116 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
The practical use of such diagrams, in ascertaining the power and the mode of 
action of the steam in steam-engines, where the curve AP 3 P 2 A is described by a 
pencil attached to a pressure-gauge, on a card whose motion corresponds with that 
of the piston, is sufficiently well known. 
( 2 .) It appears that the earliest application of diagrams of energy (as they may be 
called) to prove and illustrate the theoretical principles of the mechanical action of 
heat, was made either by Carnot, or by M. Clapeyron in his account of Carnot’s 
theory ; but the conclusions of those authors were in a great measure vitiated by 
the assumption of the substantiality of heat. 
In the fifth section of a paper on the Mechanical Action of Heat, published in the 
Transactions of the Royal Society of Edinburgh, vol. xx., a diagram of energy is 
employed to demonstrate the general law of the economy of heat in thermo-dynamic 
engines according to the correct principle of the action of such machines, viz. that 
the area of the diagram represents at once the potential energy or motive power 
which is developed at each stroke, and the mechanical equivalent of the actual 
energy, or heat, which permanently disappears. 
As the principles of the expansive action of heat are capable of being presented to 
the mind more clearly by the aid of diagrams of energy than by means of words and 
algebraical symbols alone, I purpose, in the present paper, to apply those diagrams, 
partly to the illustration and demonstration of propositions already proved by other 
means, but chiefly to the solution of new questions, especially those relating to the 
action of heat in all classes of engines, whether worked by air, or by steam, or by 
any other material ; so as to present, in a systematic form, those theoretical prin- 
ciples which are applicable to all methods of transforming heat to motive power by 
means of the changes of volume of an elastic substance. 
Throughout the whole of this investigation, quantities of heat, and coefficients of 
specific heat, are expressed, not by units of temperature in a unit of weight of water, 
but by equivalent quantities of mechanical power, stated in foot-pounds, according 
to the ratio established by Mr. Joule’s experiments on friction (Phil. Trans. 1850) ; 
that is to say, 
772 foot-pounds per degree of Fahr., or 
1389 - 6 foot-pounds per Centigrade degree, 
applied to one pound of liquid water at atmospheric temperatures. 
(3.) Of Isothermal Curves, and Curves of No Transmission of Heat. 
A curve described on a diagram of energy, such that its ordinates represent the 
pressures of a homogeneous substance corresponding to various volumes, while the 
total sensible or actual heat present in the body is maintained at a constant value, 
denoted, for example, by Q, may be called the Isothermal Curve of Q for the given 
substance. (See fig. 2 .) Suppose, for instance, that the co-ordinates of the point A, V A 
and P A , represent respectively a volume and a pressure of a given substance, at which 
the actual heat is Q ; and the co-ordinates of the point B, viz. V B and P B , another 
