78 PROCEEDINGS OF THE AMERICAN ACADEMY. 



a d'Arsonval galvanometer due to a given change of the flux of magnetic 

 induction through its circuit is usually to be quantitatively explained 

 only by attributing to the resistance of the circuit a value much greater 

 than the real one. This apparent resistance 11 may be many times 

 as great as tjie real resistance; its value depends upon the constants 

 of the motion of the coil, and it not infrequently happens that a knowl- 

 edge of these "constants" is important, even though the amplitudes 

 do not always decrease exactly according to the assumption that the 

 resistance to the motion is equivalent to a couple of moment propor- 

 tional to the angular velocity. 



If a coil of the ordinary Ayrton-Mather form, without a damping 

 vane, swing between the poles of its magnet with the coil circuit open, 

 the amplitude generally decreases slowly, and if the coil be hung suc- 

 cessively by pieces of gimp of different lengths or stiffnesses, the 

 period changes with the restoring moment, and the damping coefficient 

 (a) remains small, though it often changes somewhat with the ampli- 

 tude. If with a given suspension we determine the quantity a in 

 the equation y = A- e~ at from two amplitudes of about 5° near the 

 beginning of the motion, and then from two amplitudes of about 2° 

 after the coil has made twenty or thirty swings, the latter value will 

 usually be sensibly smaller than the other, but the difference is not 

 very great unless the restoring force is weak, as it is in very sensitive 

 instruments. 



VI. In the case of a certain galvanometer of the Ayrton-Mather 

 type which I studied at length, the value of a fell from 0.00403 to 

 0.00356 as the motion progressed, when a piece of very fine steel gimp 

 was used to hang the coil. When stiff gimp was employed, the 

 value of a remained much more nearly constant while the amplitude 

 decreased, and was nearly the same for different lengths of the gimp. 

 The first column in the next table shows the period as determined 

 principally by the stiffness of the gimp, the second column gives the 

 corresponding value of a determined after twenty or thirty swings 

 had been executed and the double amplitude had fallen below 4°. 



11 Robinson, The Electrician, 1901. White, Physical Review, 1904. Peirce, 

 These Proceedings, 1906. 



