Abstract
BY appropriate general treatment, it may be shown that solutions involving the path time are invariant, that is, can exist in any set of space co-ordinates. Starting, then, with the solution for the electron velocity ripple in terms of the transit half-angle1, it may be shown, by analogy with van der Pol's treatment of waves in n dimensions2, that this ripple satisfies certain conditions. The most important of these is that the ripple satisfies a five-dimensional wave equation, the wave velocity being that of the particle, provided the frequency of the ripple is such that θ « √2, where ç is the transit half angle (= ωτ/2). It will be convenient to regard this ripple as that part of the particle vibration which corresponds to free, as distinct from forced, oscillation. The factor ½ must be associated with the fifth dimension, as follows: where c5 is the velocity appropriate to the waves.
Similar content being viewed by others
Article PDF
References
Benham, W. E., Phil Mag., 5, 648 (March 1928).
van der Pol, B., Physica, 3, 385–392 (June 1936).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
BENHAM, W. Waves Associated with Moving Corpuscles. Nature 142, 160 (1938). https://doi.org/10.1038/142160a0
Issue Date:
DOI: https://doi.org/10.1038/142160a0
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.