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TWO SERIES MACHINES.

175

Hastie has introduced a water-motor with variable crankradius, the latter being automatically adjusted to the work done by a spring. A contrivance of this nature, although extremely ingenious, adds considerably to the cost and complication of the machine and represents an additional chance of break-down. On the other hand, electricity can be used without any separate contrivance for regulation, and has thus a great advantage over hydraulic transmission.

The system of transmitting energy by means of two series-wound dynamos has the other advantage of being almost perfectly self-regulating as regards the speed of the motor. This is a point which has as yet received hardly any attention from writers on the subject, and therefore a somewhat detailed explanation of this valuable property in this place will be opportune.

It has been shown how a motor intended to be worked by a constant current can be made self-regulating, that is, can be arranged to run always at the same predetermined speed, whatever load may be thrown on it. It has also been shown how motors can be made self-regulating, if supplied with current at constant pressure. In the first case, the electro-motive force must increase as the load increases; and, in the second place, the current must increase as the load increases, one or the other being kept automatically constant at the generating station. But with a series-wound dynamo, neither the current nor the electro-motive force are constant, but vary in a certain dependence on each other. It might thus, at first sight, seem as if the problem of making the motor self-regulating were thereby rendered very much more difficult. This is not the case. The evil, if we may so regard it, in the dynamo becomes of itself the remedy in the motor.

Let, in Fig. 67, O E represent the ordinary characteristic of the series-wound generator, the curve being drawn for a constant speed of, say, 1,000 revolutions a minute. Let e represent the characteristic of the motor also for the speed of, say, 1,000 revolutions. The counter-electro-motive force developed in the armature of the motor at that speed is therefore represented by the ordinates of the curve O e. Thus to a current O C will be opposed an electro-motive force C B, to a current O C1 will be opposed an electro-motive force C1 B1, and

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so on. In the dynamo the electro-motive force corresponding to the current O C is C D, and that corresponding to the current O C, is C, D,. Draw O R under such an inclination to the horizontal that the tangent of the angle RO X represents to the scale of the diagram the numerical value of the sum of the resistances (R + r + s) of dynamo, motor, and line, then the electro-motive force lost in overcoming these resistances is for the current O C, evidently C A, for the current O C1, C1 A1 and so on. The ordinates between the straight line O R and the characteristic curve OE represent, therefore, the counter-electro-motive forces which must be developed in

TWO SERIES MACHINES.

177 the armature of the motor at various currents. If the current is O C, the counter-electro-motive force is A D, if the current is O C, the counter-electro-motive force is A, D1, and so on. Now the counter-electro-motive force of the motor, if running at a constant speed of 1,000 revolutions a minute, is given by the curve O e, and it will be seen that if the ordinates of this curve are for every current equal to the ordinates contained between O R and O E, then the motor suits perfectly the requirements of the generator, and it will run at a constant speed. The motor will run at that speed whether the current be O C1 or O C, provided that C1 A1 = B1 D1, and C A = B D. The solution of the problem consists, therefore, in the proper choice of motor and dynamo, so that their characteristics fit each other as near as possible, as explained. Beyond this, no other precaution or apparatus is necessary to make the system perfectly self-regulating. Even if the characteristics should not fulfil the condition CA = B D over their entire range, it will, as a rule, not be difficult to find two points, C, and C, tolerably far apart, for which the condition is fulfilled, and between which the deviation of one curve from the form demanded by the other is very trifling. The system will, therefore, be practically self-regulating between these limits. Two years ago the author has had occasion to practically test the soundness of this theory. He had occasion to use electric transmission of energy within the limits of an engineering works, for the purpose of supplying with power the pattern-makers' shop, which on account of its location could not be reached by any mechanical transmission. The power required by the wood-working machines in that shop, including band and circular saws, was, of course, very variable, and it became a matter of

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the greatest importance to keep the main shaft-from which the different tools were worked by belting-revolving at a constant speed. This object was attained by the method just described. The generator was a Bürgin dynamo, driven at a constant speed from the main engine in another part of the works, and the motor was also a Bürgin dynamo, but wound for a lower electro-motive force. There was a considerable distance between the two characteristics O E and O e, Fig. 68, and to find two points, O C, and O C, for which the condition CA = B D should be fulfilled, it was necessary to increase the inclination of the line OR by placing a little additional resistance into the circuit. This, of course, entailed some small loss of energy, but was in no way a fault of the system. It was occasioned simply by the necessity of using the two dynamos which happened to be at hand. If the machines could have been designed for this very purpose, no additional resistance would have been required, and the automatic regulation would have been equally good.

CHAPTER VII.

The Line-Relation between Capital Outlay and Waste of Energy-Most Economical Size of Conductor-Formula for Maximum Current-Formula for Mean Current-Tables for Finding Most Economical SizeHeating of Conductor-Table for Rise of Temperature.

BOTH as regards first cost and economy of working, the line forms a very important item in any extended system of electric transmission of energy. We have to consider two separate cases. The one, where energy from a central station is transmitted to and divided between a number of small working centres all grafted upon a network of conductors forming the main circuit, and the other, where all the energy is conveyed to a single receiving station along a pair of conductors without any ramifications. The first case would occur in a system of town supply where electricity is furnished for lighting and power purposes, and where the lamps and motors are all connected in parallel to the mains. The second is that occurring when energy from an hitherto inaccessible source is conveyed to a convenient point of application, the distance being considerable. Whatever particular form of transmission and distribution the system may have, it will be clear that the first cost of the conductors, and the annual expenditure represented by the energy wasted in heating the conductors, follow opposite laws. To economize energy it is necessary to employ leads of low resistance, and, therefore, of considerable cross-sec

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