426 Mr. S. Lupton on the Reduction of 



which was abandoned by Kegnault, are well known ; one is 

 that the stopper does not go in to exactly the same position 

 when unequally pressed or moistened with different liquids. 



(4) Mr. Pickering does not mention any precaution taken 

 to reduce the flask and weights to their true weights in vacuo ; 

 to remove the oxygen and nitrogen dissolved in the liquid, 

 which might amount to half a cubic centimetre at 10° C, or 

 the air retained between the liquid and the glass. Though he 

 states that *0002 gram may be taken as the safe limit of 

 error, this is about the weight of a sixth of a cubic centi- 

 metre of air. 



The question of the value of the method is of far greater 

 importance than that of any individual series of experiments. 



(1) Mr. Pickering complains that his method has been per- 

 sistently misunderstood. " It does not consist in fitting sundry 



equations on to curves It is quite true that if a curve 



differentiates into a straight line an equation of a certain 

 form must represent that curve " (Journ. C. S. 1890, p. 122). 

 It is unfortunate that Mr. Pickering has used well-known 

 words and symbols with entirely new meanings. The opera- 

 tion of differentiation as usually understood cannot be applied 

 to a curve, but only to the equation of which the curve is 

 the graph. The differentials he uses are not infinitesimal 

 but considerable (finite) differences. 



What Mr. Pickering does, seems to be, to plot the experi- 

 mental results and draw a smooth curve through them ; to 

 measure first differences (except in the case of densities), plot 

 them out and draw a smoothed curve through them, measure 

 second differences, plot them out and find them represented 

 by a series of straight lines. If this account of the method 

 be correct there seem to be five chances of personal error 

 needlessly introduced, while the smoothing process, if accu- 

 rately performed, ought to get rid of those slight changes in 

 first differences which in the second differences mark changes 

 of curvature, and therefore by hypothesis changes of hydra- 

 tion. The method seems to be distinct from that of Mendeleeff, 

 though stated by Mr. Pickering to be the same. 



(2) Mr. Pickering further says : — a The method would give 

 absolutely true results only if these differences were infinitely 

 small ; if they are reduced too much, generally below 1 per 

 cent., the experimental errors attain such relatively large pro- 

 portions that the results are useless." " When a second 

 differentiation has to be performed it is hardly possible to 

 apply it to the experimental values themselves, as the quantities 

 dealt with would be about the same magnitude as the experi- 

 mental errors themselves" (Journ. C. S. 1890, p. 67). 



