Thermodynamics of Fluids. 331 



a motion parallel to the axis of entropy, the work done is 0, and the 

 heat received is equal to the increase of the energy. These two 

 propositions are true either for elementary paths or for those of finite 

 length. In general, the work for any element of a path is equal to 

 the product of the pi'essure in that part of the diagram into the hori- 

 zontal projection of the element of the path, and the heat received is 

 equal to the product of the temperature into the vertical projection 

 of the element of the path. 



If we wish to estimate the value of the integrals fpdv and ftdrj, 

 which represent the work and heat of any path, by means of measure- 

 m.ents upon the diagram, or if we wish to appreciate readily by the 

 eye the approximate value of these expressions, or if we merely wish 

 to illustrate their meaning by means of the diagram ; for any of these 

 purposes the diagram which we are now considering will have the 

 advantage that it represents the differentials dv and dij more simply 

 and clearly than any other. 



But we may also estimate the work and heat of any path by means 

 of an integration extending over the elements of an area, viz : by the 

 formula? of jiage 315, 



y 

 y 



In regard to the limits of integration in these formula?, we see that for 

 the work of any path which is not a circuit, the bounding line is com- 

 posed of the path, the line of no pressure and two vertical lines, and 

 for the heat of the path, the bounding line is composed of the path, 

 the line of absolute cold and two horizontal lines. 



As the sign of y, as well as that of 6 A, will be indeterminate until 

 we decide in which direction an area must be circumscribed in order 

 to be considered positive, we will call an area positive which is cir- 

 cumscribed in the direction in which the hands of a watch move. 

 This choice, with the positions of the axes of volume and entropy 

 which we have supposed, Avill make the value of y in most cases posi- 

 tive, as we shall see hei'eafter. 



The value of y, in a diagram drawn according to this method, will 

 depend upon the properties of the body for which the diagram is 

 drawn. In this respect, this method difiers from all the others which 



Trans. Connecticut Acad., Vol. II. 26 April, 187H 



