Solution of a Problem in Fluxions. 69 



imder my notice, relating to the mineralogical resources of this dis* 

 trict, accompanied by a geological map of the state of New York. 



A. E. 



Eensselaer School, Troy, July 28, 1829. 



N. B. Any statement of facts, calculated to explain the geology of 

 any part of North America, addressed to Mr. Cortlandt Van Rensse- 

 laer, of Albany, will be thankfully received. But it must be under- 

 stood, that we may take the liberty to express the subject matters of 

 such communications in our own condensed manner ; and that we 

 introduce and leave out, according to the plan of the proposed geo- 

 logical report and map. 



Art. VTI. — Solution of a Problem in Fluxions; by Prof. Theo- 

 dore Strong. 



(Continued from Vol. XVI. p. 283.) 



TO PROFESSOR SILLIMAIV. 



New Brunswick, July 29, 1829. 



Dear Sir — ^You will oblige me by inserting the following continua- 

 tion of my last paper in the next Journal. Yours respectfully, 



T. Strong. 



The same notation being retained ; I assume -j~^ = ? 



/7M -1 • „ T^ Ti -, J^dy-ydx\ (zdx-xdz\ 

 (o) becomes identically b =Jb , and a I — -r. — j =0, d I -j. — ) =0, 



^(zdy — ydz\ 



Equations {i) show that the particle is not acted on by any force 

 except F, in the direction r. Indeed [g) are tlie equations that 

 would result from the decomposition of a centripetal force, F, (act- 

 ing in the direction r,) in the directions of x, y, z, respectively. The 



xdi/ — ydx zdx — xdz zdy — iidz 



integrals of (^) are "^ "= A, j^ =B, "^^ =C, (k) ; 



(A, B, C, being arbitrary constants;) .'-As-f By -Ca;=0, (/); the 

 equation of a plane passing through the centre of force j in which s 



