272 Prof. Potter on the Law of the Expansion 



standard to which the liquid and solid thermometers were com- 

 pared, but also with respect to the chemical hypothesis of equi- 

 valent combining-volumes of gases. 



The laws of the expansion of the gases by equal increments, 

 proposed by Gay-Lussac, and of uniform expansion, proposed by 

 Dalton, give results which differ very little between the points of 

 the freezing and boiling of water, but they diverge greatly at 

 higher temperatures. Dalton's law, expressed in the formula 



V = V .e a '°, where V is the volume of a gas at /° above the 

 zero-point of the thermometric scale, and V the volume at the 

 zero of the scale, had a greater prima facie claim to be considered 

 a physical law than that of Gay-Lussac, of which the formula is 



Y = Y (l-\-at°), because, the expansion for one degree in the 



V —V 



latter being — *= — -=«, obtained by putting £°=1°, we do not 



v o 

 see why any temperature for a gas may not be taken as reason- 

 SV 

 ably as the freezing-point of water, and that generally -^- =« = 



constant: then integrating we obtain for Dakon's law V= V .e a '° ; 

 and expanding we have 



/ « 2 /° 2 a s t° s \ 



V = V e- = V (l + ^ + ^ + I ^ r8+& c). 



By stopping at the term with the first power of u=^q on 

 Fahrenheit's scale nearly, we have Gay-Lussac's law. Never- 

 theless I now think that Gay-Lussac* s law is a nearer approxi- 

 mation than Dalton' s in ordinary temperatures, and a very much 

 nearer one for high temperatures. 



The important experiments of M. Regnault show that the 

 coefficient of expansion for air increases with the density, or as 

 the molecules are nearer together*. Carbonic acid gas exhibits the 

 same property still more strongly, and sulphurous acid gas shows 

 it in a still higher degree. The expansion or value of a for the 

 interval between the freezing- and boiling-points of water at 

 ordinary atmospheric pressure for carbonic acid gas being "37099, 

 it becomes '38455 at a pressure of rather more than three atmo- 

 spheres j whilst hydrogen gas shows no reliable variation. 



Now as the atoms of a gas approach each other when the 

 temperature is diminished, we have a right to expect the same 

 result at lower temperatures at the same pressure : and Gay- 

 Lussac* s law gives such a result ; for the constant increment 



V —V 



«=— ■— — -bears asmallerratiototheactualvolumeV=V (l +uf) 





 as the degrees t° are increased, and a greater ratio as the degrees 



— 1° are more below the freezing-point of water. 



* Relation des Experiences, &c, vol. i. p. 110. 



