186 BELL SYSTEM TECHNICAL JOURNAL 



relay operates at this value of current. If the expression for /(/) is 



written for each of the conditions which may occur, and is found to 



equal 1/2 at the transition points, the proof is complete. For this 



purpose the summation signs may be eliminated by substituting from 



any of the six simultaneous equations numerical values in place of 



summations of terms, in the equation for /(/), with the following 



results : 



Conditions 



a,/ = io = U=\ /(/)= ;^[ii+i2 + 23 + i4 + i5 + 1.42 + z:i(-l) 



+Z5(-l) + l(2.29)] = i, 

 co/ = a *o = H=\ /W- y^[l+^2+i3+^'4+i5+1.42 + l(2.71) 



+ ^2(-l)+i3(-l)+n(-l) 



+^-,(-l) + l(1.29-2.71)] = L 

 co/ = 2a ii = ^2=1 /{7)=^[0+l+?3 + /4+i'5 + 1.42 + 0(2.71) 



/ .4z 



or 

 ii=\ ^2 = 



+ l(2.71) + /3(-l)+i4(-l) 

 +^5(-l) + l(.29-1.71)] = i. 



co/ = 3a ^2 = ^3=1 /(/)=y^[ii + 0+l+/-4 + ^5+1.42 + z-i(-l) 



or 

 ii =1 ^3 = 



+ 0(2.71) + l(2.71)+i4(-l) 

 +Z5(-l) + l(-.71-.71)] = oi, 



co/ = 4a «3 = u=\ /(/)= ^(ti + /:2 + + l+i5 + 1.42+i,(-l) 



or 

 iz =1 ^4 = 



+«2(-l)+0(2.71) + l(2.71) 

 +i5(-l) + l(-1.71 + .29)] = i 



a>/ = 5a i4 = k=\ /(/)-y^[n + /2 + /3 + 0+l + 1.42 + /i(-l) 



or 



ii =1 i5 = 



+Z2(-l)+i3(-l)+0(2.71) 



+ l(2.71) + l(-2.71 + 1.29)] = i 



co/ = 6a ^5 = /6-1 /(/)= ^[ii+i2+i3+i4 + + 1.42 + /i(-l) 



+ i'2(-l)+^'3(-l)+i'4(-l) 



+ 0(2.71) + l(2.29)] = i 



Hence it is concluded that if an admittance can be found such that 

 "Blank" T, O, M, V and "Letters" are transmitted without distor- 

 tion any other teletypewriter signal may be transmitted on a repeated 

 basis, since the correct current value (1/2) will be obtained at any 

 transition regardless of what other signal combination is used for the 

 remainder of the character. 



