142 Mr. S. U. Pickering on the Densities 



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will not help us to decide between their respective merits : 

 but whereas Prof. Pucker's equation is artificial and is a very 

 improbable representation of physical facts, the parabola is a 

 form of curve which has been found to express physical facts 

 " in the great majority of cases in physics and chemistry " 

 (Lupton, loc. cit. p. 421), and for the application of which in 

 the preseut case we have the theoretical considerations ad- 

 vanced by so high an authority as Mendeleeff*. Considering, 

 moreover, that the mathematical continuity expressed by 

 Prof. Pucker's curve does not even help us to assert that there 

 is not a change in the nature of the solutions attaining 

 recognizable dimensions just at the point where the parabolas 

 indicate that such a change occurs, we can, I think, have but 

 little hesitation in making a choice in favour of the latter. 



Two points of minor importance remain to be noticed. On 

 p. 310 Prof. Pucker suggests that errors, similar to those 

 which I found in making up solutions from two different lots 

 of stock acid, may exist in making up different solutions from 

 the same stock lot. This, I think, is surely not the case ; 

 for in using different samples of acid the results depend on 

 the comparison by analysis, or by some other means, of the 

 strength of the two, and this cannot be done with an accuracy 

 in any way approaching to that attainable by mixing weighed 

 quantities of two substances. 



Prof. Rucker alludes to my having omitted certain points 

 which I considered exhibited exceptionally large errors, while 

 I insisted on changes dependent on differences of smaller 

 amount. In dealing with a " differential " figure, an error in 

 one of the experiments affects two consecutive differential 

 points in the opposite direction, making them too high and too 

 low respectively ; and it is only in cases where this appearance 

 is evident that we should be justified in assuming, provisionally 

 at any rate, the existence of an exceptional error. Jt was 

 only in such cases that I assumed it ; but at the same time I 

 quoted fully the determinations which I considered to be 

 erroneous, so that others might use them in whatever way they 

 thought fit. These questionable determinations should, no 

 doubt, have been repeated, but to do this in every case would 

 have meant an additional amount of work which would have 

 been prohibitory. It was open to me to obtain evidence in 

 favour of my views either by the study of one or two cases 

 worked up to the highest pitch of perfection, or to accumulate 

 a considerable mass of less perfect instances from independent 



* Chem. Soc. Trans. 1887, p. 778. MendeleefT concluded that the para- 

 bolas would have one term less than my work would show them to have ; 

 this was due, no doubt, to his having assumed that the various hydrates 

 present were practically undissociated. 



