iicv. iv.] DISSERTATION SECOND. 135 



mer. It was by the views thus presented that he was led 

 to the method of constructing and calculating eclipses, by 

 means of projections, without taking into consideration the 

 diurnal parallax. These are valuable improvements, but 

 they were, however, obscured by the greatness of his fu- 

 ture discoveries. 



The planes of the orbits of the planets were naturally, 

 in the Ptolemaick system, supposed to pass through the 

 earth, and the reformation of Copernicus did not go so far 

 as to change the notions on that subject which had gene- 

 rally been adopted. Kepler observed that the orbits of the 

 planets are in planes passing through the sun, and that, of 

 consequence, the lines of their nodes all intersect in the 

 centre of that luminary. This discovery contributed es- 

 sentially to those which followed. 



The oppositions of the planets, or their places when 

 they pass the meridian at midnight, offer the most favour- 

 able opportunities for observing them, both because they 

 are at that time nearest to the earth, and because their 

 places seen from thence are the same as if they were seen 

 from the sun. The true time of the opposition had, how- 

 ever, been till now mistaken by astronomers, who held it to 

 be at the moment when the apparent place of the planet 

 was opposite to the mean place of the sun. It ought, how- 

 ever, to have been, when the apparent places of both were 

 opposed to one another. This reformation was proposed 

 by Kepler, and, though strenuously resisted by Tycho, 

 was finally received. 



Having undertaken to examine the orbit of Mars, in which 

 the irregularities are most considerable, Kepler discovered, 

 by comparing together seven oppositions of that planet, 

 that its orbit is elliptical ; that the sun is placed in one of 

 the foci ; and that there is no point round which the angu- 

 lar motion is uniform. In the pursuit of this inquiry he 



