Dr. Mills's Researches on Thermometry, 9 



rect, is legitimate. An}- one who has experience in the mathe- 

 matical expression of the results of experiment must soon be 

 strongly impressed with the untrustworthiness of empirical 

 formulae when their application is extended beyond the range 

 of the observations themselves. The same series of figures 

 can often be represented with almost equal exactness by 

 very different mathematical expressions ; and the curves to 

 which these are the equations, though closely concordant 

 for the range of the experiments, may have outside that range 

 very different geometrical properties. We may indeed, in 

 some cases, determine the constants in a formula which rests 

 upon a theoretical basis from a limited series of experiments, 

 and then extend its application ; but it is very dangerous to 

 argue from the form of a purely empirical equation. Instances 

 may be quoted where such a formula has a posteriori been 

 proved to hold for a much greater range than could have been 

 anticipated ; but it must be admitted that a determination of 

 the position of a maximum or minimum from an empirical 

 equation is worth very little, even when it lies within limits 

 of the experiments, unless special precautions are taken, and 

 that deductions as to the position, or even as to the existence, 

 of such points when lying far outside those limits are abso- 

 lutely untrustworthy. No one, for example, believes that the 

 point of maximum density of ethyl alcohol is either at — 56°*6 

 or at — 89°*5, as deduced by Muncke from two separate and 

 fairly concordant expressions for its expansion between 0° and 

 its boiling-point. Dr. Mills, however, seems to trust his 

 formulas implicitly. Henrici observed a thermometer between 

 50° and 100°; and Dr. Mills infers a point of maximum descent 

 at 143 0, 5. Thermometers 3 and c were observed for ranges 

 of 80° and 190° respectively; and in each case conclusions are 

 drawn respecting points about 140° above the highest tem- 

 peratures observed. We venture to think, not that there is 

 grave doubt as to the exact positions of the alleged maxima 

 and minima (that, of course, would be granted), but that the 

 formulae afford no evidence of their existence. Even in the 

 case of thermometer 455 it is an open question whether a point 

 of maximum ascent or a point of final repose was being 

 approached. 



We turn next to the explanation given of the motions of the 

 zero-point. " The first effect of heat on the bulb is ordinary 

 expansion attended with a ' set.' The second or further effect 

 is to cause the thin part of the glass to become sufficiently 

 plastic to yield to the influence of barometric pressure, which 

 causes a gradual collapse. In the third, or final, stage, at 

 which the vapour of mercury has a sensible tension, the bulb 



