and like the “physiological division of labour” in individual organisms, has been not only a specialisation of functions, but a continuous helping of each division by all the others, and of all by each.  Every particular class of inquirers has, as it were, secreted its own particular order of truths from the general mass of material which observation accumulates; and all other classes of inquirers have made use of these truths as fast as they were elaborated, with the effect of enabling them the better to elaborate each its own order of truths.

It was thus in sundry of the cases we have quoted as at variance with M. Comte’s doctrine.  It was thus with the application of Huyghens’s optical discovery to astronomical observation by Galileo.  It was thus with the application of the isochronism of the pendulum to the making of instruments for measuring intervals, astronomical and other.  It was thus when the discovery that the refraction and dispersion of light did not follow the same law of variation, affected both astronomy and physiology by giving us achromatic telescopes and microscopes.  It was thus when Bradley’s discovery of the aberration of light enabled him to make the first step towards ascertaining the motions of the stars.  It was thus when Cavendish’s torsion-balance experiment determined the specific gravity of the earth, and so gave a datum for calculating the specific gravities of the sun and planets.  It was thus when tables of atmospheric refraction enabled observers to write down the real places of the heavenly bodies instead of their apparent places.  It was thus when the discovery of the different expansibilities of metals by heat, gave us the means of correcting our chronometrical measurements of astronomical periods.  It was thus when the lines of the prismatic spectrum were used to distinguish the heavenly bodies that are of like nature with the sun from those which are not.  It was thus when, as recently, an electro-telegraphic instrument was invented for the more accurate registration of meridional transits.  It was thus when the difference in the rates of a clock at the equator, and nearer the poles, gave data for calculating the oblateness of the earth, and accounting for the precession of the equinoxes.  It was thus—­but it is needless to continue.

Here, within our own limited knowledge of its history, we have named ten additional cases in which the single science of astronomy has owed its advance to sciences coming after it in M. Comte’s series.  Not only its secondary steps, but its greatest revolutions have been thus determined.  Kepler could not have discovered his celebrated laws had it not been for Tycho Brahe’s accurate observations; and it was only after some progress in physical and chemical science that the improved instruments with which those observations were made, became possible.  The heliocentric theory of the solar system had to wait until the invention of the telescope before it could be finally established.