134 
into ten columns, and each time that I note the end of a 
vibration I make a mark on the slate, counting at the same 
time the ticking of the clock. Every time that the end of 
a vibration appears to be sensibly coincident with the beat 
of the clock I write the number of seconds on the slate 
alongside the usual mark. After observing the vibrations, 
which ought not to exceed 3° of amplitude, for about ten 
minutes, materials will have been collected for obtaining a 
sufficiently accurate determination of the time of vibration 
by dividing the times between the several coincidences by 
the number of intervening vibrations and taking the mean 
of the whole. 
As has been shown by Gauss and Weber, if M be the 
force of the magnetic bars in absolute measure, 0 the angle 
of deflection produced at the distance It, and T the absolute 
horizontal intensity of the earth’s magnetism, 
M_ R 3 tan 0 
T 2 ’ 
but approximately only, because the deflecting power of a 
bar decreases in a more rapid ratio than the inverse cube of 
the distance, on account of its o wn magnetic length. Hence 
the necessity of a correction which may be found by observ- 
ing the deflections at two distances R and It, from which we 
0fl 3 — 
obtain L 2 : 
2(0R— 0^) 
where L signifies the virtual half 
length of the bar. Then we obtain the closely correct value 
jjL— jj l — -L 2 R tan 0. Calling this quantity r, as in 
1 / 120 
Gauss and Weber’s equation, we have finally T=-l — , 
where t is the time of vibration in seconds, C is the mo- 
ment of inertia of the bars multiplied by 7r 2 , and 12 is the 
coefficient to reduce from inches to feet. 
The following were the data for determining the horizon- 
tal intensity on four several occasions. 
