286 
POPULAR SCIENCE REVIEW. 
pended ball is swinging in the arc of a circle, we know that near the end of 
a swing the attachments of the ball have to resist a tendency for the ball to 
turn. For since the ball has been turned in passing from its lowest to its 
highest position, it would continue to turn were it not stopped by the wire 
itself. At the end of every swing, then, there must be a slight kick ; so that 
in fact the ball will make minor swings about its point of attachment all the 
time of the motion. To make this kick less perceptible, we must make the 
fastening of the wire to the ball capable of resisting the tendency of the 
ball to continue its turning motion. If we do this by soldering the wire, a 
smaller kick will result, and will be due to the bending-moment of the wire 
resisting the turning action. If there were no difficulty of construction, it 
might be better to get rid of this kick difficulty by making the bob capable 
of rotating in the plane of swinging about an axis through its centre of 
gravity. 
2. Next, with regard to the stretching of the wire arising from variations 
in the centrifugal force of the ball while swinging. Since the time of a 
complete vibration of their pendulum was nearly 6 seconds and the arc about 
30 centimetres, the velocity of the middle of its path was 15*7 centimetres 
per second ; hence the pull on the wire, which at the end of the swing was 
equal to the weight or the wire, or 2352*2 grammes, was increased by less 
than a gramme, so that no practical extension of the wire arose from cen- 
trifugal force. 
3. Shortening of the length of the wire, due to its curvature, arising from 
the resistance of the air making it concave in the direction of motion. It is 
easy to see that the shortening of the pendulum due to this cause is exces- 
sively small, and is of the same order as the lengthening arising from the 
centrifugal force ; so that these two very small errors may be regarded as 
balancing one another. 
Also, since it may be calculated that the period of transverse vibration of 
the wire is less than one-fortieth of the periodic time of the pendulum, the 
resistance of the air cannot tend to cause amplification of the lateral vibra- 
tions in the wire itself. 
It may, therefore, be assumed that the pendulum vibrated like a rigid 
body, consisting of a ball of brass, a straight steel wire, and a triangular steel 
prism, of which the edge was the fixed axis. 
The steel knife-edge had a length of about 4 centimetres, a breadth of 
about 1 centimetre, and a depth of ^ a centimetre ; hence its weight was 
about 7*8 grammes, its moment of inertia about the axis of rotation 0*98 
(gramme, centimetre), and the distance of its centre of gravity from the axis 
of rotation 0*33 centimetre. The weight of the wire was 11*6 grammes, 
and its length 934*99 centimetres at 0° C. Its moment of inertia was there- 
fore 3*3803 4- 10 6 (gramme, centimetre), and the distance of its centre of 
gravity from the axis of rotation 467*49 centimetres. The weight of the 
brass ball was 2352*2 grammes, its moment of inertia about the axis of 
rotation 2*0744 + 10 9 , and the distance of its centre of gravity 939*09 centi- 
metres at 0° C. Of the whole system, then, the weight was 2371*6 grammes, 
the moment of inertia about the axis of rotation 2*0778 + 10 9 (gramme, 
centimetre), and the distance of its centre of gravity 2*2144 + 10 6 . Con- 
sequently 
