330 
MR. AIRY’S ACCOUNT OF THE BARTON EXPERIMENT 
In Series 1, e=+ 420. 
In Series 2, e=+ 135. 
In Series 3 , e=+ 203. 
In Series 4, e=+ 173. 
And hence the probable errors and weights of the mean results are 
93 
For First Series, probable error =+ 10*4, weight = p^^^* 
899 
For Second Series, probable error =+ 3*3, weight = Jq^^* 
82 
For Third Series, probable error =+ ITO, weight = Ibbbb' 
114 
For Fourth Series, probable error =+ 9*4, weight = Yobbo' 
45. Combining the results of the First and Third Series, with the weights just 
found, and still adopting as unit, in the probable error, the unity of the 8th decimal 
of logarithms. 
Log. Rate of Pendulum 8 below upon Pendulum 1821 above 
=:9*99928558 + 7'5. 
Combining the results of the Second and Fourth Series, 
Log. Rate of Pendulum 1821 below upon Pendulum 8 above 
= 0*00073694 + 3*1. 
And, remarking that Log. below these logarithms, we have finally 
Gravity above 
Gravity below 
Gravity above 
Gravity below 
Log. gS^|^=0-00002252±8.2. 
or — ^-i =1*00005185+0*00000019: 
Gravity above — 
or we may otherwise express it. 
Gravity below is greater than Gravity above by pboye uncertainty of 
5 ^ part of the excess. 
The acceleration of a seconds’ pendulum below is 2®*24 per day, with an uncertainty 
of less than 0®*01. 
46. But it is to be remarked that this estimate of the amount of uncertainty is 
obtained from the amount of uncertainty in each mean as deduced separately from 
the discordances of the individual results in the group contributing to that mean. In 
comparing the means, we shall see reason to suppose that the ultimate uncertainty is 
greater. Thus, though the probable errors of the means of Series 1 and 3 are 10*4 
and iro, tlie dilference of the means is 48: though the probable errors of the means 
of Series 2 and 4 are 3*3 and 9*4, the difference of the mean is 24. It is likely there- 
fore that some cause of irregularity has occurred, special to each series. The most 
