It is this last method of transmission which remains to be discussed. The author, however, feels himself obliged to restrict himself in this matter to a mere summary; and, indeed, it is English physicists and engineers who have taken the technology of electricity out of the region of empiricism and have placed it on a scientific and rational basis. Moreover, they are also taking the lead in the progress which is being accomplished in this branch of knowledge, and are best qualified to determine its true bearings. When an electric current, with an intensity, i, is produced, either by chemical or mechanical work, in a circuit having a total resistance, R, a quantity of heat is developed in the circuit, and this heat is the exact equivalent of the force expended, so long as the current is not made use of for doing any external work. The expression for this quantity of heat, per unit of time, is Ai²R; A being the thermal equivalent of the unit of power corresponding to the units of current and resistance, in which i and R are respectively expressed. The product, i²R, is a certain quantity of power, which the author proposes to call power transformed into electricity. When mechanical power is employed for producing a current by means of a magneto-electric or dynamo-electric machine--or, to use a better expression, by means of a mechanical generator of electricity--it is necessary in reality to expend a greater quantity of power than i²R in order to make up for losses which result either from ordinary friction or from certain electro magnetic reactions which occur. The ratio of the quantity, i²R, to the power, W, actually expended per unit of time is called the efficiency of the generator. Designating it by K, we obtain, W = i²R/K. It is very important to ascertain the value of this efficiency, considering that it necessarily enters as a factor into the evaluation of all the effects to be produced by help of the generator in question. The following table gives the results of certain experiments made early in 1879, with a Gramme machine, by an able physicist, M Hagenbach, Professor at the University at Basle, and kindly furnished by him to the author:
Revolutions per minute 935 919.5 900.5 893
Total resistance in Siemens' units 2.55 3.82 4.94 6.06
Total resistance in absolute units 2.435 3.648 4.718 5.787
x10^9 x10^9 x10^9 x10^9
Intensity in chemical units 17.67 10.99 8.09 6.28
Intensity in absolute units 2.828 1.759 1.295 1.005
Work done i²R in absolute units 1948.6 1129.2 791.3 584.9
x10^7 x10^7 x10^7 x10^7
Work done i²R in kilogrammes 198.6 115.1 80.66 59.62
Power expended in kilogrammes 301.5 141.0 86.25 83.25
Efficiency, per cent. 65.9 81.6 93.5 71.6
M. Hagenbach's dynamometric measurements were made by the aid of a brake. After each experiment on the electric machine, he applied the brake to the engine which he employed, taking care to make it run at precisely the same speed, with the same pressure of steam, and with the same expansion as during experiment. It would certainly be better to measure the force expended during and not after the experiment, by means of a registering dynamometer. Moreover, M. Hagenbach writes that his measurements by means of the brake were very much prejudiced by external circumstances; doubtless this is the reason of the divergences between the results obtained.
About the same time Dr. Hopkinson communicated to this institution the results of some very careful experiments made on a Siemens machine. He measured the force expended by means of a registering dynamometer, and obtained very high coefficients of efficiency, amounting to nearly 90 per cent. M. Hagenbach also obtained from one machine a result only a little less than unity. Mechanical generators of electricity are certainly capable of being improved in several respects, especially as regards their adaptation to certain definite classes of work. But there appears to remain hardly any margin for further progress as regards efficiency. Force transformed into electricity in a generator may be expressed by i ω M C; ω being the angular velocity of rotation; M the magnetism of one of the poles, inducing or induced, which intervenes; and C a constant specially belonging to each apparatus, and which is independent of the units adopted. This constant could not be determined except by an integration practically impossible; and the product, M C, must be considered indivisible. Even in a magneto-electric machine (with permanent inducing magnets), and much more in a dynamo-electric machine (inducing by means of electro-magnets excited by the very current produced) the product, M C, is a function of the intensity. From the identity of the expressions, i²R and i ω M C we obtain the relation M C = IR/ω which indicates the course to be pursued to determine experimentally the law which connects the variations of M C with those of i. Some experiments made in 1876, by M. Hagenbach, on a Gramme dynamo-electric machine, appear to indicate that the magnetism, M C, does not increase indefinitely with the intensity, but that there is some maximum value for this quantity. If, instead of working a generator by an external motive force, a current is passed through its circuit in a certain given direction, the movable part of the machine will begin to turn in an opposite direction to that in which it would have been necessary to turn it in order to obtain a current in the aforesaid direction. In virtue of this motion the electro-magnetic forces which are generated may be used to overcome a resisting force. The machine will then work as a motor or receiver. Let i be the intensity of the external current which works the motor, when the motor is kept at rest. If it is now allowed to move, its motion produces, in virtue of the laws of induction, a current in the circuit of intensity, i1, in the opposite direction to the external current; the effective intensity of the current traversing the circuit is thus reduced to i - i1. The intensity of the counter current is given, like that of the generating current, by the equation, i12R = i1 ω1 M1 C1, or i1R = ω1 M1 C1, the index, 1, denoting the quantities relating to the motor. Here M1 C1 is a function of i - i1, not of i. As in a generator the force transformed into electricity