of the Gases by increase of Temperature. 



273 



The air-thermometer being taken as the standard, we are not 

 able to employ it to show its own errors, but must have recourse 

 to the liquefiable gases, where the deviation from Gay-Lussac's 

 law becomes very great compared with that of air, and will con- 

 sequently be well ascertained by taking the air-thermometer as 

 exact in the first instance, and afterwards attributing to air the 

 same law, with different constants, as that found for the lique- 

 fiable gas. In this manner we shall find that the air-thermo- 

 meters must give place to a thermometer formed with hydrogen 

 gas, or the mercurial thermometer accurately graduated for the 

 law of uniform expansion, or otherwise for low temperatures the 

 spirit-thermometer accurately graduated according to the law of 

 the hyperbolic expansion of alcohol, when critically exact tempe- 

 ratures are required to be known. 



M. Regnault found* that a thermometer formed with sulphu- 

 rous acid gas, on being compared with an air-thermometer, gave 

 the following results for the mean value of a. for Centigrade 

 degrees : — 



From 6 Centigrade to 98-12 C. the mean value of a = -003825] 

 102-45 „ „ =-0038225 



185-42 

 257-17 

 299 90 

 31031 



= •0037999 

 = •0037923 

 = •0037913 

 = •0037893 



In seeking for the law 

 which, will include these 

 results, we shall find that 

 they conform to a hyper- 

 bolic law of expansion; 

 and Gay-Lussac's law arises 

 from taking at great dis- 

 tances from the centre 

 the asymptote of the hy- 

 perbola for the arc; and 

 thus Gay-Lussac's law be- 

 comes an exceedingly near 

 approximation for hydrogen gas, and a very near one for oxygen, 

 nitrogen, and atmospheric air. 



To apply the equation of the hyperbola to the results for sul- 

 phurous acid, in the figure let C x, Cy be the axes of coordi- 

 nates to the origin C as centre of the hyperbolic arc P A P ; ; let 

 C T, C T' be the asymptotes ; let O be any origin from which 

 the temperatures are represented along the axis of x, whilst the 



* Relation des Experiences, &c, vol. i. pp. 188, 189. 



