82 PROCEEDINGS OF THE AMERICAN ACADEMY. 



ternal magnetic field about the magnet, and the moment of the magnet 

 in that field, but such values of I as my observations give do not seem 

 to change in any such manner as Stokes's formula for the sphere de- 

 mands. Of course the two cases are mathematically quite different. 



If the magnetic field about the magnet is relatively intense, and if 

 the original deflection is as great as 10°, the system swings through 

 its position of equilibrium, when it is released, to an elongation on the 

 other side only a fraction (perhaps a half or a quarter) of the original 

 deflection. From this time on the amplitude decreases slowly and 

 regularly, much as in the case figured in Diagram C. 



If a seasoned magnet placed in G be subjected to a magnetic field 

 of several units' strength, the magnetic moment changes, and it is 

 necessary to determine the amount of this change with some care if 

 one needs to know the restoring couple which acts upon the swinging 

 system. I have used for measurements of this kind a simple induction- 

 coefficient apparatus shown diagrammatically in Figure 4 (Plate 2). P 

 and Q are two similar solenoids which may be set anywhere on a hori- 

 zontal east-west track vw. O is a mirror magnetometer the deflections 

 of the needle of which can be determined by the telescope and scale 

 (T, S). A horizontal scale ab in the meridian carries a wooden holder 

 which contains a seasoned magnet (Mo) protected from sudden tem- 

 perature changes, in Gauss's B Position with respect to the magnet- 

 ometer needle. P and Q are so connected in series with a storage 

 battery, a rheostat, and a standard centiamperemeter that a current 

 can be sent in opposite directions through the solenoids; it is then 

 easy, when a current stronger than any to be used in the subsequent 

 determinations is passing through the circuit, to arrange the positions 

 of P and Q near O on vw, so that the current shall not affect the needle. 

 After this adjustment has been made, the magnet to be tested is placed 

 in P somewhere near the middle of the solenoid and so near the needle 

 that the latter is deflected off scale, and the wooden holder containing 

 Mo is placed on ab at such a distance from the needle that the latter 

 is brought back exactly to its undeflected position. If then a current 

 of suitable, small intensity be sent through the solenoid circuit, the 

 change of the moment of the magnet in P from M to M ' causes a scale 

 reading z owing to a deflection (8) of the needle; and if the current 

 has not been too strong, this deflection disappears when the circuit is 

 broken. If the field to which the magnet has been exposed has been 

 fairly large, however, the moment is permanently changed by a small 

 amount, and it is then necessary to follow the same magnetic journey 

 in the testing which is to be taken in the damping experiments. 



