170 Prof. Barnard on the comparative Expenditure of Heat 
Then FBC G=P(W-W)=Pv(= s 1) =—pyi (Ee " 
" Vel W\ y— Wi git 
And copu=/ pr (~ )’do=—S (1-(7-)" aes (1-2) 
vi ma 
OD V, mee. wl! 
1\ 9-1 
Also KEDL=P,{V,-V,)=P,V,,(4--1] =py(z)’ (7 -1) 
PV] /Vi\elY pro, 
ae Fe a ee 
In the third expression above, we have es the value of which 
we obtain by observing that, : 
q\ MY Vo waa 
iw! a Ww : eo 
Vj=¥"(—\74, and V,=V/(—)7 1. = (24 
T, tT, Ve Vy! T,T 

i rp eae Se 
And K EDL=Py™| © (= a 2 1 | 
ONES o! 
1 
ak 
Whence the area FG HLK=Pv[ (2 -1)-2("s"1 =) | 
Pv’ qu 4, t, ‘ 
+ La (1-3) —( -*) an 
The value of M is of the same form as before, since it depends 
only on V’ and V”. 

7,0" 71 
Ww. yok 7,1! \2, 7 tT! 1 es 
RSE 2 eee Ci eo ee ? = ag asia 
Hence =H y (1 BY. og) +5(1-aoa 
qi -t, 
Wheti't, #2: 2%) "6 this expression becomes, as before =H 
When the maximum and minimum temperatures are given, the 
economy of working, in an engine of this description, depends 0” 
the intermediate temperatures t, and 7’. If, when the foregoing 
proportion holds, we vary t, and not 7’, we lose, either way. But 
there may be a slight increase in the economical ratio, by increa® 
Mu 
ing 7’ a little above the value a This fact is illustrated in ™Y 
f 
article published in the March No. of this Journal. ‘The efect 
of an increase of 1’, is upon the whole to elevate the source of 
the heat, since all that is absorbed is received above this tempe 
ature. It is hardly necessary to say that these two quantities may, 
be made to vary, by varying the proportions of the cylinders of 
the engine, or the position of. the cut-off. 
