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'We may... have surmised nebulae to be no other than clusters of stars disguised by their very great distance, but a longer experience and better acquaintance with the nature of nebulae, will not allow a general admission of such a principle, although undoubtedly a cluster of stars may assume a nebulous appearance when it is too remote for us to discern the stars of which it is composed.
I come now to another part of my system, and because it suggests a lofty idea of the plan of creation, it appears to me as the most seductive. The sequence of ideas that led us to it is very simple and natural. They are as follows: let us imagine a system of stars gathered together in a common plane, like those of the Milky Way, but situated so far away from us that even with the telescope we cannot distinguish the stars composing it; let us assume that its distance, compared to that separating us from the stars of the Milky Way, is the same proportion as the Milky Way is to the distance from the earth to the sun; such a stellar world will appear to the observer, who contemplates it at so enormous a distance, only as a little spot feebly illumined and subtending a very small angle; its shape will be circular, if its plane is perpendicular to the line of sight, elliptical, if it is seen obliquely. The faintness of its light, its form, and its appreciable diameter will obviously distinguish such a phenomenon from the isolated stars around it.
We do not need to seek far in the observations of astronomers to meet with such phenomena. They have been seen by various observers, who have wondered at their strange appearance, have speculated about them, and have suggested some times the most amazing explanations, sometimes theories which were more rational, but which had no more foundation than the former. We refer to the nebulæ, or, more precisely, to a particular kind of celestial body which M. de Maupertius describes as follows:
"These are small luminous patches, only slightly more brilliant than the dark background of the sky; they have this in common, that their shapes are more or less open elipses; and their light is far more feeble than that of any other objects to be perceived in the heavens."
...It is much more natural and reasonable to assume that a nebula is not a unique and solitary sun, but a system of numerous suns, which appear crowded, because of their distance, into a space so limited that their light, which would be imperceptible were each of them isolated, suffices, owing to their enormous numbers, to give a pale and uniform luster. Their analogy with our own system of stars; their form, which is precisely what it should be according to our theory; the faintness of their light, which denotes an infinite distance; all are in admirable accord and lead us to consider these elliptical spots as systems of the same order as our own—in a word, to be Milky Ways similar to the one whose constitution we have explained. And if these hypotheses, in which analogy and observation consistently lend mutual support, have the same merit as formal demonstrations, we must consider the existence of such systems as demonstrated...
We see that scattered through space out to infinite distances, there exist similar systems of stars [nebulous stars, nebulæ], and that creation, in the whole extent of its infinite grandeur, is everywhere organized into systems whose members are in relation with one another.... A vast field lies open to discoveries, and observations alone will give the key.
The number of compound nebulæ... being so considerable, it will follow, that if they owe their origin to the breaking up of some former extensive nebulosities of the same nature with those which have been shewn to exist at present, we might expect that the number of separate nebulæ should far exceed the former, and that moreover these scattered nebulas should be found not only in great abundance, but also in proximity or continuity with each other... Now this is exactly what by observation, we find to be the state of the heavens.
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Gaseous nebulae offer outstanding opportunities to atomic physicists, spectroscopists, plasma experts, and to observers and theoreticians alike for the study of attenuated ionized gases. These nebulae are often dusty, heated by radiation fields and by shocks. They are short-lived phenomena on the scale of a stellar lifetime, but their chemical compositions and internal kinematics may give important clues to advanced stages of stellar evolution.
I compared also the present appearance of this nebula with the delineation which Huyghens has given of it in his Systema Saturnium... The changes that are thus proved to have already happened, prepare us for those that may be expected hereafter to take place, by the gradual condensation of the nebulous matter; for had we no where an instance of any alteration in the appearance of nebula, they might be looked upon as permanent celestial bodies, and the successive changes, to which by the action of an attracting principle they have been conceived to be subject, might be rejected as being unsupported by observation.
Apart from life and thought, there is no reason to regard one form of material distribution as in any respect superior to another. A solar system may be more interesting than its parent nebula ; it may be more beautiful. But if there be none to unravel its intricacies or admire its splendours, in what respect is it better ? Its constituent atoms are more definitely grouped, the groups move in assignable orbits ; but why should the process by which these results have been achieved be regarded as other than one of purposeless change super-induced upon meaningless uniformity?
Seeing in our astral system many thousands of worlds in all stages of formation, from the most rudimental to that immediately preceding the present condition of those we deem perfect, it is unavoidable to conclude that all the perfect have gone through the various stages which we see in the rudimental. This leads us at once to the conclusion that the whole of our firmament was at one time a diffused mass of nebulous matter, extending through the space which it still occupies. So also, of course, must have been the other astral systems. Indeed, we must presume the whole to have been originally in one connected mass, the astral systems being only the first division into parts, and solar systems the second.
[T]he astronomical data give the number N of nebulae counted out to a given inferred "distance" <math>d</math>, and in order to determine the curvature... we must express N, or equivalently <math>V</math>, to which it is assumed proportional, in terms of <math>d</math>. ...from the second of formulae (3) and... (4)... to the approximation here adopted, 5)<math>V = \frac{4}{3} \pi d^2 (1 + \frac{3}{10} K d^2 + ...);</math>...plotting N against... <math>d</math> and comparing... with the formula (5), it should be possible operationally to determine the "curvature" <math>K</math>.
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