Results of Experiments. 427 



These sentences seem to carry with them the condemnation 

 of the method. If the original results are not sufficiently 

 accurate to warrant second differences, no manipulation of a 

 steel lath, however skilful, can make them so. Hence in the 

 case of experiments of such extreme delicacy it seems pre- 

 ferable to throw over the graphical method altogether, and 

 tabulate the finite differences as suggested under empirical 

 methods, more especially as they afford a test of how far it is 

 safe to carry the reduced results. The following Table is thus 

 obtained from Mr. Pickering's results. The frequent changes 

 of value and sign in the third differences shows that the 

 accuracy of the experiments does not warrant us in carrying 

 the equation to the third power of the variable. Let us then 

 attempt to find an equation of the second degree which 

 adequately expresses Mr. Pickering's results : — 



c = &u = -000047 1 nearly. 



b = hi-x 2 + x l &u = -01071616 -119-9711 x '0000471 

 = •00506552. 



a=w-^-^ 2 = l-4809752--00506552 x 58'992484 



-•0000471x3512-6. 

 a = l'016704. 



.-. ^=1-016704 + -00506552^ + -0000471a; 2 ; 



from which the column of calculated values has been obtained. 

 Since no one of the calculated results differs from that ob- 

 served by so much as one part in five thousand, the equation 

 probably expresses the results well within the limits of experi- 

 mental error, and with far greater accuracy than could be 

 attained by even the most careful drawing. Probably with 

 greater arithmetical labour the calculated and observed results 

 could be brought even more closely together. But the fact of 

 this continuous curve running so well among the experimental 

 results seems to throw very grave suspicion on the definite 

 hydrate H 2 S0 4 3 - 92H 2 containing 57 per cent, of real acid 

 which Mr. Pickering obtains from these experiments. 



The whole question then seems to depend upon the extent to 

 which we can safely rely upon the experimental, results. If 

 the limits of accuracy are 1/5000, the results can be expressed 

 by a (smooth) single curve represented by an equation of the 

 second degree ; and this equation when differentiated gives 

 an equation of the first degree, which can be expressed by a 

 straight line. 



