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Transactions of the Wisconsin Academy of Sciences, Arts and Letters
volume IV (1876-1877)

Davies, J. E.
Report on recent progress in theoretical physics,   pp. 241-264 PDF (6.7 MB)

Page 248

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248     Wisconsin Academy of Sciences, Arts, ard Letters.
when compounded together, to a rectilinear vibration. The peri-
odic time of this plane vibration is equal to that of the circular
vibrations, its amplitude is double, and its direction is in the line
joining the points at which two particles describing the circular
vibrations, in opposite directions round the same circle, would
meet.&quot;
The theorem may be illustrated as follows:
If, in any space like that represented in Fig. 10, we have a great
Fig. 10.            number of spins, more or less
completely filling the space en-
Oz4&gt;  By  a&lt;\  closed by the larger
circle,
and
plane of the paper, the resultant
will be equivalent to a spin of
single axis likewise perpendic-
ular to the to the plane of the
paper; the magnitude of this
cm t  J   /      resultant spin being determined
by the intensity, relative dis-
tances, and number, of the component spins which go to make its
up, Regarding this resultant spin only, the velocity of a particle
at any distance from the axis can be decomposed into component-
velocities, asin Fig. 11, where      Fig. 11
the uniform circular motion           y
of F, from X to Y. can be de-
composed into =_r. cos 0 and  /      E
v=r. sin 6, in such a man-
ner that the Lotion of D, to                     Irv
and fro on the line X? and
the motion of E to and fro on
on the line Y. correspond
constantly in position to the
motion of F around the cir-
cle. In such a case, we say
that the circular harmonic
motion of F is compounded of two rectilinear harmonic motions
along X and Y, of equal periods and amplitude, bat differing by

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