320 
LORD RAYLEIGH AND MRS. H. SIDGWICK ON THE ABSOLUTE 
quote in detail the results of one day’s observations. On October 19, with a certain 
loading of the interrupter-fork, the cycle of the pendulum occupied about 78 seconds, 
and the beats were at the rate of about six per minute. The interrupter was then 
sharpened , after which several observations were taken of the duration of live cycles 
of the pendulum, and of 16 beats between the forks. For the former the times 
found were 210, 210, 212 seconds; for the latter by simultaneous observation 58, 
58, 59, 59, 59, 60, 60 seconds. The temperature, as given by the thermometer, 
ranged from 17°'2 to 17°’4. After the sharpening of the interrupter, the frequency 
both of the wheel and of the auxiliary fork was increased, so that the sign of 16a in 
the expression written above is determined to be + and that of h to be —. Using 
the mean values we find 
whence 
16a=-3797, h= -2712 
128 + 16« —&=128’108 
To this we must add '009, making altogether 128‘117, to allow for the gaining 
rate of the clock, which was 6^ seconds per diem. This corresponds to a mean 
temperature 17 0, 3. 
The procedure adopted was quite good enough for our purpose; but if it were 
desired to push the power of the method to its limit, the work should be undertaken 
at an astronomical observatory, and extended over the whole time required to rate the 
clock by observations of the stars. In this way the comparison of the period of 
vibration of the standard fork with the mean solar second could be effected with the 
same degree of accuracy as that to which the former quantity is capable of defini¬ 
tion. Without this precaution we cannot be quite sure that the rate of the clock 
at the time of the observations is identical with the mean rate employed in the 
calculation. It is scarcely necessary to say that the uncertainty which arises under 
this head is common to every method by which absolute pitch could be determined. 
The results obtained, including those recorded previously," are given in the accom¬ 
panying table. They are well represented by the formula 
128T40 X {1—(£ —16)°X ‘00011}, 
in which the temperature coefficient used ( - 00011) is that found by M‘Leod and 
Clarke.1' The numbers in the fourth column are calculated from the formula. 
* 
* Proc. Roy. Soc., May, 1881, p. 138. 
f Phil. Trans., Part I., 1880. 
