acceleration of the pendulum in different latitudes. 167 
ascertained by a mean of meridian altitudes observed in No- 
vember 1818, with a sextant and artificial horizon, by Cap- 
tain Parry, who on this and on all occasions most kindly 
studied to render me every assistance in his power, consist- 
ent with the due performance of his own duties. The house 
being close to the sea, the height of the clock above low 
water mark was ascertained by direct measurement 24 feet. 
In the subjoined table is given an account of the going of 
the clock, as compared with No. 1024; the clock was set up 
on the afternoon of the 30th of April, but the account was 
not commenced until time had been allowed for the pendulum 
to acquire the temperature of the room. The temperatures 
and arcs of vibration are a mean of frequent observations in 
the times to which they correspond ; and as these were of 
irregular duration, the corrections due to the several means 
have been given an influence on the general correction, pro- 
portioned to the length of their respective periods. 
The correction for the arc is the number of vibrations lost 
by the pendulum in 24 hours, from its vibrating in a circular, 
instead of a cycloidal arc ; the arcs being less than two de- 
grees, the time of a vibration in a circular arc, whose radius 
is r: the time of a vibration in a cycloid whose axis is \ r : : 
1 -}- -d- : t,[a being the versed sine of the arc), and the errors 
arising from the greater length of the vibration in a circular 
arc being nearly as the square of the arc, when the number 
of vibrations lost by the pendulum at each station in 24 hours 
by vibrating in an arc of 1 degree has been ascertained, the 
corrections due to the arcs in which the pendulum did ac- 
tually vibrate are obtained by multiplying the square of these 
arcs by the loss for one degree. 
