THE HYDRATE THEORY OF SOLUTIONS 143 



cent. H0SO4. This deviation could be eliminated by grafting on 

 to the original formula the expression 



tf+n~ x 



which raised the calculated value 



by 0*000055 a t 6roi per cent., 



by o'ooooio at 52*91 per cent, and 69*10 per cent., 



by 0.000002 at 46*94 per cent, and 74*98 per cent., 



and by inappreciable amounts at higher or lower concentrations. 

 When this addition was made to the original equation it agreed 

 in a highly satisfactory manner with the experimental obser- 

 vations over the whole range, covering the supposed breaks at 

 51 per cent., 58 per cent., 72*8 per cent., and 78 per cent. Picker- 

 ing, commenting on this equation {Phil. Mag. 1892, 33, 139), 

 called attention to the fact that the correcting factor in Rucker's 

 formula reached a "practically appreciable" magnitude (0*000004) 

 at 72 per cent., and at 50 per cent, corresponding closely with 

 the positions of two of the breaks which he had postulated, and 

 thus affording additional evidence in favour of his " principal 

 contention " — the " practical starting of a fresh order of things 

 at certain definite points." 



So far as I am aware, it has invariably been assumed that 

 this " fresh order of things " must be one resulting from the 

 formation of a hydrate corresponding in composition with the 

 concentration at which the break occurs. Pickering's contention 

 certainly contains, however, at least the rudiments of an alter- 

 native explanation of the breaks. It may be supposed that the 

 bulk of the solution consists, at dilutions below 80 per cent., 

 of a welter of hydrates of small stability, and therefore so 

 highly dissociated as to give a smooth density curve such as 

 that represented by Rucker's original equation. Into this 

 complex mass of hydrates it may be imagined that the penta- 

 hydrate S0 3 .5H 2 is introduced as an aggregate of greater 

 stability and somewhat higher density than the hydrates with 

 slightly larger or slightly smaller proportions of water. The 

 effect would be to increase the density to an extent depending 

 on the proportion of pentahydrate in the solution — i.e. to a 

 maximum extent at 58 per cent. H 2 S0 4 (corresponding with the 

 formula H 2 S0 4 . 4H 2 of the hydrate) and to a progressively 

 smaller extent at higher and lower concentrations. There would 



