hi Reply to a Paper in the Quarterly Journal. 
ber of vibrations made in a mean solar day, to the nearest thou-^ 
sandtli of a vibration ; and this is all that I contend for. But 
not to rest the cause upon mere urifounded assertions, as Z has 
done, let us see how the facts stand ; and for this purpose, let us 
resume the 5th set of Experiments, marked (E), since it ap- 
pears to be entitled to, at least, as much credit as any one of the 
series, and, I imagine, to more than the first, third and fourth 
sets, because of the great irregularity which is found to obtain 
in the decrease of the arcs of vibration in geometrical progres- 
sion ; so much so, that I should not hesitate to reject them as 
defective, and insufficient for the purpose for which they were 
intended. Then the great weight being below, we shall find, 
by the appropriate formula given in my last paper, the follow- 
ing corrections for the circular arcs of vibration, viz. 2,1648 ; 
1,7534 ; 1,4156 ; and 1, 1273 : which being added to the cor- 
responding number of vibrations made in 24 hours, less 0'^,18 ; 
and the mean of the whole being taken, there will result 
86058,7703, the number of vibrations performed by the pendu- 
lum of experiment in the same time. Captain Kater makes it 
only 86058,76, which is not true even to the nearest Imndredih 
of a vibration. And as the clock gains 0"5l8 on m_ean solar 
time, it follows, that the pendulum of experiment will perform 
86058,9503 vibrations in a mean solar day. The distance be- 
tween the knife edges being 395 44085 inches at the temperature of 
62®, and the mean expansion in parts of this distance, due to a 
change of temperature of one degree of Fahrenheit’s thermo- 
meter, being equal to its 0,000009959th part, the distance be- 
tween the knife edges at the temperature of 69^,3 will be found 
= 39,443717 inches, the length of the experimental pendulum 
in air, at the altitude of 83 feet above the level of the sea. 
To find the length of the seconds pendulum we have the fol- 
lowing proportion : 
inch. inch. 
864002 : 8,6058,95032 : : 39,443717 : 39,132935, the length 
of the seconds pendulum in air ; add to this 0,00542 the cor- 
rection due to the buoyancy of the atmosphere, and we shall 
inch. 
have 39,138355, the length of the seconds pendulum in vacuo, 
at 83 feet above the level of the sea. 
