176 Mr. T. R. Edmonds on the Elastic Force of 



that M. Regnault' s adjusted Table is a composite Table consist- 

 ing of three separate series, each regulated by its specific con- 

 stants, whether three or five in number. When this mode of 

 construction is taken into account, it will not be expected that 

 such a Table will be in complete harmony with a theoretical 

 Table deduced from one uniform law throughout the whole 

 range of temperature observed. Disagreement between Tables 

 so differently constructed is most likely to occur at the tempera- 

 tures 0° and 100° C, the points at which the different series ot 

 Regnault are intended to join one another. 



At page 606, however, M. Regnault gives another formula 

 (H) according to Biot, with five special constants_, which formula 

 is intended to be applied generally to the whole range of tempe- 

 rature observed, and to prove to the reader that the single formula 

 (H), with its five special constants, will yield nearly the same 

 results as those contained in the principal or adjusted Table of 

 M. Regnault, and obtained by three sets of constants, amounting 

 to thirteen in number. The greatest proportional difference 

 between the elastic forces of steam, as given by Regnault' s ad- 

 justed Table and by my new theoretical Table, occurs at the 

 temperature 0° C, or at the temperature of melting ice. But 

 the elastic force at the same temperature given by the general 

 formula (H) already described, differs from the result of my 

 formula in an opposite direction. The elastic force at tempera- 

 ture 0° C. is, in millimetres, 4*60 according to Regnault's ad- 

 justed Table; m my theoretical Table it is 4*52 millims. ; whilst 

 by the general formula (H) it is 4*48 millims. This will be 

 seen on reference to Table II. hereunto annexed. In the same 

 Table II. is included a column (extracted from page 608) of 

 elastic forces, at intervals of 10° C, measured on a copper 

 engraving which contains a geometrical construction of the 

 results of M. Regnault' s observations, and which represents by 

 a continuous curve the elastic forces observed at every tempera- 

 ture, or which represents rather those observations which were 

 thought most worthy of being relied upon. The values exhi- 

 bited according to this " graphic curve " (as it is designated 

 by M. Regnault) are of doubtful authority in respect of the 

 small deviations at temperatures below 10° C. from the law 

 now offered as the true law ; for it is not improbable that M. 

 Regnault, biassed by his favourable opinion of the formula of 

 Roche, has selected for adoption those experiments which were 

 most in harmony with that erroneous formula. 



The general formula above given for the elastic force in terms 



of the temperature may, by expanding the exponential I 1 + - \ 

 by the binomial theorem, be expressed in the series following : 



