Royal Society. 447 



where it will be observed that, 92 = 5(7), an( ^ w = 6(8), the num- 

 bers of allotrious points are 2 and 4 respectively ; but since in 

 each of these cases one point is saturate, they give only the 

 numbers 1 and 3 respectively. It might be mathematically 

 possible to obtain a general solution; but there would be little 

 use in this ; and for even the next succeeding case, No. of biva- 

 lent diagrams C w H 2ra ; the extreme complexity of the question 

 would, it is probable, prevent the attainment of a general solution. 

 Passing to the chemical signification of the formulae, and 

 instead of the radicals C n H 2n+1 considering the corresponding 

 alcohols C n H 2W+1 . OH, then, 71 = 1, 2, 3,4, the numbers of known 

 alcohols are 1, ], 2, 4, agreeing with the foregoing theoretic num- 

 ber (see Sehorlemmer's 'Carbon Compounds/ 1874); butrc = 4, 

 the number of known alcohols is =2, instead of the foregoing 

 theoretic number 8. It is, of course, no objection to the theory 

 that the number of theoretic forms should exceed the number of 

 known compounds ; the missing ones may be simply unknown ; 

 or they may be only capable of existing under conceivable, but 

 unattained, physical conditions (for instance, of temperature) ; 

 and if defect from the theoretic number of compounds can be 

 thus accounted for, the theory holds good without modifica- 

 tion. But it is also possible that the diagrams, in order that 

 they may represent chemical compounds, may be subject to 

 some as yet undetermined conditions; viz. in this case the 

 theory would stand good as far as it goes, but would require 

 modification. 



LVIII. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from p. 391.] 



December 11, 1873. — Joseph Dalton Hooker, C.B., President, 

 in the Chair. 



HPHE following communication was read : — 

 -*- "A Quantitative Investigation of certain Relations between the 

 Gaseous, the Liquid, and the Solid States of Water-Substance." By 

 Professor James Thomson, LL.D., Queen's College, Belfast. 



In two communications made by me to the British Associa- 

 tion, at its Meetings at Edinburgh in 1871 and at Brighton in 

 1872, and printed as abstracts in the Transactions of the Sections 

 for those years, considerations were adduced on relations between 

 the gaseous, the liquid, and the solid states of matter. The new 

 subject of the present paper constitutes a further development of 

 some of those previous considerations ; and a brief sketch of these 



