1921.] Kobxnson.—Cable Spans with Suspension Insulators. 281 
P P 
Now, t , -„ q , at are all small, and hence to a first approximation 
hj it 
from (4), neglecting small quantities of the second degree, we have 
and from (3) and (5) 
X («• + E + P t — P q ) _ 
X 
(am + Pt - Pq) 
E 
.( 5 ) 
E 
= Ax 
(:x + A x) 3 q ± 2 ^ 2 x 3 q 2 s 2 
6P t 2 
6 Pq 2 
..( 6 ) 
Now, if pin insulators are used, the span is of constant length, i.e., A x = 0, 
and if q 1 = 1, this equation reduces to equation (9) of Mr. Parry’s 
pamphlet. 
With suspension insulators, anchor-posts with strain insulators are put 
in at certain distances, and it can be assumed that the point of support at 
the anchor-post does not move. Now, in any stretch between such anchor- 
posts, if account is taken of the sign of Ax , then 
22a;z - 0,...(7) 
providing the summation extends over all the spans comprising the stretch 
between the anchor-posts. For each span in the stretch an equation of the 
form of (6) is obtained, x being the only variable. 
Summing all these equations we have 
a ; E + P t - Pj Sa . = 3 (« + Ax) 3 — AJ 2* 3 ....(8) 
Now, 2 Ax = 0, and x is large, while ax is small, so that (8) becomes to a 
first approximation 
(«*E + Pt - Pq) 2^ 3 ?i 2 S 2 
i.e., 
*t 8 
+ L 2 ( 
E 
'$x 3 q 2 $ 2 
2^6 P q 2 
2 x 3 q 2 & 2 
2 x 6 P t 2 2 x 6 P q 2 ’ 
(9) 
P q + cEi] - 
2s 3 g 1 2 8 2 E 
%x 6 
= 0. 
Writing 
x = 
2 x 
u 3 
+ V (W- +~) 
X 2 gq 2 S 2 E 
6 P 2 
q 
= 0 ....( 10 ) 
If q ± = 1, this equation becomes the same as equation (9) of Mr. Parry’s 
pamphlet for a half-span, X. 
Equation (10) gives the value of the tension in the stretch between two 
.anchor-posts. 
V 2 x s 
—— , all the equations and 
• A X 
graphs given in Cable Spans can be used. . 
