264 K. IKEDA 



essential, and warn us not to theorize too freely from any such hasty 

 generalization. That there are more than one formulae, which have 

 no essential relation to each other, to express one and the same connec- 

 tion, seems in itself to be a strong proof of their being of an accidental 

 nature. A thing (A) may depend entirely on another (-£>)■; but if (B) 

 can influence a third (C), or is always (or even usually) accompanied by 

 it, then the proposition connecting (A) and ((,') will sometimes have 

 the appearance of a law. If it holds good for a great number of 

 instances, then it may be assumed to be true within certain limits, ;ind 

 can be used as a sort of a law, though theoretically it is not. Just as, 

 in using a circle oi a certain radius to represent a short piece of 

 almost any curve, we must assign a strict limit to the length of the 

 substituted arc lest the error grow inadmissively large; so here, 

 these accidental laws must not be stretched too far. The formulas 

 developed in this paper do not apply to the case of water. This 

 may be owing to the fact that water has a very small molecular 

 magnitude compared with the substances treated of in this paper, so 

 that it does not lie within the limit of applicability of the formulae. 

 Or it may be due to the fact that water has a critical temperature so ab- 

 normally high that it is not comparable with other substances at the 

 temperature at which the vapor pressure is equal to a certain fixed 

 quantity. Or it may be due to some unknown cause, as is the case with 

 the magnetic rotation of light, where water has a far greater value than 

 can be inferred from its composition. But one thing is certain that 

 this abnormally high capillary constant for Avater is not due to the 

 complexity of its molecular structure, for the larger the molecule, the 

 less must be the capillary attraction, supposing the formulae to be 

 true. This difficulty can, of course, be eluded by giving oxygen 

 combined with two hydrogen atoms a certain arbitrary value, so as 

 to make the calculated value of K agree with the observed. This, 



