Karl Pearson 
259 
that I was as a mere statistician struck by the appearance of the curves as I turned 
over the pages of the Proceedings. I have considered the cases of 2 and 4 amperes 
for the anode, Diagram I. The data for individual experiments are given on 
Prof. Duffield's diagrams, but his tables only give mean values. I have therefore 
had to measiire off individual values from his diagrams. The means obtained 
from these measurements agree in the main with the author's recorded means, 
but in a few cases it would appear that there is some discordance between table 
and diagram. On the diagrams curves are drawn presumably representing in 
each case the smoothed relation which the author considers to hold between loss 
of weight and length of arc. My object is to enquire how far these curves are 
probable representations of the phenomena in question. It will be seen that the 
observations are usually made in pairs, more rarely in triplicate or are even 
quadruple. There are a considerable number of isolated observations. We have 
thus rather slender material from which to determine the error of a single observa- 
tion, and clearly but little conclusion could be drawn did we not assume that a 
measurement at each arc length was of equal weight*. 
The following table exhibits the work — first for the 4-ampere curve; the 
weight lost being per coulomb x 10^ grammes. 
Arc 
length 
rip 
Weight 
lost, Wi, 
rrip 
IVp - 10 
rUp - 10 
mp - m,, 
8 {nj,{mp- mpY) 
1 
2 1 
„ / 
! ) 
! } 
5 
7 
I } 
10 1 
„ / 
■! } 
15 
20 
1 
2 
2 
2 
] 
1 
2 
2 
2 
1 
1 
17-62 
17- 92) 
18- 30/ 
1919/ 
19- 62/ 
19- 70/ 
20- 32/ 
21- 43 
21- 35 
22- 40/ 
22-63/ 
21- 371^ 
22- 89) 
22- 55/ 
23- 07/ 
22-69 
22-89 
17- 620 
18- 110 
19- 405 
20- 010 
21- 430 
21- 350 
22- 515 
22-130 
22-810 
22-690 
22-890 
17- 52 
18- 24 
1915 
20- 12 
21- 29 
22- 26 
22-51 
22-71 
22-79 
22-79 
22-79 
- 3-32 
- 3-02/ 
- 2-64/ 
- 1-751 
- 1-32/ 
- 1-24/ 
- -62/ 
+ -49 
+ -41 
+ 1-461 
+ 1-69/ 
+ -43 1 
+ 1-95/ 
+ 1-611 
+ 2-13/ 
+ 1-75 
+ 1-95 
- 3-32 
- 2-83 
- 1-54 
- -93 
+ -49 
+ -41 
+ 1-57 
+ 1-19 
+ 1-87 
+ 1-75 
+ 1-95 
+ -10 
- -13 
+ -25 
- -11 
+ -14 
- -91 
•00 
- -58 
+ -02 
- -10 
+ -10 
-0100 
-0338 
•1250 
■0242 
•0196 
•8281 
•0000 
•6728 
•0008 
•0100 
•0100 
Totals 
17 
355-94 
Sum of squares 
= 57-2166 
= 55-5422 
b7343 
= S{np{mp-m^,f] 
(7;= 20-94 
0-,/ = 3-3657 
22 = 3-2672 
<yj{^- t) 
= -0985 
n' = 
n + 
1 = 11 + 1 = 
12, .-. P = 
= -0920 
= -9709 
* This is probably not true, but there is no evidence of multiple measurements at points where the 
measurements might be assumed to be critical. 
17—2 
