266 M. 0. Szily on the Dynamical Signification of the 



depends also on the temporary course (in other words, on the 

 way and manner) of the importation of energy. Further, up 

 to the present the period has been quite undetermined during 

 which the quantity of heat d<& is communicated to the body ; 

 it is now evident that d<& refers to the period of an oscillation, 

 and that it signifies that quantity of energy which should be 

 brought to the body during one oscillation. 



Let us now examine the relation of the absolute temperature 

 to the vis viva. Provisionally let /3 be the proportionality- 

 factor, so that 



T=/3(a+t). 

 As the temperature is independent of the mass (for a small 

 mass may have the same temperature as a large one), while T 

 depends on the mass, it is simplest to suppose (3 proportional 

 to the mass of the body. Thus 



{3=M.c, 

 where M denotes the mass of the body, and c a pure number 

 which, beside the chosen units of measurement, can only de- 

 pend on the nature of the body. We then have 



a+t =WTc> < 7 > 



that is, the absolute temperature of the body is to the mean value 

 of the vis viva in direct, and to the mass in inverse ratio. The 

 measuring unit is the vis viva divided by the mass, or (what 

 is the same thing) the square of the unit of length divided by 

 the square of the unit of time. 



Let us moreover determine what is signified by the number 

 c. Let us imagine the entire heat communicated applied only 

 to the augmentation of the mean value of the vis viva, and 

 therefore 



dQ = cE, 

 and consequently, according to equation (7), 

 dQ t = Mc.dt. 



From this it follows that c denotes the true heat-capacity — that 

 is, the number that states how much heat the unit of mass re- 

 quires in order that the temperature may be raised one 

 degree. 



As an example, the application of equation (8) to the per- 

 manent gases may serve. In these, according to the experi- 

 ments of Joule and Thomson, the specific heat at constant 

 volume differs but very little from the true heat-capacity. 

 Therefore, if V is the volume of the body, v its specific volume, 

 o the specific heat at constant volume referred to the unit of 



