419 
1910-11.] A Modified Form of Atwood’s Machine. 
The string used was a strong silk fishing line, fitting well into the groove 
and continued beneath the pans to form an endless loop. The effective fall 
for one pulley revolution was determined by attaching a 10-metre tape to 
one of the pans and reading against a fixed point the distances covered 
between successive markings of the chronograph while the pulley was 
slowly rotated. The mean of fourteen separate measurements gave an 
effective fall of 38*92 cm., and consequently a mean pulley radius ^p = 6T94 
cm. The constancy of these individual measurements showed that the 
string did not slip appreciably in the Y-groove. 
3. Dynamical Equations and Data. 
Putting 
L = load on each side, including pans and string, 
w — driving weight, 
P = weight of revolving pulley, 
p> — effective radius of pulley, 
k — radius of gyration of pulley, 
a — observed acceleration, 
a = radius of spindle, 
and a sin X = effective friction radius, 
the friction moment becomes 2L + P + — a sin X, and we readily obtain 
the well-known result 
2L + w[ 1 - - sin \ ) + P- 
p J p A _ 
w 
+ g- sin Xr2L + « 0 + P1 
V 
U) 
Frictional retardation, a , is determined by observing the time taken to 
come to rest after communicating a certain speed to the system symmetri- 
cally loaded. This is also done on the chronograph, it being now necessary 
to observe and record on pen No. 3 the moment at which motion ceases. 
To get as near as possible to the same conditions of load as those obtaining 
qjj 
in the actual a experiment, it is well to observe a with a load L' — 
on each side, and in that case a is given by 
g- sin X[2L + w + P] 
2L + w + P 
k' A 
Hence equation (1) reduces to the very simple form 
<7 = 
a + a 
'to 
& 2 ' 
2L + W + P11 
p*. 
( 2 ) 
