158 THE PRINCIPLES OF SCIENCE. 



(4) Lastly, there may and does exist knowledge of 

 phenomena accepted solely on the ground of theory, and 

 which is incapable of experimental confirmation, at least 

 with the instrumental means at the time in our pos- 

 session. 



It is a work of much interest to compare and illustrate 

 in some degree the relative extent and value of these 

 four groups of knowledge. As a general rule we shall 

 observe that every great branch of science originates 

 in facts observed accidentally, or without any distinct 

 consciousness of what is to be expected. But as science 

 progresses, its power of foresight rapidly increases, until 

 the mathematician in his study seems to acquire the 

 power of anticipating nature, and predicting what will 

 happen in stated circumstances before the eye of man has 

 ever witnessed the event. 



Empirical Knowledge. 



By empirical knowledge we mean such as is derived 

 directly from the examination of certain detached facts, 

 and rests entirely on those facts, without corroboration or 

 connexion with other branches of knowledge. It is con- 

 trasted to generalised and theoretical knowledge, which 

 embraces many series of facts under a few simple and 

 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 

 portions of rivers, isolated mountains, and undefined 

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

 branch of knowledge often consists of groups of facts, each 

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

 one part to another. 



Before the time of Descartes, and Newton, and Huy- 

 ghens, there was much empirical knowledge of the 



