180 
ME. MACQTJOEN EANKINE ON THE THEEMO-DYNAAnC THEOET 
in which t, and are the two values of t corresponding to one given value of (p, and the 
other similar symbols have analogous meanings. 
Equation 4, expressed in words, means — The heat which disappears dunng a cycle of 
operations is egual to the work performed. Another mode of expressmg the pi-inciple of 
equation 4 is as follows : — t \ \ 
dt.d!p=dp.dv 
The following is a summary of that graphic representation of the General Equation 
of Thermo-dynamics which was first demonstrated in the Philosophical Transactions for 
1854. 
In fig. 1, let OP, OV be rectangular axes of coordinates; and let ordinates measured 
parallel to’ OP and OV respectively represent pressures and volumes, so that areas 
represent quantities of energy. Let the coordinates of a line of any figm-e, such as AE. 
represent a series of changes of pressure and volume undergone by an elastic body. 
Let AM, BN be curves traversing A and B, of the class called adiabatic cunes. oi 
curves of no transmission ; that is, curves whose coordinates show the law of vanation 
of the pressure and volume of the body when it neither receives nor emits heat. Those 
curves are indefinitely extended both ways, and OV is theii’ asymptote. 
Then the heat which the body receives during the change from A to B, is represented by 
the area contained between the line AB and the curves AM and BN, indefinitely extended 
in the direction OV. 
To show the connexion between this and the algebraical expression of the same law 
in equation 1, let <p be a function which is constant for a given adiabatic curie, and of 
such a nature that dt.'d^^dp.dv. Divide the area MABN into an indefinite number 
of indefinitely-narrow bands by a series of adiabatic curves. Let mabn be one ot these 
bands. Let the difference of the values of the function <p for the curves anu bn, be dl : 
let t be the absolute temperature corresponding to the element ab of the line AB ; then- 
area mab7i=td<p ; area MABN=jf^?f. 
