226 



Communicated by Colonel Sabine, R.A., Treas. V.P.R.S. &c. 

 Received June 17, 1852. 



This paper has reference to a former communication On a Ge- 

 neral Law of Density in Saturated Vapours." In the present paper 

 the author states that the formulae that embrace MM. Dulong and 

 Petit's four standard mean values of the relative expansion of air, 

 mercury and glass, exhibit the temperature by the air- thermometer in 

 advance of the mercurial thermometer, between 0° and 100° C. The 

 amount of difference increases from 0° to 48°, and then diminishes 

 to 100°; the maximum value being 0°*5i3. The most eminent 

 modern authorities deny the existence of any such difference, or 

 appear tacitly to admit that it is too small to be observed. For 

 this reason no correction was made on temperatures below 100° in 

 Chart No. 2, where indeed it could hardly be perceptible. Al- 

 though of little practical importance, this difference, if it exists, 

 cannot safely be neglected in theoretical researches, inasmuch as 

 the value of a degree of the mercurial thermometer must in such 

 case be a variable quantity, differing in the ratio of 23 to 24 from 

 100° C. to 0°. 



Having at last obtained satisfactory proof of the existence and 

 amount of the correction between 0° and 100°, he has thought it of 

 sufficient importance to give a detailed account of the method em- 

 ployed to extract the required evidence from M. Regnault's obser- 

 vations on the tension of low pressure steam. 



As the law of density, illustrated in Chart No. 2, has clearly refer- 

 ence to the air- thermometer, if a series of observations were perfectly 

 correct, they must perfectly exhibit this difference — if it really exists 

 — when projected on the chart ; because the divergence from the 

 line that joins the points at 0° and 100° must exactly correspond 

 with the correction required at the intermediate temperatures. In 

 short, the line of density would appear as a curve slightly concave 

 towards the axis, and if the proper correction were made on the 

 temperatures, that curve would be converted into a straight line. 

 This view is illustrated by a sketch, in which the curvature is pur- 

 posely much exaggerated. In this a straight line is drawn, as the 

 gradient of density, and in which the points range if the tempe- 

 ratures are by the air-thermometer. This line is inclined to the 

 axis X of temperature, at an angle of which h is the cotangent (see 

 ' Proceedings,' vol. vi. p. 98). At points in it corresponding to 

 temperatures 50°, 60°, 70°, &c., straight lines are drawn parallel to 

 the axis x ; and at distances in these equal to the respective com- 

 puted differences, straight lines are drawn at right angles to the 

 axis X, and meeting the lines of constant pressure drawn through 

 the corresponding points of the straight line which represents the 

 gradient of density. The curved line passing through the points of 

 intersection, is that in which the points of density range if laid off 

 to the temperatures by the mercurial thermometer. 



The author then states that the first attempt was made by ob- 

 taining the value of the constants g and h (' Proceedings,' vol. vi. 

 p. 98) from the observation at 50° and 100°; then computing the 



