254 TJie Proposed Pendulum Operations for India. . [No/ 4, 



rection* must be determined experimentally. Captain Kater' immersed 

 Lis pendulum in fluids of different temperatures, and measured Avith 

 a micrometric arrangement the alterations in its length. Captain (now 

 General) Sabine observed the change in the number of vibrations 

 made by a pendulum 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 has to 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 in the same proportion. In the very large majority of ob- 

 servations, the correction has been computed on this consideration 

 solely ; but Bessel demonstrated in 1828t 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 t be the standard temperature which is 

 generally taken as Qi a Fahrenheit ; t the observed temperature of the pendulum : 

 /its factor of expansion for 1° Fahrenheit, then correction = J n. f. (t—r). 

 positive when t > t. 



f This circumstance was most c]early pointed out by the Chevalier du Buat 

 in 1786, who made a number of experiments with pendulums formed of different 

 substances, but his researches, which created a great sensation at the time, 

 appeal' 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) 



C X i i Q02 3 7*332°) where ^' is the hei g at of Barometer, and *, the tem- 

 perature during the interval of observation. C is a constant for the same 

 yjKii.dulvim, and is determined from the forraJla 

 _2\T" — jy' 

 C = -/— ^r, [1 + -0023 (t°— 32°)] in which IT is the number of 



vibrations in a mean solar day, j3' and t' the barometer and thermometer read- 

 ings, in air ; and N," fi," t" the same quantities in a highly rarified medium, 

 t° = h («' X t".) 



