Miwella- 
tio on 
—_—— 
a 
466 FLUXLONS. 
the theory of 
of the 
=px BC; 
“ge—=py, (1) 
From the first of these, . 
Se pps + py—qe=O0," > 
and taking the fluxions, considering x and y as con- 
se ee 
“fires aie i 
ape ; a os “eRe 
therefore 2 20; bat frem equation (2); taking the 
fuxions, eee and hence ga 
wid by the first equation 2 = 1—, therefore 
> atic and sub- 
stitating for g* its value dyphncte hy sa (2), we get 
qz=2ap; ce, and by 
A= ptt aa A cdned te 
we have these two 
earns (2); 
) boc ad 
2a prery Me 
paeneteen ~ ay’ 
42°? = (Sa? —4ay—2*) 2. 
Hence, 44 y = 4a* —x*, and this is the equation of 
the curve which is evidently a having 
‘common intersection of all the 'para- 
ae on hot 
rameter = 4a.) 00 / of) on Ee 
d = yydee eoyutit 3 
ee aryieey ) “ye -rdz=0, 
i constant quantity ; but besides 
Bie hat gulps satan ‘ 
—s=0, 
Son aichengh i edunic” an arbi Same praia a 
uation, 
peeps voit ithe eee The bounds 
within w ne to confine this treatise, have 
not allowed us to enter into this branch of the subject, 
pope although interesting, is Ly rs penceye - On 
this subject, see Euler, Instit, vol et 8 
cap. 4. ; = m, Mom, de dead . 1774; also, 
‘on, 5, 16, and 17; La- 
place, Mem, de l Acad. Par, 1772; dre, Mem. 
on. 1790; Poisson, Journal de ? Ecole Polytechnique 
5. to be 
given by position, and that the force of each is. reel 
procally as the nth power of the distance from it; it is 
to find a curve in any of which a needle 
Gade i _ , its direction; when at 
Hes 
iff 
ia 
ee 
: 
or rejected, it be- . 
iican ‘etd ‘Seonbtibeal 
curve, We are now to 
number of points in it may 
‘Let the CNS=— and CSN 8 
the are of the curve NC. It appears 
roula 6,) that the tangent of the angle ACN el 
=r, therefore its secant carne 
but the numerator Sa ete ee 
of, We 6 formula 2,) Piette. 4 rec. ACN = 
‘ sign in,positive, s eaninh ; Et, to 
gether:) we have therefore p*:q":: 
and pl :g"1::— de: dy; ‘bit teh NCS, 
scigoas eae road Aa orenanae! 
seistign eee hence we geen ay = 
Eriery =e =» nore ¢ 
an eae fe 
ie 
ah 
aid JSsin.gd Oto} tnsshihah se4 ‘ is exo 
or taking the fluents, ; CATIA 
WPS a4 cos. hia io 
