202 HOLTZMANN ON THE HEAT AND ELASTICITY 
gives the force of expansion = 4°529 millimetres. This is the 
mean of seven experiments by Magnus, and of sixteen experi- 
ments of the tenth series by Regnault; this number is one of 
the bases on which the calculation of the coefficients is founded. 
The greatest deviations of the formula from the results of ex- 
periments are 0°83 and 0°77 degree of temperature, and it might 
be thought that this is too much, but in this case 0°8 corre- 
spond to a difference of only 0°5 millimetre pressure; and even 
the formula advanced by Magnus, which was advanced with re- 
ference to these two observations (I have only made use of the 
eight others), differs as much in this instance from the result of 
experiment. 
With the exception of these two differences all the others are 
very small, and come wholly within the limits of errors of ob- 
servation, which includes even the highest pressure observed by 
Arago and Dulong, proving both the accuracy of Magnus’s ex- 
periments and the correctness of the formula above advanced, 
and the theory on which it is founded. 
The formula here obtained for the expansive force of vapours 
is moreover the identical one to which formerly Roche and sub- 
sequently Von Wrede arrived, but in different ways, in which 
the import of the coefficient B, to which I shall subsequently 
return, was not perceived by them*. 
If it be desired to commence reckoning the temperature from 
0° C., and to indicate the pressures in millimetres of the height 
of mercury, we may first substitute in the formula (3.) ¢; — 100 
for ¢: this gives 
p _ 5°2555.t, — 525°55_ 
PE Ai elk alt Re aes 
5 760 93602 4%, ° 
consequently we have then in formula (3.) for = — 100, p 
= 4°529, 4°529 —525°55 
log a ee — 
760 236°22 
If we subtract these two equations from each other, 
525-55 
9 3 
‘ {5 555 + Se oe b Zi 
> 
4529 236-92 + t, 
74804. ¢; 
236°22 + t,’ 
* I am not acquainted with Roche’s treatise, this, therefore, is merely sup- 
position with reference to him. 
log 
ms log p = 0°65600 + 
