Gaseous t Liquid, and Solid States of Water, 453 



or whether we may suppose that possibly there may have been 

 some experimental observations which attracted the curve down- 

 wards, but were afterwards rejected on a supposition of their being 

 untrustworthy, it appears that such a bend is a feature which 

 the curve really ought to possess, and is one which even after 

 being partially smoothed off by way of correction is not obliterated, 

 but still remains clearly discoverable in the final numerical tables of 

 results. 



This is best brought to light by means of the empirical for- 

 mulae devised and employed by Eegnault for the collating of 

 his results. He proceeded evidently under the idea of the curve 

 being continuous in its nature, so that a single formula might 

 represent the pressures of aqueous vapour throughout the whole 

 of his experiments ; but before seeking for such a formula he pro- 

 ceeded to calculate several local formulae of which each should 

 represent very exactly his experiments between limits of tempe- 

 rature not wide apart; and afterwards he worked out several general 

 formulae, each adapted singly for the whole range of his experi- 

 ments. 



In regard to the one of these general formulae which he desig- 

 nates as formula (H) *, he says that it represents the aggregate of 

 his determinations of the pressures of the vapour of water, referred 

 to the air-thermometer, and extending between the extreme tem- 

 peratures of —33° and +232° with such precision that there could 

 not be any hope of attaining to representing them better by any 

 other mode of interpolation, because the differences, he says, be- 

 tween the calculated numbers and the numbers deduced from his 

 graphic constructions are always smaller than the probable errors 

 of observation. Still, for making out his final general Table of 

 pressures of steam for every degree of the air-thermometer from 

 —30° to -J- 230°, he used three local formulae, finding that by them 

 he could get slightly closer agreements with his experimental deter- 

 minations than by using the single formula (H) for the whole 

 range. Thus between — 32° and 0° he used his formula designated 

 as (E) ; from 0° to 100° he used his formula (D) ; and between 

 100° and 230° he used his formula (H). He points out (page 623) 

 that he might have calculated this Table throughout its entire ex- 

 tent by the single formula (H), and that he would thus have got 

 almost identically the same values by it from 100° down to 40° as 

 those he calculated by the formula (D), but that between + 40° and 

 —20° the pressures given by the formula (H) would be slightly too 

 small. This gives indication of the existence of the feature which 

 it is my object at present to bring into view ; and an examina- 

 tion of the column of Differences in Eegnault's Table on his page 

 608, adapted for comparing the pressures got from experiments as 



* This and other formulas in M. Regnault's memoir are here referred to only 

 by their letters of reference, because to cite the formulas themselves with their 

 necessary accompanying explanations, would extend the present paper to too 

 great a length ; and any person wishing to scrutinize the formulas would na- 

 turally prefer to have recourse to the original memoir. 



