.1921.] Robinson.—Cable Spans with Suspension Insulators. 285 
Now, we have 
'%x 3 q 1 2 
2a? 
See 3 __ 300 3 + 300 3 
HaT ~ 300 + 300 — 
300 3 x l 2 + 300 3 X 4-22 
600 ~ 
300 2 ; 
- == 300 2 x 9-405. 
Substituting in equation (12) we have 
p t 3 + p t 
2 /300 2 x 7-69 2 X 1-172 2 x 8 x 10 f 
6 X 14.000 2 
300 2 x 9-41 2 x 1-172 2 x 8 x 10« 
~6 
14, 'XX) + 12-8 x 10 _6 .X 8 x 10 6 x 24) 
= 0 , 
4.C.. 
P t 3 + Pt 2 38,290 - 1-55 X 10 12 = 0 ; 
12 
whence, Pt = 5,9501b. per square inch, which is very close to the approxi¬ 
mations of 5,962 and 6,023 given by Lyndon (p. 312). 
Returning to equation (11) we have 
300 3 x LI 72 2 / 7-69 2 4*22 2 \ , /2,460 + 5,950 - 14,000\ _ 
=-e-ViLooo 2 - M50 2 ' + V -8 xTo®- ) 300 
= - 1*45. 
The movement of the insulator is therefore 2-90 ft. As found by the 
formula given by Lyndon (p. 309) it is 2*82 ft. 
The above investigation applies only to suspension insulators, giving the 
wire free-swinging points of support. The case of lines supported on pin 
insulators is assumed in all standard works to consist of a number of fixed 
points of support. This is, of course, only approximately correct, as the 
poles themselves are elastic, and their elastic deflection corresponds to a 
considerable degree with the swing of the suspension insulators. Taking 
this into account, the formulae for cable spans would require modification. 
The result will apparently be intermediate between those obtained on the 
usual assumption of fixed points of support and those obtained above on 
the assumption of free points of support. This po ; nt, however, will be the 
subject of a further investigation. 
I wish to thank Mr. L. Birks, Chief Electrical Engineer, Public Works 
Department, and Mr. A. C. Owen, Electrical Engineer, Public Works 
Department, for their help and valuable suggestions. 
/ 
