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ing velocity. It varies inversely as the square root of the distance from the sun, hence, four times away from the sun, it is only half as great. The rule for finding the limiting velocity at any point in space is very simple. It is to take the speed of a planet passing through that point in a circular orbit, and multiply it by the square root of 2. This is 1.414. . . .

It follows that if the astronomer, by means of his observations, can find the velocity with which a comet is passing a known point of its orbit, he can determine the distance to which it will fly from the sun and the period of its return. By a careful comparison of observation made during the whole period of visibility of the comet he can generally reach a definite conclusion on the subject.

It is a curious fact that no comet has yet been seen of which the speed certainly exceeds the limit which we have described. It is true that, in many cases, a slight excess has been calculated from the observations, but this excess was no greater than might result from the necessary errors of observations on bodies of this kind. Commonly the speed is so near the limit that it is impossible to say whether it exceeds it or not. It is then certain that the comet will fly out to an immense distance, not returning for hundreds, thousands, or tens of thousands of years. There are also cases in which the speed of the comet is found to be less than the limit by a considerable amount. Such comets complete their revolutions in shorter periods and are called periodic comets.

So far as we know, the history of the motion of the