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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 251

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Recent Progress in Theoretical Physics.
that the undulation lengths for the two rays are not equal. The
annexed figure may serve to illustrate the mutual action of these
rays. Suppose M A D B, to be the orbit in which a force P tends
to urge a molecule M, to revolve around the center C, to which it
is drawn by the force M C. Suppose the equal force Q to urge
the same molecule to describe the same orbit in the opposite
direction. These forces holding each other in equilibrio, the mole-
cule will follow the direction of the third force, M C.
Now suppose the force Q suspended, the molecule will take
the direction of the circle A D B, and will continue to revolve in
it so long as the force P (supposed always tangential) continues
to act. But its movemehts will impart to the molecule next
below it a similar motion, and that to the next, and so on; so that,
as these successive molecules take up their movements later and
later, there will be a series in different degrees of advancement in
their several circles, forming a spiral; and when the molecule M
shall have returned to its original position, the series will occupy
a position like the curve M F L N' 0 R. If, now, P be supposed
to be in turn suspended, while the force Q continues to act, the
effect of Q will be to produce a contrary spiral, which may be
represented by M S K T V. If M D be a diameter of the circle
M A D B, drawn from M, and D H N' be a line parallel to the
axis C0 G of the cylindrical surface, which is the locus of the
spirals, then, if the undulating lengths are the same for both
movements, the two spirals will intersect D H in the same point,
the intersection marking the completions of a half undulation for
each. But if these lengths be unequal, the intersection with D II
will take place at different points as N and N'.
Let now a plane intersect the cylinder at any distance below
M A D B, as at E, parallel to M A D B. It is conceivable that
this plane may be made to pass through the point where the
spirals intersect each other. If I mark the point of intersection,
and we draw the tangents I P' and I Q' in the plane of the circle
E H I, then there will be a molecule at the point I which will be
in the circumstances of the molecule in [Fig. 12 at the point a'-
that is to say, solicited by three forces, of which two, I P' and I Q'
are equal and opposite, and the third is directed in the line I G0
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