Mar. 19, 1874] 



NATURE 



393 



at the triple-point (0° C. nearly), and M to denote the rate of 

 absorption at which heat must be supplied to a body consisting 

 of steam and water at the triple point, per unit augmentation of 

 volume of that whole heterogeneous body, to let it expand with- 

 out varying in temperature, and using 'Jj- and M' to denote the 



corresponding rates for steam vpith ice at the triple point, we 

 have 'ip 



dt__ M_ 

 d£ ~ M' 

 dt 

 The latent heat of evaporation of one pound of water at the 

 freezing-point (or at the triple point) into steam at the same 

 temperature, as determined by Kegnault, is 6o6'5 thermic units, 

 the thermic unit being here taken as the heat which would raise 

 the temperature of I lb. of water i" C, and the latent heat of 

 fusion of ice is about 7S or 79 of the same thermic units. 

 Hence, though M and M' belonsj each to a cubic foot of steam at 



. M . 

 the triple point, not to a pound mass of it, still the ratio ^, is = 



606 



This shows that for any small descent in temperature from 

 the triple point (where the pressure of steam with ice is the 

 same as that of steam with water), the pressure of steam with 

 ice falls off 1-13 times as much as does the pressure of steam 

 with water. 



In submitting the quantitative calculation now given, I have 

 preferred to adopt the method proposed and developed by my 

 brother rather than that which I had myself previously devised, 

 because his method is simpler, and brings out the results more 

 briefly by established principles from existing experimental data. 

 I may say, however, that the method devised by myself was also 

 a true method, and that I have since worked it out to its nume- 

 rical results, and have found that these are quite in accordance 

 with those brought out by my brother. The two indeed may be 

 regarded as being essentially of the same nature ; and I think it 

 unnecessary to occupy space by giving any details of the method 

 I planned and have carried out. Its general character may be 

 sufficiently gathered from the concluding passages of the British 

 Association' 1872 paper, as printed in the Transactions of the 

 Sections, Brighton Meeting. 



In order to discover whether the feature now developed by 

 theoretical considerations is to be found showing itself in any 

 degree in the experimental results of Regnault on the pressures 

 of steam at different temperatures *, I have made careful exami- 

 nations of his engraved curve (Plate viii. of his Memoir), 

 and of his empirical formula adapted to fit very closely 

 to the results exhibited in that curve, and of his final tables 

 of results at the close of his Memoir ; and by every mode 

 of scrutiny which I have brought t.i bear on the subject— in fact 

 by each of some seven or eight varied modes— I have met with 

 clear indication of the existence of the expected feature ; and by 

 someof them Ihavefound that itcan readily bebroughtpromniently 

 into notice. The engraved curve drawn on the copperplate by 

 Regnault himself is offered by him as the definitive expression of 

 his°experiments, as being an expression which satisfies as well as 

 possible the aggregate of his observations ; subject, however, to 

 a very slight alteration, which he has pointed out as a requisite 

 amendment in the part of the curve immediately below the freez- 

 ing-point, a part with which the investigations in the present 

 paper are specially concerned. 



Aftertelling (p. 581 of his Memoir) of the great care with which 

 he had marked the curve on the copperplate and got it engraved, 



he says: "Je n'ai pas pu eviter cependant quelques petites 



irregularitcsdanslescourbes; mais une seule deces irregularites me 

 parait assez importante pour devoir itre signalee. Elle se presente 

 pour les basses temperatures comprises entre 0° et- 16°, la courbe 

 creuse trop vers I'axe des temperatures, elle laisse, notablement 

 au-dessus d'elle, toutes les determinations experimentales qui 

 ont ete faites entre o" et-lo°. Ainsi les valeurs, que cette 



• Regnault. " Des forces elastiqvie>; de la v.ipeur d'eau aux differentes 

 temperatures" Memoires de I'Academie des Sciences, 1847. 



