4oG Trof. Potter on the Definition of the Temperature of Bodies, 



thermometer, because the differences between an arithmetic and 

 geometric series having the first and last terms equal become less 

 as the common ratio of the latter is nearer to unity. 



To compare the two scales for the mercurial thermometer at 

 the temperature halfway between the freezing- and boiling-points, 

 where the difference is the greatest for that range, we have, from 

 equal increments and tf° = 90°, 



v-v a+rf)-Y.(i + . n »_) 

 ■*® 



— \ . e 



whence 



v-r-**Gn) 



;o _ -0089687 

 ' - -00009921 ~ yU 4U 



and the difference from 90° is 0°*40, or less than ^ degree. 

 M. Regnault concluded from his experiments* that the ordinary 

 mercurial thermometer had an error of o, 2 Centigrade, or o, 36 

 Fahrenheit, by comparison with the air thermometer graduated 

 for equal increments at this temperature. 



Since mercury is admitted not to expand according to the law 

 of equal increments, we are not entitled to compare the higher 

 temperatures on the two scales ; but the differences are found to 

 be small, and we may conclude that the mercurial thermometer, 

 graduated according to the law of uniform expansion, is very 

 nearly, if not accurately, a normal thermometer. 



Hence in future the expansion of the gases must be tested by 

 the mercurial thermometer correctly graduated for uniform ex- 

 pansion, and not the converse, as has hitherto been done ; and 

 Gay-Lussac's law must take its real place as an approximate 

 empirical law only. 



The general formula which must replace that of Amontons, 

 when we adopt the principle of uniform expansion in gases, is 



p = /c . p . 6 af ° 



where tc Q = — , when f=0 at the commencement of thethermo- 



Po 



metric scale; and the calculations are very easy and concise 



when we have a table of hyperbolic logarithms. 



* Annates de Chimie et de Physique for 1842, p. 98. 



