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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 Meteorological 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 0.011 gm. per cm.
Knife edge attachment, mass 53 gms. (radius of gyration

about knife edge)213.
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 knifeedge 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 :

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To observe the time of vibration the chronometer, illuminated by an incandescent lamp, was placed on a table in front of the pendulum, a small mirror fixed to wall behind it, and a telescope arranged to observe the seconds hand of the chronometer reflected in the mirror. The pendulum 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 (o to 2500, 500 to 3000, etc) and corrected for amplitude.

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=

g=4 ?

=4 02104.07

179.19
2.68845 2.04902
978.711

978.59. The difference between numbers may be accidental or may be 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° 1' south, and its altitude 1753 metres. Helmert's formula,

h
g=980.62 – 2.6 cos 20 - gives 978.50.

3300

for a table land theory would give a correction for altitude of only & as great ; it is usually stated that the table land formula is inapplicable owing to displacements in the density of the underlying strata, but this would seem not to be the case with the great South African table land, as the formula

5

h g=980.62 – 2.6 cos 20

gives g=978.70 8

3300

in agreement with the observations. Since there are only two really large table lands in the world-South Africa and Tibetsome geophysical interest attaches to the results, and it is hoped they may be repeated with better apparatus.

SECTION B.

Anthropology, Ethnology, Bacteriology, Botany, Geography, Geology, Mineralogy,

and Zoology

Section B.

CAPT. Thos. QUENTRAL, F.G.S., M.I. Mech. E., was President of

this Section, but did not submit an Official Address for publication.

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