618 PROCEEDINGS OF THE AMERICAN ACADEMY. 



A test was now made to determine whether the velocity of the sphere 

 was such as to cause a different logarithmic decrement for large arcs of 

 swing from that obtained for small arcs. The result obtained from the 

 many observations taken was that, for the range which it was proposed 

 to use, the decrement was independent of the amplitude of swing. The 

 velocity of the fluid at any point would therefore seem to have been 

 within the limit set by the mathematical conditions. Moreover, as will 

 appear from the data given later, the maximum angle through which the 

 sphere turned was about 0.015 radians, the time of one complete swing 

 was, in the case of the glass sphere, 83.52 seconds, while the radius of 

 the sphere was 0.7495 cm. The maximum velocity of a point on the 

 equator of the sphere must have been about 0.0011 cm. per second. The 

 square of this quantity is about 0.1 percent of the quantity itself. Using 

 the value 0.00017 for /xq the expression Va p/ fj. must have been about 

 0.006. 



It will be seen that the plan described above for the elimination of the 

 friction on the fibre, mirror, and wire, as well as the friction in the fibre 

 itself, is satisfactory only if the friction in the fibre remains constant dur- 

 ing the experiment. Even with quartz this state of constancy is not 

 reached until the pendulum has continued swinging for some time. With 

 this precaution a very regular value for the decrement was obtainable. 



Though the surface of the lead disk seemed to be little, if any, inferior 

 to that of the glass disk, yet to fully justify the replacing of one by the 

 other a wooden disk with a smooth surface was used as a pendulum and 

 the decrement measured. Then the same disk, having its surface black- 

 ened with graphite, was used, but no difference in tlie decrement could 

 be detected. Want of smoothness, merely, should, indeed, affect the 

 decrement only in so far as a rough surface exposes more surface to the 

 air for a given inertia than a smooth surface does. 



Conceivably, also, there might be a damping of the swinging of the 

 lead disk due to induced currents in the lead. This was tested by chang- 

 ing the intensity of the magnetic field surrounding the vibrator to two or 

 three times its original value. No change in the speed of damping could 

 be observed. 



Method of Experiment. 



The main part of the experiment was carried out as follows : After 

 the sphere and disk had been fastened on the wire in the manner already 

 described, the whole suspension was lowered into the containing vessel 

 until the cap, D, rested in its place. When the cap, D, had been ad- 



