106 LIFE AND WORKS OF KEPLER. 



g'eometer newly married;" and, to solve it, lie proceeds to discuss proi- 

 blenis of geomtitry which may be accounted among the most difficult 

 Avhich had been till then undertaken. A singular consequence deduced 

 is the following : 



" Under the influence of a good genius who was, no doubt, a geometer, 

 the constructors of casks have given them precisely the form which, for 

 a line of the same length as that measured by the gangers, aflbrds the 

 greatest possible capacity ; and, as in the neighborhood of the maximum 

 the variations are insensible, small accidental deviations exert no appre- 

 ciable influence on the capacity, the expeditious measurement of which 

 is consequently sufficiently exact." This idea respecting maxinm, thrown 

 out in passing, but in such absolute terms, by Kepler, received its devel- 

 opment twenty years later from Fermat, of whom it is one of the titles 

 to luuior. 



Kepler adds : " Who will deny that nature alone, without any process 

 of reasoning, can teach geometry, when our coopers, guided only by their 

 eyes and an instinctive sense of the becoming, are thus seen to divine 

 the form which best comports with an exact measurement V In con- 

 formity, at the same time, with his habit of mingling reminiscences of 

 the classic poets with his scientific labors, he terminates this treatise 

 on the Art of measuring caslcs with two verses, imitated from Catullus, 

 which, freely translated, signify that, when indulging in conviviality, 

 we should not count the glasses : 



Et qnam, pocnla mille mensi eriiniis, 

 ContHrhabimus ilia, nc sciamits. 



This very learned work could be of no assistance to Kepler in the 

 support of his family, becoming everj^ year more numerous; he was 

 living, therefore, with great economy and amid continual anxieties for 

 the future, when afflictions still more poignant came to embitter his 

 latter years. A letter from his sister apjjrised him that their mother, at 

 the advanced age of seventy, had just been cast into prison on an accu- 

 sation of the crime of sorcery. Ineensed at the impertinent absurdity 

 of the questions addressed to her bj^ the judge of instruction, Catharine 

 Kepler had aggravated her position by becoming accuser in turn, and 

 scornfully reju'oaching the magistrate with his abuse of office in the 

 acquisition of sudden wealth. Unhappily, public opinion held her guiltj', 

 and without any precise allegation overwhelmed her with the odium of 

 all the calamities of the vicinage ; especially was general horror excited 

 when the tact was established that she never looked any one in the face 

 and had never been seen to shed a tear. These signs of malignity, it is 

 true, were not conclusive, but as the judges, in impeachments of this 

 kind, were absolved from the ordinary restraints and had no fear before 

 their eyes but that of seeming too lenient, the usage was to extort by 

 torture such confessions as would conduct the victim to the stake. 

 Kepler hastened to the scene, and for five years of cruel apprehensions 

 struggled unceasingly for the safety of his mother. Not all the prestige 

 of his renown, however, nor his earnestness in demonstrating that 

 "these tests of patience rather than of truth," as Montaigne expressed 

 it, involve the judge in a deeper condemnation than that which he pro- 

 nounces, could avail to hinder the instruments of torture from being 

 exhibited to the aged Catharine, their uses explained to her, and their 

 application threatened if her obstinate silence could not bo otherwise 

 overcome. But nothing could shake her constancy; she declared her- 

 self ready to sufler everything, and her lofty and resigned bearing saved 

 her finally from the punishment, but not from the disgrace, which of 

 course was reflected painfully on her son. 



