of the Acceleration of Gravity for Tokio) Japan. 299 

 the velocity at the middle of its path was 



— ~ — , or 15*7 centimetres per second ; 



hence the pull on the wire, which at the end of the swing was 

 equal to the weight of the wire, or 2352*2 grammes, was in- 

 creased by 



2352-2 x (15-7) 2 

 939x979-7 grammeS 



at the middle of the swing. But this is less than a gramme, 

 so that no practical extension of the wire arose from centri- 

 fugal force. 



3. Shortening of the length of the wire, due to its curvature, 1 

 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 excessively 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 vibrations in the wire itself. 



We may therefore assume that our 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. 



Calculation of g. 



The complete formula is, of course, 



:==7r \/ 



2Qr 2 ) 

 I ^ mg 



I being the distance from the axis of rotation to the centre of 

 gravity of the pendulum. 



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 098 (gramme, centimetre), and the 

 distance of its centre of gravity from the axis of rotation 0*33 



