On the Principles of Motion, tyc. 297 



upward force, and are now seen in every inclination, from 

 vertical to horizontal. Many of the masses of rock, now on 

 the surface, seem to have been subjected to the action of 

 great heat, and although no rocks of decidedly volcanic ori- 

 gin have been observed, our knowledge is too superficial and 

 limited to warrant us in saying that such do not exist. 

 Steubenville, Ohio, March 27th, 1827. 



Art. IX. — On the Principles of Motion, and their use in the 

 higher branches of Mathematics. 



The astonishing discoveries made in natural philosophy, 

 and more particularly of those grand principles, which regu- 

 late the movements of the great bodies of the universe, are 

 to be ascribed, principally, to the skilful use made of the 

 mathematics in the development of these discoveries. As 

 this science has thus afforded the most certain and powerful 

 assistance to philosophy, the principles of the latter, com- 

 mon to both, have contributed to the extension and illustra- 

 tion of the former, in its more difficult and complicated re- 

 searches. The idea of motion, either local, or of aggrega- 

 tion, or diminution is essential to that of the generation and 

 investigation of all curvilinear figures, and is that which was 

 employed by the ancients for that purpose. Similar views 

 of quantity in general, generated by motion and regulated 

 by certain laws, originated that most extensive and impor- 

 tant of all the mathematical sciences, denominated by New- 

 ton fluxions, and by Leibnitz the differential calculus. The 

 first of these great men illustrated the doctrine by motion, 

 and demonstrated it by the ancient method of limits, show- 

 ing the comparative effects of a motion which is uniform, 

 and of one which is varied in any ratio of this, or according 

 to any law dependent on the uniform motion. The latter 

 estimated the same effects by that, which has been denomi- 

 nated by Aristotle the motion of aggregation, or the rate by 

 which the infinitely small elements, or parts of any quantity 

 are aggregated. There appear to be no just grounds of 

 objection to either of these modes of conception, in the gen- 

 eration of quantity, as both are susceptible of demonstra- 

 tions of equal validity and clearness with those of other 

 branches of the mathematics, whose direct relations cannot 

 be inferred. Our ideas of quantity, (the whole subject of the 



Vol. XIV.— No. 2. 12 



