and on its Measurement by Thermometers. 453 



zero of temperature would be found by making l+«£°=0, or 



t°= , which is not in accordance with the results of Dulong 



u 



and Petit, whose law of the cooling of bodies in a vacuum gives 

 the absolute zero of cold at minus infinity of degrees below the 

 freezing-point of water. According to Dalton's view, the cor- 

 rect law of uniform expansion exists in gases ; or, for them, for 



6T 

 each change of a degree of temperature we have t==- = constant ; 



dV . 



and putting this into a differential form, -~- = ctdt° } which, by 



integrating and correcting the integral, gives V=V .e a *°, and 

 the degrees t° may be counted + from any starting-point at 

 which the volume of the gas is V . The volume V becomes 

 zero now only when £°= — oo , or at the absolute zero of Dulong 

 and Petit. It is clear that the science of Molecular Phvsics is 

 not yet sufficiently advanced to assist us in discriminating the 

 true law of the expansion of gases for increase of temperatures 

 independently of experiments. 



For any bodies whatever, to find the volume Vat a temperature 

 t°, when the volume V at the commencement of the scale and 

 the constant a are known, we have the formulae 



for expansion by equal increments Y = Y (l+ut°) 



for uniform expansion .... V = V .e ai!O 



Now for mercury the most careful experiments were those of 

 MM. Dulong and Petit*, who found that the expansion of mer- 

 cury between the freezing- and boiling-points of water was ^r^th 

 part, for the next equal increase of temperature it was ^- 5 th 



part, for the next equal increase again it was ^jr^rd part, the 

 two second intervals being subject to any irregularity the air 

 thermometer possessed by which they were measured. It is 

 clear that the expansion of mercury is not by the law of equal 

 increments, which has puzzled De Luc, Dalton, and others ; but 

 it is, we shall find, conformable to the law of uniform expansion, 

 and, when properly graduated, the mercurial thermometer ap- 

 proximates exceedingly near to a normal thermometer — the 

 proper correction for the expansion of the containing glass bulb 

 and tube being employed. 



Let V be the volume of any mass of mercury at the freezing- 

 point of water, Y Y its volume at the boiling-point, V 2 its volume 

 at another equal increase of temperature above the boiling-point, 

 V 3 its volume at another equal increase of temperature above 



the last. 



* Anncdesde Qhimie et de Physique, 1817. 



