Williams. — On the Fourth Dimension. 507 



By combining the equation Mw/TV'— with the well-known 

 law of Van t'Hoff, D = -02T7w, the result is D = KMTv / M ) 



d 



where D is the molecular depression of the solvent and K a 

 constant. Hence the molecular depression of any body can 

 now be calculated without a knowledge of the latent heat of 

 fusion. 



Trouton's law states that — 



MW/T 1 = K 1 . 



But Mfr/Tv'M = K ; 



io/W = c Tv^/T 1 . 



That is, the latent heat of fusion is to the latent heat of 

 vaporization as the freezing-point multiplied by the cube root 

 of the specific volume is to the boiling-point. This, of course, 

 is only true when Trouton's law is true — that is, when the 

 molecular condition of the body is unchanged in passing from 

 the liquid to the gaseous state. 



Art. L. — Some Observations on the Fourth Dimension. 

 By the Rev. Herbert W. Williams, M.A. 



[Read before the Hawke's Bay Philosophical Institute, 9th September, 



1901.] 



Helmholtz was the earliest writer to attempt to present the 

 conception of transcendental space in a form inviting popular 

 investigation, and his efforts have been ably seconded in 

 recent times by the author of " Flatland,"* in the first place, 

 and by Mr. C. H. Hinton,f in the second place. The former 

 has produced a work which has attractions beyond the mere 

 consideration of the fairyland of mathematics ; while the 

 latter, beginning with pamphlets of a distinctly popular 

 nature, has in his latest work laid down, still without ab- 

 struse mathematics, a scheme of mental training the avowed 

 object of which is to enable the student to form a perfect 

 mental image of a figure in four dimensions. 



*"Flatland, A Romance in Two Dimensions, by a Square." Seeley 

 and Co. 



f Author of "Scientific Romances" and "A New Era of Thought." 

 Swann, Sonnenechem, and Co. 