petite portion de la courbe donne pour les forces elastiques, 

 sont un pen trop faibles, et j'ai eu soin de les augmenter, 

 de la quantite convenable, dans les nombres que je don- 

 nerai plus loin." Whether we are now to think that this 

 bend downwards* of the curve towards the axis of temperatures 

 involving what Regnault regarded as a small faulty departure ot 

 his drawn curve from his actual experiments, was introduced 

 merely by a casual want of accuracy in drawing, or whether we 

 may suppose that possibly there may have been some experi- 

 mental observations which attracted the curve downwards, but 

 were afterwards rejected on a supposition of their being untrust- 

 worthy, it appears that such a bend is a feature which the curve 

 really ought to possess, and is one which, even after being par- 

 tially 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- 

 mula devised and employed by Regnault 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 re- 

 present the pressures of aqueous vapour throughout the whole 

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

 proceeded to calculate several l6cal formula; of which each 

 should represent very exactly his experiments between limits of 

 temperature not wide apart ; and afterwards he worked out 

 several general formula;, each adapted singly for the whole 

 range of his experiments. 



I^owinthe paper communicated to the Royal Society, and 

 printed in the Proceedings for December 11, 1S73, from which 

 the present paper is an abridgment, the details of a scrutiny of 

 the chief of these formula; are given (the formulx, especially, 

 which were adopted by Regnault for deducing his final general 

 table extending from — 32° C. to 4- 230° C), from which it ap- 

 pears that they present clear indications that at and veiy close to 

 the freezing-point (or rather the triple-point) the rate of ir crease 

 of pressure lor increase of temperature is decidedly less in the 

 case of steam with water than in that of steam with ice ; or, in 

 other words, that at and very close to the triple-point the steep- 

 ness of the curve for steam with water is decidedly less than that 

 of the curve for steam with ice ; or, to state the same a little 

 more fully, that while the steepness is increasing as we ascend 

 from temperatures below the triple-point up to the triple-point, 

 with ice in contact with steam, there is a sudden abatement of the 

 steepness in passing the triple-point, where the change occurs 

 from steam with ice to steam with water, after which, with con- 

 tinued rise of temperature, the steepness goes on again increasing. 

 In fact the result comes out that these formula;, expressing an 

 aggregate of experimental results of Regnault, would indicate 

 dp 



for — at the freezing-point, or the triple-point, not the value i 

 (// 



It 

 (as would be the case if a curve continuous past the triple-point 

 would express the pressure of steam or aqueous vapour, for dif- 

 ferent temperatures, in contact with ice below the triple-point 

 and with water above it), but fog or I'iO, which makes a near 

 approach to the residt I 'IS found by my brother's quantitative 

 calculation already here cited. The decimal fractions in excess 

 of unity, here represent the quantitative relation between the 

 greatness of the feature under consideration as brought out by 

 the theoretical investigation on the one hand, and as deduced 

 from Regnault's results on the other hand : and ihus we may say 

 that this feature can be brought to view as existing in Regnault's 

 principal results in a degree about i\ or \° of that in which the 

 theoretical investigation shows that it must really exist, and 

 ought to be found expeiimentally, if the experiments had a suf- 

 ficiently minute exactitude to detect it and to measure it. 



Regnault also gives, in the same Memoir, another statement of 

 results deduced from his experiments, and put in the form of a 

 table intended chiefly for meteorological purposes ; which table 

 shows the pressures of aqueous vapour for temperatures ranging 

 below and above the freezing-point at very small intervals of 

 temperature, Tirth of a degree centigrade each. In this table, 

 the numbers inserted as representing the pressures below the 

 freezing-point are slightly diiferent from the corresponding ones 

 in his general table, which, with the formula: used in making it, 

 has just now been referred to ; and he mentions that this slight 



* In M. Regnault's curve the temperatures are measured horizontally 

 across the sheet and pressures are measured upwards. 



