304 HO W KEPLER SOL VED IT. 



that the differences in longitude amounted to eight or nine 

 minutes. Now, observations so exact as those of Tycho were 

 altogether incompatible with such great error.* Therefore, the 

 geometrical hypothesis which gave these errors was false ; the 

 orbit of Mars could not be a circle, and to save these eight or 

 nine minutes, furnished by observation but in disaccord with 

 theory, it would be needful to recommence all the calculations 

 of astronomy. This conclusion, not less legitimate than daring, 

 supplied Kepler with the first decisive step in the task he had 

 undertaken. 



This is not the place to- relate all the essays and miscarriages 

 through which this man of genius passed before finally com- 

 pleting his discovery of the rules that bear his name. But 

 we may put before the reader the construction which led to 

 them. 



On a sheet of paper let us mark down by a point (Fig. 68) 

 the place occupied by the earth in relation to the sun.t 

 From this point o, we draw a right line terminating at a, the 

 sun's noon-day position (for example, on the ist of January) ; 

 the succeeding lines shall touch upon a a", which the sun 

 occupies successively after the same interval of time (twenty-four 



* The reader should turn to Kepler's immortal work, " De Motibus Stellse 

 Martis," for the manifold attempts of the astronomer to bring calculation 

 into agreement with observation. In every page is revealed what has been 

 finely called "the passionate patience of genius." 



*h There is certainly no exaggeration in comparing the earth to a point, 

 since the diameter of the sun is 112 times that of the earth, and its mean 

 distance a little more than 12,000 terrestrial diameters: the earth is but 

 a microscopical point in space, if we compare it to the place occupied by 

 the central luminary. 



