of Air- and Mercury-Thermorneto's. 221 



changed to CDj. The absolute amount of the deviation is ^ x g^, 

 that is, CDi exceeds twice CD by ^ x CD,, or ^ x CD. In 



the same way CD2 exceeds twice CD, by ^ 272 " ^ ^^-' "'" 

 ^ X CD; and CD„ exceeds twice CD„_, by g„ ^ ^^^ x CD„, 



orixCD. Put/3 = ^andCD = l, wehave 



CD, = 3+p, 



CD2=2CDi + p = 4 + 3p, 



CD3=8 + 7p, 



CD„=2" + p(2''-l) = (l+p)2", 

 when n is indefinitely great. If we now return from CD„ with 

 a gas that strictly conforms to the law of Mariotte, and suppose 

 the volume to be diminished until the tension of one atmosphere 

 is regained, it is evident that at this point the volume, instead of 



being CD = 1, is CS = (l+p) = l+ 3j^; and generally for any 

 pressure m atmospheres at this temperature, the ratio of non- 

 deviation to deviation volumes is — =^, and the absolute value 

 of the difference of these volumes in terms of volume unity at 

 one atmosphere is ,r^, a constant absolute magnitude*. 



§ 15. Thus far, while confining our view to one temperature, 

 we require to make no assumption in advance of the results 

 strictly derived from Messrs. Thomson and Joule's experiments, 

 but the influence of a change of temperature has not as yet been 

 distinctly made out. 



In passing carbonic acid through plugs at temperatures up to 

 nearly 100°, the thermal effect seemed to vary in the inverse 

 ratio of the square of (AQ) the G temperature. (Phil. Trans. 

 1854, p. 336.) t 



If this is the case with one gas, it is probably a general law 

 applicable at least approximately to all. Assuming it to apply 



* This result is dependent on the assumption that the thermal effect is, 

 at constant temperature, proportional to the difference of pressures. 



t This law is indicated hy Prof. Thomson's equation at p. 337, Thil. 

 Trans. 1864, which is constructed on a formula of Mr. Rankme. This 

 formula is palpably erroneous, nevertheless Prof. Thomson's computed 

 results agree exactly with, experiment ! See paper ou Deviation referred to 

 iD§ 11. 



