370 Prof. W. K. Clifford on the Classification of Loci. [May 9, 



(3.) Giant cells. Multinu clear masses of protoplasm. 



(4.) Concentric corpuscles of various sizes, sometimes attached to 

 one another by long processes. The corpuscles are formed of two 

 parts— a central portion, which is granular, and is acted on in a 

 peculiar manner by staining fluids ; and a peripheral portion formed 

 of flattened epitheloid cells continuous with the reticulum. The 

 concentric corpuscles are concerned in the formation of blood-vessels 

 and trabecule. 



The granular cells, giant cells, and concentric corpuscles, are almost 

 entirely confined to the central portions of the follicles. 



In fresh preparations, colourless nucleated cells are seen, which 

 contain granules and spherules of haemoglobin ; these cells either form 

 parts of the concentric corpuscles, or are in close connexion with 

 them. 



The blood-vessels of the cortical portions of the follicle are of small 

 size ; they run in lines from the periphery of the follicle to the edge of 

 fche medullary portion. The medullary portion of the follicle is sur- 

 rounded by a ring of blood-vessels ; the vessels are larger in the 

 medullary portion than in the cortical portion of the follicle. 



III. " On the Classification of Loci/' By W. K. Clifford, F.R.S., 

 Professor of Applied Mathematics in University College, 

 London. Received April 8, 1878. 



(Abstract.) 



" A curve," is to be understood to mean a continuous one-dimen- 

 sional aggregate of any sort of elements, and therefore not merely a 

 curve in the ordinary geometrical sense, but also a singly infinite 

 system of curves, surfaces, complexes, &c., such that one condition 

 is sufficient to determine a finite number of them. The elements may 

 be regarded as determined by h co-ordinates ; and if these be connected 

 by h— 1 equations of any order, the curve is either the aggregate of 

 common solutions, or, when this breaks up into algebraically distinct 

 parts, the curve is one of these parts. 



In the paper, of which this is an abstract, theorems are established 

 relating to the nature of the space in which such curves can exist, to 

 the mode of representing them in flat space of lower dimensions, and to 

 some of their properties. The following are the leading theorems : — 



I. Every proper curve of the nth order is in a flat space of n dimen- 

 sions or less. 



II. A curve of order n in flat space of h dimensions (or less) may 

 be represented, point for point, on a curve of order n — k 2 in a 

 plane. 



