A PENDULUM FOR THE REDUCTION TO A VACUUM. 
471 
Captain Sabine however has preferred trusting to actual experiment for 
this minute correction : and, considering that the result shown by the knife 
edge A is the nearest to the truth, he has rested on the establishment of that 
result, without the requisite corroboration, by an equal number of trials, from 
the other knife edge ; which are, in fact, equally essential to the establishment 
of the accuracy of the whole. Thus, he has swung the pendulum 188 hours 
on the knife edge A, and only 54 hours on the knife edge B. But, had this 
latter knife edge been employed during a longer period, it might probably have 
tended to correct the anomaly that occurs on the face of the observations. 
For, it appears that when the slider was moved about T33 inch, it caused an 
increase of 0T0 vibration in a day, on the knife edge A; whilst it caused a 
decrease of 1T2 vibration on the knife edge B. But, this is contrary to the 
known principles of the pendulum, since the effect of a slider of this sort is to 
cause an alteration of the same kind in each knife edge, differing only in degree : 
the relative proportions of which may he ascertained by determining the di- 
stance of the centre of gravity from each knife edge In the state of the pen- 
dulum in question, when last used by Captain Sabine for the experiments here 
alluded to (the tail pieces being wholly removed), the distance of the centre of 
gravity from the knife edge A, I found by actual measurement, to be 26'23 
£6"23 
inches ; and from the knife edge B, 13‘21 inches. We have therefore = 
1‘985 as the factor by which any alteration in the results of knife edge A must 
be multiplied, in order to show the corresponding alteration produced in the 
knife edge B : which will be both positive, or both negative. And if this is not 
shown by the experiment, we may reasonably suspect some error in the obser- 
13*21 
vations. Also, we have _ 1 g. c , 1 = 1 - 015 as the factor by which the dif- 
ference in the number of vibrations between A and B must be multiplied, to 
obtain the correction that should be applied to A, in order to ascertain the 
number of vibrations that the pendulum would make, if rendered perfectly 
synchronous : and which is the quantity to be used in determining the length 
* The truth of this would have been shown, and the absolute amount easily determined, had Cap- 
tain Sabine moved the slider through a larger space (one or two inches, for instance), so as to have 
produced a decided and powerful effect on the number of vibrations ; sufficient to counterbalance the 
unavoidable errors of observation. 
3 p 2 
