72 PROCEEDINGS OF THE AMERICAN ACADEMY. 



which, taken at the proper time interval (T), should have the lengths 

 indicated above. 



If, however, we assume that when t = 0, y = 1260, and use the 

 other numbers given above, in succession for determining a T, we get 

 for this product the different values 0.225, 0.238, 0.224, 0.221, 0.220, 

 0.217, 0.214, 0.212, 0.210, 0.207, and it is evidently impossible to find 

 the curve sought exactly. The differences, while much too great to be 

 accidental, are intrinsically not very large, and a curve of the family 

 y = A ■ e~ at may be drawn which will pass through the fourth, fifth, 

 and sixth points, and the ordinates of which at the ends of the series 

 will be 1231 and 116, instead of 1260 and 131. Corresponding ordi- 

 nates of the observed and calculated curves are shown in the following 

 table. The calculated curve has, as a whole, a less curvature than the 

 observed curve, and the ratio of any excursion to the next decreases 

 slightly with the time. The period was about l/100th of a second. 



In the case of this particular quickly oscillating system, therefore, 

 the first double amplitude of which was not larger than 6°, the motion 

 can be explained during a considerable part of its course with fair 

 approximation on the assumption that the resistance due to the air 

 and to frictional forces in the fibre is proportional to the angular 

 velocity. The deviations from this law, while real, are not greater 

 than one often finds in the motion of a suspended magnet or the coil 

 of a d'Arsonval galvanometer, when swinging slowly over a small arc. 

 Indeed two d'Arsonval galvanometers of the same type and apparently 

 very like each other may depart from the usual law in opposite direc- 

 tions if the periods are long; in one the logarithmic decrement may 

 grow larger as the amplitudes of a long series of swings decay, while in 

 the other it may become smaller. In the case of a galvanometer of this 

 kind in the Jefferson Laboratory, the ratio of one excursion to the next 

 increased from 1.063 to 1.086 in an hour and a quarter, while the am- 

 plitude decreased to about four tenths of its original value. The com- 

 plete period of swing was 158 seconds. A similar galvanometer in the 



