ELASTIC RADIAL DEFORMATIONS OF FLYWHEELS. 303 
The equation to the curve of the rim may be obtained by 
applying Fourier’s theorem‘ for the analysis of a complex 
Ssingle-valued periodic curve into its constituents. 
In the case of the flywheels under consideration, the 
periodic portion lies between two arms; and is repeated 
for each bay if we consider the deformations the same in 
each bay. Since the curve between two arms corresponds 
to one whole period, then we may call this 360°. The curve 
is divided into 24 parts (say) each equal to 15°. 
Let y= the ordinate at any point. The values of y cor- 
responding to each of these divisions is found from the 
accompanying curves. A table is formed in which are 
columns giving the positions on the curve (1 to 24 in present 
case) and the corresponding values of y, « (angle) sin x, 
y X sin x, cos xX, y X Cos x, sin 2x, y X Sin 2x etc. 
Then we have 
y=A.+Bo+ Ai? + B;? sin (« + 9) 
eee cin 2a Ol) 
a MSE 
where 
A. + Bo = mean of all the 24 numbers under y column 
A, = Lwice mean of. ;, a UE SINE KA 5 
B, = 7 7 me y X COSX,, 
As = Oe a 3 y X sin 24x,, 
B, = re) oy) 99 y x COS 2%,, 
B 
‘t 6G— —t f' — 
ga Te ic ie 
On testing the equations derived, it will be found un- 
hecessary to proceed to any higher degree of complexity 
than that shewn. The data used in the derivation of the 
equations are given in the following table :— 
’ Fleming’s Alternate Current Transformer, p. 87. 
