SCIENTIFIC SUMMARY. 
285 
indicated the number of vibrations of the long pendulum in that time. At 
the commencement of the experiment, after the pendulum had been set 
swinging, and the paper was running out at a fairly uniform speed, a mark 
was made on it by tapping sharply the armature up with the finger when a 
chronometer, lying beside the Morse instrument, indicated a certain time ; 
and after an hour or so, the paper being kept running all the time, a second 
mark was sharply made on the paper when the chronometer indicated a 
certain other noted time. So much paper had then run out in the interval 
of time shown by the chronometer ; and the breaks in the line, counted 
carefully afterwards by two independent students, gave the whole number 
of vibrations of the pendulum in that time. The fraction of a vibration 
could also, of course, be ascertained by comparing with the length of the 
first line made after the first break had been produced, on tapping the arma- 
ture, and repeating the same process at the end of the paper. The experi- 
ment is independent of the rate at which the paper runs out, provided, 
of course, it is never allowed to run so slowly that there is any difficulty 
in distinguishing the different breaks electrically made by the long vibrating 
pendulum. The mean temperature of the wire was carefully taken at each 
experiment. 
The next point was to measure accurately the length of the wire. As it 
was impossible to do this satisfactorily with the wire hanging up, it was 
taken down 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 hori- 
zontal 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 centimetres of similar fine steel 
wire being weighed, a simple integration 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, J apan, calculated from the result of 
about eighty thousand vibrations of the long pendulum, 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 was found of any practical consequence, on account of 
the very small angle through which the pendulum usually swung, and that 
the decrement of the amplitude of the vibrations was imperceptible, even 
after many swings. Although, however, such a pendulum as they 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 effect 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 bad and the other end to a steel knife-edge. When a sus- 
