NUMBER THEORY IN SPLICING OF CABLES 275 



that this instruction follow the simplest possible system — e.g., any two 

 adjacent conductor units in one length of cable shall connect to two 

 conductor units having a constant separation in count in the next 

 length. The exposition which follows makes no attempt to solve the 

 general problem, and seeks only to establish the results which can be 

 realized when the above two simplifying restrictions are imposed. At 

 the conclusion is added a description of a minor and acceptable devia- 

 tion from the second restriction which will enable the practical worker 

 to supplement these results and achieve the maximum possibilities in a 

 number of cases sufificient for his needs. The problem now will be 

 formulated. 



Fig. 1 Fig. 2 Fig. 3 



The three tabulations exhibited in Figs. 1, 2, and 3 show possible 

 ways of splicing two pieces of eleven-unit cable together in systematic 

 fashion. The left-hand columns indicate the consecutively adjacent 

 conductor units in the first or reference piece of cable (remembering 

 that No. 1 and No. 11 are adjacent), and the numbers opposite in the 

 right hand columns indicate the conductor units in the second piece of 

 cable to which splice is made. No importance attaches to the splicing 

 of unit No. 1 to unit No. 1 in each instance. This is simply one of 

 eleven possible "starts," and from the point of view of this discussion 

 there is no preference among these. Note that with Fig. 1 two con- 

 ductor units which lie adjacent in the first piece of cable connect to 

 conductor units separated by a count of one (adjacent) in the second 

 piece. With Fig. 2 conductor units which lie adjacent in the first piece 

 connect to conductor units separated by a count of two in the second 

 piece. With Fig. 3 conductor units which lie adjacent in the first piece 

 connect to conductor units separated by a count of three in the second 

 piece. Splices made in accordance with the schemes of Figs. 1, 2, or 3 



