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XXVII. In the sixth rank of prerogative instances we 

 will place similar or proportionate instances, which we are 

 also wont to call physical parallels, or resemblances. They 

 are such as exhibit the resemblances and connection of 

 things, not in minor forms (as the constitutive do), but at 

 once in the concrete. They are, therefore, as it were, the 

 first and lowest steps toward the union of nature; nor do 

 they immediately establish any axiom, but merely indicate 

 and observe a certain relation of bodies to each other. But 



instance, and materially assisted in securing the admission of the Copernican 

 system. We have here in miniature, and displayed at one view, a system anal 

 ogous to that of the planets about the sun, of which, from the circumstance of 

 our being involved in it, and unfavorably 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 presented in such num 

 bers at once, as to make the induction of their law a matter of ocular inspec 

 tion. For example, the parabolic form assumed by a jet 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 plate vibrates, and in consequence 

 afford us an insight into the law which regulates their arrangement and se 

 quence throughout the whole surface. The richly colored 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 expres 

 sion of the law which regulates their production. Such collective instances as 

 these lead us to a general law by an induction which offers itself spontaneously, 

 and thus furnish advanced posts in philosophical exploration. The laws of 

 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 aa 

 the cubes of their mean distance from the sun. This collective instance &quot;opened 

 the way&quot; to the discovery of the Newtonian law of gravitation. Ed. 



