6p=—b, (1), 
4q= —C¢, (2), 
Op? — 36r=d, (3), 
12pq+-72s=e, (4), 
1 1 
a? — px’ 7 (p? +8r)x* —5(288f-++q? +-9pr)x* — 
1 
gir? +2qs)z? —s?=0, (5). 
These five equations, joined to (B’)=0, are sufficient to de- 
termine y. 
We evidently have, at the same time, 
1 1 
g (Spy? +4qy)x° + 3(sy* + 3psy)x* =0 5 
or better, , 
(3py +4q)x? +2sy? +6ps=0, an indentical equation. 
Art. XII.—Solution of a Problem in Fluxions; by Prof. 
THEODORE Strona. 
TO PROFESSOR SILLIMAN. 
New Brunswick, June 8, 1829. 
Dear Sir—Should you consider the following solution of 
a well known problem of sufficient importance, you will 
oblige me by giving it a place in the Journal. 
shakin oases that a particle of matter, projected 
from a given point, in a given direction, with a given veloci- 
ty, is deflected from its rectilineal course into a curve line ; 
It is required to determine the equations of its motion. 
Solution.—Let its motion be defined by the three rec- 
tangular axes (x, y, z,) Z=P. COs. 9 COS. v, Y=F. COS. # Sin. v, 
y x 
z=r.sin. 9, .!. r?=02? +y2 +2? (1), 7 tan. v (2), > ==COs. v 
cot. 6 (3), * =sin. v cot.9 (4). Let t denote the time, (or 
the independent quantity, which varies as the time, increas- 
equal elements dt, in equal elements of the time.) _ 
he question requires that 2x, y, z, r, 9, v, found in 
y, &e. are to be considered as functions of t. Put X= —7,5+ 
