296 Messrs. Ayrton and Perry on the Determination 



wire. As it was impossible to do this satisfactorily with the 

 wire hanging up, it was taken clown without disconnecting 

 either the knife-edge carrying it or the ball at the other end. 

 The knife-edge was then fixed at one end of a horizontal rail, 

 and the other end of the wire close to the ball hung over a 

 wheel with very little friction. By this arrangement the wire 

 in a horizontal position was, of course, stretched as much as it 

 was in the vertical position, as far as the effect of the weight 

 of the ball was concerned. A correction had, however, to be 

 made for the weight of the wire itself, which of course caused 

 the tension to be a little less at the bottom than at the top 

 when the pendulum was hanging up vertically. A few cen- 

 timetres of similar fine steel wire being weighed, a simple inte- 

 gration gave the small additional weight necessary to be added. 

 This being done, the final result obtained was that the length 

 of the pendulum equalled 939*09 centimetres at 0° C; and the 

 consequent value of g in air for Tokio, Japan, calculated from 

 the result of about eighty thousand vibrations of the long pen- 

 dulum, would be 980*06 centimetres per second per second, 

 if the pendulum could be regarded as a simple mathematical 

 pendulum. 



Correcting Factors. 



1. The two most obvious corrections to apply to this result 

 are the corrections for infinitely small arcs and for the air- 

 friction — neither of which were found of any practical conse- 

 quence, on account of the very small angle through which the 

 pendulum usually swung, and that the decrement of the am- 

 plitude of the vibrations was imperceptible even after many 

 swings. Although, however, such a pendulum as we were 

 using approaches very nearly a perfect simple pendulum, there 

 are certain causes of possible error arising from its flexibility 

 and slight elasticity which would not affect a rigid compound 

 pendulum. To estimate the practical effect of these possible 

 errors, it is necessary to solve generally the complete problem 

 of a heavy ball supported by an elastic wire, one end of which 

 is soldered to the ball and the other end to a steel knife-edge. 

 When a suspended 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 



