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 arc 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 

 !--§■ rz \ 6 ~, 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 b, and call the retarding 

 force by which the ring is brought to rest when vibrating alone r, 

 and the retarding force of the magnet R, then r + 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 : r -f- R : : b : a, or ra =r (r -f- R) b ; that is to say, 



R zz r -g— ^j or R — r, ^g — 1). Now r 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 £ \ 9 which 



formula I have found to agree in a remarkable way with 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 



