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LII. Acceleration of Gravity at Johannesburg. 

 By Prof. R. A. Lehfeldt, D.Sc* 



THE value of gravity has not, so far as I am aware, been 

 measured anywhere on the South-African tableland. 

 On taking charge of the physical laboratory at Johannesburg 

 I thought it desirable to make a provisional determination 

 with such means as were at hand. There was a pendulum, 

 intended for student's use, of the usual (Borda's) pattern ; 

 the only standard of length available was the scale and 

 vernier of a cathetometer (by Pye, of Cambridge), the scale 

 being engraved on the steel upright of the instrument. For 

 time measurements there was a chronometer, which, by the 

 kindness of Mr. Innes, Director of the Government Meteoro- 

 logical Observatory, Johannesburg, could be rated tele- 

 phonically by comparison with the observatory standard 

 clock. 



The dimensions of the pendulum were as follows : — 



Ball: diameter 7*783 cms., mass 1730 gms. 



Nut at top of ball : thickness 0238 cm. 



Wire (pianoforte steel) : mass O'Oll gm. per cm. 



Knife-edge attachment : mass 53 gms. (radius of gyra- 

 tion about knife-edge) 2 = 13, centre of inertia 2'1 ems. 

 below knife-edge. 



The laboratory possessed a steel beam, two metres long, 

 forming part of an optical bench. In this a V groove was cut, 

 and a set of eight steel bars, each about 248 mms. loiw with 

 rounded ends, were made to slide in the groove. The beam 

 was mounted vertically alongside the pendulum, and a set- 

 square used to mark the position of (a) the top of the nut on 

 the ball, (b) the plane (of glass) on which the knife-edge 

 works. These levels were marked by scratches on paper 

 pasted across the steel beam ; the length of the suspending 

 wire was so chosen that the distance between the scratches 

 was a £ew T millimetres longer than the length of a whole 

 number of the steel bars. The beam was then laid hori- 

 zontally, the bars placed in the groove, and the short lengths 

 over at the ends measured by a travelling microscope. The 

 lengths of the bars themselves were measured by the scale 

 and vernier of the cathetometer, using the instrument as a 

 pair of calipers. 



Since the chief error of Borda's pendulum is usually taken 

 to he the uncertainty as to whether the centre of inertia of 



* Communicated by the Author. Read before the South African 

 Association for the Advancement of Science at Kmibeiiev, 1906. 



