Mr. A. Cay ley's Note on a Nodal Curve, 437 



A determination with another silver plate gave 



D = 0-00005985 millim. ; - = - 0-05 ; 



a 



and thence, by equation (9), 



7i = 0-6, 



The difference between the two determinations 0*3 and 0*6 

 will not appear strange, since, as I have already remarked*, much 

 greater differences occur in the refractive index of the same 

 metal ; and a metallic plate has its refractive index altered by 

 simple standing, so that it becomes even greater than 1. 



For the rest it may be remarked that by the aid of the theory 

 Eisenlohrf has deduced from Jamin's observations for the ellip- 

 tical polarization of light of the colour of Fraunhofer's line F, 

 which was reflected on a polished silver plate, 



r<=0-4971, 

 a value which lies between those found by me. 



Hence the result of the above-mentioned researches is, that 

 the refractive index of the metals is dependent upon the angle of 

 incidence, and increases with an increasing angle of incidence. 



LXVII. Note on the Nodal Curve of the Developable derived from 

 the Quartic Equation (a, b, c, d, eTt, 1 ) 4 =0. By A. Cayley, 

 Esq.% 



CONSIDERING the coefficients (a, b, c, d, e) as linear 

 functions of the coordinates x, y, z, w, then the equation 



Disct. {a, b } c, d, ejj, 1) 4 = 0, 



or, as it may be written, 



(ae-4 ! bd+3c' 2 ) 3 -27{ace + 2bcd-ad <2 -b*e-e s )* = 



represents, as is known, a developable surface or " torse/' having 

 for its edge of regression (or cuspidal curve) the sextic curve the 

 equations where©f are 



ae — 4M + 3c 2 = 0, 



ace + 2bcd-ad 2 -b*e— c 3 =0; 



and for its nodal curve, a curve the equations whereof (equivalent 

 to two independent relations between the coordinates) are 



ac—b 2 _ ad— be _ ae + 2bd—3c 2 _ be — cd_ ce—d*^ 

 a ~ 2b ~~ 6c ~~2cT"~ e~ ' 



* Phil. Mag. vol. xxvii. p. 172, 

 t Pogg. Ann. vol. civ. p. 375. 

 X Communicated by the Author. 



