The first law of light is an algebraic formula: The intensity of the fluid decreases as the square of the distance increases, and vice versâ.
The second law is equally mathematical: The angles of incidence and reflection are equivalent for every ray. Thus a sunbeam, falling on the table before me at an angle of forty-five degrees, will be reflected at the same angle.
Here, then, in the development of these two general laws, we behold the miracle of innumerable squares, circles, angles, such as sweep over countless millions of leagues in the stellar spaces, with a regularity that no Euclid or Legendre might ever hope to trace. And can it be possible that after all the great cause which thus geometrizes may be devoid of all geometrical knowledge—nay, of even the faculty of rationality? If so, then might a blind mole, or the abstraction of a nonentity, compose a system of beauty and order superior in both accuracy and splendor to the Principia of Newton or the sublime theories of La Place!
You can scarcely commence the estimation of chances in reference to these luminous angles being continually formed all over the material universe. Even imagination reels before the immensity of the conception. Think of all the fire-beams that emanate from the sun during one long summer day—of all the rays which flash out from the high stars for only a single night! Then let the mind travel back over the march of dim and distant centuries, gathering age upon age, rolling cycle after cycle, in those vast segments of eternity where the Alps and Andes seem evanescent as the snow-flakes that ride on the gyrations of the whirlwind around their hoary summits; where Platonic years are fleeting as the pulsations of the pendulum, and even the starry galaxies come and go “like rainbows.” Then bid your soaring fancy lift her lightning-wings away from world to world, and behold the horizon of the space which hath no limits, still opening for ever onwards and upwards, and thickening all around with serial columns of suns and stars, and undulating like some shoreless sea with its waves of nebulous light. Then tell me the number of rays that have shot athwart this teeming expanse of immensity since the sons of heaven shouted their choral hymns in the morning of creation. And answer me, who shall calculate the chances against the sceptical hypothesis here? Only a God of infinite intelligence may solve this infinite problem.
INSTANCE V.—ASTRONOMY.
The first law of the celestial motions discovered by Kepler, like all the rest, expresses a mathematical formula: All the planetary orbits are regular ellipses, in the lower focus of which stands the sun.
Now, as the ellipse contains an infinite number of geometrical points, it follows that the chances against the repetition of this figure by the progress of the same body along the same path in space must be infinity multiplied into infinity, compared with zero.
The second law is equally decisive. It may be stated thus: The times occupied by a planet in describing any given arc of its orbit are always as the areas of the sectors, formed by straight lines from the beginning and end of the arcs to the sun as a common centre. And here it cannot fail to be remarked that every term of the enunciation is purely mathematical.
But the third law of Kepler is still more astonishing. The squares of the periods of the planetary revolutions vary as the cubes of their distances from the sun.
What amazing evolutions are these to be the work of unthinking masses of matter! What angel’s music is this among the stars to be chimed by the choir of tongueless atoms! And well might the inspired old man exclaim when the heavenly harmony first broke upon his ear: “I have stolen the golden secret of the Egyptians. I triumph. I will indulge my sacred fury. I care not whether my book be read now or by posterity. I can afford to wait a century for readers, when God himself has waited six thousand years for an observer.”