MAGNETICAL OBSERVATIONS IN IRELAND. 
119 
arc. The principle, however, seems hardly applicable in the 
present instance. It is assumed that the successive arcs of vi¬ 
bration decrease in geometric progression, as they must necessa¬ 
rily do if the resistance of the air be proportional to the velocity. 
This is found to hold good in the vibrations of the pendulum 
when the arcs are very small; but it is by no means true when 
they are so considerable as those in which the horizontal mag¬ 
netic pendulum is made to vibrate. Where, however, the vi¬ 
brations commence from the same arc, and the terminal arc does 
not much vary, the correction itself may perhaps be disregarded. 
In the following observations, in which the initial arc was 20°, 
the 360th or terminal arc was generally 2 |°, and was in all cases 
included between the limits 1° and 4°. In such cases, then, 
the correction must be, nearly, a constant cpiantity; its appli¬ 
cation to the observed times is therefore nearly ecpiivalent to 
their multiplication by a constant coefficient, and the ratio of the 
times (with which alone we are concerned in this class of ob¬ 
servations) remains unaltered. For these reasons no attempt has 
been made to introduce a correction for the arcs in the following 
results; but the terminal arcs are given, so as to put the reader 
in possession of all the circumstances of the observation. 
3. By far the most important correction is that due to tem¬ 
perature. If T' be the observed time of 100 vibrations corre¬ 
sponding to the actual temperature and T the corrected time 
corresponding to the standard temperature t , the correction is 
T - T' = a T' (t - t '); 
a bring a constant coefficient whose value is to be determined 
experimentally for each needle. 
The following observations were made with the cylinders 
L («), L (Z>), in order to determine the value of the coefficient 
a for each. The apparatus being inclosed in a large glass bell, 
the time of 100 vibrations of cylinder L («), commencing with 
the arc of 10°, was observed at the mean temperature of the 
room, and when the air of the bell was heated artificially from 
below, by means of a spirit lamp. The final arc varied between 
4° and 5°. The observations with cylinder L (Z>), were made in 
the bell without the apparatus. In this case no means were 
taken to observe with any accuracy the arc of vibration; and 
in order to reduce as much as possible any error arising from 
this source, the observations were continued in each instance 
until the arcs were reduced to the smallest appreciable, and the 
mean of the last five intervals of 100 vibrations then taken as 
the result. The chronometer’s rate varied from + 0 //e 6 to -f l //s 4 
