INDUCTIVE EPOCH OF KEPLER. 447 



able to metaphysics." But before he attempts to 

 correct this erroneous part of his hypothesis he 

 sets about discovering the law according to which 

 the different parts of the orbit are described in 

 the case of the earth, in which case the eccentricity 

 is so small that the effect of the oval form is in- 

 sensible. The result of this inquiry was 7 the Rule, 

 that the time of describing any arc of the orbit 

 is proportional to the area intercepted between the 

 curve and two lines drawn to the extremities of 

 the arc. It is to be observed that this rule, at 

 first, though it had the recommendation of being 

 selected after the unavoidable abandonment of 

 many, which were suggested by the notions of those 

 times, was far from being adopted upon any very 

 rigid or cautious grounds. A rule had been proved 

 at the apsides of the orbit, by calculation from 

 observations, and had then been extended by con- 

 jecture to other parts of the orbit; and the rule 

 of the areas was only an approximate and inac- 

 curate mode of representing this rule, employed 

 for the purpose of brevity and convenience, in 

 consequence of the difficulty of applying, geome- 

 trically, that which Kepler now conceived to be 

 the true rule, and which required him to find the 

 sum of the lines drawn from the sun to every 

 point of the orbit. When he proceeded to apply 

 this rule to Mars, in whose orbit the oval form is 

 7 Ibid. p. 194. 



