192 DISSERTATION SECOND. [parti, 



and he proved, that the curves, proper for generating such 

 superficies by their revolution, are all comprehended 

 under one general character, viz. that there are always 

 two given points, from which, if straight lines be drawn to 

 any point in the curve, the one of these, phis or wunws, 

 that which has a given ratio to the other, is equal to a given 

 line. 



It is evident, when the given ratio here mentioned is a 

 ratio of equality, that the curve is a conick section, and 

 the two given points ils two foci. The curves, in general, 

 are of the fourth or the second order, and have been dis- 

 tinguished by the name of the ovals of Descartes. 



From this very ingenious investigation no practical re- 

 sult of advantage in the construction of lenses has been 

 derived. The mechanical difficulties of working a super- 

 ficies into any figure but a spherical one are so great, that, 

 notwithstanding all the efforts of Descartes himself, and of 

 many of his followers, they have never been overcome, so 

 that the great improvements in optical instruments have 

 arisen in a quarter entirely different. 



Descartes gave also a full explanation of the rainbow, l 

 as far as colour was not concerned, a part of the problem 

 which remained for Newton to resolve. The path of the 

 ray was traced, and the angles of the incident ray, with 

 that which emerges after two refractions and one reflection, 

 was accurately determined. Descartes paid little atten- 

 tion to those who had gone before him, and, as already re- 

 marked, never once mentioned the Archbishop of Spala- 

 tro. Like Aristotle, he seems to have formed the de- 

 sign of cutting off the memory of all his predecessors, bujt 

 the invention of printing had made this a far more hope- 

 less undertaking than it was in the days of the Greek philo- 

 sopher. 



' Meteorum, cap. 8vum, 



