28 
Proceedings of the Royal Society of Edinburgh. [Sess. 
the adsorbent is already partially saturated may be derived in a similar 
manner. It is, however, desirable to take into account the variation of 
A, and this we now proceed to do in the differentiation of equations (5) 
and (6). We have 
1 f 0 2 E _ i d 2 v f 1 J0E dv ^ 1 J 0 2 E dv ^ d 2 v y 
’ P dndff ' TH0/> + P dp I = T Iwf + 3T +; Mr/ 
T f dpdT dpd r 
or 
/0E\ 
,0®T 
/dv\ 
( dv\ 
(13) 
Now 
dv\ 
0T )g P 
0r „,0r 
0 p/s,T \dp)s, T \ 0 TAi» , 
v = (n - I\j)V. 
= _«y( — ) +{n-Ts)( d —) 
\ 0 /VT 
T /0r 
8\'[ : 
\3T 
f = W ( P'Jr + TlA ) - ( n — Ts )( pAL. _}_ T 
\dp Js, T 
dp 0T 
+ (n - Ys) 
0Y 
dp 
■ - ,T { T (l) r '>')! t (" ■ r, X T (l), ■ >’) 
\ dp ) t 
0Y 
Pr 
0Y 
0T 
'dp' 
v0T/ 
0Y 
dp 
(»L--' v 1 T (l)r'') 
/0E 
+ n - Vs • 11 . 
\3V 
0V 
0r 
The second term on the right represents the change in energy of the un- 
adsorbed gas. Since — 0 approximately for a gas, this second term 
may in general be neglected, and we may write 
1 
(-) 
s \0iy s , T 
T (l) -*} T 
(14) 
In ordinary adsorption observations s and T are not directly measured, 
but rather g and a. It will therefore be of interest to convert the equation 
into terms of g and a. We have 
/0E 
But 
and 
u-l =(A) +(y) - V ", ■ 
\op )(,, T- \ op J s, T V OS J p, T \cp/ g, T 
ds \ 
0E' \ 
dp Js, T 
V 
0r\ 
dp) s, 
T 1 
Jdv 
\0T 
(13) 
S,p 
dv\ 
dg)p,> 
(i) = 
\dpjs, T 
dv\ 
dp) g, T 
d(f 
v — (n — ag )\ , g — s(A 
dv\ , )dv\ fdg 
- + 
dp) t \dgjp, t \dp)s, t 
-M' 
da\ 
+ n -ag 
dp) S, T 
\dp ) [ 
- aV --vO'- 
0V\ 
dp / t 
