SIE B. C. BEODIE ON THE ACTION OF ELECTEICITY ON OASES. 
89 
In order to form a just estimate of the value to be attached to these experiments, which 
exhibit considerable divergences from the mean, I have calculated the probable error of 
the result, as in the Tables given in my previous paper, by the method of least squares. 
The data for the calculation are given below. 
v Y ~ Y ' 
Differences from 
the mean. 
Squares of 
the differences. 
1*44 
-•46 
•2116 
2-00 
+ •1 
•01 
1-55 
— ‘35 
•1225 
2-08 
+ •18 
•0324 
2-35 
+ •45 
•2025 
2-14 
+ •24 
•0576 
1-95 
+ •05 
•0025 
1-79 
+ •11 
•0121 
2-08 
+ •18 
•0324 
2-07 
+ •17 
•0289 
1-50 
-•4 
•16 
1-86 
-•04 
•0016 
Mean = 1*90 
Sum = *874 1 
The number of these experiments is 12. 
The probable error of the result = 0 , 6745 a / - 41 
r V 12x11 
= - 054 cub. centim. 
and also 
the probable error of a single experiment =\/l2 x '054 
= T9 cub. centim. 
It appears, therefore, from these experiments that it is an equal chance that the true 
y_V 
value of the ratio — fjt- 1 lies between the limits T95 and T85 ; also, from the calculated 
value of the probable error of a single experiment T9, half the values of this ratio given 
in the preceding Table might theoretically be expected to be found within the limits 
2‘09 and T71. Of the twelve experiments, seven experiments are within these limits, 
and five experiments outside these limits. 
As might be expected from the comparatively rough method of experimentation and 
the small quantities of gas operated upon, the probable error in these experiments is 
much greater than in the case of the similar experiments made with the electrized oxygen, 
where, in the case of a set of seventeen such experiments, the probable error amounted 
only to '017 cub. centim. In the case of those experiments the limits of probable error 
were 2 and 2'04, which agree with theory; whereas in the case of the present experi- 
ments the theoretical value 2 is not contained within the limits of probable error, and 
indeed lies considerably outside those limits. These experiments, therefore, are not in 
themselves adequate to sustain this theory, and we should not be justified in basing it 
upon them ; but the theory has been conclusively demonstrated by perfectly independent 
mdccclxxiv. s 
