LITMIR.BIZ

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the sphere inscribed in it will be Venus’s orbit. In Venus inscribe an octahedron; the sphere inscribed in it will be Mercury’s.’

      The above quotation is an instance of Kepler’s wild and imaginative genius, which ultimately led him to make those sublime discoveries associated with planetary motion which are known as ‘Kepler’s Laws.’

      He describes himself as ‘troublesome and choleric in politics and domestic matters;’ but in his relations with scientific men he was affable and pleasant. He showed no jealousy of a rival, and was always ready to recognise merit in others; nor did he hesitate to acknowledge any error of his own when more recent discoveries proved that he was wrong.

      Some of his works contain passages, written in a jocular strain, indicative of a bright and cheerful temperament. The following characteristic paragraph refers to the opinions of the Epicureans with regard to the appearance of a new star, which they ascribed to a fortuitous concourse of atoms: ‘When I was a youth, with plenty of idle time on my hands, I was much taken with the vanity, of which some grown men are not ashamed, of making anagrams by transposing the letters of my name written in Latin so as to make another sentence. Out of Ioannes Keplerus came Serpens in akuleo (a serpent in his sting); but not being satisfied with the meaning of these words, and being unable to make another, I trusted the thing to chance, and, taking out of a pack of playing-cards as many as there were letters in the name, I wrote one upon each, and then began to shuffle them, and at each shuffle to read them in the order they came, to see if any meaning came of it. Now, may all the Epicurean gods and goddesses confound this same chance, which, although I have spent a good deal of time over it, never showed me anything like sense, even from a distance. So I gave up my cards to the Epicurean eternity, to be carried away into infinity; and it is said they are still flying about there, in the utmost confusion, among the atoms, and have never yet come to any meaning. I will tell those disputants, my opponents, not my own opinion, but my wife’s. Yesterday, when weary with writing, and my mind quite dusty with considering these atoms, I was called to supper, and a salad I had asked for was set before me. “It seems, then,” said I aloud, “that if pewter dishes, leaves of lettuce, grains of salt, drops of water, vinegar and oil, and slices of egg, had been flying about in the air from all eternity, it might at last happen by chance that there would come a salad.” “Yes,” says my wife, “but not so nice and well dressed as this of mine is.”‘

      Notwithstanding the frequent interruptions which, owing to various reasons, retarded his labours, Kepler was able to bring to a successful completion the numerous and important works upon which he was engaged during his lifetime, the voluminous nature of which may be imagined when it is stated that he published thirty-three separate works, besides leaving behind twenty-two volumes of manuscript.

      During his researches on the motions of Mars, Kepler discovered that the planet sometimes travelled at an accelerated rate of speed, and at another time its pace was diminished. At one time he observed it to be in advance of the place where he calculated it should be found, and at another time it was behind it. This caused him considerable perplexity, and, feeling convinced in his mind that the form of the planet’s orbit could not be circular, he was compelled to turn his attention to some other closed curve, by which those inequalities of motion could be explained.

      After years of careful observation and study, Kepler arrived at the conclusion that the form of the planet’s orbit is an ellipse, and that the Sun occupies one of the foci. He afterwards determined that the orbits of all the planets are of an elliptical form.

      Having discovered the true form of the planetary orbits, Kepler next endeavoured to ascertain the cause which regulates the unequal motion that a planet pursues in its path. He observed that when a planet approached the Sun its motion was accelerated, and as it receded from him its pace became slower.

      This he explained in his next great discovery by proving that an imaginary line, or radius-vector, extending from the centre of the Sun to the centre of the planet ‘describes equal areas in equal times.’ When near the Sun, or at perihelion, a planet traverses a larger portion of its arc in the same period of time than it does when at the opposite part of its orbit, or when at aphelion; but, as the areas of both are equal, it follows that the planet does not always maintain the same rate of speed, and that its velocity is greatest when nearest the Sun, and least when most distant from him.

      By the application of his first and second laws Kepler was able to formulate a third law. He found that there existed a remarkable relationship between the mean distances of the planets and the times in which they complete their revolutions round the Sun, and discovered ‘that the squares of the periodic times are to each in the same proportion as the cubes of the mean distances.’ The periodic time of a planet having been ascertained, the square of the mean distance and the mean distance itself can be obtained. It is by the application of this law that the distances of the planets are usually calculated.

       These discoveries are known as Kepler’s Laws, and are usually classified as follows:—

      1. ‘The orbit described by every planet is an ellipse, of which the centre of the Sun occupies one of the foci.

      2. ‘Every planet moves round the Sun in a plane orbit, and the radius-vector, or imaginary line joining the centre of the planet and the centre of the Sun, describes equal areas in equal times.

      3. ‘The squares of the periodic times of any two planets are proportional to the cubes of their mean distances from the Sun.’[1]

      These remarkable discoveries do not embrace all the achievements by which Kepler has immortalised his name, and earned for himself the proud title of ‘Legislator of the Heavens;’ he predicted transits of Mercury and Venus, made important discoveries in optics, and was the inventor of the astronomical telescope.

      Galileo Galilei, the famous Italian astronomer and philosopher, and the contemporary of Kepler and of Milton, was born at Pisa on February 15, 1564.

      His father, who traced his descent from an ancient Florentine family, was desirous that his son should adopt the profession of medicine, and with this intention he entered him as a student at the University of Pisa. Galileo, however, soon discovered that the study of mathematics and mechanical science possessed a greater attraction for his mind, and, following his inclinations, he resolved to devote his energies to acquiring proficiency in those subjects.

      In 1583 his attention was attracted by the oscillation of a brass lamp suspended from the ceiling of the cathedral at Pisa. Galileo was impressed with the regularity of its motion as it swung backwards and forwards, and was led to imagine that the pendulum movement might prove a valuable method for the correct measurement of time. The practical application of this idea he afterwards adopted in the construction of an astronomical clock.

      Having become proficient in mathematics, Galileo, whilst engaged in studying the writings of Archimedes, wrote an essay on ‘The Hydrostatic Balance,’ and composed a treatise on ‘The Centre of Gravity in Solid Bodies.’ The reputation which he earned by these contributions to science procured for him the appointment of Lecturer on Mathematics at the University of Pisa. Galileo next directed his attention to the works of Aristotle, and made no attempt to conceal the disfavour with which he regarded many of the doctrines taught by the Greek philosopher; nor had he any difficulty in exposing their inaccuracies. One of these, which maintained that the heavier of two bodies descended to the earth with the greater rapidity, he proved to be incorrect, and demonstrated by experiment from the top of the tower at Pisa that, except for the unequal resistance of the air, all bodies fell to the ground with the same velocity.

       As the chief expounder of the new philosophy, Galileo had to encounter the prejudices of the followers of Aristotle, and of all those who disliked any innovation or change in the established order of things. The antagonism which existed between Galileo and his opponents, who were both numerous and influential, was intensified by the bitterness and sarcasm which he imparted into his controversies, and the attitude assumed by his enemies at last became so threatening that he deemed it prudent to resign the Chair of Mathematics in the University of Pisa.

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