92 Mr. S. U. Pickering on Mr. Lupton's Method of 



through my papers : he raises numerous minor objections, 

 nearly all of which I have fully answered, and his chief 

 weapon of offence is the representation of a small portion of 

 one of the sets of my density results by a parabola deduced 

 mathematically, and which, if strictly applicable, would nega- 

 tive the existence of one of the changes of curvature which I 

 considered probable, in ignorance of the fact that I myself 

 had applied the same method of examination to the same 

 portion of all but the same curve, and had shown why the 

 results obtained did not negative the existence of the change 

 in question (Chem. Soc. Trans. 1890, p. 78). From this ex- 

 amination Mr. Lupton arrives at a similar provisional conclu- 

 sion to what I did, " if the limits of accuracy are 5 q 00 " then 

 this small portion of this series of my " results can be ex- 

 pressed by a single curve." But, apparently, " the hurry of 

 modern life"" prevented Mr. Lupton from ascertaining whether 

 the experimental error teas 5-qVo? an ^ whether, therefore, 

 this result led to any argument against my conclusions. 

 But 5 q 00 is a somewhat large quantity when it refers to the 

 weight of 25 c.c. of strong sulphuric-acid solutions; it is 

 about 8 milligrams; and had Mr. Lupton taken the trouble to 

 ascertain from the numerous values available for this purpose 

 (Trans. 1890, pp. 70, 71 ; Phil. Mag. xxx. p. 402) what the 

 probable experimental error really was, he would have found 

 that it was not ^ m , not -^i m , and scarcely even 5 ooVoo- 

 As Mr. Lupton's argument depends entirely on the con- 

 cordance between the values calculated from his equation and 

 the experimental values, it was certainly incumbent on him 

 to make sure that his calculations were correct ; but this he 

 did not do, and of the two errors which he made one was a 

 very important one*. I therefore take the liberty of giving 

 the following amended version of the first and last columns 

 of his table, in which x is the percentage strength of the 

 solution, and u calc. — u obs. the differences between the 

 actual densities and those calculated according to Mr. Lupton's 

 equation, which represents these results as forming one con- 

 tinuous parabolic curve. In two cases only out of the 10 

 results which Mr. Lupton investigated (50 to 68 per cent.) 

 does the difference even approach to 50 ^ 00 , while the average 

 difference is yo (Too? that * s ^0 times greater than the probable 

 error mentioned above, and 23 times greater than the liberal 

 maximum which I allowed as, and also found to be, the limit 

 of error in the majority of cases (Chem. Soc. Trans. 1890, 

 p. 71) ; but, independently of this, the arrangement of the 



* _ -000098 for + -000218 in the last column. 



