The only other thermometer we shall notice, is One proposed by M. Aebard of Berlin for measur ing high temperatures. The substance employed was the well known fusible metal composed of bis muth, lead, and tin, which liquefies below the tem perature of boiling water; the bulb was proposed to be of porcelain. This idea is a very ingenious one, but from practical difficulties, never has, as far as we know, been brought into use, and we suspect it never will. The only instrument of the kind we have seen, failed, from the sudden expansion of the metal in the act of consolidation, which burst the bulb.
Having finished our account of the simple ther mometer, let us pause a moment and apply this in slantia crucis to the whole subject. How arc we sure that any fluid corresponds by its expansions to equal increments of heat? The question admits of no mathematically demonstrable answer, for every attempt to measure heat, (a principle, as we have observed, admitting of no independent or ab solutely comparable measure,) involves a certain degree of hypothesis. By far the simplest and most convincing plan which has been proposed, is the mixture of definite volumes of water at different temperatures, attempted first by Renaldini of Pa dua, but not accurately performed till undertaken by Dr. Brooke Taylor, who made his experiments in 1723 with the oil thermometer,* yet Deluc attri butes the first adoption of the plan to Le Sage, who published an account of it in 17764 Deluc him self is the first who has made these delicate re searches with sufficient nicety, and has found that even mercury, which we have already stated to be the most accurate thermometric fluid, is liable to small deviations from the true scale of heat discov ered by the method of mixtures just noticed; the accuracy of the principle depends on the assump tion that the specific caloric of hot and cold water is the same, for if not, equal weights of both would not have a temperature exactly at the mean of the two, but somewhat different, as explained in the case of the mixture of mercury and water. Our limits necessarily confine us to a very brief sketch of this refined part of the subject.
The following results by Deluc of the absolute quantities of heat in every 5° of his thermometer may be taken as very correct, since one accurate observer has considered the deviation to be some what too small, and another§ too large.
We have added the second differences, which show a considerable irregularity attributable to er rors of experiment. We may add, that the cause of the near coincidence of mercury with the stages of absolute heat appears to be owing to the dis tance of the range of temperature above given, from the boiling point of the fluid, for near that point, all substances show great irregularities; this ap pears from the following table by Petit and Du long, in which the temperatures are centigrade.
Mr. Dalton, with that fondness for general and speculative conclusions which that distinguished chemist has too often given way to, has suggested that mercury and all other fluids expand in a ratio proportional to the squares of the temperature above their respective freezing points, but this opinion is by the best observers considered desti tute of foundation. M. Biotll has probably simpli fied the matter as far as is practicable, by a refer ence to the expansibility of a variety of substances to that of mercury by the following formula; where is the true dilatation in parts of unity of volume at temperature of melting ice, t being the temperature on the mercurial thermometer, and a b c coefficients depending upon the nature of the fluid. By this formula he has even satisfied the conditions of the singular phenomena of water, the only known fluid which does not in all parts of the scale expand with heat, its point of maximum den sity and minimum volume being between 39° and 40°,11 below which it expands until congelation.
The deviations of the mercurial thermometer from the truth we have seen to be small. But a far more practically important inquiry of the same na ture regards the spirit thermometer, which, as it is necessarily employed for several purposes, it be comes desirable to ascertain whether these irregu larities are so very great as has been stated. We confess that it is with diffidence that we object to the conclusions which Deluc, and all who have suc ceeded him in the same investigation, have drawn as to the indications of the spirit thermometer; yet we think we can produce unanswerable arguments to show that they have done great injustice to the instrument, by subjecting it to trials for which it was never intended.