ELASTIC RADIAL DEFORMATIONS OF FLYWHEELS. 305 
In each case A,, Ao etc., are zero, since the sine values 
cancel, the curves being symmetrical with regard to the 
centres of the bays. Thus tan 9=@ i.e. 9= 0 = 90°” 
The equations are therefore, for the three-armed wheel : 
y = 14°54 — 5°95 sin (w + =| + 1°14 sin Qe + + 
for the four-armed wheel: 
y = 12°34 — 3°17 sin (x + 5) + 0°58 sin (2a + - 
for the six-armed wheel: 
= e ae 5 . a & : 9 7 
y = 8°37 — 3°47 sin (« +5) 4 1°13 sin 2x +2) 
The above equations when plotted will give the shape of 
the rim very approximately at 14 revolutions per second, 
or in other words, will give the deflection of the rim past 
its zero position. Arrangements are at present being made 
to obtain the bursting speed of these flywheels, to compare 
with any theoretical bursting speeds which may be deduced 
from the above experimental results. 
The author desires to express his thanks to Professor 
Warren, M. Inst. c.B., Wh.Sc, and to Mr. 8. H. Barraclough, B.E., 
M.M.E., for their advice on many points during the course 
of these experiments, and to the former also for kindly 
allowing him the use of the workshop and appliances in 
the laboratory. 
