374 PROCEEDINGS OF THE AMERICAN ACADEMY § 5 



in which formula we see that even if both liquids A and 

 B satisfy the equations, 



JL'D' = E'^T, and JL"D" = E"^T, 

 it will not in general be true that a mixture of the two 

 liquids will do the same. 



Trcatinof alcohol as a mixture of ether and water we 

 have, from the table in § 3, since 



^ = li. and ^ = -li , 

 92 92 



the value 1.86 indicated* for the principal ratio, at 0° cen- 

 tigrade, against 2.17 observed. 



Independent of the theory, from a mechanical point of 

 view, it may be interesting to note the values of the sepa- 

 rate quantities indicated, namely: for the latent heat, 182, 

 which is correct at 100° according to Zeuner; for the 

 density, .787, which is true at about 25°; for the modulus 

 of elasticity, 9,899,000,000, which would probably be right 

 in the neighborhood of 35° (see Everett, page 52); and for 

 the coefficient of expansion, .001196, which is the value at 

 about 45° according to Pierre. 



It is not inconsistent with the modern theories of mo- 

 lecular structure to suppose that those parts of different 

 inolecules which may have greater mutual cohesion than 

 the rest should be drawn together so as to form a nucleus; 

 and it is possibly the clustering of the '■'•hydroxyV rad- 

 icals, in alcohol, which enables us to treat it so success- 

 fully as a mixture of ether and water. On the other hand, 

 it is the impossibility, perhaps, of the formation of such 

 nuclei that causes the approximate agreement of the first 

 three liquids with the theory for elementary substances. 



The investigation of the case of water, which alone re- 

 mains, will be deferred until after the analytical treatment of 



*JLD ^ 42,000,000 (l^ 86-5 + ^ 575) (|^ 0.736 + ^|) 



-^<^ 20,200,000,000 X 8,800,000,000 ,^, „ ^ , 



— , .„ o o (l^ 0.0015 —as 0.00005) X 273 



7.1. 20,200,000,000 + ^a 8,800,000,000 ^9i^ ^ 5sr ^J '•> 



