LAW OF CAUSATION. 861 



a sphere and another a cylinder, of equal height and diameter, 

 the one will be exactly two-thirds of the other, let the nature 

 and quality of the material be what it will. Again, each body, 

 and each point of a body, must occupy some place or position 

 among other bodies ; and the position of two bodies relatively 

 to each other, of whatever nature the bodies be, may be un 

 erringly inferred from the position of each of them relatively 

 to any third body. 



In the laws of number, then, and in those of space, we re 

 cognise in the most unqualified manner, the rigorous univer 

 sality of which we are in quest. Those laws have been in all 

 ages the type of certainty, the standard of comparison for all 

 inferior degrees of evidence. Their invariability is so perfect, 

 that it renders us unable even to conceive any exception to 

 them ; and philosophers have been led, though (as I have en 

 deavoured to show) erroneously, to consider their evidence as 

 lying not in experience, but in the original constitution of the 

 intellect. If therefore, from the laws of space and number, we 

 were able to deduce uniformities of any other description, this 

 would be conclusive evidence to us that those other uniformi 

 ties possessed the same rigorous certainty. But this we cannot 

 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 oar 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 inferred. 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 



