18 GRAPHICAL METHODS IN THE 



Hence, in the diagrams of different gases, CD-:-BC will be propor- 

 tional to the specific heat determined for equal volumes and for 

 constant volume. 



As the specific heat, thus determined, has probably the same value 

 for most simple gases, the isentropics will have the same inclination 

 in diagrams of this kind for most simple gases. This inclination may 

 easily be found by a method which is independent of any units of 

 measurement, for 



BD:CD:: 



\d log tv, ' \d log v/t ' \dv/^ ' \dv/t 



i.e., BD-r-CD is equal to the quotient of the co-efficient of elasticity 

 under the condition of no transmission of heat, divided by the co- 

 efficient of elasticity at constant temperature. This quotient for a 

 simple gas is generally given as 1*408 or 1*421. As 



BD is very nearly equal to CA (for simple gases), which relation it 

 may be convenient to use in the construction of the diagram. 



In regard to compound gases the rule seems to be, that the specific 

 heat (determined for equal volumes and for constant volume) is to the 

 specific heat of a simple gas inversely as the volume of the compound 

 is to the volume of its constituents (in the condition of gas) ; that is, 

 the value of BC-j-CD for a compound gas is to the value of BC-J-CD 

 for a simple gas, as the volume of the compound is to the volume of 

 its constituents. Therefore, if we compare the diagrams (formed by 

 this method) for a simple and a compound gas, the distance DA and 

 therefore CD being the same in each, BC in the diagram of the com- 

 pound gas will be to BC in the diagram of the simple gas as the 

 volume of the compound is to the volume of its constituents. 



Although the inclination of the isentropics is independent of the 

 quantity of gas under consideration, the rate of increase of r\ will vary 

 with this quantity. In regard to the rate of increase of t, it is evident 

 that if the whole diagram be divided into squares by isopiestics and 

 isometrics drawn at equal distances, and isothermals be drawn as 

 diagonals to these squares, the volumes of the isometrics, the pressures 

 of the isopiestics and the temperatures of the isothermals will each 

 form a geometrical series, and in all these series the ratio of two 

 contiguous terms will be the same. 



The properties of the diagrams obtained by the other methods men- 

 tioned on page 17 do not differ essentially from those just described. 

 For example, in any such diagram, if through any point we draw an 

 isentropic, an isothermal and an isopiestic, which cut any isometric 

 not passing through the same point, the ratio of the segments of the 

 isometric will have the value which has been found for BC : CD. 



In treating the case of vapors also, it may be convenient to use 



