THE NEW NATIONAL STANDAED OF LENGTH, AND ITS PEINCIPAL COPIES. G73 
Table (continued). 
Excess above Bronze 7. 
Name of Bar. 
Observer. 
Position of 
Bronze 7. 
Excess 
when 
Bronze 7 
is outside. 
Excess 
when 
Bronze 7 
is inside. 
Number of 
observa- 
tions. 
Probable 
Error of 
Mean. 
Symbol for Excess, 
independent of posi- 
tion but dependent 
on observer. 
Bronze 10 <( 
Sheepshanks 
Henderson < 
Dunkin < 
W. Simms, jun. ... 
Outside. 
Inside. 
Outside. 
Inside. 
Outside. 
Inside. 
Outside. 
Inside. 
d. 
— 2-711 
— 1-210 
-2-390 
— 0-350 
d. 
— 2-142 
— 1-360 
— 1-630 
— 1-530 
28 
24 
10 
10 
10 
10 
4 
4 
d. 
0-1008 
0-0973 
0-1454 
0-1744 
0-1653 
0-2988 
0-0506 
0-1728 
' 
■ 
’ ^2 ^44 
’ ^48 
’ ^50 
' ^10 ^46 
It must be remarked that the “ probable error ” in the Table is the probable chance- 
error in the mean of observations of the bar under given circumstances, derived in the 
usual way from the discordances of the observations under those circumstances, and not 
applying in any degree to a constant error of the observer or a constant error depending 
on position. 
The results were now treated in the following way : — 
From examination of Mr. Sheepshanks’s probable errors, it appeared that tlie probable 
error of a single “ observation ” by Mr. Sheepshanks is about 0‘^’55. This quantity will 
be called E. 
On comparing the probable errors of the other observers with those of Mr. Sheep- 
shanks, it appeared that theii’ proportions are nearly as follows : — 
Hendeeson 
Sheepshanks : 
9 : 8 
Dunkin 
Sheepshanks : 
I : I 
Simms 
Sheepshanks : 
3 : 4 
W, Simms, jun. 
Sheepshanks : 
5 : 8 
De la Eue 
Sheepshanks : 
G : 7 
It appeared from these that no sensible error would be committed by assuming the 
observations of all the observers to be equally good, except those of W. Simms, jun., one 
of whose observations is equivalent to two of any other observer, (This estimate agrees 
entirely with the high opinion of Mr. W. Simms’s accuracy which Mr. Sheepshanks had 
often expressed to me long before this time.) In other words, the probable error of one 
E 
of Mr. W. Simms’s observations will be that for any other observer being E. And, 
to make the probable error, of the equation formed for the mean of n observations, 
equal to E, the equation must be multiplied, for observers in general, by \/n : but for 
Mr. AY, Simms, jun. it must be multiplied hy s/'lii. 
Now let ^2 be Mr. vSheepshanks’s value of the excess of Bronze 10 above Bronze 28; 
y the increase in this value produced by the circumstance of Bronze 28 being Outside 
