Solution of a Problem in Fluxions. 69 
under my notice, relating to the mineralogical resources of this dis= 
trict, accompanied by a geological map of the state of New York. 
Rensselaer 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 pected geo- 
logical report and map. 
Arr. ViIl.—Solution of a Problem in Fluaxions; by Prof. Tuxro- 
DORE STRONG. 
(Continued from Vol. XVI. p. 283.) 
TO PROFESSOR SILLIMAN. 
New Brunswick, July 29, 1829. 
Dear Sir—You will doles me by inserting the following continua- 
tion of my last paper in the next Journal. Yours respectfully, 
T. Strrone. 
2 
The same notation being retained; I assume a = a=, 
d?y a d#z') 2% V (d? x)? + a 2+ (d?z)* 
dy—yd. dx- re 
(b) becomes identically F=F, and d (re) =0, d (cto = )=o, 
dy — yd. 
— anne 0, (i); -F’=0, F”=0. 
a (i) show that the particle is not acted on by any force 
except F, in the direction r. Indeed (g) are the equations that 
would result from the decomposition of a centripetal force, F’, (act- 
ing in the direction "2 in the directions of 2, y, 2; respectively. ‘The 
dx dx — xrdz zdy - ydz 
integrals of (i) are oa I = A, a eB, ge Ooh) 
(A, B, C, being variety constants;) .”-Az+By — Cail, (2); the 
equation of a plane passing through the centre of force; in which s 
