74 
ME. CLERK MAXWELL OX THE DTXAMICAL THEORY OE GASES. 
tube had its lower tenth part filled with a heavy gas, and the remaining nine-tenths with 
a lighter gas. After the lapse of a known time the upper tenth part of the tube was 
shut off, and the gas in it analyzed, so as to determine the quantity of the heavier gas 
which had ascended into the upper tenth of the tube during the given time. 
In this case we have 0, (82) 
*»,=- (S3) 
§l^ A lP dX 
and by the equation of continuity, 
$+B(f.«.)=0. (84) 
whence 
d Pi = . P 1 P 2 I <^Pi . /g5 1 
dt §i§^ A i P dx 2 5 ^ ' 
or if w r e put D= JEiBz- I, 
P 
( 86 ) 
The solution of this equation is 
C 2 e~” 2D 'cos (w#+a)+ &c (87) 
If the length of the tube is a, and if it is closed at both ends, 
^ 1 = C 1 -|-C 2 «e - '^ ri cos^-}-C3^ 4-H;ri cos2^+ &c., (88) 
where C 15 C 2 , C 3 are to be determined by the condition that when t— 0, p, =p, from 
to A=xb( 2 3 and ^=0 from x—^a to x—a. The general expression for the case 
in which the first gas originally extends from x—0 to x=b, and in which after a time t 
the gas from x— 0 to x—c is collected, is 
P\ b 2a ( _z!£f . irb . ttc 1 _ 4 . 2t rb . 2ttc ) . 
—=-4 — sm — sm — \~ 7 ^e « 2 sin — sm — + &c. >, . . . (89) 
p a 1 ir z c ( a a 1 2' a a 1 j ’ v ' 
where ~ is the proportion of the first gas to the whole in the portion from x—0 to 
x—c. 
In Mr. Graham’s experiments, in which one-tenth of the tube was filled with the first 
gas, and the proportion of the first gas in the tenth of the tube at the other end ascer- 
tained after a time t, this proportion will be 
]j=i5-^f^' si i l A- <? "^‘ sinl2 ^+ <! ‘ 3 ’^' sin ’ 3 n)— &c -}- • • • ( 9 °) 
We find for a series of values of — taken at equal intervals of time T, where 
log e 10 a 2 
io?r 2 IT 