has a value, i ω M C, so in a motor the force developed by electricity is (i - i1) ω1 M1 C1. On account, however, of the losses which occur, the effective power, that is the disposable power on the shaft of the motor, will have a smaller value, and in order to arrive at it a coefficient of efficiency, K1, must be added. We shall then have W1 = K1 (i-i1) ω1 M1 C1. The author has no knowledge of any experiments having been made for obtaining this efficiency, K1. Next let us suppose that the current feeding the motor is furnished by a generator, so that actual transmission by electricity is taking place. The circuit, whose resistance is R, comprises the coils, both fixed and movable, of the generator and motor, and of the conductors which connect them. The intensity of the current which traverses the circuit had the value, i, when the motor was at rest; by the working of the motor it is reduced to i - i1. The power applied to the generator is itself reduced to W-[(i-i1)ω M C]/K. The prime mover is relieved by the action of the counter current, precisely as the consumption of zinc in the battery would be reduced by the same cause, if the battery was the source of the current. The efficiency of the transmission is W1/W. Calculation shows that it is expressed by the following equations:W1/W = K K1 [(ω11 M1 C1)/(ω1 M C)], or = K K1 [(ω11 M1 C)/(ω11 M1 C1 + (i-i1) R)]; expressions in which it must be remembered M C and M1 C1 are really functions of (i-i1). This efficiency is, then, the product of three distinct factors, each evidently less than unity, namely, the efficiency belonging to the generator, the efficiency belonging to the motor, and a third factor depending on the rate of rotation of the motor and the resistance of the circuit. The influence which these elements exert on the value of the third factor cannot be estimated, unless the law is first known according to which the magnetisms, M C, M1 C C1, vary with the intensity of the current.
GENERAL RESULTS.
Casting a retrospective glance at the four methods of transmission of power which have been examined, it would appear that transmission by ropes forms a class by itself, while the three other methods combine into a natural group, because they possess a character in common of the greatest importance. It may be said that all three involve a temporary transformation of the mechanical power to be utilized into potential energy. Also in each of these methods the efficiency of transmission is the product of three factors or partial efficiencies, which correspond exactly--namely, first, the efficiency of the instrument which converts the actual energy of the prime mover into potential energy; second, the efficiency of the instrument which reconverts this potential energy into actual energy, that is, into motion, and delivers it up in this shape for the actual operations which accomplish industrial work; third, the efficiency of the intermediate agency which serves for the conveyance of potential energy from the first instrument to the second.
This last factor has just been given for transmission by electricity. It is the exact correlative of the efficiency of the pipe in the case of compressed air or of pressure water. It is as useful in the case of electric transmission, as of any other method, to be able, in studying the system, to estimate beforehand what results it is able to furnish, and for this purpose it is necessary to calculate exactly the factors which compose the efficiency.
In order to obtain this desirable knowledge, the author considers that the three following points should form the aim of experimentalists: First, the determination of the efficiency, K, of the principal kinds of magneto-electric, or dynamo-electric machines working as generators; second, the determination of the efficiency, K1, of the same machines working as motors; third, the determination of the law according to which the magnetism of the cores of these machines varies with the intensity of the current. The author is of opinion that experiments made with these objects in view would be more useful than those conducted for determining the general efficiency of transmission, for the latter give results only available under precisely similar conditions. However, it is clear that they have their value and must not be neglected.
There are, moreover, many other questions requiring to be elucidated by experiment, especially as regards the arrangement of the conducting wires: but it is needless to dwell further upon this subject, which has been ably treated by many English men of science--for instance, Dr. Siemens and Professor Ayrton. Nevertheless, for further information the author would refer to the able articles published at Paris, by M. Mascart, in the Journal de Physique, in 1877 and 1878. The author would gladly have concluded this paper with a comparison of the efficiencies of the four systems which have been examined, or what amounts to the same thing--with a comparison of the losses of power which they occasion. Unfortunately, such a comparison has never been made experimentally, because hitherto the opportunity of doing it in a demonstrative manner has been wanting, for the transmission of power to a distance belongs rather to the future than to the present time. Transmission by electricity is still in its infancy; it has only been applied on a small scale and experimentally.
Of the three other systems, transmission by means of ropes is the only one that has been employed for general industrial purposes, while compressed air and water under pressure have been applied only to special purposes, and their use has been due much more to their special suitableness for these purposes than from any considerations relative to loss of power. Thus the effective work of the compressed air used in driving the tunnels through the Alps, assuming its determination to be possible, was undoubtedly very low; nevertheless, in the present state of our appliances it is the only process by which such operations can be accomplished. The author believes that transmission by ropes furnishes the highest proportion of useful work, but that as regards a wide distribution of the transmitted power the other two methods, by air and water, might merit a preference.