In the mathematician, astronomer, physicist, and philosopher, J. H. Lambert (1728-1777), Kant found a genius akin to his own, and through him hoped for a reformation of philosophy on the basis of the study of science. Lambert like his contemporary was a disciple of Newton, and in 1761 he published a book in the form of letters expressing views in reference to the Milky Way, fixed stars, central sun, very similar to those published by Kant in 1755. Lambert had heard of Wright's work, so similar to his own, a year after the latter was written.

Comets, now robbed of many of the terrors with which ancient superstition endowed them, might, he says, seem to threaten catastrophe, by colliding with the planets or by carrying off a satellite. But the same hand which has cast the celestial spheres in space, has traced their course in the heavens, and does not allow them to wander at random to disturb and destroy each other. Lambert imagines that all these bodies have exactly the volume, weight, position, direction, and speed necessary for the avoidance of collisions. If we confess a Supreme Ruler who brought order from chaos, and gave form to the universe; it follows that this universe is a perfect work, the impress, picture, reflex of its Creator's perfection. Nothing is left to blind chance. Means are fitted to ends. There is order throughout, and in this order the dust beneath our feet, the stars above our heads, atoms and worlds, are alike comprehended.

Laplace in his statement of the nebular hypothesis made no mention of Kant. He sets forth, in the Exposition of the Solar System, the astronomical data that the theory is designed to explain: the movements of the planets in the same direction and almost in the same plane; the movements of the satellites in the same direction as those of the planets; the rotation of these different bodies and of the sun in the same direction as their projection, and in planes little different; the small eccentricity of the orbits of planets and satellites; the great eccentricity of the orbits of comets. How on the ground of these data are we to arrive at the cause of the earliest movements of the planetary system?

A fluid of immense extent must be assumed, embracing all these bodies. It must have circulated about the sun like an atmosphere and, in virtue of the excessive heat which was engendered, it may be assumed that this atmosphere originally extended beyond the orbits of all the planets, and was contracted by stages to its present form. In its primitive state the sun resembled the nebulæ, which are to be observed through the telescope, with fiery centers and cloudy periphery. One can imagine a more and more diffuse state of the nebulous matter.

Planets were formed, in the plane of the equator and at the successive limits of the nebulous atmosphere, by the condensation of the different zones which it abandoned as it cooled and contracted. The force of gravity and the centrifugal force sufficed to maintain in its orbit each successive planet. From the cooling and contracting masses that were to constitute the planets smaller zones and rings were formed. In the case of Saturn there was such regularity in the rings that the annular form was maintained; as a rule from the zones abandoned by the planet-mass satellites resulted. Differences of temperature and density of the parts of the original mass account for the eccentricity of orbits, and deviations from the plane of the equator.

In his Celestial Mechanics (1825) Laplace states that, according to Herschel's observations, Saturn's rotation is slightly quicker than that of its rings. This seemed a confirmation of the hypothesis of the Exposition du Système du Monde.

When Laplace presented the first edition of this earlier work to Napoleon, the First Consul said: "Newton has spoken of God in his book. I have already gone through yours, and I have not found that name in it a single time." To this Laplace is said to have replied: "First Citizen Consul, I have not had need of that hypothesis." The astronomer did not, however, profess atheism; like Kant he felt competent to explain on mechanical principles the development of the solar system from the point at which he undertook it. In his later years he desired that the misleading anecdote should be suppressed. So far was he from self-sufficiency and dogmatism that his last utterance proclaimed the limitations of even the greatest intellects: "What we know is little enough, what we don't know is immense" (Ce que nous connaissons est peu de chose, ce que nous ignorons est immense).

Sir William Herschel's observations, extended over many years, confirmed both the nebular hypothesis and the theory of the systematic arrangement of the stars. He made use of telescopes 20 and 40 feet in focal length, and of 18.7 and 48 inches aperture, and was thereby enabled, as Humboldt said, to sink a plummet amid the fixed stars, or, in his own phrase, to gauge the heavens. The Construction of the Heavens was always the ultimate object of his observations. In a contribution on this subject submitted to the Royal Society in 1787 he announced the discovery of 466 new nebulæ and clusters of stars. The sidereal heavens are not to be regarded as the concave surface of a sphere, from the center of which the observer might be supposed to look, but rather as resembling a rich extent of ground or chains of mountains in which the geologist discovers many strata consisting of various materials. The Milky Way is one stratum and in it our sun is placed, though perhaps not in the very center of its thickness.

By 1811 he had greatly increased his observations of the nebulæ and could arrange them in series differing in extent, condensation, brightness, general form, possession of nuclei, situation, and in resemblance to comets and to stars. They ranged from a faint trace of extensive diffuse nebulosity to a nebulous star with a mere vestige of cloudiness. Herschel was able to make the series so complete that the difference between the members was no more than could be found in a series of pictures of the human figure taken from the birth of a child till he comes to be a man in his prime. The difference between the diffuse nebulous matter and the star is so striking that the idea of conversion from one to the other would hardly occur to any one without evidence of the intermediate steps. It is highly probable that each successive state is the result of the action of gravity.

In his last statement, 1818, he admitted that to his telescopes the Milky Way had proved fathomless, but on "either side of this assemblage of stars, presumably in ceaseless motion round their common center of gravity, Herschel discovered a canopy of discrete nebulous masses, such as those from the condensation of which he supposed the whole stellar universe to be formed."