But such instances are few and far between, and we should receive a very erroneous impression as to the population of the celestial regions by bodies devoid of light if we thought that the few whose presence has been occasionally disclosed in some very indirect and casual manner bore anything like a considerable proportion to the total number which actually exist. It is just at this point that the theory of probabilities comes to supplement our knowledge, and the results to which it conducts us are of a most startling description. By this theory we are assured, with a logic which cannot be controverted, that the invisible bodies must be vastly more numerous than the visible stars, so that even the millions of bright stars which we see afford only an utterly inadequate conception of the full extent of the material universe. Remember, I am not now referring to objects beyond our ken merely because they lie so far off. What I mean is that even within the sphere which contains the visible stars that we know, there is such a stupendous quantity of matter of a dark character, that the visible part bears an almost imperceptible proportion to it. It may well be asked how we know that there is this exuberant abundance of invisible matter. Let the theory of probabilities answer the question.
I shall suppose that we have to deal with a lapse of time, which for our present argument may be regarded as indefinitely long. It can be demonstrated that the conditions under which a mass of matter becomes so highly heated as to shine with star-like radiance are wholly exceptional in their character. So far as our present knowledge goes it would seem that the brightness of any sun-like body is to be attributed solely to the transforma-
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