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MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
is known, in each case, from previous experiments on the properties of the gas em- 
ployed ; and this area, by Proposition VI., is equal to the area MGAHN ; to which 
adding the area NH/m, ascertained by experiment, we obtain the area MG hn, that 
is, the latent heat of expansion from the volume V G to the volume V ft ,at the constant 
actual heat Q„ denoted symbolically by 
H =QwL PrfV=Q,(F i -F G ). 
V G 
, Now the problem to be solved is of this kind. We know the differences of actual 
heat corresponding to a certain series of isothermal curves for the substance employed ; 
and we have to ascertain the absolute quantities of actual heat corresponding to those 
curves. Of the above expression for the area MGA«, therefore, the factor Qj is to be 
determined, while the other factor, being the difference between two thermo-dynamic 
functions, is known ; and the experiments of Messrs. Thomson and Joule, by giving 
the value of the product, enable us to calculate that of the unknown factor, and 
thence to determine the point on the thermometric scale corresponding to absolute 
privation of heat. 
(17.) Proposition VII. — Problem. To determine the ratio of the Apparent Specific 
Heats of a substance at Constant V olume and at Constant Pressure, for a given Pressure 
and Volume ; the isothermal curves and the curves of no transmission being known. 
* 
(Solution.) In fig. 12, let A be the point whose co-ordinates represent the given 
volume V A and pressure P A ; QAQ the isothermal curve passing through A ; q q an- 
Fig. 12. 
other isothermal curve, very near to QQ. Through A draw the ordinate V A Aa parallel 
to OY, cutting qq in a ; draw also AB parallel to OX, cutting qq in B. From A, a, B, 
draw the three indefinitely-prolonged curves of no transmission AM, am, BN. 
Then the heat absorbed in passing from the actual heat Q to the actual heat q , at 
the constant volume V A , is represented by the indefinitely-prolonged area MAam, 
while at the constant pressure P A it is represented by the area MABN. Let the curve 
qq be supposed to approximate indefinitely to QQ. Then will the three-sided area 
AaB diminish indefinitely as compared with the areas between the curves of no 
transmission AM, am, BN ; and consequently the area MABN will approximate in- 
