442 JAMES CLERK MAXWELL. [CHAP. XIV. 



It is a metaphysical doctrine that from the same ante- 

 cedents follow the same consequents. No one can gainsay 

 this. But it is not of much use in a world like this, in 

 which the same antecedents never again concur, and nothing 

 ever happens twice. Indeed, for aught we know, one of the 

 antecedents might be the precise date and place of the event, 

 in which case experience would go for nothing. The meta- 

 physical axiom would be of use only to a being possessed of 

 the knowledge of contingent events, scientia simplicis intelli- 

 gentice, a degree of knowledge to which mere omniscience of 

 all facts, scientia visionis, is but ignorance. 



The physical axiom which has a somewhat similar 

 aspect is "That from like antecedents follow like conse- 

 quents." But here we have passed from sameness to likeness, 

 from absolute accuracy to a more or less rough approximation. 

 There are certain classes of phenomena, as I have said, in 

 which a small error in the data only introduces a small error 

 in the result. Such are, among others, the larger phenomena 

 of the Solar System, and those in which the more elementary 

 laws in Dynamics contribute the greater part of the result. 

 The course of events in these cases is stable. 



There are other classes of phenomena which are more 

 complicated, and in which cases of instability may occur, the 

 number of such cases increasing, in an exceedingly rapid 

 manner, as the number of variables increases. Thus, to take 

 a case from a branch of science which comes next to 

 astronomy itself as a manifestation of order : In the refrac- 

 tion of light, the direction of the refracted ray depends on 

 that of the incident ray, so that in general, if the one direc- 

 tion be slightly altered, the other also will be slightly altered. 

 In doubly refracting media there are two refracting rays, but 

 it is true of each of them that like causes produce like effects. 

 But if the direction of the ray within a biaxal crystal is 

 nearly but not exactly coincident with that of the ray-axis of 

 the crystal, a small change in direction will produce a great 

 change in the direction of the emergent ray. Of course, this 

 arises from a singularity in the properties of the ray-axis, and 

 there are only two ray-axes among the infinite number of 



