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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 249


Recent Progress in Theoretical Physics.
a quarter of a complete oscillation. If there be two equal and op-
posite tendencies operating upon F, one to carry it toward Y,
and the other toward X, the result will be, that the tangential
tendencies at F will neutralize each other, while the normal com-
ponents will coincide and carry the particle towards C along r (Fig
11), and a rectilinear motion              Fig. 13.
will be the result, as in Fig.
12 or Fig. 13. Thus two tend-
encies to gyrate in opposite
directions may result in mere
rectilinear vibrations. If one
      Fig. 12.    of these                     1   i
              re  tenden-
                   cies be
                   stronger /
                   other, so
                   that of it-
self it would produce a more rapid rotation in its direction, than
the other component in its, then the motion will be elliptical in an
orbit of which the major axis changes at each complete oscillation
             Pig. 15.- by some angle 0, the magnitude
        ,+ *f 1~ I  Iof which will depend upon the
                                  excess of velocity in one direc-
                                  tion over that in the opposite.
                                  This is easily seen by reference
                                  to Figs. 14 or   Fig. 14.2
                                  15, where the
                                  motion would
                                  be along ab, 7
                                  were both cir-
                             j   cular compo-
                                  nents  equal,
                   - I'          whereas t he
 ' The engraver has very imperfectly copied the origiaal drawings for this
 as for some of the other figures.
 2For c in the figure, read Q, and for a and b at the extremities of one
of the
diameters, read a' and b', respectively.
249


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