Composition of Dilute Sulphuric Acid. 207 



from his breaks would have been equal to half the average 

 length of his curves. This operation is in effect that which 

 I have performed, except that I have fused into one the four 

 curves which would have been necessary to cover the range 

 considered ; but the condition still holds, that an overlap 

 at the extremities about equal to half the range of one of 

 Mr. Pickering's curves is adequate. 



Mr. Pickering finally finds seventeen breaks between per 

 cent, and 100 per cent. ; i. e. he divides the curve into 

 eighteen parts, the average range of which is 5*5 per cent. 

 Half of this is 2*7 per cent., and the overlaps of my curve are 

 2*5 per cent, and 4 per cent, at the two ends respectively. 



It is true that the distance between the breaks under con- 

 sideration is considerably over the average for the whole 

 range ; but that no argument can be based on this is proved 

 by the fact that in one case (viz. between 72*8 per cent, and 

 78 per cent.) it is a little less than the average. 



As to Mr. Pickering's argument in the footnotes on p. 138, 

 in which he urges the uncertainty of his own observations in 

 support of the view that the end of my curve may be nearer 

 to a break than appears from the numbers he himself quotes, 

 I can only say, that a research cannot be propped up by its 

 own uncertainty. 



I have discussed these arguments of Mr. Pickering because 

 I wish, as far as possible, to meet him on his own ground, but 

 I must frankly say that I do not think the discussion can with 

 advantage be carried further, and I hope that he will not 

 think that I admit the validity of any further arguments he 

 may adduce if I do not answer them. 



No definite mathematical method for deciding how the 

 results of a group of experiments can best be graphically or 

 analytically respresented exists. 



Hence the discussion becomes a wearisome argument as to 

 how a ruler may be held, whether curves have " humps " and 

 the like. 



I have answered Mr. Pickering's arguments on such points 

 because I wished at the end to take a wider point of view 

 without being charged with having evaded them. 



The state of the question appears to me now to be as 

 follows : — 



Mr. Pickering claims to have established the existence of 

 certain hydrates of sulphuric acid by detecting discontinuities 

 in the curves which represent the physical properties of 

 solutions of the acid. He asserts that the evidence is cumu- 

 lative, but it would avowedly take months to examine it all in 

 minute detail. I have therefore sampled it. I took what I 

 have every reason to believe Mr. Pickering considers to be 

 the best part of his work, the determination of the densities. 



