A PENDULUM FOR THE REDUCTION TO A VACUUM. 
459 
CC 
displaced by the body ; then p + P will express its weight in vacuo, and 
p p % 
“ will be the ratio of gravity in the two cases : whence we obtain 
1= a X 
P + P 
“ This formula would give correctly the length of the pendulum, if the body 
“ in moving did not drag with it a certain quantity of the same fluid, which 
“ varies very little by the difference of velocity : so that the mass, when in 
“ motion, consists not only of the mass of the body itself, but also of the fluid 
“ dragged with it He then proceeds to show (page 229) that “ if n be any 
“ constant number such that n P expresses in all cases the weight of the fluid 
“ displaced and also that of the dragged fluid, the mass, when in motion (or its 
“ weight in vacuo) is no longer p + P, but is represented by p + n P ; whilst 
“ its weight in water is always expressed by p. The correct formula therefore 
“ will be 
l — a X — /— r, 
p + n 
“ whence we deduce 
M. Du Buat then gives the result of 44 experiments made by swinging pen- 
dulums formed of spheres of lead, glass and wood, of different weights, and sus- 
pended by lines of different lengths : and the conclusion at which he arrives 
is, that the value of n (which, in his experiments, varies, with only 4 slight ex- 
ceptions, from T67 to 1*45) may be assumed equal to T585 f. This certainly 
agrees with the fact much more nearly than might be expected from the rough 
manner in which those enquiries were conducted, as compared with more 
modern experiments. And, although it cannot be placed in competition with 
the more rigid investigations of M. Bessel, or the results detailed in this 
paper, yet it evinces the great talent and zeal of the author in being able to 
extract so near an approximation from such a mode of procedure. M. Du 
Buat then gives the result also of a vast variety of similar experiments on 
cylinders, prisms, cubes, &c. : and found in each of them a complete confirma- 
tion of his opinion relative to the dragging of the fluid in which the vibrations 
f Ibid, page 257. 
* Edition 1816, vol. ii. page 226. 
