It was separately excited and kept

The

Pacinotti armature. running at a constant speed of 1,600 revolutions a minute, whilst the current which was permitted to flow through the armature was varied by means of a rheostat. line E, Fig. 60, represents the internal electro-motive force corresponding to the constant exciting power if there were no reactions. The line Eb represents the electromotive force which would be found at the brushes if

EXPERIMENT WITH PHENIX DYNAMO.

there were no reaction, and the line Eb1 was that actually observed. The difference of the ordinates of Eb and Eb1 represents the loss of electro-motive force due to selfinduction, weakening and distorting of the field. The same influences which tend to lower the electro-motive force of a dynamo tend, on the other hand, to increase the counter-electro-motive force of a motor. This has been investigated by the author, experimentally, by separately exciting the field magnets of a Bürgin dynamo, and mea

suring the electro-motive force under the following three conditions 1st, No current was allowed to flow through the armature; 2nd, A current was allowed to flow doing external work by heating resistance coils; 3rd, A current from another dynamo was sent in an opposite direction through the armature, causing it to revolve and produce external work on a Prony brake. We have now to dis

Fig. 61.

Counter

Static

-Dynamic

tinguish between the static electro-motive force found by experiment 1; the dynamic electro-motive force found by experiment 2; and the counter-electro-motive force found by experiment 3. By repeating the experiments under different conditions, three internal characteristics were obtained occupying relatively to each other the position shown in Fig. 61.

CHAPTER V.

Graphic Treatment of Problems—Maximum External Energy-Maximum Theoretical Efficiency-Determination of best Speed for Maximum Commercial Efficiency-Variation of Speed in Shunt Motors-The Compound Machine as Generator-System of Transmission at Constant SpeedPractical Difficulty.

THE treatment of problems relating to the electrical transmission of energy is greatly simplified by the use of the curves explained in the preceding chapter, and by other graphic methods, of which we may mention that due to Professor Silvanus Thompson. The problem is as follows. Let a square A B C D be drawn so that the length of one of the sides shall represent the electromotive force E of the supply to any convenient scale, Fig. 62, and let the counter-electro-motive force e of the motor be represented by the length A F = A G. Draw through F and G the lines F K and G H respectively parallel to A B and A C. The energy supplied to the motor equals the product of electro-motive force E and current C, whilst the work converted into mechanical energy in the armature of the motor equals the product of counter-electro-motive force e and current C. Let R repreE-e,

sent the total resistance in the circuit, then C =

R

which in our diagram is represented by the length F C divided by R. The energy delivered to the motor is evidently

Now the area of the rectangle FKDCE (E — e) and the area of the rectangle GBK Le (Ee) ; and since R is a constant, we find that these areas-shaded in our diagram-are proportional to the work expended and recovered.

Thompson's diagram can immediately be used to solve

graphically two of the problems which have already been treated analytically in the first chapter (page 38). These are the following: First, what is the condition of maximum work obtained from the motor? and, secondly, what is the condition of maximum efficiency?

The answer to the first question is easily found by inspecting our diagram, Fig. 62. Since the rectangle GBK L, which represents the work of the motor, is inscribed between the diagonal AD and the sides A B, DB; the question resolves into that of finding which of all possible rectangles inscribed within these lines has a maximum of area. This is evidently a square, the sides

GRAPHIC TREATMENT OF PROBLEMS.

129

of which are half as long as those of the external square. In this case the work expended is represented by a rectangle of half the area of the external square, and the efficiency is therefore 50 per cent.

As regards the second question it will readily be seen that the discrepancy in the area of the two rectangles, Fig. 62, is the greater, the nearer the point is to A, or in other words, the smaller the counter-electro-motive force. In the same measure as the latter increases, point L is pushed further towards D, and the areas of the two rectangles become more and more equal. The efficiency, therefore, tends towards unity as the counter-electromotive force of the motor tends towards the electro-motive force of the source of supply of electricity. This statement has already been made in the first chapter, and it is theoretically quite accurate; but from a practical point of view it requires some qualification. It will be seen that when the counter-electro-motive force of the motor approaches very closely the electro-motive force of the supply, the current becomes very small, and the work expended and converted becomes also very small. Now the work converted in the motor is not all available in the shape of external mechanical energy, and it may well happen that in this case, after the resistance of mechanical and magnetic friction has been overcome, no margin remains for useful external work. The commercial efficiency would therefore be Zero, although the theoretical efficiency is a maximum. To put the matter

K