422 
Proceedings of the Royal Society of Edinburgh. [Sess. 
5. Discussion of Results. 
Considering the magnitude of the frictional correction for the particular 
apparatus used in these experiments and the slight uncertainty in its 
numerical value, the remarkably good mean value obtained for g must be 
regarded as somewhat fortuitous. That there are irregularities is evident 
from the above values of a, which, as a varies as 
1 + P 
1 
If -| 
p 2 
7,2 
21/ + P-k 
, 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 individual 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 measure- 
ment 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 become 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 acceleration. What should be attempted, 
therefore, is the reduction of the absolute value of a to a minimum. Since 
a 
a =g p sm X 
1 + P 
1 p 2 
21/ + P 
/c 2 
/c 2 
for a given load L', with P fixed by con- 
siderations of stability, the desired result will be attained by making a and 
X a minimum, and k as nearly equal to p as possible. This means that the 
supporting pivots must be thin and well lubricated, and that the mass of 
the pulley must be concentrated in the rim, the spokes being as light as 
possible, consistent with the load they have to bear. 
In conclusion, it might be well to draw attention to the fact that the 
only modification in the usual type of Atwood pulley necessary to adapt 
it to the foregoing method is the very simple one of forming the wheel 
