84 PROCEEDINGS OF THE AMERICAN ACADEMY. 



decreased gradually and regularly. The field here was about 19.3 

 units. Figures 8, 9 (Plate 4) show the effect of suddenly applying a 

 comparatively strong field (14.3 gausses) when the system is already 

 swinging in a field of about 2 units. 



The curious irregularity in the spacing of the record in the last dia- 

 gram after the strong field was applied came from the fact that the 

 magnet was making oscillations in a vertical plane with an amplitude 

 of about 2'. When the system was at rest, the axis of the magnet and 

 the axis of the solenoid were in the same vertical plane but differed 

 from each other in direction by a small fraction of one degree. 



To illustrate the fact that in a weak field where the period of the 

 oscillation is long the amplitude of the motion decreases regularly with 

 a practically constant decrement, and that in somewhat stronger fields 

 the departure from this law is nearly inappreciable, except perhaps at 

 the very beginning of the motion, two or three sets of typical measure- 

 ments will serve. In very strong fields, when the initial deflections are 

 fairly large, the motion cannot be explained with any good approxi- 

 mation to accuracy on the assumption that the air resistance furnishes 

 a couple proportional to the angular velocity. 



When the periodic time was as short as 1.2 seconds, a curve of the 

 family A • e~ at which passed through the crests of the figure at the 

 middle of the diagram fell distinctly below the crests at the beginning. 



From measurements of photographic records taken with Q' for 

 eight different values of the current in the solenoid, the period (T), the 

 damping coefficient (2 a), the logarithmic decrement (A.) were deter- 

 mined for every case ; the intensity of the magnetic field (//) about the 

 magnet was then found by adding the original strength of the field to 



