they also resolved the orbits of the heavenly bodies into circular motions, discovered the precession of the equinoxes, and knew also the apparent motions of the planets and their periods.  They could predict eclipses of the sun and moon, and knew that the orbit of the sun and planets was through a belt in the heavens, of a few degrees in width, which they called the Zodiac.  They did not know, indeed, the difference between real and apparent motion, nor the distance of the sun and stars, nor their relative size and weight, nor the laws of motion, nor the principles of gravitation, nor the nature of the Milky Way, nor the existence of nebulae, nor any of the wonders which the telescope reveals; but in the severity of their mathematical calculations they were quite equal to modern astronomers.

If Copernicus revolutionized astronomy by proving the sun to be the centre of motion to our planetary system, Galileo gave it an immense impulse by his discoveries with the telescope.  These did not require such marvellous mathematical powers as made Kepler and Newton immortal,—­the equals of Ptolemy and Hipparchus in mathematical demonstration—­but only accuracy and perseverance in observations.  Doubtless he was a great mathematician, but his fame rests on his observations and the deductions he made from them.  These were more easily comprehended, and had an objective value which made him popular:  and for these discoveries he was indebted in a great measure to the labors of others,—­it was mechanical invention applied to the advancement of science.  The utilization of science was reserved to our times; and it is this utilization which makes science such a handmaid to the enrichment of its votaries, and holds it up to worship in our laboratories and schools of technology and mines, not merely for itself, but also for the substantial fruit it yields.

It was when Galileo was writing treatises on the Structure of the Universe, on Local Motion, on Sound, on Continuous Quantity, on Light, on Colors, on the Tides, on Dialing,—­subjects that also interested Lord Bacon at the same period,—­and when he was giving lectures on these subjects with immense eclat, frequently to one thousand persons (scarcely less than what Abelard enjoyed when he made fun of the more conservative schoolmen with whom he was brought in contact), that he heard, while on a visit to Venice, that a Dutch spectacle-maker had invented an instrument which was said to represent distant objects nearer than they usually appeared.  This was in 1609, when he, at the age of fifty-five, was the idol of scientific men, and was in the enjoyment of an ample revenue, giving only sixty half-hours in the year to lectures, and allowed time to prosecute his studies in that “sweet solitariness” which all true scholars prize, and without which few great attainments are made.  The rumor of the invention excited in his mind the intensest interest.  He sought for the explanation of the fact in the doctrine of refraction.  He meditated day and night.  At last he himself constructed an instrument,—­a leaden organ pipe with two spectacle glasses, both plain on one side, while one of them had its opposite side convex, and the other its second side concave.