1873.] Gaseous, Liquid, and Solid States of Water. 33 



In regard to the one of these general formulae which he designates as 

 formula (H) *, he says that it represents the aggregate of his determina- 

 tions of the pressures of the vapour of water, referred to the air-ther- 

 mometer, and extending between the extreme temperatures 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, between the calculated numbers and the numbers 

 deduced from his graphic constructions are always smaller than the pro- 

 bable errors of observation. Still, for malting out his final general Table 

 of pressures of steam for every degree of the air-thermometer from 30 

 to +230, he used three local formulae, finding that by them he could, 

 get slightly closer agreements with his experimental determinations than 

 by using the single formula (H) for the whole range. Thus between 

 32 and he used his formula designated as (E) ; from 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 extent 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 examination of the 

 column of Differences in Eegnault's Table on his page 608, adapted for 

 comparing the pressures got from experiments as expressed by his graphic 

 curve with those got from the formula (H), shows distinctly a re-entrant 

 angle, or at least a flattened place, in the curve at or about 0. Several 

 other like comparisons, by means of his other formulae, give like indica- 

 tions ; but most of these may for brevity be passed over without further 

 mention here. The most decisive indication comes out in the following 

 way. We may observe that for temperatures adjacent to the freezing- 

 point and extending both ways from it, Eegnault finally adopted as fitting 

 best to his experiments the formula (E) for temperatures descending 

 from 0, and the formula (D) for temperatures ascending from 0. He 

 tried (at pages 598, 599 of his memoir) the continuing of the application 

 of his formula (D) beyond the inferior of the two limits and 100, for 

 which he had specially aimed at adapting it to his experimental deter- 

 minations ; and he found that in calculating by it the pressures which it 

 would give for temperatures below 0, these pressures come out always 

 slightly in excess of those which were given by his experiments. I have 

 developed this mode of comparison in a more complete manner, and have 

 arrived at remarkable results. The formula (D) may be regarded as the 



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

 letters of reference, because to cite the formulae themselves with their necessary accom- 

 panying explanations, would extend the present paper to too great a length ; and any 

 person wishing to scrutinize the formula? would naturally prefer to have recourse to 

 the original memoir. 



YOL. XXII. D 



