ANNALS 



OF 



PHILOSOPHY. 



3IAr, 1826. 



Article I. 



On a new Application of the Method qfParatneters to the Deter^ 

 miuation of certain Curves. By Henry Moseley, Esq. BA. 

 of St. John's College, Cambridge. 



(To the Editors of the An.ials of Philosophy.) 



GENTLEMEN, 



If the tangent to any point (X, Y,) of a curve be given in posi- 

 tion in terms of the co-ordinates of a corresponding point (r, y,) 

 in another curve, whose equation/ j y = 0, is also given ; there 

 exist among the quantities concerned the three following equa- 

 tions by the ehmination of (jc) and(y), between which the former 

 curve is determined. 



FXYart/ =0 (1) 



-y- d X + — rf« = 0..... {^) 



d X d y -^ 



fxy = (3) 



For let the tangents to any two points in the required curve 

 intersect in the point (X', Y',) ; and let the positions of these 

 tangents be given according to the supposition in terms ot(x,y), 

 (j + A X, ?/ + A y) co-ordinates of corresponding points in the 

 given curve. 



There are, therefore given the equations 



FX'Y'ay ~ 



F X' Y' (a; + A x) (j/ -r A 5^) = 



From the last, we obtain by expansion, 



F X' Y' a- j^ + ^-^' Aa- -{- P (A xf "I , 



-f- Q (A ar) (A t/) J> = 



ilV I 



+ gA3/+Il(Ayr- J 



• F ik here written for F X Y * y. 



NeirSeWe*, VOL. XI. y 



