486 e. H. SFSAM 



in {yo—ì/r) and ali its partial derivatives witli respect to (//q. ••«/,) 

 of order n — 2 vanish identically when {>/) coincides with [x) 



except , „ ^ ,,^"/« is « which reduces to C.ro^o-^Xi^\..x,M 



Then 



is an expression of the required type. 



For, if T is any terni in the brackets which does not 



vanish identically, then ^ „ '' :--z- reduces to Ca?,V^''.»i^'....Kr'^' 



when (i/) coincides with (x). Hence - „ ^ „ — r—^ reduces to 

 Oxo^'^Xi^^K.-Xr'^'- when (//) coincides with (x). 



^n—ÌQ 



Any derivative of the type —-tT^^.^z — ^^^ — , ^ „ ^ 



when (//) coincides with {x). For, the derivative of the first term 

 reduces to Cx^'^^^^x^i^K.. x/}^\.. x,.^"-; the derivative of each of 

 the other terms reduces to zero except the derivative o 

 i^oVi — yo^'j)9j which reduces to — CxqI^^^'^Xi^k.. x/j'^^... x^'^'-. 



Every other derivative of G with respect to («/o^i ...y,) of 

 order n — 1 vanishes identically, since the derivative of each 

 term in the brackets vanishes identically, when (//) coincides 

 with (x). Hence G is an expression of the required type. 



The ~ — ~r-, — rj ,,, , equations ot condition on the coer- 



{ni-\-lìl rl{n — l)!*'! ^ 



iìcients of the general polynomial, homogeneous of degree m 



in {xq . . . X,.) and of degree n in {//o . . . //,.), are therefore inde- 



pendent. 



Hence, the equation of an hi/per coniceli connex of derp'ee m 



in (xq . . . X,.) and of degì'ee n in (vo . . . y,.) inrolves 



{m-^r)\ (n-\-r — 1)! [m — «-j-lì 



(»(+l)! (r-D! n\ r\ 

 essential homogeneous parameters (*). The equation of the connex 



(*) The expression obtained by Masoni for the number of constants in 

 the equation of the connex for the case r = 3 is incorrect. This error was 

 pointed aut by Segrk in his previously cited review of Masoni's article. 



