Nov. 20, 1879] 



NATURE 



59 



telescope a practical instrument could not lay it aside till 

 he had exhausted what it had to tell him, or that his whole 

 thoughts were turned from the mathematical and ap- 

 parently abstract entities which we have been describing 

 to discuss the system of the universe in the new light he 

 had brought to bear on it. Yet the choice he made has 

 proved to be wrong. It was through the door of mathe- 

 matics—not through the tube of the telescope— that the 

 discoveries of the true system of the universe were destined 

 to pass. Galileo's facts made it practically certain that 

 the Copernican theory was right, and that the sun was the 

 centre of the orbit of each of the planets. Kepler en- 

 larged these statements, establishing, by a patient industry 

 that was never surpassed, that the orbits are ellipses 

 nearly circles, with the sun in one focus— that the line 

 drawn from sun to planet sweeps over equal areas in 

 equal times— that the square of the time taken to describe 

 a planet's orbit, divided by the cube of its mean distance 

 from the sun, is a fraction which is the same for every 

 planet of the system. Till Newton appeared to interpret 

 them, these results were only statistical facts ; and Newton 

 himself could throw no light on them till he had invented 

 the Fluxional Calculus and discovered the properties of 

 an abstract fluent quantity, such as a speed or a curvature, 

 which is continuously changing. 



And yet how near Galileo came to the secret ! We 

 have seen that he was in fact compelled to deal with the 

 fundamental problems of the Fluxional Calculus in dis- 

 cussing falling bodies and projectiles. It was his famous 

 scholar Cavalleri whose Calculus of Indivisibles fore- 

 shadowed the Fluxional Calculus of Newton. It is diffi- 

 cult to say how much of Cavalleri's views were developed 

 out of the note-books of his master's lectures and out of 

 his own consideration of the problems that master had 

 triumphantly solved. Like many of Galileo's pupils, he 

 had published works of his own, in which it was doubtless 

 difficult to separate what was original from what was 

 borrowed. From about 1592 till about 1638 — forty-six 

 years— Galileo had published scarcely anything except on 

 the planetary system. The inclined planes, the falling 

 bodies, the pendulums, the cycloids, were so many pro- 

 blems worked out in his youth — during the early years of 

 his professoriates at Pisa and Padua — scattered in students' 

 note-books, and germinating in students' minds through- 

 out the world. It was so with his theory of projectiles; 

 and Cavalleri, who was one of his old students and his 

 successor at the University of Padua, published the theory 

 of projectiles without referring it to its real author. 

 Challenged by Galileo, he allowed his obligations frankly, 

 and their friendship was not interrupted. Cavalleri pub- 

 lished his theory of indivisibles in Galileo's old age (1635), 

 calling it " Geometria indivisibilibus continuorum nova 

 quadam ratione promota," after he had apologised for his 

 former awkward error. The shape of the new theory was 

 Cavalleri's own — the impulse came almost certainly from 

 the discoverer of the true theory of falling bodies and of 

 projectiles. 



We owe the theory of indivisibles to Cavalleri, and not 

 to Galileo, partly, no doubt, because for the greater por- 

 tion of his manhood his astronomical discoveries, and the 

 discussions they brought with them, filled Galileo's mind 

 almost exclusively ; partly because for the last five-and- 

 twenty years of his life most of his thought had to be 

 spent on his relations with the Church, to which he was 

 sincerely attached. In 1616 he was warned that the 

 Copernican hypothesis was to be considered as false. 

