and on its Measurement by Thermometers. 451 



velocity of cooling, equals the number of degrees lost in a unit 

 of time, considered constant through that time. 



By equating the value of t l ° to the value of t° before found, we 

 have 



F . 



me 



J =e 



for any interval through which c might be taken constant. 



Though these expressions do not immediately guide us in our 

 search for a normal thermometer, yet they are of the greatest 

 use in pointing out the errors we have to avoid when empirical 

 results and approximate laws are discussed. 



In the first instance, the scales of degrees of both the air and 

 liquid thermometers would naturally be formed in series at equal 

 intervals, and the theory of a correct scale would only come under 

 discussion when discrepancies between the different instruments 

 became evident. De Luc found a discrepancy in the scales of 

 the air and mercurial thermometers*, and concluded that, if a 

 mass of mercury expanded 29 parts between the freezing- and 

 boiling-points of water, then the expansion was 14 parts in the 

 first half of the scale, and 15 parts in the last half. Dalton 

 thought the irregularity in the expansion of mercury consider- 

 ably greater than as stated by De Luc, and proposed a new 

 scale for the mercurial thermometer, for which a Table is given 

 in Henry's ( Chemistry/ In the Appendix, however, to part 1 

 of vol. ii. of his ' New System of Chemical Philosophy/ published 

 in 1827, he says he then thought the differences between the 

 air and mercurial thermometers to be less than he formerly con- 

 cluded them to be. 



From Gay-Lussac's empirical law for the expansion of the 

 gases, the air thermometer has been considered the normal 

 thermometer; and Dulong and Petit accept this, although it 

 leads to consequences at variance with their experiments on the 

 cooling of bodies. 



M. Regnault, from more recent researches, concludes that the 

 air thermometer must lose its position'of a normal thermometer 

 and take its place with the others as an abnormal one. 



When we come to review the whole subject as discussed by 

 the many eminent men who have written upon heat, we find 

 continual use of the expression the uniform expansion of some 

 body which might be employed to form a normal thermometer. 

 Now it appears that we must find out, in the first place, what is 

 the true mathematical expression for uniform expansion, before we 

 can be expected to arrive at a true thermometric scale of degrees. 



* Henry's ' Chemistry/ vol. i. p. 81. • * 



