m 



10. The explanation of the dynamic system. 



Tlie aiTangement of tlie families in the dynamic system given in the 

 foregoing pages is somewliat comparable to that of nnmerous images of objects 

 reflected by two mirrors standing at obtuse angles to each other, wliich objects 

 lie between the two miiTors. Tliis thought came to my mind, as I was read- 

 ing the proofe of tliis paper ; and I at once thought of myself as standing, 

 as it were, just in fi-ont of the min-ors and looking at the innumerable images 

 reflected in them. 



Such an arrangement of families, as tliat in my system, should necessarily 

 satisfy the following condition : — Pi-ovided that a family, say A, in the middle 

 cohimn of the system is compared with another family, say B, or other famiHes, 

 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 infalUbly lias, in its timi, family A at its side. In order to accord 

 with this condition, I have, wliile reading the proof, inserted in my system as 

 many "reflected images " up to the Hmit of my knowl6dge, as all the families 

 there mentioned should have. In the com'se 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 consfcructing a d;yTiamic system. 



As I have stated above, you first construct the system by placing the 

 familias of the framework in the middle vertical column in the same order as they 

 originally appear in the same work, and T)y 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. Tlien 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 corabination of each one, say A, of all the families in the 



