A PENDULUM FOR THE REDUCTION TO A VACUUM. 
407 
tied medium, nearly approaching to a vacuum. Let N' denote the number of 
vibrations made by a pendulum in a mean solar day (corrected in the usual 
manner for the rate of the clock, the arc of vibration and the temperature of 
the room, but not for the height of the barometer ), /3' the height of the baro- 
meter, and / the height of the thermometer when the pendulum is swung un- 
der the full pressure of the atmosphere : and let N", (3", t" denote respectively 
the same quantities, when it is swung in a highly rarefied medium. Then will 
N" — N' . . 
0 , -—r express the true correction for one inch pressure of the atmosphere 
at the temperature t° ; where f = ^ {£ -f- f) : which, being multiplied by 
1 + *0023 ( f — 32°), will give the true constant 
N" — N' r 1 
c = -jrzrjr X [l + -0023 (t° - 32°)] (6) 
for the same pressure, and at the freezing point : whence we obtain the fol- 
lowing expression for the true correction, at any pressure (3 , and at any tem- 
perature t : viz. 
^ X 1 +-0023 (t — 32°) 0) 
agreeably to which formula I have deduced the value of C' in the experiments 
about to be detailed. 
Now, the value of C' is always greater than C : and, in order to determine 
the factor by which C must be multiplied in order to produce the true correc- 
tion, (which factor will vary according to the form and construction of the pen- 
dulum,) we must make C' = n C : whence we obtain, for the factor required, 
n = § ( 8 ) 
and it is in this manner that the value of the factor (n) has been deduced in 
the following experiments. And it may be proper to state that the quantity 
which is here denoted by n, M. Bessel expresses by (1 + ft). 
Description of the Pendulums. 
The number of pendulums, for which I have deduced the comparative re- 
sults, by swinging them in a vacuum apparatus, amounts to forty-one * ; vary- 
ing from each other in figure, dimension, weight, specific gravity, length, mode 
* This number has been more than doubled by the experiments hereafter alluded to, made subse- 
quent to the reading of this paper. 
3 g 2 
