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MR. A. B. KEMPE OR THE THEORY OF MATHEMATICAL FORM. 
composed as many systems as there are types of component collections of a full set 
of 2 n classes. 
390. If n=A, so that C has 16 component units, the number of these types will 
be 397, so that a class system containing 16 classes has 397 different sorts of com¬ 
ponent collections. # It must be noted that it is distinguished collections, and not 
distinguished aspects of collections, with which we are here dealing. 
391. The number of types in a system of 4 units is 5. In one of 8 units it 
is 21. In both cases components containing all units of the systems are included. 
* See Professor Clifford “ On tie Types of Compound Statement involving Four Classes,” in the 
‘ Proceedings of the Manchester Philosophical Society,’ vol. vi., Third Series. In this paper Professor 
Clifford denotes the 2 16 classes of a system derived from four unrestricted classes A, B, C, D, by state¬ 
ments or propositions. He regards the classes A, B, C, D, and their obverses a, b, c, d, as distinguished 
from all other classes of the system, and thus regards the separated classes as constituting a full system, 
and consequently gets the division of all the classes into 396 sorts, not including the aggregate of all 
the classes. In the view taken in this memoir, the 2 16 classes should all be regarded as undistinguished 
from each other, the distinction raised between the classes A, B, C, D, a, b, c, d, and others, being due 
to the accident of particular classes being selected to be denoted by single letters, and not to any 
essential differences. This does not, of course, affect the conclusion that the number of distinct types of 
component collections of a system of 16 classes is, if we do not include the collection which is the 
aggregate of all the classes, 396, or if we do include such collection, 397. 
