MAGNETISM. 



'63 



that direction, and placed in the inclined 

 position AB, it is well known that 

 the rotatory action of the force of gra- 

 vity acting upon all its particles is equi- 

 valent to a single force acting upon a 

 point, O, which is called the centre of os- 

 cillation ; and also that, in order to esti- 

 mate what portion of that force OE con- 

 tributes to its rotation on its axis, we 

 must resolve it into one in the direction 

 O x y and another in the direction O r, 

 at right angles to it ; this latter force 

 hein^ in all cases proportional to the sine 

 of the angle EO.r, or its equal EXb. 

 The only difference between this case 

 and the one we have been considering, 

 is that here the force is single, whereas 

 there are two forces acting upon the 

 magnetic poles. 



(3 1 9.) These two forces being always 

 precisely equal and in opposite direc- 

 tions, perfectly balance one another 

 with reference to any motion of the 

 whole needle, either towards or from the 

 earth. This admits of experimental 

 proof ; for, in the first place, were there 

 any balance remaining in favour either 

 of the attractive or repulsive forces 

 emanating from the earth, the effect 

 would be shown by an apparent change 

 in the weight of the needle ; if, when 

 magnetised, it were on the whole at- 

 tracted to the earth, it would appear 

 heavier than before ; if repelled, lighter. 

 But no such change is observed to take 

 place. Neither is there any tendency 

 manifested in a magnetised bar to a 

 lateral or horizontal motion. This may 

 be proved by placing it at the end of a 

 light frame of wood, AB, Jig. 72, which 

 is suspended at its centre C by means 

 of a fine silk thread, T ; a weight, W, 



Fig. 72. 



being placed at the other end to act as a 

 counterpoise to the magnet NS. When 

 left to itself, it will be found that the 

 whole apparatus will turn round until 

 the direction of the needle coincides ex- 



actly with the plane of the magnetic me- 

 ridian, just as if it had been suspended 

 by its own centre. Had there existed 

 any force impelling it horizontally, it 

 would have occasioned a deviation from 

 this plane, acting as it must have done 

 with the advantage of the lever AC. But 

 the two equal forces acting differently 

 upon the two magnetic poles, though 

 opposed with respect to any motion of 

 translation, yet concur in their rotatory 

 action, and may, consequently, as far as 

 relates to this action, be regarded as a 

 single force of twice the intensity of 

 either of them taken singly. 



(320.) It is evident, then, that the 

 same dynamical laws which regulate 

 the motions of a compound pendulum, 

 actuated by terrestrial gravity, will also 

 regulate those of a magnetic needle, ba- 

 lanced on its centre of gravity, and ac- 

 tuated by terrestrial magnetism. The 

 same pendulum, it is well known, per- 

 forms all its vibrations in equal times, 

 whatever be the length of the arc in 

 which they are performed, provided 

 that arc be not too great. If we esti- 

 mate the length of a pendulum by the 

 distance between its centre of motion 

 and its centre of oscillation, then, in 

 pendulums of different lengths, and in 

 situations where the force of gravity is 

 different, the squares of the times of 

 performing a given number of vibra- 

 tions are directly proportional to the 

 lengths of the pendulums, and in- 

 versely proportional to the force of 

 gravity. Now the number of vibrations 

 performed in a given time is inversely 

 as the time employed in each vibra- 

 tion ; therefore, the square of the num- 

 ber of vibrations in a given time will be 

 inversely proportional to the length, and 

 directly proportional to the force of 

 gravity. 



(321.) The same formula being ap- 

 plicable to the vibrations of magnets, 

 a very simple computation will enable 

 us to arrive at an estimate of the com- 

 parative forces acting on the same mag- 

 net in different inclinations of the axis, 

 and in different situations with respect 

 to the position of equilibrium in the 

 plane of motion. We have only to dis- 

 turb it slightly from this position, and 

 count the number of vibrations it makes 

 in a given time, a minute for example, 

 in different cases: then, taking the 

 squares of these numbers, they will be 

 proportional to the intensities of the ter- 

 restrial magnetic forces that are in ope* 

 ration in these several instances, 



