340 



INDUCTION. 



ferent, if the causes co-existed in 

 different proportions, or with any 

 difference in those of their relations 

 by which the effects are influenced. 

 If, for example, the sun's attraction 

 and the original projectile force had 

 existed in some other ratio to one 

 another than they did, (and we know 

 of no reason why this should not have 

 been the case,) the derivative laws of 

 the heavenly motions might have been 

 quite different from what they are. 

 The proportions which exist happen 

 to be such as to produce regular 

 elliptical motions ; any other propor- 

 tions would have produced different 

 ellipses, or circular, or parabolic, or 

 hyperbolic motions, but still regular 

 ones ; because the effects of each of 

 the agents accumulate according to 

 an uniform law ; and two regular 

 series of quantities, when their cor- 

 responding terms are added, must 

 produce a regular series of some sort, 

 whatever the quantities themselves 



§ 3. Now this last-mentioned ele- 

 ment in the resolution of a derivative 

 law, the element which is not a law 

 of causation, but a collocation of 

 causes, cannot itself be reduced to 

 any law. There is (as formerly re- 

 marked*) no uniformity, no norma, 

 principle, or rule, perceivable in the 

 distribution of the primeval natural 

 agents through the universe. The 

 different substances composing the 

 earth, the powers that pervade the 

 universe, stand in no constant relation 

 to one another. One substance is 

 more abundant than others, one power 

 acts through a larger extent of space 

 than others, without any pervading 

 analogy that we can discover. We 

 not only do not know of any reason 

 why the sun's attraction and the 

 force in the direction of the tangent 

 co-exist in the exact proportion they 

 do, but we can trace no coincidence 

 between it and the proportions in 

 which any other elementary powers 



* Supra, book iii. ch. v. { 7. 



in the universe are intermingled. The 

 utmost disorder is apparent in the 

 combination of the causes ; which is 

 consistent with the most regular order 

 in their effects ; for when each agent 

 carries on its own operations accord- 

 ing to an uniform law, even the most 

 capricious combination of agencies 

 will generate a regularity of some sort ; 

 as we see in the kaleidoscope, where 

 any casual arrangement of coloured 

 bits of glass produces by the laws of 

 reflection a beautiful regularity in the 

 effect. 



§ 4. In the above considerations 

 lies the justification of the limited 

 degree of reliance which scientific 

 inquirers are accustomed to place in 

 empirical laws. 



A derivative law which results 

 wholly from the operation of some 

 one cause will be as universally true 

 as the laws of the cause itself : that 

 is, it will always be true except where 

 some one of those effects of the cause, 

 on which the derivative law depends, 

 is defeated by a counteracting cause. 

 But when the derivative law results 

 not from different effects of one cause, 

 but from effects of several causes, we 

 cannot be certain that it will be true 

 under any variation in the mode of 

 co-existence of those causes, or of the 

 primitive natural agents on which 

 the causes ultimately depend. The 

 proposition that coal-beds rest on 

 certain descriptions of strata exclu- 

 sively, though true on the earth so 

 far as our observation has reached, 

 cannot be extended to the moon or 

 the other planets, supposing coal to 

 exist there ; because we cannot be 

 assured that the original constitution 

 of any other planet was such as to 

 produce the different depositions in 

 the same order as in our globe. The 

 derivative law in this case depends 

 not solely on laws, but on a colloca- 

 tion ; and collocations cannot be re- 

 duced to any law. 



Now it is the very nature of a 

 derivative law which has not yet 

 been resolved into its elements, in 



