PROFESSOR W. K. CLIFFORD ON THE CLASSIFICATION OF LOCI. 
681 
If p>n — k, then 2k is not greater than n. 
Conversely, if k > fn, p is at most equal to n — k. 
YVe may also state the proposition in this way. A curve of order n and deficiency 
p, not greater than |n, can at most exist in n— p dimensions. 
[It appears, therefore, that the theorems at the beginning of the paper may be 
extended, and that in n dimensions we have the curve of order n which is unicursal, 
the curve of order n-\- 1, and deficiency at most 1, of order n + 2, and deficiency at 
most 2, and so on till we come to the order 2 n, wliich is the first case of exception, 
and may have deficiency r+ 1. This curve is the natural geometric representation of 
the general Abelian functions, its multiple tangent flats playing the same part as the 
double tangents of the quartic curve in Riemann’s beautiful paper on the case j>—o. 
H. Weber has noticed that in four dimensions this curve is the complete intersection 
of three quadric loci.- — January, 1879.] 
