294 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



fits in with the control contact network. Again, this is a multi-terminal 

 network problem and the procedure is to design two-terminal networks 

 that combine most readily. Since it is impractical to illustrate all the 

 repeated trials that led to the final design, each network will be designed 

 separately with the understanding that some of the steps are imposed 

 by the form of all networks viewed collectively. 



The procedure adopted for developing the "0" lead network is as 

 follows. First set up the miniature table repeating the portion of Table 

 III that corresponds to the "0" lead. These parallel combinations should 

 then be manipulated algebraically to obtain the greatest simplification 

 possible. It is rather easy to apply some of the algebraic rules by observ- 

 ing the condition of the relay in the several combinations in the table. 

 A simple "shorthand" rule to follow is: if in the table of combinations 

 describing a particular two terminal network, all possible combinations 

 of certain relays appear in conjunction with a single combination of other 

 relaj^s, the network contacts on the former relays may be neglected. In 

 other words when 2" different combinations of any number of variables 

 m, are identical in all but n columns, contacts on the corresponding n 

 relays are not required. This procedure is carried out below. 



B C D E 



Thus we have the follo^^^ng algebraic expression for the "0" lead, 

 which can be simplified as shown. 



(B + C + D')(B' -f- C + E')iB + (" -j- E)iC' + /)' + E) 



[C + (B + D'){B + E)(D' + E)]{B' + C + E') (3b) 



[C + (E + BD')(B -f D')](B' + C -\- E') (3b) 



This is shown on Fig. 4a. A somewhat different manipulation of the 

 equation permits placing the network in the bridge form of Fig. 4b. 

 The algebraic equation, given below, can easily be shown to be the 

 equivalent of the original. 



[E + C + B{B' + D')](B' + C + E')(B + C -f D') 



