A FORM OF ATWOOD'S MACHINE 107 

 fortuitous. That there are irregularities is evident from the 



1+p 



above values of a', which, as a! varies as 



should decrease asymptotically as the load increases ; but it 

 would also seem that the effect of these disturbances can be 

 determined by a proper evaluation of friction for each indi- 

 vidual experiment. No doubt, more carefully constructed 

 friction rollers would prove more regular in action ; but as 

 the accuracy here attained is more than sufficient for the 

 author's immediate purpose, he did not think it necessary to 

 have another wheel constructed in order to be able to test this 

 point further. 



It is, perhaps, of interest to examine under what conditions 

 greatest accuracy may be attained. For a given absolute 

 possibility of time measurement a should be as small as possible 

 in order that it should be known with the highest relative 

 accuracy, but then the difficulty arises that a! is a large fraction 

 of the total, and any slight uncertainty in its value affects the 

 result accordingly. On the other hand, to increase a so as to 

 make a' relatively small would entail less accuracy in the time 

 measurement, the square of which is involved, and, moreover, 

 air resistance at such comparatively high speeds would be- 

 come appreciable even during the earlier stages of the fall. 

 It is, perhaps, significant that the worst value amongst the 

 foregoing results is that obtained from the greatest accelera- 

 tion. What should be attempted, therefore, is the reduc- 

 tion of the absolute value of a' to a minimum. Since 



af=g a sin X 

 P 



, for a given load L', with P fixed 



by considerations of stability, the desired result will be attained 



