620 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



Experiment I. 



In the firsi experiment the sphere was made of ivory. Its diameter 

 was 0.8653 cm., and together with the ivory disk weighed 5.4C0 grams. 

 Tiie moment of inertia of the mirror and wire alone was found to be 

 0.0016 in C. G. S. units, while that of the vibrator as determined from 

 the different cylinders, which in this case were made of ivory, was 

 1.6409, 1.6424, and 1.6479, the mean of which is 1.644. The tempera- 

 ture corrected by a standard thermometer was 23°. 0, and the pressure 

 75.65 cm. The logarithmic decrement obtained when the disk was on 

 the wire was 0.00859 and the time of swing 38.83 seconds. The decre- 

 ment for the sphere and ivory disk was 0.02424, and the time 38.94 

 seconds. To change the former decrement to what it would be were the 

 time of swing 38.94 seconds the approximate formula A (1 — t^jt^) was 

 used. It expresses the amount to be added to A, the decrement when 

 the time is ti in order to get what that decrement would become when 

 the time had Changed to t^ and is obtained by considering the pendulum 

 as being damped by a resistance proportional to the angular velocity. It 

 is sufficiently accurate for this correction, which must be small, since 

 the difference in time is small. In this case the correction was —0.0002, 

 so that the corrected decrement for the lead disk was 0.00857 and the 

 decrement due to the resistance to the sphere alone must have been 

 0.01567. To the base e, this becomes 0.03608. 



The following table gives the data necessary for the calculation of jx : 



TABLE I. 



The insertion of these values in the expression for the logarithmic decre- 

 ment in Stokes's formula leads to an equation of the fourth degree from 

 which to determine /* . The solution gives 



/i233.o = 0.0001825. 



Holman * has obtained the formula 



/,,, = /io (1 + .002751 1 — .00000034/2) 



* riiil. Mag., 21, 1886. 



