LAW OF CAUSATION. 235 



this would be conclusive evidence to us that those other uniformities pos- 

 sessed the same rigorous certainty. But this we can not do. From laws 

 of space and number alone, nothing can be deduced but laws of space and 

 number. 



Of all truths relating to phenomena, the most valuable to us are those 

 which relate to the order of their succession. On a knowledge of these is 

 founded every reasonable anticipation of future facts, and whatever power 

 we possess of influencing those facts to our advantage. Even the laws of 

 geometry are chiefly of practical importance to us as being a portion of the 

 premises from which the order of the succession of phenomena may be in- 

 ferred. Inasmuch as the motion of bodies, the action of forces, and the 

 propagation of influences of all sorts, take place in certain lines and over 

 definite spaces, the properties of those lines and spaces are an important 

 part of the laws to which those phenomena are themselves subject. Again, 

 motions, forces, or other influences, and times, are numerable quantities ; 

 and the properties of number are applicable to them as to all other things. 

 But though the laws of number and space are important elements in the 

 ascertainment of imiformities of succession, they can do nothing toward it 

 when taken by themselves. They can only be made instrumental to that 

 purpose when we combine with them additional premises, expressive of 

 uniformities of succession already known. By taking, for instance, as 

 premises these propositions, that bodies acted upon by an instantaneous 

 force move with uniform velocity in straight lines ; that bodies acted upon 

 by a continuous furce move with accelerated velocity in straight lines ; and 

 that bodies acted upon by two forces in different directions move in the 

 diagonal of a parallelogram, whose sides represent the direction and quan- 

 tity of those forces ; we may by combining these truths with propositions 

 relating to the properties of straight lines and of parallelograms (as that a 

 triangle is half q, parallelogram of the same base and altitude), deduce an- 

 other important uniformity of succession, viz., that a body moving round 

 a centre of force describes areas proportional to the times. But unless 

 there had been laws of succession in our premises, there could have been 

 no truths of succession in our conclusions. A similar remark might be 

 extended to every other class of phenomena really peculiar ; and, had it 

 been attended to, would have prevented many chimerical attempts at dem- 

 onstrations of the indemonstrable, and explanations which do not explain. 



It is not, therefore, enough for us that the laws of space, which are only 

 laws of simultaneous phenomenon, and the laws of number, which though 

 true of successive phenomena do not relate to their succession, possess the 

 rigorous certainty and universality of which we are in search. We must 

 endeavor to find some law of succession which has those same attributes, 

 and is therefore fit to be made the foundation of processes for discovering, 

 and of a test for verifying, all other uniformities of succession. This fun- 

 damental law must resemble the truths of geometry in their most remark- 

 able peculiarity, that of never being, in any instance whatever, defeated or 

 suspended by any change of circumstances. 



Now among all those uniformities in the succession of phenomena, which 

 common observation is sufiicient to bring to light, there are very few which 

 have any, even apparent, pretension to this rigorous indefeasibility : and of 

 those few, one only has been found capable of completely sustaining it. In 

 that one, however, we recognize a law which is universal also in another 

 sense ; it is co-extensive with the entire field of successive phenomena, all 

 instances whatever of succession being examples of it. This law is the 



