260 
" Goodness of Fit " in Statistics and Phi/sics 
Thus the probabihty, if the inscribed curve represented the phenomenon, that 
a system of observations as unfavourable or more unfavourable than the observed 
would arise is about 1 in 11, i.e. in eleven trials we should have had one result as 
bad. This is not very great odds (10 to 1) against the inscribed curve describing 
the facts, but it cannot be called a highly satisfactory concordance. 
I now take the anode 2 ampere's data. The work is given in the following 
table : 
Arc 
length 
n„ 
Weight lost, 
Wp - w 
nip - w 
nip 
- mp 
tip {nip - rapY 
I } 
! } 
4 1 
'] 
2 
3 
2 
2 
4 
25- 311 
26- 04J 
20-04^ 
26-77 
26-95 
26-831 
28-30J 
28-93 
2915J 
34-00' 
34-28 
34- 89 
35- 11 
I 
\ 
1 
25- 08 
26- 59 
27- 57 
29-04 
34-57 
25- 68 
26- 46 
27- 68 
30-73 
34-46 
- 4-801 
- 4-07 
- 4-07= 
- 3-34 
- 3-16 
- 3-281 
- 1-81J 
- 1-181 
- -96 J 
+ 3-89' 
+ 4-17 
+ 4-78 
+ 5-00, 
1 
■ 
- 4-43 
- 3-52 
- 9.p;4 
- 1-07 
+ 4-46 
+ 
+ 
+ 
-02 
•13 
•11 
1-69 
•11 
•0008 
•0507 
•0242 
5-7122 
•0484 
! } 
2 
33-981 
35-OOJ 
\ 
34-49 
34-61 
+ 3-871 
+ 4-89 J 
\ 
+ 4-38 
•12 
•0288 
Totals 
15 
451-58 
Sum of squares 
= 212-92 
S{np {mp-wf\ 
= 209-51 
5-8651 
= 8{[np{mp-mpY-\ 
w = 30-11 
<tJ = 14-1947 
22 = 13-9673 
•2274 
= 25^72 
n' = n + 1 = 
6 + 1 = 
V, . 
•. P = 
0003 
= -9839 
Thus only three times in 10,000 trials if the inscribed curve actually represented 
the phenomenon would a series of observations so widely divergent as those 
observed arise. In other words the inscribed curve must be definitely rejected 
as a probable description of the series of phenomena. Now the great advantage 
of this "goodness of fit" method is that by the very working of it out the actual 
regions at which the theoretical results diverge with a maximum of improbability 
from the observations are indicated, and the investigator is able to say here are the 
points where discordance is greatest and where theory or observation needs modi- 
fication. Clearly in this case the whole burden of the discordance falls on the 
observations at arc length 4. The special examples selected are of no real import- 
ance ; the author probably laid no stress on his inscribed curves, and a little better 
draughtsmanship might have bettered them to some extent. They are used simply 
to illustrate that a new instrument is ready to the hand of the physicist. He must 
have felt very desirous at times in the past of being certain how far his observations 
were in accord with theory. How many times must he not have put to himself the 
