328 
MR. AIRY’S ACCOUNT OF THE HARTON EXPERIMENT 
60, 63, 64, 63, 15. Combining the separate results by these weights, we obtain 
the following mean results : — 
First Series. 
Log. Rate of Pendulum 8 below upon Pendulum 1821 above 
= 9-99928536. 
Second Series. 
Log. Rate of Pendulum 1821 below upon Pendulum 8 above 
=0-00073691. 
Third Series. 
Log. Rate of Pendulum 8 below upon Pendulum 1821 above 
= 9-99928584. 
Fourth Series. 
Log. Rate of Pendulum 1821 below upon Pendulum 8 above 
=0-00073715. 
43. For ascertaining the probable error e I have used the following process. 
Let Eo, El, Eg, &c., as before, be the actual errors of comparison, estimated by the 
effect which they produce on a 4-hours’ rate, in the 8 th decimal place of logarithms ; 
let Ri, Rg, &c. be the successive individual results for the rate of the lower pendulum 
on the upper pendulum ; and let A be the adopted value of that rate. Now if A 
were rigorously correct, we should have the following equations : — 
Eo= Eo 
Ei = Eo+Ri — A=E o-|- R] — A 
Eg=Ei-)-Rg — A=Eo-l-(Ri-|-Rg) — 2 A 
E3=Eg-)-R3 — A=Eo-l“(R, -I-R 2 -I-R 3 ) — 3 A 
&c. 
and, adding all for the First Series, which terminates with Rge and Ege, 
26‘25 
Eo+Ei-)- &c. -l-Eg6=27Eo-l-26Ri-l-25Rg-l- &c. -I-R 26 2 
Eo is yet undetermined. Now the Theory of Probabilities which we have used 
requires that the chances of positive and negative errors be equal, and therefore that 
(subject to the irregularities of chance) Eo+Ei-p &c. +E 2 e= 0 . This gives 
ofi-qpi 1 
Eo= 2-27 ^ ^ (26Ri+25Rg-l- &c. 4 -R 26 ) ; 
and, substituting this for Ej in the different expressions above, Ej, Eg, &c. will be 
