We have passed over the name of Descartes, almost contemporary with Galileo, the founder of modern dynamics, but his initiation of one of the greatest improvements of mathematical method cannot be overlooked. This era was the beginning of the Golden Age of Mathematics that embraced the lives of the versatile Euler, equally at home in dynamics and optics and the lunar theory; of La Grange, author of the elegant "Mécanique Analytique"; and La Place, of the unparalleled "Mécanique Céleste." With them and a fully elaborated calculus Newton's universal law had been extended to all the motions of the cosmos. Even the tides and precession of the equinoxes and Bradley's nutation were accounted for and explained. Mathematical or gravitational astronomy had attained its pinnacle—it seemed to be a finished science: all who were to come after must be but followers.

The culmination of one great period, however, proved to be but the inception of another epoch in the development of the living science.

The greatest observer of all time, with a telescope built by his own hands, had discovered a great planet far beyond the then confines of the solar system. Mathematicians would take care of Uranus, and Herschel was left free to build bigger telescopes still, and study the construction of the stellar universe. Down to his day astronomy had dealt almost wholly with the positions and motions of the celestial bodies—astronomy was a science of where. To inquire what the heavenly bodies are, seemed to Herschel worthy of his keenest attention also. While "a knowledge of the construction of the heavens has always been the ultimate object of my observations," as he said, and his ingenious method of star-gauging was the first practicable attempt to investigate the construction of the sidereal universe, he nevertheless devoted much time to the description of nebulæ and their nature, as well as their distribution in space. He was the founder of double-star astronomy, and his researches on the light of the stars by the simple method of sequences were the inception of the vast fields of stellar photometry and variable stars. The physics of the sun, also, was by no means neglected; and his lifework earned for him the title of father of descriptive astronomy.

While progress and discovery in the earlier fields of astronomy were going on, the initial discoveries in the vast group of small planets were made at the beginning of the nineteenth century. The great Bessel added new life to the science by revolutionizing the methods and instruments of accurate observation, his work culminating in the measure of the distance of 61 Cygni, first of all the stars whose distance from the sun became known.

Wonderful as was this achievement, however, a greater marvel still was announced just before the middle of the century—a new planet far beyond Uranus, whose discovery was made as a direct result of mathematical researches by Adams and Le Verrier, and affording an extraordinary verification of the great Newtonian law. These were the days of great discoveries, and about this time the giant of all the astronomical tools of the century was erected by Lord Rosse, the "Leviathan" reflector with a speculum six feet in diameter, which remained for more than half a century the greatest telescope in the world, and whose epochal discovery of spiral nebulæ has greater significance than we yet know or perhaps even surmise.

The living science was now at the height of a vigorous development, when a revolutionary discovery was announced by Kirchhoff which had been hanging fire nearly half a century—the half century, too, which had witnessed the invention of photography, the steam engine, the railroad, and the telegraph: three simple laws by which the dark absorption lines of a spectrum are interpreted, and the physical and chemical constitution of sun and stars ascertained, no matter what their distance from us.

Huggins in England and Secchi in Italy were quick to apply the discovery to the stars, and Draper and Pickering by masterly organization have photographed and classified the spectra of many hundred thousand stars of both hemispheres, a research of the highest importance which has proved of unique service in studies of stellar movements and the structure of the universe by Eddington and Shapley, Campbell and Kapteyn, with many others who are still engaged in pushing our knowledge far beyond the former confines of the universe.

Few are the branches of astronomy that have not been modified by photography and the spectroscope. It has become a measuring tool of the first order of accuracy; measuring the speed of stars and nebulæ toward and from us; measuring the rotational speed of sun and planets, corona and Saturnian ring; measuring the distances of whole classes of stars from the solar system; measuring afresh even the distance of the sun—the yardstick of our immediate universe; measuring the drift of the sun with his entire family of planets twelve miles every second in the direction of Alpha Lyræ; and discovering and measuring the speed of binary suns too close together for our telescopes, and so making real the astronomy of the invisible.

Impatient of the handicap of a turbulent atmosphere, the living science has sought out mountain tops and there erected telescopes vastly greater than the "Leviathan" of a past century. There the sun in every detail of disk and spectrum is photographed by day, and stars with their spectra and the nebulæ by night. Great streams of stars are discovered and the speed and direction of their drift ascertained. The marvels of the spiral nebulæ are unfolded, their multitudinous forms portrayed and deciphered.

And their distances? And the distances of the still more wonderful clusters? Far, inconceivably far beyond the Milky Way. And are they "island universes"? And can man, the measurer, measure the distance of the "mainland" beyond?