224 Mr. J. J. Waterston on a Difference in the march 



100°, which can only be accounted for by some fault in tlie observa- 

 tions. Take the tension at 111°"74, as given by M. Regnault, and 

 compute its projection on fig. 2. The cotangent is T 65406 (see 

 Table, ante), and the difference •OS'iSo. This gives Tas the position 

 of this point (fig. 2), and P Q R S T as the line of M. Rcgnault's ob- 

 servations. It will be remarked that the law of continuity is mani- 

 festly broken at S, the critical point at which the mode of observa- 

 tion underwent a change. Compare RST with QRS, or FSH 

 with E F S ; also the angle p R S with s S R. 



II. 



When the gradients radiate from the same point, it is evident that 



in the general equation e= < — > t, the value of g is the same 



for all. Hence comparing the densities of two vapours thus related, 

 it is obvious that at the same temperature they must vary inversely 

 as the sixth power of h : also the tensions must be in this proportion. 

 Thus between pure alcohol and aqueous vapour the ratio at the same 

 temperature will be found to be 2' 3 192. 



When two gradients are parallel, the value of g differs by a con- 

 stant amount, and h is the same for both ; hence on comparing the 

 densities of two vapours thus related, we find equal densities not at 

 the same temperatures, but at the same constant interval of tempe- 

 rature {g — g'). As an example, the vapour of sulphuric aether taken 

 at 69°-55 below the temperature at which the density of the vapour 

 of water may happen to have been observed, will be found at all 

 parts of the scale to have 4i times its specific gravity, being the rela- 

 tive proportion of their chemical equivalents. This applies to Dal- 

 ton's observations only. 



This formula is 



III. 



in which f^ jg temperature by air-thermometer, 



tm temperature by mercury-thermometer, 

 log 6=3-7145723 logD=0-7S587 

 logA=4539°-617 log 0^ = 6-43303. 

 The data upon which it is constructed are taken from the original 



memoir of MM. Dulong and Petit, " On the Expansion of Mercury 



and Standard of Temperature " {Ann. de Chim. vol. vii. 1817, p. 136). 



They are as follows : — 



Between 0° and 100° the rate of expansion of mercury is 

 Between 0° and 200° (by air-thermometer) the rate is . 

 Between 0° and 300° (by air-thermometer) the rate is 



