§ l8 OF ARTS AND SCIENCES. 423 



tween the fourth and the square; that is, we should expect 

 to find 6 ^ X ^ ^. 



The effect of diminishing x will be evidently to increase 

 the elasticity and to diminish the expansion in like pro- 

 portion, so that the product £e T will not be affected, and 

 hence the principal ratio. A", will remain the same; but 

 the specific heat, which involves the product Ee"^ T^ will be 

 diminished, as we have already seen is the case in solid 

 bodies. 



A diminution of .v would, however, increase the calcula- 

 ted value of the critical temperature, which we have seen 

 is already too high, and this alone is sufficient to counter- 

 balance the weight of the argument founded upon expan- 

 sion. 



By giving different values to x^ all possible relations may 

 be represented between e and its derivative; by assigning 

 arbitrary values to x at different temperatures, any law of 

 expansion can be expressed; and if our reasoning has been 

 correct, when the true relations between the derivatives 

 shall have been determined with still greater accuracy than 

 at present, we shall be able to conclude precisely by what 

 law the cohesion actually varies in different states of aggre- 

 gation, and we may then class under the head of accurate 

 knowledge what has so far been only hypothetical. 



§ 18. The above sections were already in the press 

 when the communication of D. Mendelejeff, On the Ex- 

 pansion of Liquids, published in the April Journal of the 

 Chemical Society at London, first came to my notice. 

 The table for the expansion of liquids, quoted from 

 Thorpe, has been reprinted in full (Table VIII.) and is a 

 most striking confirmation of the uniformity of the law of 

 expansion of liquids, pointed out in § 9. One can hardly 

 avoid the conclusion that the experiments of Thorpe must 



