310 



Prof. A. W. Riicker on the Density and 



obtain it I have had to carry Mr. Pickering's own calculation 

 of the value of ds/dp from his experiments to a place beyond 

 that at which he — very properly in my opinion — stopped. 



In the third column (/3) the last figure is affected — in the 

 case of the higher percentages — by the third decimal in the 

 percentages, which. I have ignored. The error thus committed 

 is, however, small. 



As regards the fourth column (7), small errors may be 

 introduced into the last place by the method of calculation. 



If, then, we discard the last place and express each value of 

 ft — a, and 7 — a in terms of the number of units in the last 

 place but one to which it most nearly approximates, we get 

 the following Table, in which, for brevity, the values ofp 



and signs are omitted :- 



Table V. 



(3 — a, 

 1 



y-». 



3 



P-m. 



y-a. 







j8 — a. 



y-cc. 











(?) 



1 



3 



1 







1 



1 



5* 



5 











3* 



2 







1 



3* 



3 



1 







6* 



8 







1 



1 







1 





7# 



7 



1 





1 





2 



1 

















1 











1 



It is evident from this Table that, taking a broad view of 

 the relative claims of one continuous or five discontinuous 

 curves to represent the results, there is not much to choose 

 between them. 



, There are five points (marked with asterisks) at which 

 both systems indicate large errors. These are partly accounted 

 for by the fact that at most of them the differences between 

 the values of p by means of which dsjdp was calculated were 

 unusually small. At all of them also the two points required 

 were obtained by means of different solutions, so that sources 

 of error not included in Mr. Pickering's estimate of the 

 maximum affected the results. 



These points Mr. Pickering regards as abnormal. I will 

 therefore neglect them, only remarking that if sources of error 

 of such magnitude are introduced by a change in the funda- 

 mental solution from which the mixtures are made up, similar 

 unreckoned errors may be introduced in the process of form- 

 ing the individual mixtures. An inspection of the curves at 

 8°, 28°, and 30° confirms this suspicion. 



