* i38, 139] Optical Work: Study of Mars 183 



suggestion for the construction of a telescope by the use 

 of two convex lenses, which is the form now most commonly 

 adopted, and is a notable improvement on Galilei's instru- 

 ment (chapter vi., 118), one of the lenses of which is 

 concave ; but Kepler does not seem himself to have had 

 enough mechanical skill to actually construct a telescope 

 on this plan, or to have had access to workmen capable 

 of doing so for him ; and it is probable that Galilei's 

 enemy Scheiner (chapter vi., 124, 125) was the first 

 person to use (about 1613) an instrument of this kind. 



139. It has already been mentioned (chapter v., 108) 

 that when Tycho was dividing the work of his observatory 

 among his assistants he assigned to Kepler the study of 

 the planet Mars, probably as presenting more difficulties 

 than the subjects assigned to the others. It had been 

 known since the time of Coppernicus that the planets, 

 including the earth, revolved round the sun in paths that 

 were at any rate not very different from circles, and 

 that the deviations from uniform circular motion could be 

 represented roughly by systems of eccentrics and epicycles. 

 The deviations from uniform circular motion were, however, 

 notably different in amount in different planets, being, 

 for example, very small in the case of Venus, relatively large 

 in the case of Mars, and larger still in that of Mercury. 

 The Prussian Tables calculated by Reinhold on a Copper- 

 nican basis (chapter v., 94) were soon found to represent 

 the actual motions very imperfectly, errors of 4 and 5 

 having been noted by Tycho and Kepler, so that the 

 principles on which the tables were calculated were evi- 

 dently at fault. 



The solution of the problem was clearly more likely 

 to be found by the study of a planet in which the de 4 - 

 viations from circular motion were as great as possible. 

 In the case of Mercury satisfactory observations were 

 scarce, whereas in the case of Mars there was an abundant 

 series recorded by Tycho, and hence it was true insight on 

 Tycho's part to assign to his ablest assistant this particular 

 planet, and on Kepler's to continue the research with un- 

 wearied patience. The particular system of epicycles used 

 by Coppernicus (chapter iv., 87) having proved defective, 

 Kepler set to work to devise other geometrical schemes, the 



