not more than eight people in the world who were able to understand the full meaning of his calculations and reasonings; and though his theory of gravitation was well received, and his name became one of the most renowned and honoured in the world, yet it was more than fifty years before his work was thoroughly appreciated.

It may therefore easily be imagined that it is not possible to give a simple sketch of what is contained in the 'Principia;' but some idea may perhaps be formed of the grandeur of the law of gravitation from an enumeration of some of the problems which Newton explained by its action.

1. He explained those laws of motion which Galileo had proved by experiment, and showed that it is the force of gravity which causes the weight of bodies; and determines, when combined with other laws, the rate at which they fall, and the path they describe.

2. He worked out the specific gravity of the planets, showing, for example, that the matter of which Saturn is composed is about nine times lighter than the matter of our earth.

3. He showed how the attractions of the sun and of the moon cause the tides of the sea, and worked out accurately the reason of the spring and neap tides.

4. He proved that the earth could not be a perfect globe, and measured almost exactly how great the bulge at the equator and the flattening at the poles must be. And this he did entirely by calculation, for no measurements had then been made, to lead anyone to doubt that the earth was a perfect globe.

5. He gave a complete explanation of the cause of the 'precession of the equinoxes,' the occurrence of which, as you will remember, Hipparchus had discovered (see p. 30).

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6. He not only showed why the planets move in ellipses while a line joining the sun and a planet cuts off equal areas in equal times; but he also accounted for many irregularities in these movements, arising from their mutual attractions, thus showing that gravitation explains not only the general laws but even apparent exceptions.

7. Of all bodies comets are apparently the most irregular, yet Newton calculated that they probably move in a peculiar curve called a parabola, and since his time it has been proved that the motions of all comets can be sufficiently well explained by this theory, with the exception of a few which move in ordinary ellipses like the planets, and return periodically. These and many other problems of the universe Newton showed could all be referred to the action of gravitation; and he concluded his work with a grand description of the mechanism of the heavens, dwelling with deep reverence upon the thought of that Infinite Mind which gave rise to such a wonderful and complex machinery, working in perfect order.

Chief Works consulted.-Brewster's Life of Newton;''Lives of Eminent Persons'--Lib. of Useful Knowledge; Airy's 'Elementary Astronomy;' Airy, 'On Gravitation.'

CHAPTER XIX.

SCIENCE OF THE SEVENTEENTH CENTURY (CONTINUED). Transits of Mercury and Venus-Kepler foretells their occurrence-1631, Gassendi observes a Transit of Mercury-1639, Horrocks foretells and observes a Transit of Venus-1676, Halley sees a Transit of Mercury, and it suggests to him a method for Measuring the Distance of the Sun-1691-1716, Halley describes this method to the Royal Society—Explanation of Halley's method.

First transits ever observed of Mercury and Venus, 16311639. We must now pause for a moment before passing on to Newton's discoveries in Optics, in order to mention a remarkable astronomical suggestion made about this time by the astronomer Halley (born 1656, died 1742), who was the friend and disciple of Newton.

You cannot fail to have heard and read something about the expeditions sent last December, 1874, into all parts of the world to observe the Transit (or Passage) of Venus across the sun. The object of these observations was to measure the sun's distance from the earth; and Halley was the first to propose this method of measurement, in 1691, and to show how it might be accomplished.

You know that the two planets Mercury and Venus are nearer to the sun than our earth is, and are therefore constantly passing between us and it. But usually they pass either below or above the sun, and it is only rarely that they cross over the bright disc, so as to be seen through

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the telescope as a round black spot upon the sun's face. With Mercury this happens at intervals of from seven to thirteen years; but with Venus it is much more rare, for though two transits generally come together with an interval of only eight years between them, yet after this there is a gap of more than a hundred years before another transit occurs.

After Kepler had finished the famous Rudolphine Tables he was able to use them to calculate when these transits would take place; and he showed that both Mercury and Venus would cross the sun's disc on certain days in the year 1631. A French philosopher named Gassendi took advantage of this prediction, and managed to observe Mercury passing across the face of the sun on November 7, 1631. He was the first who ever observed a transit. With Venus he was not so fortunate, for the transit of that planet took place when it was night at Paris, and so Gassendi had no chance of observing it.

It was not long, however, before this too was seen. You will remember that two transits of Venus occur close together with only eight years between them. Now Kepler had imagined that in 1639 Venus would pass a little to the south of the sun, and so no transit would take place. A young Englishman, however, named Jeremiah Horrocks, only twenty years of age, after going carefully over Kepler's tables, felt convinced that there would be a transit, and he even calculated within a few minutes the time when Venus would enter upon the sun's face. Full of enthusiasm at the chance of seeing this grand sight, he wrote to a friend at a distance, begging him also to watch through the telescope at three o'clock on the afternoon of December 4, 1639. His expectations were not disappointed, for at fifteen minutes

past three on that day the planet began to creep over the face of the sun. For twenty minutes Horrocks watched it, and then the sun set and he could see no more. He had been able to notice, however, that Venus was much smaller in comparison with the sun than had been formerly supposed. Horrocks and his friend Crabtree were the only people in the whole world who saw this transit of Venus, the first one ever observed.

Halley suggests that the Sun's distance may be measured by the Transit of Venus, 1691.-This was all that was known about transits when Halley went to St. Helena in 1676 to study the stars of the southern hemisphere. Here he also observed a transit of Mercury, and after watching the small black spot travelling across the face of the sun, and noting the time it took in going from one side to the other, the idea occurred to him that it would be possible to learn the distance of the sun by measuring the path of a planet across its face. As Mercury, however, is very far from us, and near to the sun, it would not answer the purpose so well as Venus, which is much nearer the earth.

Halley knew that another transit of Venus would take place in 1761, and as he could not hope to live till then, he read a paper to the Royal Society in 1691, and another in 1716, beseeching the astronomers who should live after him not to let such an opportunity pass, and describing the way in which the observations should be made. It is this method which we must now try to understand as far as it is possible without mathematics.

First of all I must tell you two facts which astronomers knew already. The proportion of the distances of the planets was ascertained, as you will remember, by Kepler (see p. 100). Therefore it was known that Venus is (in round