of Sulphuric- Acid Solutions. 139 



substitute for my five discontinuous curves (pp. 308, 310) ; 

 it does not do so; all that it does is to cover three of my 

 curves, and small, altogether insufficient portions of two others. 



This leaves but two breaks which could possibly be materially 

 affected by the calculations, and one of these I certainly would 

 never have ventured to uphold on the strength of this one 

 series of results, for the only conclusion which 1 drew respect- 

 ing it, even from the four concordant series of density 

 determinations at different temperatures, was that it was " of 

 a very doubtful character " {loc. cit. p. 76), so that the calcula- 

 tions can be said to materially affect but one of the breaks whose 

 existence I asserted — that at 72'8 per cent.: and what evidence 

 does it afford respecting this one ? 



The hump in Prof. Sucker's equation begins to be appre- 

 ciable at a certain point, and again becomes inappreciable at 

 another point, and if the quantities constituting it have any 

 physical meaning at all, they must mean that a certain sub- 

 stance is present, or that certain physical conditions exist, to 

 an appreciable extent between these points only, and are 

 altogether inappreciable throughout the whole of the rest of 

 the solutions, whether stronger or weaker. This is precisely 

 what occurs with a hydrate, according to my views. But let 

 us go further and see at what points this temporary distur- 

 bance begins and ceases. Without much error we may say, 

 I think, that any deviation would first begin to be practically 

 appreciable when it attained a magnitude of about ^ to \ that 

 of the mean experimental error, say J ; this would be 4 X 10 -6 

 in the present case ; and the point at which the fourth term in 

 the equation attains this magnitude is 72 per cent., almost 

 the exact point at which my break occurs, +72*8 per cent. ; 

 and, further still, it diminishes to this magnitude, and again 

 becomes inappreciable, at 49'9 per cent., just where another 

 of my breaks occurs — 51 per cent, in the present series of 

 experiments, 49'9 per cent, in the mean of all my experiments. 

 I should, however, not place much value on the concordance 

 in this second case, owing to Prof. Riicker's equation extend- 

 ing such a short distance beyond this point. We are 

 forced, I think, therefore, to regard Prof. Riicker's results as 

 affording additional evidence in favour of my principal con- 

 tention — the practical starting of a fresh order of things at 

 certain definite points. In fact, the only dilemma on to the 

 horns of which Prof. Riicker's results have placed me is, not 

 that which he imagines (loc. cit. p. 313), but that of having 

 to decide whether the graphic or mathematical method is host 

 suited for discovering those points at which practical changes 

 in solutions occur. 



