175 



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, wliich 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 w T ork, aiid 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 

 tliat may have been omitted. In practice, you make a set of cards, on each 

 of Avhich is written a combination of each one, say A, of all the families in the 



