BOOK IL] constitutive INSTANCES. 491 



Aj^ain, as an other example, let the required nature be the 

 communication of quality, without intermixture of substance. 

 The instance of light will afford or constitute one species of com- 

 munication, heat and the magnet another. For the communica- 

 tion of light is momentary and immediately arrested upon the 

 removal of the original light. But heat, and the magnetic force, 

 when once transmitted to or excited in another body, remain 

 fixed for a considerable time after the removal of the source. 



In fine, the prerogative of constitutive instances is considerable, 

 for they materiall}'- assist the definitions (especially in detail) and 

 the divisions or partitions of natures, concerning which Plato has 

 well said, " He who can properly define and divide is to be con- 

 sidered a god."* 



" The collective instances here meant are no other than genei-al 

 facts or laws of some degree of generality, and are themselves the 

 result oi induction, For example, the system of Jupiter, or Saturn 

 with its satellites, is a collective instance, and materially assisted in 

 securing the admission of the Copernican system. We have here in 

 miniature, and displayed at one view, a system analogous to that of the 

 planets about the sun, of which, from the circumstance ot our being 

 involved in it, and unfavourably situated for seeing it otherwise than in 

 detail, we are incapacitated from forming a general idea, but by slow 

 and progressive efforts of reason. 



But there is a species of collective instance which Bacon does not 

 seem to have contemplated, in which particular phenomena are pre- 

 sented in such numbers at once, as to make the induction of their law 

 a matter of ocular inspection. For example, the parabolic form as- 

 sumed by a iet of water spouted out of a hole is a collective instance of 

 the velocities and directions of the motions of all the particles which 

 compose it seen together, and which thus leads us without trouble to 

 recognize 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 ])late vibrates, and in 

 consequence afford us an insight into the law which regulates their 

 arrangement and sequence throughout the whole surface. The richly 

 coloured lemniscates seen around the optic axis of crystals exposed to 

 polarized light afford a striking instance of the same kind, pointing at 

 once to the general mathematical expression of the law which regulates 

 their production. Such collective instances as these lead us to a general 

 law by an induction which offers itselt spontaneously, and thus furnish 

 advanced posts in philosophical exploration. The laws ol Kepler, 

 which Bacon ignored on account of his want of mathematical taste, 

 may be cited as a collective instance. The first is, that the planets 

 move in elliptical orbits, having the sun for their common focus. The 

 second, that about this focus the radius vector of each planet describes 

 equal areas in equal times. The third, that the squares of the periodic 

 times of the planets are as the cubes of their mean distance from the 

 3un. This collective instance "opened the way" to the discovery ol 

 tbc Newtt^nii^n l^w of gravitation, ^'d. 



