of Superheated Vapours. 423 



the attainment of the gaseous state a greater superheating is 



70 



required than -^ . 10 or 350°. 



We thus see that, wherever a sensible deviation of purely 

 saturated vapour from the gaseous state has place, a very con- 

 siderable elevation of temperature is necessary in order by super- 

 heating in constant volume to make it pass into the gaseous 

 condition. 



For practical application we hence obtain the not unimportant 

 result, that, at least so long as the limits of these experiments 

 are not exceeded (therefore to about 4 atmospheres pressure) , 

 only trifling errors are entailed by putting the coefficient of pres- 

 sure-expansion for a constant volume simply equal to the coeffi- 

 cient of expansion of air, provided the limits of the temperatures 

 under consideration are not too wide, say not more than 50°. 



For the theoretical side of the question, however, such a tri- 

 fling augmentation of </> is perfectly sufficient to cause the pro- 

 portions to appear quite different from what they would be with 

 <f) constant. To see this it is best to keep in view the two di- 

 rections in which I have followed the variability of the vapour- 

 densities. The earlier experiments give the variableness which 

 occurs when at a constant temperature the vapour expands its 

 volume ; the present when, the volume remaining constant, the 

 temperature is raised. In both ways the gaseous state is gra- 

 dually reached. Now in the latter this takes place with singular 

 slowness. Nevertheless we can as yet only say further that, in 

 the cases discussed, fully twice the absolute temperature of the 

 vapour is necessary. Looking at the variations occurring when 

 the first way is taken, my earlier experiments show that in indi- 

 vidual cases an increase of the volume to four or five times may 

 be required in order to attain the gaseous state. 



Accordingly, if in 



pv=cj>{27S + t) 

 we regard <£ as a function of v and t, we have the partial differ- 

 ential quotients l-j-j for constant temperature and (-tH for 

 constant volume to be equally taken account of, and must not 

 neglect the latter on account of the small values of ■—■ which 



have been obtained. 



Lastly, the numerical value of the coefficient of pressure-ex- 

 pansion of vapours, w 7 hich is not so directly to be learned from 

 the variations of <p, may be fixed, and compared with the num- 

 bers given by Regnault for gases, in order to obtain points of 

 support on this side also. For the coefficient of pressure-cxpan- 



