oa MAGNUS ON THE EXPANSIVE FORCE OF STEAM. 
surface in the vessel was encountered. The various observations 
yielded some lower and some higher numbers than 4'525; they, 
however, in no case attained the previously adopted value, 5:06. 
The mean from them would be 4°62, I however give the prefer- 
ence to the number found by my method, 4°525™™", because the 
single observations offer smaller differences. 
In order to calculate the expansive forces for entire degrees of 
temperature from the found values, a formula of interpolation 
was requisite. If we were acquainted with a law of the de- 
pendency of the expansive force of the temperature and all the 
other quantities which necessarily come into consideration, we 
should be able to suggest a theoretical formula which would 
certainly be preferable to all others, but unfortunately up to the 
present nothing is known of this law. Roche has attempted to 
give such a theoretical formula, but the reporter of the French 
Commission* says of the considerations upon which it is based, 
that they are not deserving of the approbation of physicists. 
Recently Von Wrede+ has likewise proposed a theoretical for- 
mula; but however ingenious its derivation, it still depends on 
some hypotheses which have not hitherto been sufficiently esta- 
blished; I therefore thought it right to content myself with a 
purely empirical formula, 7. e. with such a one as represents with 
sufficient accuracy the results of the observations. 
At present we already possess an immense number of formulze 
for the same purpose. That none of these could suit my ob- 
servations is evident, since their coefficients have been deter- 
mined from other experiments ; but it was interesting to ascer- 
tain what form of these different equations might probably cor- 
respond with them best. 
Several examinations of the form of the equation suggested by 
Laplace and modified by Biot {, which expresses the expansive 
forces by a series arranged according to ascending powers of 
the temperatures as well as of that proposed by Egen§, which 
expresses the temperatures by a series arranged according to 
ascending powers of the logarithm of the expansive force, have 
shown that these forms can only be made to agree with the ob- 
servations when the whole of them are used for the determina- 
* Annales de Chimie, xliii. p. 105. 
+ Poggendorff’s Annalen, lii. p. 223. 
{ Biot, 7raité, i. p. 273. 
§ Poggendorff’s Annalen, xxvii. p. 9. 
