32 THERMODYNAMICS OF FLUIDS. 



function of the state of the body, can be reduced to the preceding by 

 the substitution of pdv for dW, or that of tdrj for dH. 



In the foregoing discussion, the equations which express the funda- 

 mental principles of thermodynamics in an analytical form have been 

 assumed, and the aim has only been to show how the same relations 

 may be expressed geometrically. It would, however, be easy, starting 

 from the first and second laws of thermodynamics as usually enun- 

 ciated, to arrive at the same results without the aid of analytical 

 formulae, to arrive, for example, at the conception of energy, of 

 entropy, of absolute temperature, in the construction of the diagram 

 without the analytical definitions of these quantities, and to obtain the 

 various properties of the diagram without the analytical expression 

 of the thermodynamic properties which they involve. Such a course 

 would have been better fitted to show the independence and sufficiency 

 of a graphical method, but perhaps less suitable for an examination 

 of the comparative advantages or disadvantages of different graphical 

 methods. 



The possibility of treating the thermodynamics of fluids by such 

 graphical methods as have been described evidently arises from the 

 fact that the state of the body considered, like the position of a point 

 in a plane, is capable of two and only two independent variations. 

 It is, perhaps, worthy of notice, that when the diagram is only used 

 to demonstrate or illustrate general theorems, it is not necessary, 

 although it may be convenient, to assume any particular method of 

 forming the diagram ; it is enough to suppose the different stages of 

 the body to be represented continuously by points upon a sheet. 



