134 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
of a curve of no transmission at the same point, or of the specific heat at constant 
pressure to the specific heat at constant volume. 
This is a geometrical proof of Laplace’s law for all possible fluids. The same law 
is deduced from the Hypothesis of Molecular Vortices in the paper before referred to 
on the Centrifugal Theory of Elasticity. 
(20.) Proposition VIII. — Problem. The isothermal curves for a given substance 
being known, and the quantities of heat required to produce all variations of actual heat 
at a given constant volume ; it is required to find any number of points in a curve of 
no transmission passing through a given point in the ordinate corresponding to that 
volume. 
(Solution). In fig. 13, let V a Aj be the given ordinate ; QjQj, A 2 Q 2 isothermal curves 
meeting it in A 1? A 2 , respectively ; and let it be required, for example, to find the 
Fig. 13. 
point where the curve of no transmission passing through Aj intersects the isothermal 
curve A 2 Q 2 . On the line V A A 2 A n as an axis of abscissa?, describe a curve CC, whose 
ordinates (such as A 2 C 2 , a 4 c 4 , &c) are proportional to the specific heat of the substance 
at the constant volume V A , and at the degrees of actual heat corresponding to the 
points where they are erected, divided by the corresponding rate of increase of press- 
ure with actual heat; so that the area of this curve between any two ordinates (e. g. 
the area a 4 c 4 c 3 a 3 ) may represent the mechanical equivalent of the heat absorbed in 
augmenting the actual heat from the amount corresponding to the lower ordinate to 
that corresponding to the higher ( e . g. from the amount corresponding to « 4 to that 
corresponding to « 3 ). 
Very near to the isothermal curve A 2 Q 2 , draw another isothermal curve a 2 ^ 2 , and 
let the difference of actual heat corresponding to the interval between these curves 
be SQ. Draw a curve DD, such that the part cut off by it from each ordinate of the 
