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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
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Page 251

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 251

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