of Sulphuric -Acid Solutions. 137 



bolic form, with seven constants, to agree very closely indeed 

 with fourteen of the points ; and the number of points with 

 which an equation could be made to coincide might be further 

 increased considerably by the fact that eight of the points lie 

 very nearly on a single straight line. When to these con- 

 siderations we add that of an operator of the highest skill and 

 ingenuity, it would indeed be remarkable if Prof. Riicker's 

 seven-constant equation did not show a very close agreement 

 with the twenty experimental points investigated. I say 

 twenty points advisedly, for of the twenty-four points inserted 

 by Prof. Pucker, four (those at 80*04, 79*12, 65*12, and 57*94 

 per cent.) are deduced from determinations (by taking alter- 

 nate experiments) which have already been used to their full 

 extent in supplying the other points given in his tables. 



But Prof. Pucker has not confined himself to the use of the 

 parabola or any other simple equation, but has used an equa- 

 tion of a complex and highly artificial form, for which, I 

 believe, there is no precedent, and for which, as an expression 

 of physical facts, there would seem to be (I speak under cor- 

 rection) no probability whatever. Prof. Rucker first finds an 

 equation (a combination of an exponential curve with a straight 

 line) y = a + bx — cd z , which agrees well with two or three ex- 

 perimental points between 47 and 51 per cent., and again with 

 those between 72 and 80'5 per cent., these two portions con- 

 stituting together but ^ths of the total length of the figure. 

 For all solutions weaker than 47, and stronger than 80*5 per 

 cent, there is no semblance of an agreement; and the whole of 

 the middle portion of the curve between 51 and 72 per cent. 

 " lies a little below that given by experiment," and cannot 

 therefore be accepted as a representation of the experiments. 

 In order to rectify this defect and to raise this portion of his 

 curve, Prof. Rucker ingrafts on to it a " hump " by means of 

 a fourth term, m/(n x + n~ x ). Now it is obviously possible in 

 the case of any figure such as that under discussion, where any 

 changes of curvature which exist are by no means very abrupt, 

 but are only " minor changes," to mould a curve to the exact 

 form of the experimental figure, if it is lawful to pare it down, 

 or plaster it up wherever it may be necessary*, and the mere 

 fact of obtaining such an equation to fit can, I maintain, 

 prove nothing beyond the skill of the operator. 



Even, however, if such an operation could disprove the 

 existence of breaks, Prof. Riicker's estimate of the number of 

 my breaks which he has disproved would have to be materially 

 reduced. 



* For the whole of the density-results an equation of this sort would 

 at a moderate estimate contain about 21 constants. 



