96 DISSERTATION SECOND. [rAR* i. 



certainty is one of their properties, of which it does not ap- 

 pear that even Bacon himself was aware. 



Again, from the intimate connexion which prevails 

 among the principles of science, the success of one investi- 

 gation must often contribute to the success of another, in 

 such a degree as to make it unnecessary to employ the 

 complete apparatus of induction from the beginning. — 

 When certain leading principles have been once established, 

 they serve, in new investigations, to narrow the limits with- 

 in which the thing sought for is contained, and enable the 

 • inquirer to arrive more speedily at the truth. 



Thus, suppose that, after the nature of the reflection and 

 refraction of light, and particularly of the colours produc- 

 ed by the latter, had been discovered by experiment, the 

 cause of the rainbow were to be inquired into. It would, 

 after a little consideration, appear probable, that the phe- 

 nomenon to be explained depends on the reflection and re- 

 fraction of light by the rain falling from a cloud opposite 

 to the sun. Now, since the nature of reflection and re- 

 fraction are supposed known, we have the principles pre- 

 viously ascertained which are likely to assist in the ex- 

 planation of the rainbow. We hare no occasion, there- 

 fore, to enter on the inquiry, as if the powers to be inves- 

 tigated were wholly unknown. It is the combination of 

 them only which is unknown, and our business is to seek 

 so to combine them, that the result may correspond with 

 the appearances. This last is precisely what Newton ac- 

 complished, when, by deducing from the known laws of 

 refraction and reflection the breadth of the coloured arch, 

 the diameter of the circle of which it is a part, and the re- 

 lation of the latter to the place of the spectator and of the 

 sun, he found all these to come out from his calculus, 

 just as they are observed in nature. Thus he proved the 



