154 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
then the heat to be stored, according to equation (49 a.), is 
888*3 
72,233 + 26214-4 X hyp. log --^=72,233+1 1 ,157 
= 83,390 foot-pounds per pound of working air per stroke. 
The large proportions borne by these quantities to the whole heat expended, show 
the importance of efficient action in the regenerator to economy of fuel. The quan- 
tity of heat to be stored, however, becomes smaller, as the curves of equal transmis- 
sion approach those of no transmission, for which it is null. The additional expan- 
sion requisite in this last case is found by the following computation, — 
Vc_Vp_ 
v B -v A - 
/T\±T 0 \ 
U+tJ 
_i_ 
N qO'41 
= 5-423, 
the result of which shows the great additional bulk of engine required, in order to 
obtain the maximum efficiency without a regenerator. 
Supposing one pound of coal, by its combustion, to be capable of communicating 
heat to the air working in an engine corresponding with the above example, to an 
amount equivalent to 
6,000,000 foot-pounds 
(an amount which would evaporate about 7 lbs. of water), the maximum theoretical 
duty of one pound of such coal in such an engine, without waste of heat or power, 
would be 
3,000,000 foot-pounds, 
corresponding to 
3 , 000,000 
12,010 
= 249 strokes of a pound of working air, with the effective expansion 
3 
T 
The deductions to be made from this result in practice must of course be deter- 
mined by experience. 
Section V.— PROPOSITIONS RELATIVE TO A HETEROGENEOUS MASS, OR AGGREGATE, 
ESPECIALLY IN VAPOUR-ENGINES. 
(34.) The Heterogeneous Mass to which the present investigation refers, is to be 
understood to mean an Aggregate of portions of different ingredients, in which each 
ingredient occupies a space, or a number of spaces, of sensible magnitude. 
The results arrived at are not applicable to mixtures in which there is a complete 
mutual diffusion of the molecules of the ingredients, so that every space of appre- 
ciable magnitude contains every ingredient in a fixed proportion. A mixture of this 
kind, when the relations between its pressure, volume, heat, and temperature are 
known, may be treated, so far as regards the expansive action of heat, as a homo- 
geneous substance. 
The ingredients of an aggregate are heterogeneous with respect to the expansive 
