[559 
560] 
19 
560. 
. (1873—1874), p. 112.] 
[ADDITION TO LORD RAYLEIGH’S PAPER “ ON THE NUMERICAL 
CALCULATION OF THE ROOTS OF FLUCTUATING FUNCTIONS.”] 
ailed the cyclide) is in 
viz. assuming it to be 
only be observed that 
lints, viz. these are the 
to see that it is the 
viz. the general cyclide 
[From the Proceedings of the London Mathematical Society, vol. v. (1873—1874), 
pp. 123, 124. November 22.] 
Prof Ciyley to whom Lord Rayleigh’s paper was referred, pointed out that a similar result may be 
attained by a method given in a paper by Encke, “Allgemeine Auflösung der numerischen Gleichungen,” 
Grelle, t. xxii. (1841), pp. 193—248, as follows : 
m, n) (x, y, z, l) 2 = 0 
Taking the equation 
0= 1 - ax + bx 2 - ca? + dP - ex 5 +fx 6 - gx 7 + hx s - ...; 
= 11 constants. But the 
3 of inversion, taken in 
it; in all 2 + 2 + 1, =5 
¡he number of constants 
if the equation whose roots are the squares of these is 
0 = 1 — a x x + b x x- — c^P + ..., 
then 
a x = a 2 — 2b, 
)f an Anchor King or Torus, 
= b 2 — 2ac + 2d, 
cf 2 = c- — 2 bd + 2ae - 2/, 
dj 2 = d 2 - 2ce + 2bf - 2a# + 2h, &c.; 
and we may in the same way derive a 2 , b. 2 , c 2 , &c. from a 1} b 1} c x , &c., and so on. 
As regards the function 
z n [ z 2 & ) 
J n ( z ) ~ 2 n . T (n +1) 2.2n + 2 1 2.4.2n + 2.2n + 4 j ’ 
3—2