186 R. Clausius on the Application of the 
vertable. i 
9. If we now apply equations (1) and (11) to the circular pro- 
cess which takes place in the thermo-dynamic machine during a — 
riod, we see in the first place that if the whole 5 pret of | 
beat which the mediating substance has taken up during this — 
time is given, then the work is also determined immediately by i 
he first equation, without its being necessary to know the nature q 
of the processes themselves of which the circular process con- — 
sists. In similar generality we may, by the combination of the 
two equations, determine the work from other data also, 4 
We will assume that the quantities of heat which the variable 
body receives one after the other, as well as the temperatures 
which it has at the reception of each, are given, and that there i 
only one temperature over and above, whose magnitude is not 
known @ priort, at which a quantity of heat is still communi 
ted to, or, if it be negative, taken from, the body. Let the s 
of all the known quantities of heat be Q,, and the unknow 
Then resolve the integral in equation (II) into two parts, 0 
which one extends only over the known quantity of heat Q,, and 
the other over the unknown quantity Q,. In the last part the | 
integration may be directly executed, since 7’ has in it a constant 
value 7',, and gives the expression a 
Q 
— 
= 
The equation (11) becomes hereby 
Qi 
dQ Vo _ 
i oe aes 
whence sisws " 
Qi 
Q.=-7,.f Oe aes 
o u 
Further we have according to equation (1), as, for our case, 
= Q.+ Qo: ; 
1 — 
W= 7(@.4Q)- ee 
a substitute in this equation for Q, the value just found, we 
