118 
FIFTH REPORT 
1835. 
pended so as to hang near the bottom, its deviation, if any, from 
the horizontal position will be detected by its inclination to the 
surface. It is then to be slightly moved to one side or other in 
the brass stirrup by which it is supported, until it hangs truly 
parallel to the lower surface of the box; and when this adjust¬ 
ment is once accurately made, no further alteration will be re¬ 
quired, unless the change of dip be considerable. 
When an observation is to be made, the needle is raised or 
lowered by a small roller to which the silk suspension is at¬ 
tached, so that it may hang about midway between the upper 
and lower surfaces of the box. It is then drawn aside from the 
magnetic meridian through an arc of 25° or 30°, by a piece of 
brass wire inserted in the side of the box, and is allowed to os¬ 
cillate. The registry of the oscillations is commenced when the 
amplitude of the vibration on either side of the meridian is re¬ 
duced to 20°, and it is continued during 360 vibrations; the 
moment of the completion of every 10th vibration during that 
interval being noted by a chronometer. The amplitude of the 
final arc, or of the arc of the 360th vibration, is also observed; 
and the temperature of the air in the box, as indicated by the 
interior thermometer, is noted at the beginning and end of the 
observation. 
It is obvious that in this manner seven intervals of time are 
obtained, each corresponding to 300 vibrations,—viz. the interval 
between the Oth and 300dth vibration, between the 10th and 
310th, &c., and between the 60th and 360th and the mean 
of these is taken as the result. But to this result several cor¬ 
rections must be applied. 
1 . The time as shown by the chronometer is to be corrected 
for rate\ and accordingly the chronometer’s rate must be deter¬ 
mined from time to time by comparison with a good timekeeper, 
or by astronomical observations. In the present series the rate 
was observed at the commencement and end of each group of 
observations by the former and easier method. The amount 
of the correction due to rate is in most cases very small, the cor¬ 
rection in the time of 100 vibrations corresponding to a daily rate 
of 2" being less than O''*01 with the slowest of the needles 
employed. 
2 . Professor Plansteenhas applied a correction for the arc of 
vibration, so as to reduce the time to that corresponding to in¬ 
finitely small arcs. The correction is investigated on the same 
principles as that usually applied to pendulum observations. 
It is however more complicated in its form; for, instead of a 
single series of vibrations, (as in the case of the pendulum,) we 
have here seven distinct series, each commencing from a different 
