^8 Rev. W. W he well on the principles of Dynamics^ 



voice of those who have treated of such subjects, and is in fact 

 demonstrable, that the evidence of mechanical and of geome- 

 trical science are altogether different in kind. That while the 

 latter depends for its truth on the nature of the human mind 

 alone, and its self-produced stores, the former must necessarily 

 derive some part at least, both of its materials and its rules, 

 from the impressions made on us by the external world. This 

 is more particularly the case with regard to that portion of 

 mechanics which refers to motion. For the propositions which 

 concern bodies at rest, (statics,) whether or not they are to be 

 ranked with the truths of geometry in other respects, agree 

 with these at least in this, that the certainty of them is in- 

 volved in the definitions by which they become intelligible, 

 and that they require us to borrow from experience nothing 

 but the ideas which are the subject of their operations. 



But in dynamics the case is different, and besides being 

 obliged to derive from observation the phenomena about which 

 we reason, we are also under the necessity of taking from the 

 same source the laws according to which the phenomena suc- 

 ceed and determine each other ; the business of the science 

 being to reduce these laws to the simplest form and smallest 

 number, and then by recombining these, to account for, and 

 calculate all mechanical events. Now, with respect to this 

 analysis of such complex occurrences into their simplest and 

 fewest laws, it appears that writers have arrived at different 

 results. It will therefore appear not to be superfluous or un- 

 profitable to show what is the greatest degree of simplicity to 

 which the fundamental doctrines of mechanics can be reduced ; 

 what are the considerations which make it impossible to carry 

 the simplification further than this point, and unscientific to 

 stop short of it ; and how far the mode in which the principles 

 of the science are stated in works of the most acknowledged 

 reputation can be considered as possessing this philosophical 

 simplicity combined with logical strictness. ';'^^ 



The leading distinction which may be considered as pre- 

 vailing at present upon this subject is that between the 

 English writers, who, following Newton, make three laws of 

 motion the foundation of dynamics ; and the foreign, and more 

 particularly the French writers, in whose Treatises on Mecha- 



