ELASTIC RADIAL DEFORMATIONS OF FLYWHEELS. 259 
but the method was erroneous as it was based on the 
assumption that the extension of the arms is such as to 
render the stresses due to bending one half of what they 
would be if the arms did not stretch at all, an assumption 
for which there is apparently no foundation. 
The only experimental work known to the writer is that 
which was carried out in 1898 and later, at the Case School 
of Applied Science by Mr.C. H. Benjamin.’ These experi- 
ments were carried out on small cast-iron flywheels 15 
inches and 24 inches in diameter, which were tested to 
destruction, the speed at which they burst being deter- 
mined. iach wheel was a scale model of some actual fly- 
wheel designed bya reputable firm. To attain the speed 
necessary for destruction, use was made of a Dow steam 
turbine capable of being run at any speed up to 10,000 
revolutions per minute. As the speed was too great for 
the successful use of a tachometer or a counter, a commu- 
tator of one break was arranged on the flywheel shaft and 
this connected through the battery circuit with an ear- 
phone in an adjoining room. This gave a clear musical 
tone, but it was found that the audible tone produced by 
the machine itself when running at a high speed corres- 
ponded exactly to the tone in the ear-phone, and so the 
ear-phone was discarded. 'T'wo observers with tuning forks 
determined the pitch within half a tone, the quarter tones 
being estimated. By this means it was thought that the 
error in speed did not exceed 5%. Wheels of various 
designs were tested—some with three arms or six arms, 
and others with joints in the rims of various kinds. 
These experiments indicate that, as the segments of the 
rim between the arms become weaker as beams, either 
through increase of length or decrease of thickness, there 
is a falling off in the bursting speed. The shape of fracture 
+ Trans. Am. Soc. Mech. Engrs., Vol. xx., p. 209. 
