“9 
’ ler on the cere # he of Wat 325 
— ye. but accidental. In the formulaof Mr. Roche, (which he 
rs, not as a means of interpolation, but as the expression of a 
‘gene Ree. physical law,) the temperature is itself an element of the 
index by which certain constant quantities are to be involved. 
The principles, however, upon which he has founded the expres- 
sion, are Gerrionee both by Mr. Dulong and Mr. Regnault. 
The formula of Mr. Dulong presents a smaller aggregate devia- 
tion ete fi of the others; and it would be singular if it did 
not, seeing that it was derived from | a constant furnished by his 
own experiments. But as s might also be anticipated, this con- 
‘stant, taken (to four places of decimals ) from the. result of the 
highest aah temperature, fails to apply in the lower ones, 
ad The maximum deviation under his formula, given in the last 
; table, occurs at the lowest experimental temperature ; and in fact 
“in his final table of, atmosp be pressures and corresponding tem- 
peratures, he has preferred, below the limit of four atmospheres, 
(1 5°: A Cent. or 2939-72 Fahr.,) to abandon his own formula and 
use that of Tredgold. . Below the ordinary as pressure, 
“his quantities are utterly Po as will be seen es the’ 
+4 
Bons statemen —_ 
"Pressures Tua (Centigra “ay t 2 re : 
Observed oye culated by tia Ol le: as ee 
__ Regnault. ee | Franklin Institute.| Alexander. 
78 36°16 = 39° 5oe me 
-00 10 +45 <4 4-28 
9% “00 —FF D4 is 3] 
The last two columns are added here for illustration; an 
— among other things, that the formula of the Franklin In 
gutnte is, like that of a French Academy, inapplicable to low 
n peratures and pressu — 
“Later than these, Mr. ‘Biot, in 1839, proposed another formula, 
and, in 1841, published a table calculated by it; in which the ~ 
Oe are given in metres and for every degree Centigrade from — 
= 20° to 220° Cent., corresponding to the “limits of — 4° and oi 
428° Pehtentici The patient labor requisite for this task, has : 
Let om 
ola 
y vhich todeulgedtoh impresses a more -sy. 
E; # 
the method ; but yet, in spite of the og 
