MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
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(9.) First Corollary from Proposition 11 . — Theorem. If a succession of isothermal 
curves corresponding to quantities of heat diminishing hy equal small differences c$Q, be 
drawn across any pair of curves of no transmission, they will cut off a series of equal 
small quadrilaterals. 
Second Corollary . — Theorem. In Jig. 6, let ADM, BCN be any two curves of no 
transmission, indefinitely prolonged in the direction of X, and let any two isothermal 
Fig. 6. 
curves QjQj, Q 2 Q 2 , corresponding respectively to any two quantities of actual heat 
Qi, Q 2 , be drawn across them. Then will the indefinitely -prolonged areas MABN, 
MDCN, bear to each other the simple ratio of the quantities of actual heat Q 13 Q 2 . 
Or, denoting 1 those areas respectively by H 15 H 2 — 
h 2 q 2 
h, a, (9,) 
This corollary is the geometrical expression of the law of the maximum efficiency 
of a perfect thermo-dynamic engine, already investigated by other methods. In fact, 
the area MABN represents the whole heat expended, or the latent heat of expansion, 
the actual heat at which heat is received being Q x ; MDCN, the heat lost, or the 
latent heat of compression, which is carried off by conduction at the actual heat Q 2 ; 
and ABCD (being the indicator-diagram of such an engine), the motive power, pro- 
duced by the permanent disappearance of an equivalent quantity of heat ; and the 
efficiency of the engine is expressed by the ratio of the heat converted into motive 
power to the whole heat expended, viz. — 
ABCD H 1 -H 2 _Q 1 -Q 2 
MABN' 
H, 
Q,j 
( 10 .) 
(10.) Third Corollary ( of Thermo- Dynamic Functions). 
If the two curves of no transmission in fig. 6, ADM, BCN, be indefinitely close 
together, the ratio of the heat consumed in passing from one of those curves to the 
other, to the actual heat present, will be the same, whatever may be the form and 
position of the curve indicating the mode of variation of pressure and volume, provided 
it intersects the two curves of no transmission at a finite angle ; because the area 
contained between this connecting curve and the two indefinitely-prolonged curves 
