for the elastic force of Steam. 99 



&c. upon dense matter, the law of the elastic force of vapours in 

 contact with the liquids from which they arise, at different tent- 

 peratures, is a subject of great importance. 



Many formulae have been proposed for the elastic force of 

 steam, which corresponded sufficiently nearly with the observed 

 results through moderate ranges of temperature, but failed com- 

 pletely for great ranges. It is not intended in the present paper 

 to recapitulate these attempts. 



M. Regnault has given formulas for interpolation which en- 

 abled him, from his observation through many series of experi- 

 ments, to construct most valuable tables of the elastic force of 

 the vapours of the liquids in regularly ascending temperatures. 

 These are found in his treatise " Relation des experiences .... 

 pour determiner les principales lois et les donnees numeriques 

 qui entrent dans le calcul des machines a vapeur. Par M. V. 

 Regnault," in two volumes, of which vol. i. is tome xxi., and vol. 

 ii. is tome xxvi. of the Memoirs of the Institute, but the two 

 volumes can be procured as a separate treatise; and from a 

 recent paper in this Magazine they appear not yet to be much 

 studied in this country. 



However valuable interpolation formulas may be for the pur- 

 poses to which they are applied, yet in physical inquiries we 

 naturally seek for formulas which are likely to represent the 

 physical laws of the phenomena ; which will generally be simpler 

 than the expansions in series with coefficients to be determined 

 from the experiments, which is the constitution of the interpo- 

 lation formulas. 



In the Number of this Magazine for January 1849 there is an 

 important paper, reprinted from Silliman's American Journal of 

 Science for September 1848, and entitled " On a new Empirical 

 Formula for ascertaining the Tension of Vapour of Water at any 

 Temperature. By J. H. Alexander, Esq." In this paper is a 

 Table occupying four pages, in which the results of the formula 

 are compared with the observations of Regnault, 1844; the 

 Franklin Institute, 1836; the French Academicians, 1829; 

 Taylor, 1822; Arzberger, 1819; Ure, 1818; Dalton, 1801 

 and 1820-; Southern, 1797 and 1803 ; Betancourt, 1790; Robi- 

 son, 1778; and Watt, 1774. Though the formula shows consi- 

 derable differences from even the more recent experiments in 

 some cases, yet the differences are not more than are found 

 between the experimental results themselves of the different ob- 

 servers at nearly the same temperatures. As the range of tem- 

 perature is from — 27°'112 to 435°'227 Fahr., through which 

 the general accordance of the formula with the experiments 

 holds good, we must admit the argument of Mr. Alexander, 

 that his formula accords with the observations of the different 



H2 



