BOOLEAN ALGEBRA AND CIRCUIT DESIGN 289 



for Avhich .Y is closed. Hence h(X) may be o])taiiie(l from r{X) by iiotiiifi; 

 I hat li(X) is the negative of r(X). Thei'efore the entire control i)ath of 

 any relay can be expressed geiuMally as 



f(X) = <AX)[X + h(X)] = ,AX)[X + (/-(A'))'] 



Thns for the .1 relay 



g(A) = L' + B' 



r{A) ^ L' + B 



h{A) = [L' + B]' = LB' (7a) 



and 



/(.4) = (U + B')(A + LB') 



= (L' + B')iA + L)(A + B') (3b) 



= (L + AXL' + B') (12a) 



Also for the B relay 



g(B) =L + A 



r{B) = L + A' 



h(B) = [L + A']' = L'A (7a) 



and 



f(B) = (L + AXB + L'A) 



= (L + .4)(5 + L')(5 + .4) (3b, 



= (L + ,4)(L' + B) (12a) 



The schematic forms of the A and B control circuits as represented by 

 the above algebraic expressions are sho^\^l in Fig. 2a and 2b. Since the 

 general reciuirements of the basic problem specify only one transfer on 

 the L relay, only simple makes and breaks on the A and B relays and no 

 shunt release paths (to avoid reduction in speed of operation), the combi- 

 nation of the above specific circuits is not possible without recourse to 

 double windings. Another factor which affects the practical form of the 

 circuit is the finite transit time of the L relay armature spring. Switching 

 aigebi-a presupposes instantaneous action of relay contacts and in certain 

 cases, when the use of a break-make transfer is required, additional con- 

 tacts are necessary to cover the open contact interval. The final circuit 

 form, conceived by F. K. Low, is shown on Fig. 2c and uses an added A 



