in Fig. 13. The five groups of lamps represented by the light vertical lines are connected together by two conductors, which are shown as heavy horizontal lines. These conductors correspond to the so-called mains in electrical distribution systems, to which are connected the leads or small branch wires actually supplying the lamps. The mains receive their current through feeders, AA and BB, which connect them with the generating plant D, as represented in Fig. 12. As a general rule no lamps are connected directly to the feeders. The celebrated "Feeder and Main" patent of Edison* covered this arrangement of electrical conductors. In the first case, represented in Fig. 13, the mains are supposed to be fed at one end, the feeding-points being represented by short vertical lines marked + and - respectively. The mains are assumed to consist of No. 0000 wire, A. W. G., which would weigh 1,025 pounds for 1,600 feet required. Each section of the mains consists of 200 feet of No. 0000 wire, and has a resistance of about Fig. 13. Feeding at One End of Mains; 1025 lbs. Copper; 2 Volts Max. Difference Between Lamps; 111 Volts at Feeding-Points; 1.2 Volts Average Drop. = .01 ohm. The current in the first section of the main is 40 amperes, since it supplies 4 groups of lamps taking 10 amperes each, hence the drop is 40 x .01 .4 volt. Similarly the drops in the other three sections are found to be .3 .2 and .1 volts respectively. The drop in the main has exactly the same values, but is in the opposite direction, the fall of potential being always in the * U. S. Patent, No. 264,642, Sept. 19, 1882. direction in which the current flows. The distribution of potential is shown in an exaggerated manner in Fig. 14. It will be seen that a potential of 111 volts, supplied at the feeding-points, gives 109 volts at the other end, therefore no lamp receives a pressure more than one volt greater or less than the normal value of 110 volts. The horizontal axis OO would represent the line of zero potential when the system is uniformly insulated, in which case the potentials of the mains at the feeding-points would be + 55.5 volts and 55.5 volts respectively. A defect in the insulation at any point would tend to cause the potential of that point to approach zero, as already explained in connection with Figs. 4 and 5; and if the feeding-point were grounded, the + feeding-point would become + 111 volts, all the potentials having positive values. But the potential difference would remain the same in all cases. Tapering Conductors. The use of tapering or "conical" conductors in place of the ordinary cylindrical ones is hardly practicable, on account of the difficulty of making a wire or rod of that form. It is possible, however, to use a jointed conductor composed of sections of different sizes of wire. The object of such an arrangement is to proportion the cross-section of the conductor to the current which it has to carry in cases where the current varies from point to point, this being the usual condition in parallel distribution. If Fig. 13 be modified in such a way that the size of each section of the main is proportional to the current passing through it, Fig. 15 is obtained. In this case the drop in each. section will be .25 volts, being the same for all. Hence the potential falls uniformly from the + feeding-point to the end of the main, and would be represented by a straight line, instead of the broken one in Fig. 14. It is sometimes stated that the use of tapering mains secures economy in copper, but such is not the case in ordinary parallel distribution. The weight of copper required in Fig. 15 is 1,013 lbs., which is practically the same as the 1,025 lbs. called for in Fig. 13. The fallacy arises from the fact that the conductor is assumed to be a true cone, the elements of which are straight lines. As a matter of fact, the elements would curve outward since the 1 cone should be one-half the cross-section, or -.707 of the √2 diameter at a point midway between the base and the apex, instead of one-half the diameter. Fig. 15, Tapering Mains; 1,013 lbs. of Copper; 2 Volts Max. Difference Between Lamps; 111 Volts at Feeding-Points; 1 Volt Average Drop. Tapering conductors give a uniform drop, as already stated; and the average drop is slightly less than with cylindrical wires, being 1.2 volt in Fig. 13, and 1 volt in Fig. 15. This is not a matter of great consequence, however, as it is customary to consider the maximum drop in electrical distribution, and that is the same for the two cases when all the lamps are connected. If only the first groups of lamps were lighted, the tapering conductors would give considerably less drop than cylindrical ones. Nevertheless, it is doubtful in practice if the advantages are worth the extra trouble of laying and connecting several different sizes of wire. Where the distances are considerable, and where joints or cut-outs would be introduced in any event, it may be desirable to vary the size of a main in proportion to the current it is to carry at different points. In this discussion it is of course assumed that the conductor must always have sufficient current capacity, whether it be tapering or cylindrical. In the next case, Fig. 16, the mains are supposed to be fed at their centers, as shown. In this arrangement No. 2 wire, weighing 321.5 lbs., gives almost exactly the same variations of potential as in the two preceding cases, the maximum pressure being 111 Fig. 16. Feeding at Middle of Mains; 321.5 lbs. Copper; 1.92 Volts Max. Difference Between Lamps; 111 Volts at Feeding-Points; 1.3 Volts Average Drop. volts and the minimum 109.08 volts. This shows that a great saving of copper is effected by simply feeding the mains in the middle rather than at the ends. Theoretically, it would only require one-quarter as much copper in the former case. This is easily seen, when it is considered that the mains in Fig. 16, on each side of the feeding-point, are one-half as long, and carry about one-half as much current, as those in Fig. 13, consequently the conductor need only have one-quarter of the cross-section to give the same drop. The weight is found to be slightly more than one-quarter in the example, because the average current is in the proportion of 15 to 25 instead of 1 to 2. The next case, Fig. 17, represents the mains fed at opposite points. This was formerly called the Werdermann system, after Fig. 17. Feeding at Opposite Ends of Mains; 202.2 lbs. Copper; 2 Volts Max. Difference Between Lamps; 116 Volts Between Feeding-Points; 6 Volts Average Drop. its inventor, but is now known as the anti-parallel or return loop method of distribution. In this case the same length (1,600 feet) of No. 4 wire, weighing only 202.2 lbs., gives an equally good distribution of potential. It is sometimes supposed that this ar rangement must give a perfectly uniform pressure at the lamps, since the sum of the distances of each lamp from the feedingpoints measured on the two mains is a constant. As a matter of fact, however, the middle lamps will receive a lower voltage than those at the ends, as shown in the diagram. This is due to the fact that the former are supplied through the portions of the main conductors which carry heavy currents, and in which the drop is greatest. For example, the drop on the mains in the case of the central group of lamps is 21.5+1.5 +27 volts, but for the end group of lamps it is only It is possible, however, to secure a perfectly uniform pressure at all points between the mains, if their cross-section is made proportional to the current in each section by the use of the so-called conical conductors already described. In this way the drop in each section will be the same, and each group of lamps will receive exactly the same pressure, being equal to the difference of potential between the feeding-points minus the drop in four sections. In the next example the mains are fed at distributed points as represented in Fig. 18. In this case No. 7 wire, weighing only Fig. 18. Feeding at Distributed Points on Mains; 101 lbs. of Copper; 2 Volts Max. Difference Between Lamps; 116 Volts Between Feeding-Points; 6 Volts Average Drop. 101 lbs., gives no greater variation in voltage (i.e. one volt from the normal) than No. 0000 wire, weighing 1,025 lbs., in Fig. 13. These examples show the great difference that is made by changing the points at which the feeders are connected to the mains. It should be carefully noted, however, that in both the last two cases (Figs. 17 and 18) the feeders must supply 116 volts to the mains instead of only 111 volts, as in the preceding examples |