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historical view op ti»e

server.” .... If you would know the precise mo-ment, the idea first came across me on the 8th of Marchof this year, 1618 ; but, chancing to make a mistake inthe calculation, I rejected it as false. I returned againto it with new force on the 15th of May; and it hasdissipated the darkness of my mind, by such an agree-ment between this idea and my seventeen years’ labouron ‘ Brahe ’s Observations,’ that at first I thought Imust be dreaming, and had taken my result for grantedin my first assumptions. But the fact is perfect; thefact is certain, that the proportion existing between theperiodic times of any two planets is exactly the sesqui-plicate proportion of the mean distances of their orbits.”That is, as we may express it with more perspicuity,the squares of the times are as the cubes of the meandistances.

Thus was the third of these important principlesestablished, as laws simply derived from induction. Infact, the essential desideratum, at this stage of thescience of the system of the world, was precisely thisdetermination of its numerical laws, deduced withoutreference to any physical hypothesis. Had such relationsbeen deduced in connection with any theory, they wouldhave been received with suspicion ; and, very probably,in the then state of philosophy, would have been thrownaside along with the theory, if it had been in its turnexploded to make way for a newer system. The greatadvantage possessed by these laws of Kepler, was theirpurely inductive character; and we cannot help recog-nising, in the extremely peculiar turn of Kepler's mind,which sought after these arithmetical relations purelyfor their own sake, the precise intellectual character re-quisite for taking this particular and essential step to-wards the establishment of the system of the world,raised up at the precise period when he was wanted, andfulfilling this one great purpose in conducing to thepromotion of truth, amid all the innumerable avenuesto error which were opened in his other speculations.

Kepler had no sooner published his epitome of the