190 LECTURES. 



the facts under investigation and some other facts of which the law is 

 known. One successful induction is the key to another. 



We must be careful not to he misled by a mere rhetorical analogy. 



(11.) A supposition or guess thus made from analogy, as to the 

 nature of the law of a class of facts, is usually called an hypothesis ^ 

 and sometimes the antecedent prohahility . 



(12.) When an hypothesis of this kind has been extended and veri- 

 fied, or in other words, when it has become an exact expression of the 

 law of a class of facts, it is then called a theory. 



(13.) Physical theories are of two kinds ; which are sometimes 

 called pure and hypothetical. The one being simply the expression 

 of a law of facts resting on experiment and observation. Such as the 

 theory of universal gravitation — the theory of sounds &c. 



The other consists of an hypothesis combined with facts of expe- 

 rience. Of this kind is the theory of electricity which attributes a 

 large class of phenomena to the operations of an hypothetical fluid 

 endowed with properties, so imagined as to render the theory an 

 expression of the law of the facts. 



On account of the abuse of theory and hypothesis, discredit has 

 been thrown even on the terms. They are, however^ of essential im- 

 portance to the advance and application of science ; since few physical 

 investigation can be made without the adoption of .some provisional 

 hypothesis ; and a good hypothetical theory such as that of electricity 

 is generally the only convenient expression of the law of a large class 

 of phenomena. 



Strictly speaking, no theory in the present state of science, can be 

 considered as an actual expression of the truth. It may, indeed, be 

 an exact expression of the law of a limited class of facts, but in the 

 advance of science, it is liable to be merged in a higher generalization 

 or the expression of a wider law. 



(14.) Although in accordance with the principles of the inductive 

 philosophy, it is acknowledged that there is no other method of estab- 

 lishing the laws of nature, than by induction founded on experience ; 

 yet many writers who profess to adojit this method, inconsistently 

 attempt to deduce some of the most important of these laws from 

 a priori considerations. 



For example, in works on mechanics we find frequent attempts to 

 prove the laws of motion by an a])plication of the principle of Leibnitz, 

 called the sulJicieiit reason, which is expressed by saying, nothing 

 exists in any state unless there is some reason for its being in that state 

 rather than in any other. This principle is evidently true in itself, 

 but its application to the proof of a law of nature presupposes in us a 

 knowledge of all the reasons for the particular existence of things. 



(15.) Another principal of Leibnitz often referred to by writers on 

 natural philosophy, is that called the law of continuity. His motto in 

 reference to this \\sis,natura non operatur per saltum — all the changes 

 in nature are produced by insensible gradations. This principle, it is 

 true, expresses a fact of frequent occurrence, yet since it does not rest 

 on a sufficient induction, we cannot consider it as a law of nature. 



