The use of hypothesis, as it is employed in astronomy, must be carried into the other sciences. This mode of procedure everywhere remains like to itself, although we do not always conceive it so clearly. “Its normal domain coincides with that of observation.” An hypothesis completes by anticipation what we know of facts and of their laws. Consequently, it is subject to be modified, corrected, or contradicted by a wider or deeper knowledge of facts. Hypotheses then are only valid during the time when they are advantageous, that is to say, as long as they serve to unite and co-ordinate our observations. As has been said, they labour to render themselves useless. But they are indispensable, and science, without them, could neither advance nor even begin. Far from giving too small a share to hypothesis, like Bacon, Comte would rather incur the reproof of having given it too large a one. He made too much use of it himself at the end of his life. But the theory which he gave of it in the _Cours de philosophie positive_ and of which certain features appeal again in Claude Bernard’s _Introduction a l’étude de la médecine experiméntale_, was a careful study of its nature and function. III. Astronomy, or at least that part of astronomy which bears the name of celestial mechanics, of all the physical sciences is the one which has been carried to the highest degree of perfection. Nowhere else have the phenomena been better reduced to a supreme law which allows us to foresee them with sufficient precision. But this result could only have been obtained by substituting the notion of a solar world to that of a universe.[123] This world is the only one which we can comprehend as a system. If the object of astronomy were the general laws of the universe, this science would be extraordinarily imperfect, not to say impossible. For what do we know about cosmic laws?[124] We do not even know whether Newton’s law applies to any or all systems of stars. We must then distinguish between astronomy as the science of our world and sidereal astronomy. The latter is not absolutely forbidden us, but we know very little on this subject, and we shall probably never know much more. Do the innumerable suns scattered in space form a general system, or do independent systems exist? Is space limitless? Is the number of celestial bodies an infinite one? philosophers ask. In truth the consideration of our world is positive. The consideration of the universe is not.