1826.] of the Length of the Peridulum at the Equator. 347 



specific gravity of the pendulum formerly found, the thermo- 

 meter having been 88° and the barometer 30*064, was 8*1085 ; 

 the difference, therefore, is not very considerable ; but 1 shall of 

 course use the Mint specific gravity in the following computa- 

 tions, and also by it re-calculate the correction for the buoyancy 

 of the atmosphere, applied to the experiments for finding the 

 length of the pendulum at Madras. 



The weight of water to that of air at 53° of the thermome- 

 ter, and 29*27 inches of the barometer, is as 836 to 1, the expan- 

 sion of air for each degreeof the thermometer being -5-1^ of its bulk. 

 The specific gravity of the pendulum at that height of the thermo- 

 meter and barometer will, therefore, be 7*5414. 



Corrections for the Buoyancy of the Atmosphere, 

 First set (L). 



Therm. Barom. Vibrations in 24 hours. 



88*63 30*151 86158*674 



53*0 29*270 



35*63 



Then 1*7417 x 35*63 = 62*0568 



30-151 : 836 :: 29*270: 811*5724 



873-6292 

 836 : 7*5414 :: 873*6292 : 7*8808 specific gravity. And 

 873-6292 x 7*8808 = 6884*8970 the pendulum heavier than air. 



Square of the number of vibrations 86158*674 = 7423317105, 

 4383 divided by 6884-8970 - 1078203*073 x the square of the 

 number of vibrations in 24 hours, and the square root of the 

 same, gives the number of vibrations in 24 hours, corrected for 

 the buoyancy of the atmosphere = 86164*931 or + 6*257 vibra^- 

 tions for the correction. 



In like manner, the corrections for the buoyancy of the atmo- 

 sphere were found for the other sets (L), and are for the second 

 set + 6*254; for the third + 6*333; and for the fourth + 

 6*269. 



The corrected number of vibrations in 24 hours will, therefore, 

 be; first set 86164*931 ; second 86165*966; third 86167-111 ; 

 fourth 86167*233. 



Following the same process with the results (R), we shall 

 have the correction on account of the buoyancy of the atmo- 

 sphere for the first set 6*2892 ; for the second 6*2685; for the 

 third 6*3486 ; and for the fourth 6*2759. 



And the corrected number of vibrations ; first set 86165-0772; 

 second 86165*9115; third 86167*3836; and the fourth 

 86167*3659. 



It now only remains to ascertain and apply the correction for 

 the height of the pendulum above the level of the sea. The 



