The theoretic law of the velocity of sound enunciated by Newton on purely mechanical considerations, was found wrong by one-sixth.  The error remained unaccounted for until the time of Laplace, who, suspecting that the heat disengaged by the compression of the undulating strata of the air, gave additional elasticity, and so produced the difference, made the needful calculations and found he was right.  Thus acoustics was arrested until thermology overtook and aided it.  When Boyle and Marriot had discovered the relation between the density of gases and the pressures they are subject to; and when it thus became possible to calculate the rate of decreasing density in the upper parts of the atmosphere, it also became possible to make approximate tables of the atmospheric refraction of light.  Thus optics, and with it astronomy, advanced with barology.  After the discovery of atmospheric pressure had led to the invention of the air-pump by Otto Guericke; and after it had become known that evaporation increases in rapidity as atmospheric pressure decreases; it became possible for Leslie, by evaporation in a vacuum, to produce the greatest cold known; and so to extend our knowledge of thermology by showing that there is no zero within reach of our researches.  When Fourier had determined the laws of conduction of heat, and when the Earth’s temperature had been found to increase below the surface one degree in every forty yards, there were data for inferring the past condition of our globe; the vast period it has taken to cool down to its present state; and the immense age of the solar system—­a purely astronomical consideration.

Chemistry having advanced sufficiently to supply the needful materials, and a physiological experiment having furnished the requisite hint, there came the discovery of galvanic electricity.  Galvanism reacting on chemistry disclosed the metallic bases of the alkalies, and inaugurated the electro-chemical theory; in the hands of Oersted and Ampere it led to the laws of magnetic action; and by its aid Faraday has detected significant facts relative to the constitution of light.  Brewster’s discoveries respecting double refraction and dipolarisation proved the essential truth of the classification of crystalline forms according to the number of axes, by showing that the molecular constitution depends upon the axes.  In these and in numerous other cases, the mutual influence of the sciences has been quite independent of any supposed hierarchical order.  Often, too, their inter-actions are more complex than as thus instanced—­involve more sciences than two.  One illustration of this must suffice.  We quote it in full from the History of the Inductive Sciences.  In book xi., chap, ii., on “The Progress of the Electrical Theory,” Dr. Whewell writes:—­