ARTICLE VII. 



New Formulae relative to Comets. By E. Nulty, Philadelphia. Read 

 September 21, 1838. 



The investigation which I here propose to make, respects the com- 

 ponent velocities of a comet, observed in three positions, at consecutive 

 and moderately small intervals of time. It has for its basis the theo- 

 rem of Maclaurin, as adapted to proximate states of a variable function, 

 and the known expressions for the sun's attractive force on the comet 

 and the earth, referred as usual to rectangular solar axes. The means 

 which I employ are therefore the same as those presented by La- 

 grange in the Mecanique Analytique, and which Mr Pontecoulant 

 has recently adopted in his Theorie Analytique du Systeme du Monde, 

 where formulae for determining the distances and orbits of comets are 

 given with appropriate developments. But the object which I have 

 here in view, is not the same as that of Lagrange, in his celebrated 

 work above mentioned ; and my investigation and results are different 

 from those of Mr Pontecoulant, and embrace a wider extent of sub- 

 ject. Similar diversity and extension, in mathematical research, are 

 in perpetual requisition. They constitute an essential and important 

 part of analytic science ; and with their peculiar attractions, always 

 lead to useful views and advantageous contrast. As to the instance 

 now adduced, the presumed novelty, and the great accuracy and sim- 

 plicity of the formulae which I have obtained, entitle them, I should 



VI. — 3 T 



