460 A. Kendrick — Damping of Bell-magnets, etc. 



reducing the inertia moment below the point required for 

 " dead-beat " vibration would be to increase the time of com- 

 ing- to rest. With a field of about T \ the value of the earth's 

 field, the time of a half vibration of Q in air was 5 seconds, 

 and in box 4, the vibration being " dead-beat," it required 

 about 30 seconds to come to rest, but with an inertia disc, that 

 increased the time in air to 10 seconds, the time of coming to 

 rest was about 30 seconds. In 4 (c) in the same field without 

 the inertia disc, the vibration being also " dead-beat," the time 

 was lengthened only about 2 seconds. 



The foregoing results were, as above stated, obtained by 

 using the magnet Q only, and similar action would naturally 

 be expected from other bell-magnets and corresponding boxes, 

 but it may be of interest to mention other forms and sizes that 

 were tried. T is of about one-half the linear dimensions of Q 

 (thickness about the same). Its time of swing in air was 

 nearly the same as that of Q when in the same field, hence the 

 ratio of inertia moment to magnetic moment for the two sus- 

 pended systems was about the same. But the magnetic moment 

 of T is about ^ of that of Q, hence the inertia moment is 

 about t l that of Q. Supposing Q in box 1 (1st), if reduced to 

 T * ff in relative magnetic moment and relative inertia moment, 

 to represent T in box 7. Producing curve III of fig. 8, so 

 that it will include the point where the magnetic moment is 

 0*1, we find the corresponding A is about # 65. We see from 

 curve I of fig. 7 that a reduction of the moment of inertia to 

 - l would at least reduce A from - 09 to 0, and, without 

 attempting to make any allowance for a further effect, if we 

 subtract 0"09 from 0*65 we get as an estimated value of A for 

 T in box 7 something less than 0'6. It was found to be 

 slightly under 0'50. S is twice as long as T, and slightly 

 thicker. The time of swing is a trifle less than that of T, and 

 so its magnetic moment is greater in proportion to its inertia 

 moment ; also, since its inertia moment is necessarily some- 

 what greater than that of T, the magnetic moment is greater, 

 and in the same box, 7, we should expect a value of A notice- 

 ably less than for T. The observed value is 0*40. In a weak- 

 ened field, the vibration of T became aperiodic in box 7 and 

 the time of coming to rest was very long. P had a magnetic 

 moment of about T 9 7 that of Q, and an inertia moment about 

 3*8 times that of Q. Estimating from the curves II of fig. 7 

 and 1Y of fig. 8, one would say that the A of P in 4 (c) might 

 be about 040. It came to rest in 11 swings, or A was approx- 

 imately 0*5. U has about -J the moment of inertia of Q, and 

 about y^ its magnetic moment ; 0*4 would be the estimate for 

 A of U in box 3, and 10 swings or approximately - 45 for A 

 was the actual damping. P has a moment of inertia about -j^- 



