NEW INVESTIGATION, &C. 403 



amount and direction, when the boundary of the 

 attracting points is any specified figure or surface, 

 has been the great object of investigation by 

 mathematicians since the theory of attractions 

 was first developed by Newton, in his great work 

 the Principia. 



No subject of inquiry, since Newton's time, 

 has been attended with greater difficulties, or 

 received the attention of more profound and en- 

 lightened minds, than the theory of attractions. 

 In pursuing the investigation, we are conducted 

 to all the resources and refinements with which 

 the domains of analysis have been enriched by the 

 great geniuses of the last century, who have left 

 upon immortal pages the deep impress of their 

 great and noble intellects. Some of the most 

 illustrious of these are Newton, James and John 

 Bernoulli, to whom we are indebted for the use- 

 ful and well known method of integration by 

 parts, which Lagrange has successfully applied in 

 order to establish his fine theory of the Calculus 

 of Variations ; Leibnitz, Euler, D'Alembert, 

 Laplace, Lagrange, Poisson, Simpson, Mac- 

 laurin, — and Ivory, who has the merit of being 

 the first in this country who studied the works of 

 the continental writers. All of these have en- 



