Oscillations of the HorizontalNeedle. 17 
graduated card, be divided by the number made between the 
same points, when put in vibration about the magnet m, Fig 8, 
then the quotient minus 1, may be taken to express the compa- 
rative force of the bar m, and we shall have a constant quantity 
for the same degree of tension, whatever extent we take between 
the first and last are of vibration. Thus, the ring of copper alone 
was observed to make 70 vibrations between 40° and 35°, and 164 
vibrations between 40° and 30°. When vibrating about the mag- 
net, it made only 30 vibrations between 40° and 35°, and only 
70 vibrations between 40° and 30°. It may be here seen that 
79 — 184, or very nearly. 
30. The formula just given for estimating differences in mag- 
netic tension, seems deducible in the following way: Let the vi- 
brations of the ring alone be called a, and the vibrations within 
the same limits made about the magnet 8, and call the retarding 
force by which the ring is brought to rest when vibrating alone 7, 
and the retarding force of the magnet R, then 7 + R is the com- 
bined or whole retarding force, where the ring vibrates about the 
magnet ; but the number of vibrations between given limits may 
be assumed to be in an inverse ratio of the retarding forces ; 
hence we have r:7-+ R::0:a, or 7a = (r + R) 6; that is to say, 
R ee or hy =, ees 1). Now~7 having been taken as the 
force by which the ring alone is brought to rest, may be considered 
as unity in every csae ; hence the value of R, or the force of the 
magnet, is comparatively expressed by the formula Ea which 
formula I have found to agree in a remarkable way witb the re- 
sults of experiments. The following instance may serve to illus- 
trate its application in a particular case. 
(c). The tension of a small magnet was estimated at each 
pole, by observing the attractive force on a small cylinder of soft 
iron at a given distance, in the way described in Vol. IX. of the 
Society’s Transactions, p. 278. The magnet was then submitted 
to further experiment with the vibrating ring of copper, as above 
VOL. XIII. PART I. c 
