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vector H becomes a hydrokinetic flow-function for the motion of the positive net; and where there is any positive charge it is a flow-function for the motion of the net plus that of the charge. Similarly the vector H is the negative of a flow-function of the motion of the negative net and charges. And in each case, equations (5) and (6) tell us that it is the solenoidal flow-function that is required.
The equation of motion is, as we expected, one which we have some difficulty in applying. But if we split it up into equations (5) to (10), and then combine them properly, we may use in electrical problems only the vectors E and H, representing the relative displacement of the positive net from the negative, and the flow-function of the relative motion. And in gravitational problems the vectors E and H disappear entirely.
Collisions of Electrons.
An interesting application of this model is to the problem of collisions of electrons, of the same or opposite signs, as in the case of a cathode particle striking an electron in the metal it hits. If they are of the same kind they will evidently become flattened as they come together. But as soon as they are within about their own length of each other, the side of either of them nearest the other will be effected not only by the displacement due to the presence of the other, but also by the displacements radiated from the other on account of its acceleration. To make the vectors balance, as required by equations (9) and (10), its acceleration must therefore be so much greater than that required by the inverse square law that they can never collide.
In the case of two electrons of different kinds, both are lengthened, and they come together faster than the inverse square law would demand. But since they may go right through each other perfectly freely, there need not be any of the destructive effects that one might expect from other theories.
Retarded Potentials. In calculating the values of the retarded potentials due to moving electrons it is found necessary to treat each electron as if its charge were not the same as when at rest, but changed in the ratio (1-B,), where ẞ, is the component of ẞ in the direction towards the point at which we wish to know the potential. This has been interpreted by some writers as indicating that all electromagnetic actions are due to some sort of pulsation of the electrons, and are
8 For information about retarded potentials, see Lorentz, "Theory of Electrons," Chap. 1.
9 L. de la Rive, Phil. Mag., 13, p. 279.
stronger if the pulsations are more rapid, so that the Doppler effect is introduced if the charge is moving. But with the model it is obvious that any such interpretation is unnecessary; for the important quantity is not the actual charge of the electron, but the volume. of the ether in which there was a spreading of the net at such a time as to affect the point in question at the time in question.
Because of the apparently absolute nature of acceleration, as well as for other reasons, we find it necessary to assume the existence of the ether, and therefore desirable to learn as much as possible of its properties. To do this, we first reduce the laws of all its phenomena, including gravitation and the relativity-principle, to five equations, and then examine their meanings; and find that two of them are probably laws of the geometrical configurations of the different parts of the ether; two more, equations partially defining two convenient vectors, and stating the indestructibility of electricity; while the fifth, Hamilton's Principle, is a law of motion, expressing the perfectly efficient cooperation of the different parts of the fundamental mechanism of the universe.
From these laws we may draw certain conclusions about the structure and properties of the ether, which are not, however, enough to enable us to determine exactly what it is. But by a few simple assumptions, we obtain an imaginable model of its actions. And since the model is based directly on the electromagnetic laws, it may be applied, without fear of error, to any electromagnetic problem, to enable us to obtain a qualitative result without mathematical analysis.
Proceedings of the American Academy of Arts and Sciences.
VOL. XLVIII. No. 13.― NOVEMBER, 1912.
CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES OF HARVARD UNIVERSITY. — Nos. 55-58.
THE HISTORY, COMPARATIVE ANATOMY AND
BY EDWARD C. JEFFREY.