at different Temperatures. 5 



spheres, it follows that the formula does not reach such high 

 temperatures. 



If we examine the formula (B) it will readily appear that 



1 a — 



the quotient ^ decreases to a minimum and then increases 



again. And that this is actually the case in nature, may be 

 proved by the experiments in our possession. Thus, taking 

 the experiment of M. Clement, we have, 



i^5 =.00-459; 



but in the Table we find •007454 in the column of quotients at 

 310°: wherefore while the temperature increased from 310° 

 to 419°, the quotient must have decreased to a minimum and 

 then increased again to its first magnitude. We learn, further, 

 that the minimum takes place at 364°^, or about 152° or 153° 

 beyond the boiling point. Now, by the formula, the minimum 

 is 311° beyond the boiling point, or at double the distance it 

 ought to be; and the experiment of M. Clement is placed 

 before the minimum, instead of after it. The formula, there- 

 fore, although it is very accurate for a long range of tempera- 

 tures, finally digresses altogether from the truth, furnishing 

 another instance of the great difficulty of detecting general 

 properties or laws by means of a comparison of particular re- 

 sults. 



It is evident, however, that the formula deviates from the 

 truth, not because the form of the expression has been erro- 

 neously assigned, but because the experiments do not enable 

 us to determine the coefficients with sufficient accuracy. For 

 this purpose it is requisite to know the exact relation be- 

 tween A and A', which we shall seek in vain to deduce from 

 the quantities furnished by observation. We have in reality 

 groped out the numerical values in the formula by consider- 

 ing the general features of tlie numbers, rather than by fol- 

 lowing any direct or accurate procedure. The experiment of 

 M, Clement has shown us in what respects the formula is 

 faulty ; and, perhaps, it might be possible so to rectify it, as 

 to make it represent all the experiments with some degree of 

 approximation. This, however, could not be accomplished 

 without long calculations, serving litde other ])uipose than to 

 oratiiy curiosity ; for it cannot be supposed that a single ex- 

 periment beyond the minimum is sufficient for fixing that 

 point witii any tolerable ])recision. 



But, setting aside Uie consideration of numerical formuke, 

 it has been proved that the (juotient of the elasticity divided 

 by the lcnii)erature is a quantity that decreases to a minimum 



and 



