218 Mr. J. J. Waterston on a Difference in the march 



between 50° and 100°. Otherwise M. Regnault's graphical 

 curve of equalized observations may thus far be removed from 

 perfect accuracy, or it may be caused by the deviation from 

 Mariotte's law aftecting the air- thermometer. (See § 18.) 



That so small an adjustment should bring M. Regnault's 

 observations into perfect harmony both with the law of density 

 and with the thermometric formula constructed upon MM. Du- 

 long and Petit^'s data, cannot be viewed as otherwise than remark- 

 able. Can such a coincidence be accidental ? Is it illusory ? 



§ 8. The coefficient of the expansion of mercury in glass must 

 change with the quality of tlie glass. M. Pierre found the co- 

 efficient of glass between 0° and 100° to vary from '0026 to 

 •0019*, which is from about ^th to ygth the coefficient of 

 mercury ; hence the absolute expansion of mercury in glass may 

 vary to the extent of oVnd part. 



How this may influence the comparison of thermometers, we 

 may perhaps most easily understand by means of a diagram 

 such as fig. 3. Let AD represent the curve of expansion of 

 mercury in glass with the greater coefficient, and A C the same 



with the lesser coefficient. Let D C = ^ D B, and A B = 100°. 



If the arch A C were flatter than the arch A D in the proportion 

 of B C to B D, there could be no diff'erence between the thermo- 

 meters, and the formula of correction for one would apply to the 

 other. The subtense of the arch of expansion represents the 

 uniform rate of the air-thermometer, and its extension beyond 

 100° is situated below the curve of expansion, showing the air- 

 thermometer to be behind the mercury. If the absolute amount 

 of this difi"erence in the two thermometers continued to have the 

 same ratio C B to C D above 100° as below, the relative amount 

 would be the same, and thermometers of diiferent kinds of glass 

 would keep pace with each other. 



§ 9. The evidence on this point is rather conflicting. 

 M. Regnault states {Ann. de Chim. vol. v. p. 102) that the 

 different kinds of glass not only have coefficients of dilatation 

 absolutely different, but they all follow different laws in the di- 

 latation. The glasses which have the smallest coefficient appear 

 to experience a less rapid augmentation of dilatation with the 

 temperature. This is precisely what is required to admit of 

 thermometers constructed of different kinds of glass keeping pace 

 with each other. On the other hand, M. Pierre states [Ann. de 

 Chim. vol. v. p. 438) that the thermometer with crystal reser- 

 voir is constantly in advance upon the thermometer with com- 

 mon glass reservoir, and the difference increasing generally with 



* Ann, de Chim, vol. xv. p. 335. 



