56 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



Objective facts which contributed nothing to the determination 

 of that construction. The relative distances of the planets 

 from the sun in Keppler's system are open to calculation and 

 comparison with data of observation. Keppler's theological 

 .prepossessions do not prevent him from recognising this truth 

 i^ the clearest manner. " Transeamus modo," he says, " ad 



orbiuin astronomiae et demonstrationes geometricos : 

 quae nisi consentiant, procul dubio omnem praecedentem operam 

 luserimus."* So the relative radii of the spheres imprisoned 

 in this complicated way between the regular solids are com- 

 puted, and the results compared with the estimates of Copernicus. 

 The concordance is practically perfect ! t 



In 1600 Keppler left his chair at Gratz, and received from 

 Tycho Brahe that introduction to the Emperor Eudolph which 

 led to consequences of the first importance in the development 

 of Science. Brahe died in the same year, and the Imperial 

 mathematician inherited his splendid collection of observations 

 on the planet Mars. In 1609 appears the famous treatise,. 

 De Motibus Stellae Martis, in which he sets forth with the 

 delightful long-windedness of a leisurely age the results of his 

 patient study of these data. After the fashion of a day when 

 philosophers reasoned even of Ethics more yeometrico, Keppler 

 prefixes to his work a collection of Axiomata pliysica de motilus 

 stellarum. These are of the highest interest, for they betray 

 a complete change (since the My sternum, Cosmographicuni) in 

 the astronomer's attitude towards his facts, To determine 

 the particulars of the orbits of the planets we are no longer 

 invited to consider that they must move "ad majorem Dei 

 gloriani : motus a spatio dependet ; planetae aguntur vi naturali ; 

 vis motrix opus habet propagation a fonte ceu effuxu " ; are 

 among the startling " axioms " that meet us. 

 ' The body of the work is largely occupied by Keppler's 



* Cap. XIII, p. 148. 



t Table in Cap. XIV, p. 151. 



