474 CAPTAIN SABINE ON THE LENGTH OF THE SECONDS PENDULUM 
If, now, we take a mean of the results in both positions of the pendulum 
a and b, and in both positions of the slider I. & II., we have 86069.38 vibra- 
tions with the weight above, and 86069.07 vibrations with the weight below, 
corresponding to the slider at 1.6 inch (being the mean between 1.633 and 
1.566) from the middle of the pendulum towards the weight. 
The vibrations with the weight above are in excess 0.31 of a vibration. To 
ascertain the fraction of the tenth of an inch which it would be necessary to 
move the slider in order to produce perfect convertibility, and the effect of 
such change in the position of the slider, upon the vibrations with the weight 
below, we have from the experiments the following data (the letters referring 
as before to the detail of the experiments at the close of the paper). 
Weight above. 
Vibrations. 
Slider at 1.5 E to G 860/0.26 4 making a difference of 1.12 vibration per 
1.566 T to V 86069.61 > diem corresponding to 0.133 inch of the 
1.633 P to S 86069. 14 J slider. 
Weight below. 
Vibrations. 
Slider at 1.5 A to D 86069.00 "} making a difference of 0.10 vibration per 
1.566 W to E E 86069.04 > diem corresponding to 0.133 inch of 
1.633 H to M 86069. 10 J the slider. 
Whence we obtain by proportion 1.637 as the position of the slider which 
renders the pendulum perfectly convertible : and the vibrations, in the posi- 
tion of perfect convertibility, 86069.09 with the weight above, and 86069.10 
with the weight below ; — a result which, it will be seen, is in the closest ac- 
cordance with the experiments H to S, during which the slider was at 1.633. 
Expansion of the Pendulum. 
The rate of the pendulum having thus been found for the temperature of 
5 7°, we have to seek its rate at 62°, being the temperature at which Captain 
Kater referred the distance between the knife edges to Sir George Shuck- 
burgh’s scale. To obtain the alteration of rate corresponding to each degree 
of Fahrenheit from the data furnished by the experiments, we have the rate 
with the weight below, observed on the 31st of January and 1st of February 
