1897-98.] Thermodynamics founded on Motivity and, Energy. 129 
From these, by elimination of hT, we find 
JMi = - ^J 1 - J JM 2 = - j etc. (14). 
These equations (11), (12), (13), and (14) express all the know- 
ledge regarding properties of matter which can be derived, accord- 
ing to suggestions of Carnot and Clapeyron, from the combined 
Carnot and Joule thermodynamic theory. 
§ 7. For some applications the following condensation of nota- 
tion and corresponding modification of formulas will be found con- 
venient. Let id denote the mechanical work performed in altering 
the apparatus from any one configuration ( t , gf, g 2 , . . .) to any 
other configuration (t, g Y , g 2 , . . .), both at the same temperature t, 
and let H be the heat absorbed during the process. Equations 
(11) and (10) demonstrate that w and H are independent of the 
particular succession of configurations through which the apparatus 
is brought from the initial to the final configuration, provided heat 
is given to it , or taken from it, by external agency , so as to keep it 
at one unchanged temperature t throughout the process. With this 
notation (11) and (10) are equivalent to the following: — 
w = x(^i>P2> • • • • •) ( 15 ) 
H - if/fag^, • • •) - 'K t >9i>92> • • •) (1G) 
where y and if/ denote two functions of the variables ; and we have 
p dw 
1== dif 
dw , 
p 9 = ^-; etc. 
- dg. 2 
(17) 
II 
^j| 
= etc. 
" dg 2 
(18). 
In terms of this condensed notation we find as an equivalent for 
(14) the following single equation : — 
■TH --ij (19) 
and by integration of (8), (9), and (7) with reference to g v g 2 , etc. 
e - w + JH + e{t,g{,gf, . . .) 
JTH 
e- m = __ + e(t,g{,g 2 , . . .) - mft,gfg 2 , . 
t _ t 
m = m + J — _H + m. I (t,g 1 ,g 2 ' , . . .) 
YOL. XXII. 9/4/98 
. .) 
( 20 ) 
( 21 ) 
(22). 
