PROPERTIES OF MATTER IN THE GASEOUS STATE. 
815 
c . 
s 
wherein f[~j varies continuously as - varies from 0 to co, having a finite value when 
c c 
is infinite and being,’ zero of the order - when - is zero. 
° s s 
Q 
101. The factor s\ — s' 2 is clearly a function of c, - and X 3 , where X 3 depends on the 
s 
Q 
nature of the impacts between the gas and the tube. And, moreover, when - is small 
and the molecules cross the tube without encounter, s\ — s'. 2 is proportional to c —it may 
be shown that in the case of a flat tube s 1 —s 2 =7rmc, and in the case of a round tube 
s 1 —s 2 =twic(i-{--J, for tubes of other shapes — s 2 would have an intermediate value 
—so in this case we put 
s\ — s' 2 =irm'c. 
Again, where - is large, then s\ — s' 2 is equal to sX 3 . 
s 
Hence, as a perfectly general form for s\ — s' 2 , we have 
s'l - s' 3 =1 m'c/J ) + s\ 3 /J ~ s 
(97) 
wherein fs(~J is zero when - is large, and unity when - is small; while f 4 (- ) is unity 
c c 
when - is large, and zero when - is small. 
The general equation of transpiration. 
102. Substituting in equation (95) from equations (96) and (97) we have 
■ ( 98 ) 
Or since Art. 72 p= p -^-, ^=K-a 2 , and Art. 98 \=X 1 / 1 ^-j-hX 2 / 2 ^j we have, remem¬ 
bering that M is constant, 
5 M 
MDCCCLXXIX. 
