864] 
457 
864 
ON RUDIO’S INVERSE CENTRO-SURFACE. 
[From the Quarterly Journal of Pure and Ajjplied Mathematics, vol. xxn. (1887), 
pp. 156—158.] 
Dr F. Rudio, in an inaugural dissertation “ Ueber diejenigen Flächen deren 
Krümmungsmittelpunktsflächen confokale Flächen zweiten Grades sind,” Berlin, 1880, 
and Grelle's Journal, t. xcv., p. 240, has determined the surfaces having for their 
centro-surface (i.e., the locus of centres of curvature) the aggregate of the confocal 
quadric surfaces 
a — y, b — y c — fj. 
or, what is the same thing, the surfaces orthotomic to the common tangents of these 
two surfaces. He obtains, as the final result of an elegant analytical investigation, the 
following formulae: 
U = 
a — u.b — u.c — u' 
A —u. fJL —u 
V = 
a — v.b — v.c — v' 
X — v./jL — v j 
0. XII. 
58