A PENDULUM FOR THE REDUCTION TO A VACUUM. 
431 
General view of the preceding Results. 
Having thus given the detail of the several experiments, I shall bring the 
mean results of the whole into one general view, in the following Table: where 
I shall first give the value of the old correction, for the reduction to a vacuum, 
for each pendulum, on the assumption that the barometer stands at 30 inches, 
that the thermometer is at 32°, and that the number of vibrations in a mean 
solar day is in each case exactly 86400 ; then the value of n, or the factor by 
which such correction must be multiplied in order to obtain the new cor- 
rection ; which new correction, as deduced from the preceding experiments, 
is given in the next column. To which I have added, in the last column, the 
weight of air adhering to and dragged by the pendulum in consequence of the 
air put in motion thereby, when vibrating in the mean state of the atmosphere 
above mentioned : or rather the quantity of air which, if applied to the centre 
of gyration of the pendulum, would produce the retardation shown by the 
experiment. This view of the subject was suggested by Professor Airy ; who, 
at the same time, favoured me with the following investigation and formula 
for the computation of the weight of adhesive air required. 
“ Let N denote the number of vibrations made by a pendulum, in a mean 
solar day, when swung in air : and let v be the additional number which it 
“ makes when swung in vacuo. Also let w be the weight of the pendulum, 
“ in grains troy ; S its vibrating specific gravity, and <r the specific gravity of 
“ the air. Now, since the force of gravity diminishes in the ratio of (N + v ) 2 
“ to N 2 , or in the ratio nearly of ^1 -f to 1, it follows that when the pen- 
“ dulum vibrates in air, it is as if, retaining the inertia of its weight w, it 
“ had the gravity of only w x v y — w (l — nearly : or, as if it had 
“ lost the weight w x But, the weight which it has really lost from the 
“ displacement of a quantity of air is w X Consequently the portion 
“ which is not accounted for by the mere displacement of the air, is 
( 9 ) 
3 k 2 
