PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 79 



The resistance of the instrument was about 21 ohms, but a considerable 

 fraction of this was in the gimp. 



When the coil circuit was closed by a resistance of 400 ohms, and 

 the coil was hung successively by several different pieces of gimp of 

 different lengths, the damping coefficient (a) slowly decreased as the 

 amplitude decreased, so that the logarithmic decrement was not quite 

 constant during the whole motion in any case, but the value of a for 

 a double amplitude of say 4° was practically the same for widely 

 different periods. 



The next two tables show the results of measurements of a good 

 number of photographic records. In the first case, as has been said, 

 the outside resistance of the circuit was 400 ohms, in the second case 

 it was 200 ohms. 



TABLE V. 



T. Damping Coefficient. 



9.28 0.0113 



4.57 0.0113 

 3.62 0.0113 



2.61 0.0114 



TABLE VI. 



T. Damping Coefficient. 



7.58 0.0193 

 4.57 0.0192 



3.62 0.0192 

 2.61 0.0191 



If the coil was deflected out of its position of equilibrium through 

 an angle of perhaps 10°, and was then suddenly released, the ampli- 

 tude fell at once to a much smaller value, especially when the coil was 

 closed through a resistance of say 400, and then decreased gradually 

 in much the same manner as the swings represented by Figure 5. 

 The phenomenon is, however, not so marked as when the damping 

 is fairly large and due wholly to air resistance. 



When the circuit of the coil of a d'Arsonval galvanometer of the 

 form described is closed through an outside resistance, x, so that the 

 whole resistance is (g + x), the damping coefficient of the motion is 

 theoretically the sum of the corresponding coefficient when the circuit 

 is open and the coefficient which the electromagnetic damping would 

 cause if the air damping were absent, and this last should be pro- 

 portional reciprocally to the apparent resistance {g' + x) of the circuit, 

 where g' is usually considerably larger than g. A set of five photo- 



