A PENDULUM FOR THE REDUCTION TO A VACUUM. 
473 
venient intervals for the coincidences. The daily rate of the pendulum clock 
has always been kept very low, for very obvious reasons : it has, in no case, 
exceeded 0 s ,80 in a day *. 
Let t denote the total interval of time, expressed in seconds, employed in 
any given series, as shown by the pendulum clock, making (86400 + r) vibra¬ 
tions in a mean solar day; r being the daily rate of the clock, which will be 
minus when losing: and let n denote the number of coincidences (always in¬ 
cluding the first) that have taken place during that interval. Then will 
be the time of the mean interval of the coincidences, expressed in seconds of 
the clock, which I shall denote by rn : and the number of vibrations (N) made 
by the pendulum of experiment, in a mean solar day, will be 
N = ^ (86400 + r) = 86400 + r ( 1 ± -) 
where the upper sign is to be taken when the pendulum of experiment goes 
faster than the clock ; and the lower sign when it goes slower. All the pen¬ 
dulums enumerated in this paper, from No. 1 to No. 20 inclusive, go faster 
than the clock, and consequently the upper sign must be used in the compu¬ 
tations. All the bar pendulums from No. 25 to No. 34, and the pendulums 
No. 40 and 41, go slower than the clock ; and therefore the lower sign must 
be adopted in those cases. In all my reductions, however, I have made N 
equal to —=— 86400 only; and have afterwards applied r ( 1 ± ~ ) as a sepa¬ 
rate correction for the rate of the clock. For the long cylindrical rod (No. 21 ) 
a special computation was made : and in the case of the cylindrical tube (No. 
35—38) the pendulum clock was adjusted so as to make 90000 vibrations in a 
day : and the correction for the variation from that rate, applied afterwards. 
In noting the coincidences I adopt the plan suggested by Professors Airy 
and Whewell, and always observe the first and last disappearance and the 
first and last reappearance of the luminous disc : the mean of the four is the 
* A sudden change may sometimes be noticed between some of the series of observations : but this 
has occurred when the pendulum of experiment has been changed, and when it was necessary to stop 
the clock, in order to alter the luminous disc. In some cases where the variation in the daily rate has 
been an appreciable quantity, I have proportioned it, in the different experiments during the day, 
according to the intervals. 
