32 Prof. J. Thomson on the [Dec. 11, 



Tables of results at the close of his memoir; and by every mode of 

 scrutiny which I have brought to 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 some of them I have 

 found that it can readily be brought prominently into notice. The 

 engraved curve drawn on the copper plate by Eegnault himself is offered 

 by him as the definitive expression of his experiments, as being an expres- 

 sion 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 

 freezing-point, a part with which the investigations in the present paper 

 are specially concerned. 



After telling (page 581) of the great care with which he had marked 

 the curve on the copper plate and got it engraved, he says : " Je n'ai 

 pas pu eviter cependant quelques petites irregularites dans les courbes ; 

 mais une seule de ces irregularites me parait assez importante pour 

 devoir etre signalee. Elle se presente pour les basses temperatures com- 

 prises entre 0et 16; la courbe creuse trop vers 1'axe des temperatures, 

 elle laisse, notablement au-dessus d'elle, toutes les determinations experi- 

 mentales qui ont ete faites entre et 10. Ainsi les valeurs, que cette 

 petite portion de la courbe donne pour les forces elastiques, sont un peu 

 trop faibles, et j'ai eu soin de les augmenter, de la quantite convenable, 

 dans les nombres que je donnerai plus loin." Whether we are now to 

 think that this bend downwards* of the curve towards the axis of tem- 

 peratures, involving what Eegnault regarded as a small faulty departure 

 of 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 experimental observations which 

 attracted the curve downwards, but were afterwards rejected on a suppo- 

 sition 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 formulae 

 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 proceeded to calculate several local for- 

 mulae of which each should represent very exactly his experiments 

 between, limits of temperature not wide apart ; and afterwards he worked 

 out several general formulae, each adapted singly for the whole range of 

 his experiments. 



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

 sheet, and pressures are measured upwards. 



