96 Mr. J. J. Waterston on certain Thermomolecular 



i. e. the temperatures reckoned from —274°, the zero of gaseous 

 tension, are taken in the same ratio as the respective values of h, 

 the tangents or exponents of the thermomolecular lines. 



§ 42. The next point to consider is, that if the above ratio of 

 molecular volume holds good throughout the whole range of ex- 

 pansion, the proportionate dilatation at the r temperatures ought 

 to follow the same ratio of h inversely, or, expressed by symbols, 



-j—cth (in which^=l ), because, if we imagine the t line to 



move upwards parallel to itself through a small increment of its 

 distance from the axis of temperature, it cuts off at each intersec- 

 tion with a vapour-line an increment of temperature proportional 

 to h, and, to maintain the same ratio in the molecular volumes 

 at the end as at the beginning of these increments, the proportionate 

 dilatations should be all equal to each other — which can only 

 take place if the proportionate increment corresponding to a 

 constant value of dt or 1° is inversely as h. This increment, 

 therefore, multiplied by h, should be a constant quantity in all 

 these four liquids. This product being a fractional quantity, we 



compute its reciprocal -r- • j from the constants of the three 



ethers found in § 32. 

 Muriatic Ether. — The t temperature is 0°, at which v= 1, hence 

 vdt, = dt , =p 3 . 48 x 186 . 4 = 64 9 



dv dv w 

 and h being 144, we have yff =4*50. 



Hydrobromic Ether. — Ther temperature is 27°, at which v = 



1-0385*, P=2-97, 7=253, and P 7 ^7 = j = 671, which, 



x by v and -4- by ^ = 158'6, gives 4*39. 



Hydriodic Ether. — The t temperature is 62°'4, at which v = 

 1-0782, P = 2-75, 7 = 312°, P(f^7)?; = 742, which, divided by 

 h = 176'9, gives 4*19. A previous result by another computation 

 is 4-32. 



Chloroform. — The r temperature is 51°'4, at which v = l'0660f, 

 P = 2-52, 7 = 334, A = 171. These give the quotient 4-48. The 



mean of the four is 4*38= -=- • -=■ for these four liquids. 



§ 43. The product of this by the previous constant - gives 



vdt 1 . P 



-j- • - =18*00, which is also a constant at the respective t tem- 



av n 



peratures of these four liquids. This third constant is indepen- 



* Ann. de Chim. et de Phys. vol. xv. p. 369. 

 t Ibid. vol. xxxiii. p. 208. 



