EMriRICAL LAWS. 367 



solvable into simpler laws, but not yet resolved into them. The ascertain- 

 ment of the empirical laws of phenomena often precedes by a long interval 

 the explanation of those laws by the Deductive Method ; and the verifica- 

 tion of a deduction usually consists in the comparison of its results with 

 empirical laws previously ascertained. 



§ 2. From a limited number of ultimate laws of causation, there are 

 necessarily generated a vast number of derivative uniformities, both of 

 succession and co-existence. Some are laws of succession or of co-existence 

 between different effects of the same cause ; of these we had examples in 

 the last chapter. Some are laws of succession between effects and their 

 remote causes, resolvable into the laws which connect each with the in- 

 termediate link. Thirdly, when causes act together and compound their 

 effects, the laws of those causes generate the fundamental law of the effect, 

 namely, that it depends on the co-existence of those causes. And, finally, 

 the order of succession or of co-existence which obtains among effects 

 necessarily depends on their causes. If they are effects of the same cause, 

 it depends on the laws of that cause; if on different causes, it depends on 

 the laws of those causes severally, and on the circumstances which deter- 

 mine their co-existence. If we inquire further when and how the causes 

 will co-exist, that, again, depends on their causes; and we may thus trace 

 back the phenomena higher and higher, until the different series of effects 

 meet in a point, and the whole is shown to have depended ultimately on 

 some common cause ; or until, instead of converging to one point, they ter- 

 minate in different points, and the order of the effects is proved to have 

 arisen from the collocation of some of the primeval causes, or natural 

 agents. For example, the order of succession and of co-existence among 

 tlie heavenly motions, which is expressed by Kepler's laws, is derived from 

 the co-existence of two primeval causes, the sun, and the original impulse 

 or projectile force belonging to each planet.* Kepler's laws are resolved 

 into the laws of these causes and the fact of their co- existence. 



Derivative laws, therefore, do not depend solely on the ultimate laws into 

 which they are resolvable ; they mostly depend on those ultimate laws, and 

 an ultimate fact ; namely, the mode of co-existence of some of the component 

 elements of the universe. The ultimate laws of causation might be the 

 same as at present, and yet the derivative laws completely different, 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 oth- 

 er 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 proportions would have produced different ellipses, or circular, 

 or parabolic, or hyperbolic motions, but still regular ones ; because the ef- 

 fects of each of the agents accumulate according to a uniform law ; and two 

 regular series of quantities, when their corresponding terms are added, must 

 produce a i-egular series of some sort, whatever the quantities themselves are. 



§ 3. !N'ow this last - mentioned element in the resolution of a derivative 

 law, the element which is not a law of causation, but a collocation of causes, 



* Or, according to Laplace's theory, the sun and the snn's rotation. 



