﻿480 Acceleration of Gravity at Johannesburg . 



the ball coincides with its centre of figure, two lengths of 

 wire were used — one about equal to seven rods, the other 

 to four. The length from knife-edge to centre of ball was 

 obtained as described, and the length of the equivalent simple 

 pendulum calculated by means of the centre of inertia and 

 moment of inertia of the whole system. The results were : — 



179-19 cms. | 104-07 cms. 



To observe the time of vibration the chronometer, illu- 

 minated by an incandescent lamp, was placed on a table in 

 front of the pendulum, a small mirror fixed to the wall 

 behind it, and a telescope arranged to observe the seconds 

 hand of the chronometer reflected in the mirror. The pen- 

 dulum wire (slightly out of focus, of course) swung in front 

 of the mirror and could therefore be seen along with the 

 chronometer. A set of five thousand complete oscillations 

 was observed, the time being noted for every hundredth up 

 to 2000 and every five hundredth from there onwards. The 

 period for the first two thousand and for the whole set was 

 calculated in the usual manner (0 to 2500, 500 to 3000 &c.) 

 and corrected for amplitude. 



Semiamplitude at start ... 8 cms. 5 J cms. 



„ finish -... 3 cms. 2^ cms. 



Temperature 10° to 18° 7° to 13° 



Chronometer loses 1 in 18,000. 



Corrected period 2'68845 | 2-0490 



17Q.1 Q 



a — A-.2 *-<* ^ _ 078.74 

 ^" 47r 2-68845 2_ J ' b ' 



. n 104-07 07Q _ 

 = ^ 2^049(F = ° 78 ° 9 ' 



The ^difference between these numbers may be accidental or 

 mayjbe due to an error in the position of the centre of inertia 

 of the ball. I think it is due to the former cause chiefly, 

 and as the measurements cannot claim an accuracy beyond 

 the^first place of decimals I take the result to be 



978-7. 



The latitude of the physical laboratory is 26° 11 / south, 

 and its altitude 1753 metres. Helmert's formula 



g = 980-62-2-6 cos 20- ^ 



gives 978-50. For a tableland theory would give a cor- 

 rection for altitude only J as great: it is usually stated 



