OF NATURAL PHILOSOPHY. l85 



it were, in violent circumstances, try their temper, 

 and bring their vigour to the test. 



(194.) Bacon's "collective instances" (instantia 

 unionis), are no other than general facts, or laws of 

 some degree of generality, and are themselves the 

 results of induction. But there is a species of col- 

 lective instance which Bacon does not seem to have 

 contemplated, of a peculiarly instructive character ; 

 and that is, where particular cases are offered to tur 

 observation in such numbers at once as to make the 

 induction of their law a matter of ocular inspection. 

 For example, the parabolic form assumed by a jet of 

 water spouted from a round hole, is a collective in- 

 stance of the velocities and directions of the motions 

 )f all the particles which compose it seen at once, 

 and which thus leads us, without trouble, to recog- 

 nize the law of the motion of a projectile. Again, 

 the beautiful figures exhibited by sand strewed on 

 regular plates of glass or metal set in vibration, 

 are collective instances of an infinite number of points 

 which remain at rest while the remainder of the 

 plate vibrates ; and in consequence afford us, as it 

 were, a sight of the law which regulates their ar- 

 rangement and sequence throughout the whole 

 surface. The beautifully coloured lemniscates seen 

 around the optic axes of crystals exposed to polar- 

 ized light afford a superb example of the same 

 kind, pointing at once to the general mathematical 

 expression of the law which regulates their pro- 

 duction.* Of such collective instances as these, it 

 is easy to see the importance, and its reason. They 

 lead us to a general law by an induction which 

 * See Phil. Trans. 1819. 



