104 ON THE ACCURACY ATTAINABLE WITH 

 Effective Force, the meaning of the equation can be grasped 

 even by a student whose dynamical knowledge is small. 



With the present apparatus it was found necessary to 

 determine a several times before and after each determination 

 of a, ; with an apparatus of more satisfactory construction this 

 would probably be unnecessary. 



To get k, the radius of gyration, the pulley wheel was 

 removed from its position on the friction rollers and was 

 attached to bi-filar suspensions. Three separate determina- 

 tions gave =4-221, 4-205, 4.230, giving a mean &=4-218. 



This, with the weight P=44-0 g, and the radius p=6-194 cm., 





 gives for the equivalent mass of the pulley P 2=20-5 g. 



The inertia of the four friction rollers was found from their 

 dimensions and their weights to be one-tenth of that of the 

 pulley wheel itself. As their angular speed is less than one- 

 tenth that of the pulley, their total kinetic energy is less than 

 one-thousandth of the kinetic energy of the pulley, and has 

 therefore been left out of account in the subsequent calculation 

 of g. 



rz 



A graphical evaluation of P-^ made in the usual way 



ftfl 



from the results appended, by plotting - , against 2L+w 



a+a 



and reading off the intercept on the load axis, led to a value 

 21-2 g. 



A graphical method may also be adopted for ascertaining 

 the fraction of a revolution at the beginning in finding a, and 

 at the conclusion in finding a'. If R is the number of revolu- 



R 



tions from and to rest respectively, we have in each case a 



constant, and so x, the unknown fraction of a revolution, can 

 be at once obtained by plotting (0, 1, 2, 3, etc.) R against 

 Tl, T\, T\, T\, etc., where T , T v etc., are the times of x,l+x, 

 2+x, etc., revolutions. In the a measurements this fraction is 



