LIFE AND V/ORKS OF KEPLER. 107 



During tbese times of trouble and disorder all Germany, agitated, as 

 it were, by a violent storm, seemed little else than a tbeater for the evo- 

 lution of armies and the calamities which accompany them. Oue of the 

 most terrible contests which history records, the war of thirty years, 

 spread desolation and the contagion of deadly maladies tlirongli all the 

 provinces. In this cruel extremity Kepler, who to assist his mother had 

 renounced the innctions of professor, was plunged in an ever-increasing 

 destitution, against which his ardent spirit struggled without respite. 

 But a last affliction was in reserve for him: he lost a daugliter of the 

 age of seventeen years. It was now that, bearing up against these dis- 

 tresses, he sought refuge in those serene regions into which the troubles 

 of earth do not penetrate, and, casting aside the ini])ortunate burden of 

 obligatory or lucrative labors, devoted all his thoughts to the composi- 

 tion of a work which, as he tells us, yielded him more pleasure than all 

 its readers together could experience in its perusal. Those inthiite 

 spaces which surround us, whose eternal silence dismayed the sceptical 

 reason of Pascal, possessed, in the harmonious diversity of movements 

 which they accomplish, an inexhaustible attraction for the mystical im- 

 aginatiou of Kepler; and as he thought that he had long heard in the 

 depth of his soul the perpetual chorus of the mysterious voices of nature, 

 he endeavored to give it utterance in the strange work entitled, "■Ear- 

 moniccs mundi, Hhri quinqne,^' Five books of the harmony of the world. 



He first studies, geometrically, many regular figures, and the analyt- 

 ical views to which he is led would have sufficed, as one of our most 

 distinguished colleagues has said, to preserve the work from oblivion. 

 He reduces his i)roblem to an equation, and interprets with exactness all 

 its solutions. This, and nothing more, is regarded as within the scope 

 of science at the present day; but sucli a result does not satisfy Kepler. 

 "It is proved," he says, "that the sides of regular polygons "must ne- 

 cessarily remain unknown, being, from tlieir nature, imdiscoverable. 

 Xor is there anything surprising in the tact that ichat occurs in the arch- 

 etype of the world cannot be expressed in the conformation of its partsP 

 Proceeding afterward to the consideration of human music, and recalling 

 the idea of Pythagoras, who, we are told, compared the planets to the 

 seven chords of the lyre, he aims to show how man, imitating the Cre- 

 ator, by a natural instinct is led, as regards the notes of his voice, to 

 make the same choice and observe the same proportion which God has 

 seen fit to introduce into the general harmony of the celestial move- 

 ments; the same thought of the Creator being thus translated into all 

 his designs, of which one may serve as the interpreter and figure for 

 another. 



Seeking harmonies wherever they are possible, Kepler devotes a 

 chapter to politics: "Cyrus," he says, "having seen in childhood a man 

 of tall stature clothed in short tunic, and near him a dwarf habited in a 

 long and llowing robe, was of opinion that they should exchange gar- 

 ments in order that each might have what suited his size; but his 

 master pronounced that each should be left in possession of what be- 

 longed to him. The two opinions might be reconciled by decreeing that 

 the first should, after the exchange, give to the dwarf a certain sum of 

 money. Every one," adds Kepler, "clearly sees by this example that a 

 geometric proportion may be harmonic, such is 1, 2, 4, or the beneficial 

 arrangement which gives to the tallest the longest robe. An arithmet- 

 ical proportion may also be harmonic: such is 2, 3, 4, or the useful ex- 

 change which allows not the dwarf, possessing a long robe, to lose his 

 property, but enables him to change it into money which he may appl}' 

 to a better purpose." 



