost identical with what equation (132) becomes as s approaches 
in value to r. If s—r, then the only difference in those two equations is in the co¬ 
efficient. In comparing these equations, however, it must be noticed that in (132) a is 
not the same as a c , for only refers to the one set of molecules—those which are 
receding from the surface, whereas a refers to both sets. 
At the surface when either - or - 2 —- are small 
s s 
« Cl + « 
a =~2~- 
Whence making this substitution in equation (132), and putting s=r the coefficient 
g 
differs from that in equation (139) by -, which shows the extent to which discon¬ 
tinuity at the surface affects the result. 
General equation of impulsion. 
115. From equations (132) and (139) we may form an equation which will hold for 
all values of 
s 
For if the surfaces are spherical 
(140) 
5 o 2 
