280 REASONING. 



plicity of these primary relations, being called up by the imagination with as much 

 vividness and clearness as could be done by any external impression, which is the 

 only meaning we can attach to the word intuition, as applied to such relations." 

 And again, of the axioms of mechanics : "As we admit no such propo- 

 sitions, other than as truths inductively collected from observation, even in 

 geometry itself, it can hardly be expected that, in a science of obviously contin- 

 gent relations, we should acquiesce in a contrary view. Let us take one of these 

 axioms and examine its evidence : for instance, that equal forces perpendicularly 

 applied at the opposite ends of equal arms of a straight lever will balance each 

 other. What but experience, we may ask, in the first place, can possibly inform 

 us that a force so applied will have any tendency to turn the lever on its centre 

 at all ? or that force can be so transmitted along a rigid line perpendicular to its 

 direction, as to act elsewhere in space than along its own line of action ? Surely 

 this is so far from being self-evident that it has even a paradoxical appearance, 

 which is only to be removed by giving our lever thickness, material composition* 

 and molecular powers. Again, we conclude, that the two forces, being equal 

 and applied under precisely similar circumstances, must, if they exert any effort 

 at all to turn the lever, exert equal and opposite efforts : but what a priori 

 reasoning can possibly assure us that they do act under precisely similar circum- 

 . stances? that points which differ in place are similarly circumstanced as regards 

 the exertion of force ? that universal space may not have relations to universal 

 force or, at all events, that the organization of the material universe may not 

 be such as to place that portion of space occupied by it in such relations to the 

 forces exerted in it, as may invalidate the absolute similarity of circumstances 

 assumed ? Or we may argue, what have we to do with the notion of angular 

 movement in the lever at all ? The case is one of rest, and of quiescent de- 

 struction of force by force. Now how is this destruction effected ? Assuredly 

 by the counter- pressure which supports the fulcrum. But would not this de- 

 struction equally arise, and by the same amount of counter- acting force, if 

 each force simply pressed its own half of the lever against the fulcrum ? And 

 what can assure us that it is not so, except removal of one or other force, and 

 consequent tilting of the lever ? The other fundamental axiom of statics, that 

 the pressure on the point of support is the sum of the weights ... is merely 

 a scientific transformation and more refined mode of stating a coarse and 

 obvious result of universal experience, viz. that the weight of a rigid body is 

 the same, handle it or suspend it in what position or by what point we will, 

 and that whatever sustains it sustains its total weight. Assuredly, as Mr. 

 Whewell justly remarks, ' No one probably ever made a trial for the purpose 

 of showing that the pressure on the support is equal to the sum of the weights.' 

 . . . But it is precisely because in every action of his life from earliest infancy 

 he has been continually making the trial, and seeing it made by every other 

 living being about him, that he never dreams of staking its result on one addi- 

 tional attempt made with scientific accuracy. This would be as if a man 

 should resolve to decide by experiment whether bis eyes were useful forthe purpose 

 of seeing, by hermetically sealing himself up for half an hour in a metal case." 

 On the " paradox of universal propositions obtained by experience," the same 

 writer says : {l If there be necessary and universal truths expressible in proposi- 

 tions of axiomatic simplicity and obviousness, and having for their subject- 



