of Vapours to Mariotte and Gay-Lussac's Law. 307 



pressure of one atmosphere for several temperatures. Although, 

 for the right determination of the coefficient of dilatation under 



o 



a constant pressure acccording to the formula a= — — 



dv 



the correct knowledge of the relation existing between t and v 



is indispensable, we may yet calculate approximately, by help of 



the not very large differences of the volumes here treated of, the 



mean coefficient of dilatation between each pair of temperatures 



v —~ v 

 by means of the formula a= — ~- — -. Therebv we obtain from 



\ yt -v t 



Hirn's statements the following values : — 



Temperature, Mean coefficients of 



Celsius. dilatation. 



o 



■f^J" 0-004181 



Hr-[ 0-004212 



;;Ji \ 0-002902 



ooo \ 0003059 



oV«J 0-003838 



These numbers naturally give only a very rough picture of the 

 relations which hold; but perhaps their course is sufficiently de- 

 terminate to point to some such minimum of the coefficient of 

 dilatation as my ow T n observations have given for chloroform 

 and bisulphide of carbon, of course under a less pressure. 



§n. 



From the considerations set forth in the last paragraph, we 

 may see that such a form of the equation of condition as Zeuner 

 first gave, in the Zeitschrift des Vereins deutscher Ingenieure, 1867, 



k—\ 



p. 49, for superheated aqueous vapour, pv = B(a + t) — Cp * , 

 where B, C, and k are constant, cannot be employed with certainty 

 for the vapours of chloroform and of bisulphide of carbon consist- 

 ently with the observations here communicated, Indeed accord- 

 ing to this equation a course of the curve Y l similar to that de- 

 scribed would not be possible. Suppose in the equation the pres- 

 sure p constant, then it follows from B(« + —pv= const, that 

 pv will correspond more closely with R(a + t), i. e. will approach 

 more nearly to a gaseous condition, the larger that (a + t) is. 

 Therefore for a constant pressure with an increasing tempera- 

 ture the vapour must, in conformity with this equation, be con- 

 tinually approximating to it. 



Zeuner deduces the equation on the grounds of two assump- 

 tions : (1) that the specific heat of aqueous vapour is constant 



