Publication: The Telegrapher
New York, NY, United States
ON THE WORKING CAPACITY OF TELEGRAPH
BY DAVID BROOKS.
IF we take two wires of the same metal, and of equal length, one of which is twice the weight of the other, the apparent difference in their sizes will not be great, and it is somewhat difficult to realize that the latter has twice the capacity of the former for the conduction of electricity, yet such is actually the case. Again, if we take two wires of the same metal whose weight per foot is the same, one of which is one foot and the other two feet in length, we find that the shorter wire has twice the conducting power of the longer one, or conversely that the electrical resistance of the longer wire is twice that of the shorter.
If a wire of any given diameter, and one foot long, is drawn out to a length of two feet, its length will be doubled, while its weight per foot will obviously be halved. Hence its conducting capacity or conductivity will be but one fourth of the original amount. We find, therefore, that the conductivity of a given weight of wire becomes reduced as it is lengthened in the ratio of the square of its length.
Applying this principle to the case of a telegraph line, we will suppose its length to be 100 miles, and the conducting wire to be of the size known as No. 8. We can get an electrical current of equal strength from the same battery through a wire 200 miles in length if we use a No. 4, or wire weighing twice as much per foot as the No. 8. We have made no allowance in this case for leakage at the insulators or supports. This relation could be preserved by doubling the distance between the posts so as not to increase their number.
In order to secure the best result in the working of a telegraph line we must make the resistance as small as possible in the route through which we wish the electricity to travel, and as great as possible in every other direction, that is to say, we must keep down the resistance in the conductor, and increase it in the insulation to the greatest practicable extent. The practical value of a telegraph line is the difference or margin between the joint resistance of the conductor and the insulation and that of the insulation alone. This difference is in all cases shown by the tension of the spring of the relay magnet, when upon what is termed a "working adjustment." It will be evident, from what has been said, that this margin may be increased by either of two methods, viz:
1. By increasing the resistance of the insulation.
2. By decreasing the resistance of the conductor; or, in other words, by increasing its conductivity.
For example, we will take a line of telegraph 100 miles in length - the weather being rainy. Suppose that the conductor has a resistance of 20 units per mile while the resistance of the insulators is 1,000,000 units per mile. Let the receiving magnet and battery be situated at one extremity of the line and the key at the other. When the key is closed, the force acting upon the armature of the magnet is in proportion to the quantity of electricity leaving the battery and passing through the magnet to the line, and this quantity is made up of that escaping through the insulation along the line, in addition to that going through the conductor to the other end of the route. When the key is open the force exerted upon the armature is due to the current passing through the insulation alone. The effective working strength is therefore the difference between the attractive forces acting upon the armature, when the key is opened, and when it is closed at the other end of the line - or in other words we may say that the working margin is the difference between the sum of the forces due to the joint conductivity of the wire and insulators and that of the insulators atone,
We have given the strength of current with key closed as 100 in both the above cases, in order to show the proportionate increase of margin. The absolute strength of current in the two cases is as 100 to 183, an increase of 83 per cent., while the increase of working margin is only 9 per cent.
We will now look at the result of an actual measurement. A new No. 9 galvanized wire, 115 miles in length, on a clear and fine day, gave a resistance of 2,400 units, or about 21 units per mile. On the same poles was a No. 10 plain wire, which had been in use nineteen years. This wire, including eight instruments in circuit, gave a resistance of 13,300 units. In a rain the insulation resistance of the good wire measured 15,300 units, and the bad wire 19,650.
The joint resistance of the good wire and its insulators was 2,077. The proportion of current escaping by the insulators was to the whole current as 13.51 to 100, giving a margin to work on of 86.49.
The joint resistance of the bad wire and its insulators was 7,982. The proportion of escape to the whole current was as 40 to 100, giving but 60 per cent. as an available working margin. This wire could not be worked except when the other circuits on the same poles remained idle, either closed or open. The good wire was worked without difficulty. The escape was apparent, but was not sufficiently great to cause any serious inconvenience. The relative working margins were in the proportion of 86.49 to 60.
On a clear and cold day the insulation of the good wire showed a resistance of 2,400,000 units, the working margin being 99.99. The bad wire showed an insulation resistance of 1,700,000 units, the working margin being 99.93. The difference in this case between the two wires was only 00.06, an amount not appreciable in practice. The poor wire worked as well as the good one, but the current was not so strong. This difference could be compensated for by increasing the battery on the former.
In the above instance we have two wires on the same poles. One is new and a good conductor, the other old and a poor conductor. In fine weather the insulation of the new wire is the most perfect, but the difference in their working is inappreciable. In rain, although the insulation of the old wire is actually the best, yet it does not work nearly so well as the new wire, and this is attributable solely to the fact that the new wire has a much greater conductive capacity.
Take another example, also from actual measurement: A new wire, 105 miles in length, on a clear day gave a resistance of 2,200 units. On the same poles was an old rusty No. 11 wire, which gave a resistance of 23,500 units. On a very wet day the insulation resistance of the new wire was 4,800 units, and of the old wire 32,000 units. The working margin of the new wire was 78, and that of the old wire 60. In this case the amount of current escaping over the insulators of the new wire was 2.7 times that passing through the old wire and its insulators combined! In other words, the current with key open on the new wire was nearly three times as strong as on the old wire when the key was closed.
In these examples the resistance of the batteries and instruments has not been taken into account, as they do not materially affect the results.
The writer has known instances where a new wire has been put up and worked as a "through circuit," its apparent insulation being judged of by comparison with an old "way wire," with as many as twenty instruments in circuit, having a resistance varying from 100 to 1,000 units each. The utter fallacy of such a comparison, as far as insulation is concerned, is well seen by the two examples give above. It is in point of fact simply a comparison of working margins, giving no indication whatever of the absolute value of the insulation, of one circuit as compared with the other. It would, in the case just mentioned, have been far better to have used the old wire for the "through" and the new wire for the "way" circuit, thus in some measure compensating with new wire of good conductivity the resistance of so many instruments.
(Concluded next week.)