 Religious persecutions were not then unknown in Pro- 

 testant countries, and people were tortured for witchcraft 

 as well as heresy. Hut it was reserved to the Catholic 

 Church in Italy to erect the Aristotelian doctrines and 

 the Ptolemaic system into an article of faith. A century 

 after Luther shook the world at Wittenberg, had brought 

 dreadful days for mathematicians, physicists, and re- 

 ormers, in Italy. When Galileo was a youth of twenty- 



three, two years before he was called to be professor at 

 Pisa. Barozzi, who had occupied himself at Venice with 

 the discussion of the asymptotes of curves, was believed 

 to be guilty of dealing in sorcery and witchcraft, of cast- 

 ing lots, and of causing the drought which reigned in the 

 Island of Cyprus. He was condemned by the Inquisi- 

 tion in 15S7, partly because he had a great number of 

 curious books and a wonderful collection of astronomical 

 and mathematical instruments. Porta, the famous author 

 of the " Magia Naturalis " — the reputed discoverer of the 

 camera obscura, — was summoned to Rome to give an 

 account of his opinions. Giordano Bruno was burned at 

 Venice in 1600, hardly less for his daring speculations in 

 religion than because he had attacked Aristotle and 

 adopted the system of Copernicus. The aged Arch- 

 bishop of Spalatro, de Domir.is, to whom Newton at- 

 tributes the successful explanation of the colours of the 

 rainbow, died in 1624 in the prisons of the Inquisition, 

 and all that death had left to the mercies of his persecu- 

 tors was publicly committed to the flames. The skies of 

 Italy were black with the smoke of these burnings, the 

 air was heavy with suspicion and terror. The Inquisition 

 tried men for heresies which had been denounced by un- 

 known enemies, and the processes of moral and intellectual 

 torture to which it subjected those who were brought 

 before its tribunals were only more oppressive because the 

 secret of their details was closely kept. Galileo wrote a 

 letter to his friend and pupil the Jesuit Castelli, in 1614, 

 copies of which were privately circulated, but which was 

 not printed till twenty years later. In that noble w-riting 

 he lays down with equal firmness and clearness the broad 

 lines with separate scientific and religious thought, and 

 shows himself deeply penetrated with religious as with 

 scientific faith. A Jesuit father denounced it, another 

 preached against him as a witness for the Copernican 

 system. Though the great works he had hitherto 

 published, that on the Solar Spots and the " Nuncius 

 Sidereus" had neither of them committed their author 

 to the Copernican theory of the universe, the Church 

 resolved to anticipate and to forbid the support by the 

 most illustrious of living astronomers of doctrines, which, 

 whatever else might be said of them, were clearly fatal to 

 the authority of the Peripatetics. 



Galileo went to Rome (in 1616) to struggle for as much 

 liberty as could be saved, but he was deeply disap- 

 pointed with the result. He retracted nothing, because 

 he had neither been tried nor convicted, but the 

 officers of the Inquisition waited on him, and left 

 him an official warning that it was not permitted to 

 teach that the sun was the fixed centre of our system, 

 and that the earth revolved around it. Silence was 

 imposed on him ; and it was only after the new Pope 

 was appointed, who, as a Cardinal, had opposed the 

 promulgation of this warning, that he ventured again 

 to think of publishing his views. The book in which 

 they appeared in 1632 was a three-cornered dialogue 

 between a Ptolemaist and a Copernican, with .1 third 

 person acting as a kind of half intelligent chorus. The 

 arguments of the Ptolemaist were, of course, the weaker, 

 as°in Galileo's hands it was impossible that it should be 

 otherwise. To secure the imprimatur of the censorship, 

 he prefixed this statement to the book — " Within the last 

 few years a salutary edict was promulgated at Rome, in 

 which, in view of dangerous scandals, silence was en- 

 joined on the supporters of the Pythagorean doctrine of 

 the movement of the earth. Some have been rash enough 

 to sav that this dogma was not arrived at after a judicious 

 examination, but was promulgated in passion and in 

 ignorance, and it has been asserted that people utterly 

 without practice in astronomical observations ought not 

 to attempt, bv a premature prohibition, to clip the wings 

 of speculation. Hearing these complaints my heart 

 burned within me, and I could not keep silence. Having 

 been fully informed of this wise decision, 1 resolved to 



