FUNDAMENTAIL PRINCIPLES. 
tion, and_g_ 7 is the drop due to that current, where » 
7 
is the resistance of each section. ‘The drop in the first 
. : ¢ : ‘ 
section from A is to—— 7, in the second section g—c— 7 
7 n 
and so on; 7. e., for the whole 7 sections the total drop 
must be 
(6) E _*_,7»(1+2+3 5o 
But the sum of this series of integers is well known, being 
n(n+1) 
e 
Hence, substituting and reducing, we have 
(7) E= 
This gives the total drop produced by » uniform loads 
uniformly spaced and aggregating C amperes. 
It is generally convenient to have working formulee 
give the cross section of conductor directly, smce that is 
most frequently the quantity to be determined. = Equa- 
tion (3) can readily be transformed for this purpose as 
follows: 
        
a2 L 
¢.om. 
(8) R= 
But since the R here concerned is the total resistance, 
and not the resistance per section 7, as in (7), we may 
write, 
11 L, 
T (em)n’ 
Then substituting this value of »in (7) and reducing, we 
have 
  
  
(9) C. m.— IICL (71+TJ 
2B Ly 
This equation gives the area of conductor required for C 
amperes supplying a line of known length equally loaded 
at # points at any required terminal drop. 
n+1 
7 
  
For a large number of sections ( ] approach- 
es unity, so that, for a given current in amperes and a