JoLY — Vector Expressions for Curves. 397 



23. Curve constructed hy three developalles. 



Unicursal curves may also be regarded as generated by the poicts 

 of intersection of homographic planes of three unicursal developables. 

 If three developables are the envelopes of 



Spi>,{t)=f,{t), Sp<^,{t)=f,{t), and Spcf.,{t)=f,{t), 



the points common to three corresponding planes is 



_ /l (0 y<f>2 (0 <^3 (0 +/2 {t) V^, {t) <f>, {t) +./3 jt) r4>, {t) Cf>, it) 

 ^ 6'c^l(0<^3 (0*^3(0 



The degree of the curve is «i + /ij + **3) where ??i, %, and n^ are 

 the degrees in which the parameter occurs in the expressions for the 

 planes of the developables. Thus, in particular, a tvtdsted cubic ia 

 the locus of intersection of three corresponding planes of homographic 

 systems through right lines ; here 



ni = 7i2 = % = 1. 



24. Inverse and pedcd curves. 

 The inverse of the curve 



^~ f{^y) ^~ ^i^i/y 



if the radius of the sphere of inversion is unity. Multiplying above 

 and below by <^{xy), the equation of the inverse is 



P T^4.{xy) 



This is of the form considered in the present Paper, the vector to a 

 point on the curve being expressed as the quotient of a vector binary 

 quantic by a scalar binary. 



