OF THE LAWS OF MOTION. 171 



This has been done in two ways: — sometimes by attending only to the 

 necessary part of each law (as the parts are stated in the last para- 

 graph but one) and by overlooking the necessity of the empirical 

 supplement and limitation to it; — at other times by asserting the part 

 which I have stated as empirical to be self-evident, no less than the 

 other part. The former way of proceeding may be found in many 

 English writers on the subject; the latter appears to direct the reason- 

 ings of many eminent French mathematicians. Some (as Laplace) have 

 allowed the empirical nature of two out of the three laws ; others, as 

 M. Poisson, have considered the first as alone empirical ; and others, as 

 D'Alembert, have assumed the self-evidence of all the three indepen- 

 dently of any reference whatever to observation. 



25. The parts of the laws which I have stated as empirical, 

 appear to me to be clearly of a different nature, as to the cogency 

 of their truth, from the parts which are necessary ; and this difference 

 is, I think, established by the fact that these propositions were de- 

 nied, contested, and modified, before they were finally established. If 

 these truths could not be denied without a self-contradiction, it is 

 difficult to understand how they could be (as they were) long and 

 obstinately controverted by mathematicians and others fully sensible to 

 the cogency of necessary truth. 



I will not however go so far as to assert that there may not be 

 some point of view in which that which I have called the empirical 

 part of these laws, (which, as we have seen, contains negatives only,) 

 may be properly said to be self-evident. But however this may be, 

 I think it can hardly be denied that there is a difference of a fun- 

 damental kind in the nature of these truths, — which we can, in our 

 imagination at least, contradict and replace by others, and which, his- 

 torically speaking, have been established by experiment; — and those 

 other truths, which have been assented to from the first, and by all, 

 and which we cannot deny without a contradiction in terms, or reject 

 without putting an end to all use of our reason on this subject. 



26. On the other hand, if any one should be disposed to maintain 

 that, inasmuch as the laws are interpreted by the aid of experience 



