248 Mr, Meikle on the Expansion of Air. 



But since DHKF = AHIB, the area AHKC is cut in the 

 same ratio by BI as by,the curve DEF; that is, in the con- 

 stant ratio of m to n. Consequently, by the lemma, each of 

 these curves is a hyperbola, having G for its centre, and GH 

 for an asymptote. 



Since, in either curve, the variations of the area denote 

 variations in the quantity of heat, while the corresponding va- 

 riations of the abscissffi denote variations of temperature on 

 the common scale, it follows, from the known properly of the 

 hyperbola, that while the variations of the quantity ot heat in 

 air, under a constant pressure, are uniform, those on the 

 common scale of an air-thermometer form a geometrical pro- 

 gression. Or, more generally, when the variations in the 

 quantity of heat are uniform, those of the volume, imder a con- 

 stant pressure, form a geometrical progression ; as do likewise 

 the variations of pressure under a constant volume. 



Such is the necessary result of the very principles from 

 which MM. de Laplace and Poisson failed to deduce a cor- 

 responding scale of temperature. Had the defect of their 

 procedure been that, instead of fairly deducing, they had as- 

 sumed the proper result, such a shift would neither have been 

 half so blameable in itself, nor so injurious to science, as an 

 erroneous assumption must always be when sanctioned by high 

 authority. However, from their not only assuming a very 

 different result, but one which is very erroneous if their data 

 be true, it is evident that these philosophers had not had so 

 much as a conjecture of what the necessary result should be. 

 So nobody wonders when a research of this sort fails in the 

 hands of an inexperienced tyro; but if those who are de- 

 servedly regarded as at the head of their profession be liable 

 to deceive themselves in so remarkable a manner, how cau- 

 tious ought we to be in receiving even what emanates from 

 high authority, if supported by nothing deserving the name of 

 argument or intelligible evidence. 



Upwaixls of twenty years ago, that distinguished philoso- 

 pher Mr. Dalton proposed what he alleged to be the true scale 

 of the mercurial thermometer, founded on the supposition that 

 the expansions of mercury were as the squares of the true 

 temperatures reckoned from its freezing-point. "With this he 

 coupled another speculation : he supposed that relatively to 

 equal increments on his new scale, the expansions of air under 

 a constant pressure formed a geometrical progression. These 

 views, however, were soon found to be incompatible : but of 

 the two hypotheses, that regarding the expansion of mercury 

 being the greater favourite with Mr. Dalton, he rather chose 

 to retain it, and abandon the geometrical expansion of nir. 

 It was absolutely necessary that one of them should be relin- 

 quished ; 



