350 X.'s Reply to Mr. Daniell. [Nov. 



degrees of difference of temperature ; whence is obtained for 

 the number of degrees which the existing temperature is above 



d 



or below 32°, the small fraction ; and not a fraction de- 



rived from that of the cubic dilatation of glass — , the number 



for which Mr. D. would insist, and which is in effect used also 

 as one of the elements in the construction of Mr. Rice's table. 

 For a scale on a plate of glass, the correction would be affirm- 

 ative for degrees above 32°, and negative for those below that 

 standard point, because in the former of these cases any line 

 on the scale would be in advance of absolute or unexpanded 

 distance, and vice versa. This, however, is contrary to what 

 Mr. D. says, if I have been able rightly to conjecture what he 

 .means by measuring upon a scale of glass. 



As there is something portentous in the manner in which Mr. 

 D. alludes to M. Biot, I shall, with due deference show where 

 his error lies ; to that gentleman truth will be acceptable from 

 whatever quarter it may come. 



In treating of absolute dilatation M. Biot says, " Elle est 

 plus forte que la dilatation apparente, comme cela doit etre," 

 but precipitately he adds, " puisque celle-ci n'est reellement 

 que l'exces de la dilatation propre du mercure sur celle du 

 verre ; " in one sense this may be true, but not in the way M. 

 Biot understood it, he having made that a case of addition, 

 which is one of division. In the preceding page (51) this ap- 

 parent dilatation of mercury is stated to be — , and it appears 



from page 161, that — is taken as the cubic dilatation of the 

 vessel, (i ' 1 = l'iss)'; 0I> course, to find that of the mer- 



' \ I 1 4<3 1 380/ 



cury M. Biot makes g^ + ^ = ^7f 2 - Now, not to mention 

 an immaterial slip in this summation, the rule itself is fal- 

 lacious, - + ^ is not the absolute dilatation in question ; 



A V 



~ — - = M* being the legitimate formula, which, as well as 



A + V + 1 => ° 



its two converse forms, holds universally true. In M. Biot's 



case therefore — is -— and not rrr^, the number used in the 



subsequent parts of his work. This oversight is not exclusively 

 M. Biot's: Dulong and Petit, together with every writer on the 

 subject, whose works I have perused, agree with the most ex- 



* Whoever chooses to investigate this, will perceive that the symbols represent the 

 volumes at 32°, as each of them plus unity does at 212° ; or in other words, they are 

 severally denominators of the fractions of the apparent, dilatation of mercury, and of 

 the absolute dilatations of the vessel and of mercury. 



