PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 83 



If the distance of the centre of the auxiliary magnet from the centre 

 of the needle is do centimeters, and if Iq is the half magnetic length of 

 this magnet, the moment of the couple which it exerted upon the 

 needle before the latter was deflected, and which just balanced the 



moment due to the magnet to be tested, was — = — j^— -j . 



(d%+i z oy 



When the magnet under the test is removed, the needle deflection 

 (Sq) caused by the auxiliary magnet alone is usually too large to be 

 easily measured by aid of the telescope and scale ; but if this magnet 

 be removed on its track to such a distance that the deflection 5' can 

 be determined, and if the distance between the centres of the magnet 

 and needle is then d', 



tan Sp d (d f * + l\f , . 



tan 8' ' (d 2 + / 2 o)'' d' ' { } 



and M' can be determined in terms of M by means of the equation 



W -M tan 8 



M tan 8 ' 



(31) 



VII. The first magnet (Q') used with this apparatus was about 4.0 

 centimeters long and weighed about 7 grams. The whole suspended 

 system had a moment of inertia in vacuo almost exactly equal to 43.0, 

 and the magnetic moment of the seasoned magnet (Q') when placed 

 with its axis perpendicular to the meridian was about 29.8 units. Its 

 induction coefficient under these circumstances was about 0.0242 ; its 

 moment in a field of 10.37 gausses was 38.7. Most of the records were 

 made with the drum revolving very slowly at the rate of a turn in 348 

 seconds: the normal length of a record was 479 millimeters. The 

 periodic time of the swinging system varied from 50.8 seconds to 

 1.20 seconds in the fields actually used. The torsion coefficient of 

 the fibre was under all circumstances here considered much too small 

 to be appreciable. 



Figures 5 (Plate 2) and 6 (Plate 3) represent oscillations of the sus- 

 pended system of which the magnet Q' was a part under fields of 

 about 2 and 12 gausses respectively. In the case shown in Figure 7 

 (Plate 3) the magnet was deflected through an angle of perhaps 10° 

 and then suddenly released. The record begins at the point O, where 

 a nearly straight line indicates that the magnet was on its way through 

 the position of equilibrium and out on the other side to a point cor- 

 responding to a deflection of about 2.5°, after which the amplitude 



