284 
The N.Z. Journal of Science and Technology. 
[Jan. 
By substituting in the above we have 
P t 3 + P t 2 3 ' 05 x 104 ~ 2-94 x 10 12 = 0, 
whence Pt = 8,6501b. per square inch. 
These results show that even with suspension insulators a considerable 
pull (along the line) may come on any post, due to the breaking of a wire. 
With steel flexible towers this is provided for by a steel earth-wire running 
along the top of the poles and fastened securely to each. 
To find the Tension when the Spans are unequally loaded. —With suspen¬ 
sion insulators in country where snow falls this is of some importance. The 
snow and ice collect on the wires and greatly increase the sag. Some spans, 
however, clear themselves, and in them the sag is small. Now, if the lines 
are vertically above one another, and in a span the top wire is ice-covered 
and the bottom one bare, the top one may foul the bottom.* 
Returning to equation (6), 
x (otEi + P t — P q ) _ {x -j- A x) 3 q 1 2 S 2 x 3 q 2 S 2 
B - A.x + jj-pj:2 -^2 • 
As before, throughout the stretch «, t, E, P t , P q , 8, and q may be 
considered constant. For each span, however, q 1 is now variable, de¬ 
pending on whether the wire in the span is snow-covered or not. Now, 
summing as before, we get 
L 3 + l 2 
q 2 S 2 E 2x 3 
6 P„ 2 v x 
P q + «E t 
8 2 E %x 3 q t 
6 2 £ 
= 0 , ...( 12 ) 
the solution of which gives the tension in the stretch. The tension and the 
loading in each span being known, the sags can easily be determined. In 
Hydro-electric Power, vol. 2, page 308, Lyndon considers the case of two 
spans with ice load on one, and the tension is found by a method which is 
only applicable to a stretch of two spans. The wire is No. 0000 B. & S. 
aluminium, and -the spans are 600 ft. On one span is an ice load Jin. thick, 
and the other span is clear. The temperature of the wire is 34° F. The 
maximum stress is 14,0001b. per square inch at a temperature of 10° F., 
with an ice load of Jin. and a wind load of 101b. per square foot. 
Weight of wire per foot-run 
Weight of ice per foot-run 
Wind load per foot-run 
Resultant load per foot-run 
Loading-value, q 
Loading-value, q 1 
Area of wire 
Weight per foot-run per square inch 
Coefficient of expansion 
Modulus of elasticity 
0*195 lb. 
0-632 lb. 
P251 lb. 
1*50 lb. 
7-69 
4-22 
0-1662 sq. in. 
1-172 lb. 
12-8 X 10- 6 . 
8 X 10 6 lb. per 
square inch. 
* Prevention of Sleet Troubles on High-tension Transmission-lines, Electrical World, 
10th March, 1917. — 
