IN THE OBSERVATORY OF GREENWICH. 
469 
Examining these observations, we have 
I. 
II. 
III. 
IV. 
V. 
Arcs 
1.31 to 1.12 
0.40 to 6.33 
6.33 to 6.30 
1.36 to 1.1 7 
Vibrations .... 
86065.17 
86066.09 
86068.53 
86068.92 
86066.10 
Correction for the arcs' 
by the formula . . . j 
+ 3.13 
+ 2-42 
+ 0.22 
+ 0.16 
+ 2.73 
Numbers which should* 
agree if the correc- 
tions computed by 
the formula were 
just compensations 
> 86068.30 
86068.51 
86068.75 
86069.08 
86068.83 
In both these series of experiments the same indication is afforded, viz. that 
the retardation of the vibration is greater in large arcs than is covered by the 
correction computed by the formula. The difference, however, between the 
results in large arcs and in small arcs, with the computed corrections applied, 
is much less than takes place when the pendulum is vibrated with the weight 
above. With the weight below, the computed corrections being multiplied by 
1.13, the results are rendered accordant with each other on both days of ex- 
periment, and the vibrations become as follows : — 
January 31st, large arcs, Exp. II. 86080.99 ; small arcs, Exp. I. & III. 86081.00. 
April 28th, large arcs, Exp. I. II. & V. 86068.92; small arcs, Exp. III. & IV. 86068.94. 
The alteration produced by the employment of this multiplier, in the final 
deduction of the rate of the pendulum from the experiments to be subsequently 
narrated, is an addition of 0.12 vibration per diem to the number of vibrations 
which would otherwise have been derived. I should have been glad to have 
employed a greater number of observations in the more assured determination 
of this multiplier, but circumstances did not permit me to pursue the inquiry 
further ; and I have only now to refer to the consistency and concurrent indi- 
cation of those results that were obtained, as an evidence that the multiplier 
derived from them is in all probability very near the truth. I may also notice, 
that a change of one unit in the second figure of decimals of this multiplier, 
would produce an alteration of something less than one hundredth of a second 
per diem in the rate of the pendulum, derived from the experiments which form 
the subject of this paper. 
It was my intention to have investigated experimentally the cause of the re- 
tardation being greater in large arcs than accords with the formula of reduction 
