( 597 ) 
whilst the differential equation for v reduces to 
ae _ ie 
de dz 
Let o be an arbitrary function of «,y,2. We shail now find 
1 do 020 020 0°20 
w= |e (5, Sa On ce ae eral 
de 
The differential equation s + “= 0, for which may be written 
ao is 
dx dy tid 
’ 
possesses as intermediate integrals 
des do do 
das ta Be GEE = f (2), 
do oo do 
where f denotes an arbitrary function. 
These results differ in form only from those formerly communi- 
cated sub VY. | 
Mathematics. — “On the locus of the centre of hyperspherical 
curvature for the normal curve of n-dimensional space”. By 
Prof. P. H. ScHours. 
At the close of the preceding paper we have pointed out that the 
characteristic numbers of the locus of the centre of hyperspherical 
curvature are lowered if some of the points of the given rational 
curve lying at infinity coincide. At present we wish to trace fora 
special case the amount of those lower numbers, viz. for the case where 
° e 1 3 e e 
the given curve is the “normal curve! N„ of the n-dimensional space 
S,, in which it is situated. It is known that this curve is represented 
on rectangular coordinates by the equations 
it, (== 2, 2, eel TM n) 9 ° ° ° e ° (1) 
