630 BELL SYSTEM TECHNICAL JOURNAL 



tions (1) and (9) alone, as the first step necessary is to determine the 

 value of R which, with a given value of T, will result in the specified 

 value of / (.070 ampere). With line current equations R can, of course, 

 be calculated by substituting .070 for /. While the line current equa- 

 tions can be set up fairly readily, they are of an extremely cumber- 

 some character. For that reason curves t'l, ii and iz, Fig. 2, were cal- 

 culated by the following method : 



From equations (1) to (9) inclusive, the line current was calculated 

 for the various values of T from 500 to 3000 ohms with various values 

 of R from to 2000 ohms in steps of 250 ohms. For each value of T 

 the line current was then plotted against R and the required value of 

 the latter read from the intersection of the curve and the .070 ordinate. 

 The values of R thus obtained were then substituted in equations (7) 

 to (9) for calculating r. These values of R and r in turn were substi- 

 tuted in equations (1) to (3). By the above method the values of R 

 within plus or minus two or three ohms can be determined. This pos- 

 sible error in R will not appreciably effect the points on the curves. 

 The point of intersection of ii, h, is, and i-o, Fig. 2 was calculated by 

 equating the right hand side of equation (10) to .0138. 



Referring to equations (1), (2) and (3) showing the relations be- 

 tween the regulating resistances and the received currents, it will be 

 noted that in the right hand member of (1) and (3), Ri and R3, respec- 

 tively, appear only as positive terms in the denominator. This shows 

 that the received current will inevitably be reduced for every increase 

 in the resistance, provided ri and rs are continuously increasing func- 

 tions of Ri and i^3 and from equations (7) and (9) it will be seen that 

 both ri and r^ increase continuously for every increase in Ri and R3, 

 respectively. In equation (2), however, R2 appears in both the 

 numerator and the denominator and in the latter it appears in both 

 the first and second powers. It is, therefore, not so easy to determine 

 from an inspection of the equation just how the received current 

 will be affected by increasing the resistance. It will be seen that this 

 difference in the received current equations offers a guide in the 

 selection of the location for the resistances which will result in the 

 greatest received current. 



From a closer inspection of equation (2), it is seen that when i^2 = 

 the received current will be and, as the denominator of the right 

 hand member contains the second power of R2, the received current 

 will approach if Ro be increased indefinitely. Also, it is clear that 

 there will be current in the receiving relay for all finite values of i?2. 

 Thus, if Ry be indefinitely increased from 0, the received current will 

 rise from to a maximum value and then descend again toward 0. 



