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MEASUREMENT OF ANGLES.

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point where the index marks the circle, say at 10°, then turning

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the index towards S, observe where it makes the circle, say 20°, the difference 10°, is the angular distance of S from B. The instruments of Ptolemy were constructed upon this principle though not so perfect, using shadows, and other contrivances, instead of simply observing through two vanes or sight holes.

Ptolemy had not intended his system to be received other than an hypothesis, which might account for the observed motions; he did not profess this to be the actual order of the world, but his successors, without their great master's love for truth and careful study, soon gave to these supposed spheres and orbs, a real existence, and the heavens became crowded with crystalline spheres moving in all directions, and with all velocities, and as often as new motions, or irregularities in the old ones were detected, new circles moving at their centres round the old ones, were added, called epicycles, so that at last cycles and epicycles, revolved in all directions, bearing the planets along with them, until amid the crowd of spheres and crystal orbs the brain grew dizzy, and could not comprehend the mysterious revolutions. Amidst all this confusion of " Cycle and epicycle, orb on orb," a bright luminary arose, and with a master hand dashed aside the crystal spheres of the successors of Ptolemy, substituting instead, the simplicity of truth. This man was Nicholas CoperniAt the time when the true system was about to be made

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known, the followers of the Egyptian school were in their glory, Purbach, professor of Astronomy at Vienna, had reviewed the whole system, and by the addition of various new spheres, had succeeded in explaining all the observed irregularities of the planets, and thus silenced forever the sneers of infidels, and particularly those of Alphonso X. King of Castile, who had observed, "Had the Deity consulted me at the creation of the universe, I could have given him some good advice." But the hour of triumph was short. Error, which had sat like a cloud npon the mountain top, overshadowing all below, was ready to vanish before the bright beams of the sun of Truth.

The obscurity which hangs over those early days, conceals the steps by which Copernicus arrived at the knowledge of the true system. It required indeed a bold mind to disregard all the religious dogmas of the time, and methodise a system, which as Tycho Brahe, himself an illustrious astronomer, observes, "Moved the earth from its foundation, stopped the revolution of the firmament, made the sun stand still, and subverted the whole ancient order of the universe." Such a mind however, Copernicus seems to have possessed, although his modesty prevented him from publishing his views, until at so late a period, that he only lived just long enough to see a printed copy of that book which was to gain him immortal honor. At this time, in the words of his admirable friend the Bishop of Culm, "He was occupied with weightier cares"-about to test the reality of that unknown world whose mysteries sages have endeavored but in vain to understand, from remotest ages. The first gleam of truth which burst upon the mind of Copernicus was doubtless the idea that the apparent revolution of the starry orbs around the earth from east to west once in 24 hours, was actually accomplished by a revolution of our earth on its axis in the same time but in the contrary direction. Refer to the following diagram and observe the simplicity of this explanation.

Here is the earth, and around it on all sides the celestial concave. Suppose now an observer situated upon the earth should see a particular star A, directly overhead at sunset, and that the earth was revolving once on its axis in 24 hours in the direction of

DIURNAL REVOLUTION OF THE EARTH,

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the letters A B, after an interval of 6 hours, the spectator would

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arrive under B, and perceive the star B directly overhead while the star A would be just ready to sink below the horizon. After an interval of 18 hours more he would again arrive under A, having performed a complete revolution. Now as all the stars are observed to have a perfectly uniform motion, moving once around the earth in 24 hours, never changing their apparent positions with regard to each other, doubtless this supposition appeared to Copernicus the most rational, and its truth is now incontestably proved, and universally admitted. The great motion of the heavens being thus shown not to be real, but only apparent, Copernicus naturally endeavored to ascertain how far certain other motions, which the followers of Ptolemy explained by innumerable cycles, and crystalline spheres, as if all their observed motions were real, might be explained by a movement of our earth instead of these bodies. The actual size of the sun and planets, as also their actual distance from the earth, not being known at that time, rendered this problem more difficult, and beside this, he was wholly unacquainted with the laws of gravitation. Hence it was no ordinary effort of mind to reduce the various complicated motions of the planets and the sun to one harmonious system. Pythagoras, the celebrated Greek philosopher who lived 500 years before Copernicus, had already suggested the idea that the sun was the central body, and that the earth and planets were revolving about the sun at various distances. He did not attempt

however to account for the irregularities observed in the planetary motions. Copernicus might have easily perceived, and no doubt did perceive, that the motion of the sun backwards in the heavens, and to which we have alluded, was only apparent, and was due to a real motion of our earth, which may be illustrated thus:

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Let S represent the sun, occupying the centre of the system, and E the earth moving in an orbit around it. Now an observer on the earth at E would perceive the sun S, apparently projected against the heavens near the star B. If the earth was stationary, then after 24 hours, turning around in the direction of the arrow, i. e., from left to right, or west to east, (the north pole in the diagram being supposed towards the eye) the sun would again appear close to the star B, and the sun and stars would come to the meridian or mid-heaven together. Now suppose the earth to have moved forward in its orbit to A, and imagine the sphere of stars figured in the diagram to be expanded to an infinite distance, it will be easy to see that the sun and the star B, will no longer come to the meridian together, the meridian being represented by the black line on A, but that, on the supposition that the earth is turning in the direction of the arrow, the sun would come to the meridian, or this line, much later than the star, and would appear among the stars at C. To explain the motions of Mercury, and

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Venus, Copernicus supposed them to be revolving around the sun, but in orbits within the earth's. This would explain why they were never seen at any considerable distance from that lumihary and also the various irregularities observed in their motions, Thus:

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Let S be the sun, E the earth, and V, Venus. In the situation represented in the diagram Venus would appear among the stars at A, the sun being at B. In this case, supposing the earth to turn on its axis in the direction of the arrow, the sun would come to the meridian or overhead, to an observer on its surface, before the planet, which consequently, setting after the sun, would be the evening star. Now supposing the earth stationary in its orbit, let Venus move from V to W. This would cause her to describe the arc A C in the heavens, gradually approaching the sun, which is apparently at B, and then appearing on the opposite side. When in the position W, still supposing the earth to turn on its axis in the direction of the arrow, Venus would come to the meridian, or rise before the sun and consequently be morning star. During the rest of her revolution in her orbit, from W to V she would seem to move backwards in the heavens, or retrograde from C to A, and at the points C and A she would appear for a short time stationary. We have supposed the earth to be at rest,

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