






















254 The Proposed Pendulum Operations for India. [No. 4, 
rection* must be determined experimentally. Captain Kater immersed 
his pendulum in fluids of different temperatures, and measured with 
a micrometric arrangement the alterations in its length. Captain (now 
General) Sabine observed the change in the number of vibrations 
made by a penduluin in different temperatures. This is the most 
direct method of obtaining the correction undoubtedly, but everything 
depends on the perfect compensation of the clock pendulum with 
which it is compared. 
Thirdly, the formula is only true for observations in a vacuum, 
and as observations have generally been made in air, or at all events 
only in a partial vacuum, the effect of the air hasto be taken into - 
account. This effect is to diminish the weight of the pendulum by 
the weight of the air displaced, or to diminish the apparent force of 
gravity inthe same proportion. In the very large majority of ob- 
servations, the correction has been computed on this consideration 
solely ; but Bessel demonstrated in 1828+ that this correction was 
insufficient, inasmuch as a portion of the surrounding air was set in 
motion by, and moved with, the pendulum so as to become part of the 
moving mass. The correction for this can only be determined prac- 
tically, as by swinging the pendulum in “ media” of different 
densities. It depends chiefly on the form of the pendulum. As this 
correction, ‘‘ reduction to a vacuum” or “ buoyancy correction” as it is 
* According to Kater’s method—if 7 be the standard temperature which is 
generally taken as 62° Fahrenheit ; ¢ the observed temperature of the pendulum ; 
fits factor of expansion for 1° Fahrenheit, then correction = } n. f. (t—7) 
positive when t > 7. 
+ This circumstance was most clearly pointed out by the Chevalier du Buat 
in 1786, who made a number of experiments with pendnlums formed of different 
substances, but his researches, which created a great sensation at the time, 
appear to have been completely lost sight of, and to have been unknown even 
to Borda, who was conducting his experiments, little more than ten years after 
the publication of Du Buat’s results. 
The true correction for buoyancy Mr, Baily has shown to be (Phil. Trans. 1832) 
B ; ‘ 
C+ i 0023 ($32) where 6 is the height of Barometer, and ¢ the tem- 
perature during the interval of observation. C is a constant for the same 
pendulum and is determined from the formula 
NIN F 
C— [1"+- .0023 (t°—32°) ] in which WN’ is the number of 
p’—p” 
vibrations in a mean solar day, 6’ and ¢’ the barometer and thermometer read- 
ings, in wir; and N,” B,” t’ the same quantities in a highly rarijied medium 
ne = a (t° + ti ) 

