14.— ACCELERATION OF GRAVITY AT JOHANNESBURG. 



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



[Abstract.] 



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

 measured anywhere on the South African table land. 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 the use 

 of students, of the usual Borda's pattern, and 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 telephonically by 

 comparison with the Observatory standard clock. The dimensions of 

 the pendulum were as follows : — 



Ball diameter 7.783 cm. Mass 1730 gms. 



Nut at top of Ball, thickness 0.238 cm. 



Wire (Pianoforte steel), mass o.oii gm. per cm. 



Knife edge attachment, mass 53 gms. (radius of gyration 



about knife edge)^i3. 

 centre of inertia 2.1 cms. 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 248 mm. long, with rounded ends, 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 few millimetres 

 longer than the length of a whole number of the steel bars. The 

 beam was then laid horizontally, 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 instruments as a pair of 

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

 to be the uncertainty as to whether the centre of inertia of 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 cm. I 104.07 cm. 



To observe the time of vibration the chronometer, illuminated by an 

 incandescent lamp, was placed on a table in front of the pendulum, 



