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10. THE EXPLANATION OF THE DYNAMIC SYSTEM. 
The arrangement of the families in the dynamic system given in the 
foregoing pages is somewhat comparable to that of numerous images of objects 
reflected by two mirrors standing at obtuse angles to each other, which objects 
lie between the two mirrors. This thought came to my mind, as I was read- 
ing the proofs of this paper; and I at once thought of myself as standing, 
as it were, just in front of the mirrors and looking at the innumerable images 
reflected in them. 
Such an arrangement of families, as that in my system, should necessarily 
satisfy the following condition : — Provided that a family, say A, in the middle 
column of the system is compared with another family, say B, or other families, 
say B, C, ... , or in other words, provided the former A has the latter 
family or families, B, C, ... , at its side; in the case that family B or one 
of the families, B, C, D, ...., is in the middle column, then the latter family 
must infallibly has, in its turn, family A at its side. In order to accord 
with this condition, I have, while reading the proof, inserted in my system as 
many “reflected images” up to the limit of my knowledge, as all the families 
there mentioned should have. In the course of the reading, I have thought of 
a process by which we can test whether or not a system constructed as above 
satisfies this condition. Though I have been unable, in my present circumstances, 
to test my system by the process given, it will not be superfluous if I now describe 
this process as a supplement to my method of constructing a dynamic system. 
As I have stated above, you first construct the system by placing the 
families of the framework in the middle vertical column in the same order as they 
originally appear in the same work, and by placing any other family or other 
families, which according to your knowledge you think is or are comparable 
with each family in the middle column, at the side of each of the families 
in the framework. Then you proceed to test whether or not the system thus 
constructed satisfies, as you expected, the necessary condition stated above, and 
at the same time, in passing, you perfect your system by adding any families 
that may have been omitted. In practice, you make a set of cards, on each 
of which is written a combination of each one, say A, of all the families in the 
