PHYSICAL AND MATHEMATICAL SCIENCES. J 45
particular, of which I pertinaciously sought the causeswhy they are not other than they are: the number, thesize, and the motion of the orbits.” He was delightedwith the simplicity of the Copernican system, andwas thus anxious to trace numerical relations amongits elements, from a firm persuasion that some abstruseprinciple of numerical harmony pervaded all nature,and regulated the proportions of all its parts. Oneafter another, he proposed, tried, and rejected every sortof numerical relation he could devise. Notwithstandingperpetual failures, he adds, — “I was comforted insome degree, and my hopes of success were supported,as well by other reasons which will follow presently, asby observing that the motions in every case seemed tobe connected with the distances, and that when therewas a great gap between the orbits, there was the samebetween the motions; and I reasoned that, if God hadadapted motions to the orbits in some relation to thedistances, it was probable that he had also arranged thedistances themselves in relation to something else.”
It is far from our intention to follow Kepler throughthe vast number of speculations which he pursued onthese points ; we merely refer to them as admirable in-dications of the spirit and character of his method ofphilosophising, and as illustrative of the genius of hisinvestigations. The theory which pleased him best,and which, though it deviated considerably from theobserved results, yet he regarded as differing only bythe errors of observation, was a geometrical construc-tion which determines the proportions of the orbits, by '
inscribing successively in them the five regular solids,each sphere being drawn to touch internally the sides ofthe solid inscribed in the preceding. This, with someother supplementary theories, forms the substance ofhis “ Mysterium Cosmographicum, ” 1596.
In 1597 he withdrew from Gratz into Hungary ,and subsequently visited Tycho at Prague . Owing tosome dissensions, it seems that he shortly after gaveup his appointment at Gratz ; and his affairs being in
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