526 THE PRINCIPLES OP SCIENCE. [CHAP. 



or without distinct consciousness of what is to be expected. 

 As a science progresses, its power of foresight rapidly 

 increases, until the mathematician in his library acquires 

 the power of anticipating nature, and predicting what will 

 happen in circumstances which the eye of man has never 

 examined. 



Empirical Knowledge. 



By empirical knowledge we mean such as is derived 

 directly from the examination of detached facts, and rests 

 entirely on those facts, without corroboration from other 

 branches of knowledge. It is contrasted with generalised 

 and theoretical knowledge, which embraces many series of 

 facts under a few comprehensive principles, so that each 

 series serves to throw light upon each other series of facts. 

 Just as, in the map of a half-explored country, we see 

 detached bits of rivers, isolated mountains, and undefined 

 plains, not connected into any complete plan, so a new 

 branch of knowledge consists of groups of facts, each group 

 standing apart, so as not to allow us to reason from one to 

 another. 



Before the time of Descartes, and Newton, and Iluyghens, 

 there was much empirical knowledge of the phenomena of 

 light. The rainbow had always struck the attention of 

 the most careless observers, and there was no difficulty 

 in perceiving that its conditions of occurrence consisted in 

 rays of the sun shining upon falling drops of rain. It was 

 impossible to overlook the resemblance of the ordinary 

 rainbow to the comparatively rare lunar rainbow, to the 

 bow which appears upon the spray of a waterfall, or even 

 upon beads of dew suspended on grass and spiders' webs. 

 In all these cases the uniform conditions are rays of light 

 and round drops of water. Koger Bacon had noticed these 

 conditions, as well as the analogy of the rainbow colours 

 to those produced by crystals. 1 But the knowledge was 

 empirical until Descartes and Newton showed how the 

 phenomena were connected with facts concerning the 

 refraction of light. 



There can be no better instance of an empirical truth 



1 Opvt Maws. Edit. 1733. Cap. x. p. 460. 



