1881.] 



solution of the equation x*+y s — 1 = 0. 



109 



as is immediately verified: hence writing ^r 2 = j, we have for the 

 value in question, y = 1, 



(m 8 - 1) (1 + cn u) - r 2 (1 -cnw)=: 0, 



or say 

 that is 



m 2 (1 + cn it) = (1 + cn u) + r 2 (1 — cn u), 



cn u = 



r 2 + l-m 2 

 r 2 - 1+m 2 



which is one of the values of cn u derived from the equation x = 0; 

 but this equation x = gives, not the foregoing equation, but 



m 



[1 + cn u) 3 = {(1 + cn w) + r 2 (1 - cn it)] 3 , 



viz. the three values of cn u are the foregoing value and the two 

 values obtained therefrom by changing m into com and com respec- 

 tively, co being an imaginary cube root of unity. In fact the curve 

 x 3 +y z = 1, has at the point x = 0, y = l an inflexion, the tangent 

 being y= 1, so that this line meets the curve in the point count- 

 ing three times; but the line x = meets the curve in the point, 

 and besides in two imaginary points. 



(2) Continued observations on the state of an eye affected with 

 a peculiar malformation. By Sir George Biddell Airy, K.C.B., 

 M.A., LL.D.jD.C.L., Honorary Fellow of Trinity College, Astronomer 

 Royal. 



Nearly ten years have elapsed since I last reported to the 

 Society the state of my eyes, as regards optical convergence of 

 pencils of rays. I subjoin the results of an examination lately 

 made, and I place them in series with those of preceding examina- 

 tions, as serving to shew clearly the gradual change which takes 

 place in the eye during a period exceeding 55 years. 



I. Distance from the cornea of the left eye at which a 

 luminous point presents the appearance of a nearly horizontal 

 line. 



Difference = — '073. 



-028. 



--006. 



--005. 



