214 Mr. J. J. Waterstou on a Difference in the march 



§ 3. The chart above referred to as being in the archives of 

 the Royal Societ^y, contains observations on the density of the 

 vapour of alcohol, sulphuric aether, and sulphuret of carbon, 

 carried up to about 200°. They were made in sealed graduated 

 tubes, so that the results should be uninfluenced by a deviation 

 from Mariotte's law, which must in some degree affect all den- 

 sities derived from measurements of tension. In projecting 

 these, the temperatures were reduced to the standard of the air- 

 thermometer by a formula derived from MM. Dulong and Petit^s 

 observations on the expansion of mercury and glass from 0° to 

 300°. [See Appendix, III.] These represent mercury in glass to 

 be 3° in advance of the air-thermometer at 200°, and I felt cer- 

 tain that with such corrections the points conformed more nearly 

 to a straight line than if they were uncorrected. M. Regnault 

 does not admit of any correction being required up to 200°, and 

 further, that at about 50° the air- thermometer is behind the 

 mercury. 



If the expansibility of mercury increases with the temperature, 

 it is plain that it must be behind the air-thermometer at tempe- 

 ratures between 100° and 0°, unless there is compensation from 

 glass diminishing in its expansibility to the same amount as 

 mercury increases in its rate of expansion. But M. Regnault 

 and M. Pierre both agree with MM. Dulong and Petit, as to glass 

 experiencing an augmentation in its coefficient of dilatation. 

 Hence, if there is continuity in the law of expansion of mercury, 

 the conclusion is inevitable that the mercury is behind the air 

 between the fixed points of the scale. The amount computed 

 by the formula is 0°-513 at 50°, 0-481 at 60°, 0-413 at 70°, 

 0-31 at 80°, and 0-171 at 90°. 



§ 4. Let us first proceed on the hypothesis that the thermo- 

 meter employed by M. Regnault in his researches on the tension 

 of aqueous vapour from 100° to 50°, corresponded with the for- 

 mula, and was actually behind a perfect air-thermometer exactly 

 the amount specified at the respective temperatures. Let us also, 

 for the present, assume that the gradient of density with the 

 temperatures thus corrected is exactly a straight line. The pro- 

 jection of M. Regnault^s observations with the temperatures un- 

 coirected will not range exactly in a straight line, but in an arch 

 concave towards the axis of temperature. Thus, e. g. 50° by the 

 mercury indicates 50°-51 by the air: we have therefore, by dis- 

 regarding the correction, applied to abscissa 50° the ordinate of 

 density that belongs to 50~-51 ; to abscissa 60° the ordinate of 

 density that belongs to 60°-47 ; to abscissa 70° the ordinate that 

 belongs to 70°-42, &c. 



Suppose the scales of projection on the chart to be so arranged 

 that the line that approximately represents M. Regnault's 



