the Determination of the Mean Density of the Earth. 221 
From this, in connection with the time of vibration of the 
unloaded pendulum, we get the magnitude gMs, which forms 
the denominator in the Gepecesion for the angle of deflection, 
tan d= ae ‘ 
where g’ is the attraction of the ALGHa mass, m the mass 
of the pendulum-bob, / the distance of its centre from the 
knife-edge. Closer consideration shows that the use of this 
method is even allowable if a correction is made for the buoy- 
ancy of the air, Bessel’s correction for the moment of inertia, 
and for a possible blunting of the knife-edge ; for the form of 
the equation does not alter, and only the ‘magnitudes gMs 
and MK? acquire a different ‘signification, 
As an example of the determination I may here give the 
results of two series of observations. In the first the duration 
of the free oscillation was :— 
T, = 59-20 
lixtra weight 1 gr. . . T, = 22:00 
” De Olea T; = 10°46 
9 ” 10 PO ac ara Tro ==) (46 
Expressed in grammes and millimetres, we have for gMs the 
values 
SELIG: we Sle 2b S189: 
In the second series the time of the free oscillation was:— 
T, = 145-20 
Hxtra weight 1 gr. . . T, = 23°64 
» OL Ot ab etre ley =o 13766 
ABM theron ol We eas a 
and for gMs, ‘ 
13°75, 18°50, 13°50. 
The concordance between these numbers, which are inde- 
pendent of each other, is also somewhat limited by the error 
of the extra weight, the amount of which was not known. 
The experiments show, however, with certainty that the value 
of the reduction may be determined with great accuracy with 
an apparatus of convenient construction. 
Besides the calculation of the gravitation of the pendulum- 
bob towards the attracting masses which is common to all 
methods, two measurements are necessary—the distance of 
the extra weight, and of the centre of the pendulum-bobs 
from the knife- edge. These measurements, however, require 
no other appliances than those which are in use with the 
reversion-pendulum. 
