ACCURACY OF NEUMANN’S METHOD. 81 
The following table gives the results obtained by 
Neumann’s method for the amount of P.O; in 10 cc. of the 
standard phosphate solutions. The errors vary consider- 
ably but are all positive. 
Table IV. 
Amounts of P.O; found in 10 ce. of standard solutions by Neumann’s 
method. 
ee eiai Result by Difference Result by | Percentage 
Neumann. from mean. | weighing as error. 
12 23°0 mg + 0:29 mg. | Mg,P.O, + 3:1 
13 Bae” 5, E000 8° |e (Sol. Bs) 4:0 
14 B28, 5, + 0:49 _,, bis 2°2 
15 Sig ee + O19 ,, 22:3 mg. 3°6 
16 7 ae = Ol, ast 7°6 
17 aad ere OxAl ye, 6°2 
i8 Be » 55 + OF 19. ,; 3°6 
Mean 23°29 .. O34 ,, 43 
19 ke a + 0°64 ,, NaPO, + 0:9 
20 LIS 9 + 0°04 ,, | (Soln. C.) 3°6 
21 7. ale + 0°24 ,, es 2°7 
22 23°3 ,, + 0:04 ,, 22°5 mg. 3°6 
23 2D) *y, — 016 ,, ee 4°4 
24 728 le + 0.04 ,, 3°6 
25 238% 55 — 0:46 ,, 5:8 
26 7 ad aN = 0:36) 5, 5-3 
Mean | 23°34,, | O20 rss be | 3°6 
The extreme difierence between any two members of the 
first series of the above results is 1°2 mg., and of the second 
series, 1°1 mg. The average difference from the mean in 
the first case is 0°34 mg., or 1°57, and in the second case, 
0°25 mg., or 1°17%. The mean of these figures is 1°37%, and 
this we may take as the average casual error of these 
results. The means of the figures for the percentage difier- 
ence of the two above sets of results from the standard 
results are 4°3 and 3°67 respectively, and the mean of these 
two figures is 407%. This value represents the average 
constant error of the results. We see from the table, 
therefore, that as a first approximation, the results obtained 
F—June 3, 1914, 
