98 On Reducing the Results of Experiments. 



just as I asked Prof. Arrhenius (from whom he seems to have 

 borrowed this argument, see Phil. Mag. xxix. p. 429), to 

 explain what he means by " accurate" or " proper" smoothing. 

 Why does he not take the whole of one of my first differential 

 density diagrams, and show how it may be accurately smoothed 

 so as to obliterate all changes of curvature ? Surely he cannot 

 think that he has sufficiently illustrated the feasibility of this 

 by taking only a small portion of the most regular part of one 

 of these figures. And even if he does, I scarcely think that 

 any one who glances at the result depicted above (woodcut, 

 p. 94) will consider that he has succeeded in the attempt. 



12. Lastly, Mr. Lupton says that I am self-condemned 

 bv having dealt with second differences deduced from the 

 smoothed first differential curve, while I admit that the indi- 

 vidual determinations through which the smooth curve was 

 drawn are scarcely accurate enough for the direct deduction 

 of second differences. Mr. Lupton has evidently not carefully 

 read p. 123 of my paper. To any one acquainted with phy- 

 sical methods it must seem absurd to state that the mean of a 

 number of determinations, or the straight line or curve drawn 

 through a number of determinations, is not, as a rule, more 

 exact at any given point than are the individual experiments. 

 Mr. Lupton might as well say that no statement could be 

 made as to the inclination of a bank of stones, because the 

 lines drawn between two neighbouring stones showed all sorts 

 of different inclinations. 



Mr. Lupton has apparently had little experience in the 

 practical manipulation of series of results ; and if I have 

 shown any deficiency in forbearance towards him, I must 

 crave his forgiveness, for he has entered on a task which 

 should have been undertaken in no light mood, and only after 

 a thorough mastery of the results which he proposed to 

 demolish. There are very few who can be expected to enter 

 into the details of work such as that now under discussion, 

 and the majority will consent to be led by the opinion of 

 a critic who has presumably made himself acquainted with 

 the intricacies of the subject, especially when he makes an 

 effective bid for their confidence by a display of whole pages 

 of equations. If, however, Mr. Lupton can for a moment 

 place himself in my position and imagine that he has a 

 thousand and more determinations of a most tedious cha- 

 racter, the constant care and unremitting labour of two whole 

 years, which are in danger of being blown to the winds by the 

 breath of a superficial critic, he will forgive me for any 

 warmth of expression which he might at first sight be inclined 

 to resent. 



