EMPIRICAL LAWS. 307 



original projectile force, had existed in some other ratio to one another 

 than thoy did (and we know of no reason why this shoidd not have 

 been the case), the derivative laws of the heavenly motions might 

 have been quite dift'erent from what they are. The proportions which 

 exist happen to be such as to produce regular elliptical motions ; any 

 other pi-oportions would have produced diflerent ellipses, or circular, 

 or parabohc, or hyperbolic motions, but still regular ones ; because the 

 effects of each of the agents accumulate according to an uniform law; 

 and two I'egular series of quantities, when their corresponding terms 

 are added, must produce a regular scries of some sort, whatever the 

 quantities themselves are. 



§ 3. Now this last mentioned element in the resolution of a deriva- 

 tive 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 

 remarked*) 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 sub- 

 stance 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 tangential force coexist in the exact propor- 

 tion they do, but we can trace no coincidence between it and the 

 proportions in which any other elementary powers in the universe are 

 intermingled. The utmost disorder is apparent in the combination of 

 the causes ; which is consistent with the most perfect order in their 

 effects ; for when each agent carries on its own operations according 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 colored 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 

 degi-ee of reliance which philosophers are accustomed to place in em- 

 pirical 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 

 coimteracting cause. But when the denvative law results not from 

 different effects of one cause, but from effects of several causes, we 

 cannot be certain that it will be tnic under any variation in the mode 

 of coexistence of those catises, or of the primitive natural agents on 

 which the causes ultimately depend. The proposition that coal beds 

 rest upon certain descriptions of strata exclusively, 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 dejjositions in the same order as 

 in our globe. The derivative law in this case depends not solely 



* Supra, p. 206. 



