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Abstract
The author commenced by stating that he had been led to make farther investigations, on the subject of his hypothesis as to the nature of comets, by some comparatively recent criticism to which that hypothesis had been subjected. Its main features had been published more than ten years ago in the “Proceedings” of the Society (May 17, 1869) and in the first volume of “Nature.” Of course, if a critic completely misstates an hypothesis, he has no difficulty in refuting it; so that to such writers the author does not attempt to reply.
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- Proceedings 1879–80
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- Copyright
- Copyright © Royal Society of Edinburgh 1880
References
page 369 note * These conclusions are found to follow easily from the very simple investigation for a circular orbit. For the approximate differences of radius-vector, and angle-vector, at the time t, of the comet and of a particle projected at time tl, with relative velocity p, from its head, in a direction making an angle ψ with the tangent, are—
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:94078:20160525040419772-0846:S0370164600043959_eqnU1.gif?pub-status=live)
and
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:60399:20160525040419772-0846:S0370164600043959_eqnU2.gif?pub-status=live)
Here a is the radius of the orbit, and w the angular velocity in it.
If w (t - t1) be a small angle χ, whose third and higher powers may be neglected, these expressions take the form—
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:42211:20160525040419772-0846:S0370164600043959_eqnU3.gif?pub-status=live)
from which we easily deduce the results stated above. It appears that in the majority of large comets ψ is nearly a right angle.