363] 
ON THE THEORY OF THE EVOLUTE. 
479 
If instead of the given curve we consider its reciprocal in regard to the absolute, 
m, n, 8, k, t, i; 0, \ /l ; t, = 0 + X + /n 
then 
are changed into 
n, to, t, l, 8, k ; 0, fi, \ ; i, = 6 + ¡i + X 
respectively. 
Hence for the evolute of the reciprocal curve we have 
n' = n + m —6 , 
to' = 3 n + k — 20 — i, 
/ / 
c = t , 
k = 6n — 3m + 3/c — 3^ — i, 
which, attending to the relation t — k = 3 (n — to), are in fact the same as the former 
values; that is, the evolute of the given curve, and the evolute of the reciprocal 
curve are curves of the same class and order, and which have the same singularities. 
Cambridge, February 22, 1865.