∑R and the useful work done is -

W' = e' (E-e)

∑R That is to say, with no greater loss in heating, more energy is transmitted and more work done. Also the efficiency is greater, for w' / W' = e'/E' : and this ratio is more nearly equal to unity than e/E - , because both E and e have received an increment arithmetically equal. Clearly, then, it is an economy to work at high electromotive force. The importance of this matter, first.pointed out by Siemens and later by Marcel Deprez, cannot be overrated. But how to obtain this higher electromotive force. One very simple expedient is that of driving both generator and motor at higher speeds. Another way is to wind the armatures of both machines with many coils of wire having many turns. This expedient has, however, the effect of putting great resistances into the circuit. This circumstance may, nevertheless, be no great drawback, if there is already a great resistance in the circuit - as, for example, the resistance of many miles of wire through which the power is to be transmitted. In this case, doubling the electromotive force will not double the resistance; Even in the case where the line resistance is insignificant, an economy is effected by raising the electromotive force.

For, as may be deduced from the equations, when E - e is kept constant, the effect of doubling the electromotive force is to double the efficiency when the resistance of the line is very small as compared with that of the machines, and to quadruple it when the resistance of the line is very great as compared with that of the machines. It is, in fact, worth while to put up with the extra resistance, which we cannot avoid, if we try to secure high electromotive force by the use of coils of fine wire of many turns. It is true that the useful effect falls off, coeteris paribus, as the resistance increases; but this is much more than counterbalanced by the fact that the useful effect increases in proportion to the square of the electromotive force.

In the recent attempt of Marcel De - prez to realize these conditions in the transmission of power from Miesbach to Munich, through a double line of telegraph wire over a distance of 34 miles, very high electromotive forces were actually employed. The machines were 2 ordinary Gramme dynamos, the magnets being series - wound, similar to one another, but their usual low - resistance coils had been replaced by coils of very many turns of fine wire. The resistance of each machine was consequently 470 ohms, whilst that of the line was 950 ohms. The velocity of the generator was 2100 revolutions per minute; that of the motor, 1400. The difference of potential at the terminals of the generator was 2400 volts; at that of the motor, 1600 volts. According to Prof. von Beetz, the mechanical efficiency was found to be 32 per cent. Deprez has given the rule that the efficiency w/W is obtained, in. the case where 2 identical machines are employed, by comparing the 2 velocities at the 2 stations. Or W/w=N/n, where N is the speed of the generator, n that of the motor.

There is, however, the objection to this formula, that the electromotive forces are not proportional to the speeds, unless the magnetic fields of the 2 machines are also equally intense, and the current running through each machine is the same. This is not the case if there is leakage along the line. Moreover, when there ire resistances in the line, the ratio of the 2 electromotive forces of the machines is not the same as the ratio of the 2 differences of potentials, as measured between the terminals of the machines.

Turning back to consider some points in the design and construction of motors, it will be found that many of the rules already suggested (pp. 118 - 24) are applicable also to motors.

In the dynamo used as a generator, the capacity for doing work increases as the fifth power of the linear dimensions; by doubling a dynamo in length, breadth, and thickness, we have a machine weighing 8 times as much, costing less than 8 times as much, but capable of doing 32 times the work, and that with a great gain, in economy in working. The same thing is true of motors.

In the prospect of an immediate field of usefulness opening out for motors, so soon as we have such a thing as regular town supplies of electric currents laid on, it is most important that motors should be designed, not simply to work with the constant electromotive force supplied at the electric mains, but designed also to work at uniform speeds. It is highly important, in driving many kinds of machinery, that the speed should be regular, and that the motor should not "run away " as soon as the stress of the cutting tool is removed. Deprez and Perry have solved a converse problem to this, namely, that of getting a dynamo to feed a circuit with currents, at a constant electromotive force, when driven with uniform speed, the solution consisting in using certain combinations for the field magnets, which give an initial magnetic field, independently of the actual current furnished by the dynamo itself. This problem may be applied conversely, and motors may be built with a combination of arrangements for their field - magnets, 6uch that, when supplied with currents at a certain constant electromotive force, their speed shall be constant, whatever the work or no work which they may be doing.

The difficulty in the problem - a mere matter for experiment and calculation - is to find the critical number of volts of electromotive force at which this will hold good. It is, in fact, the converse to the operation of finding the critical velocity at which one of Deprez's or Perry's combination dynamos must be driven, in order that it may give a constant electromotive force. Deprez has constructed motors upon this plan, which run at a perfectly uniform speed, quite irrespective of the work being done: whether lifting a load from the ground, or letting this load ran down to the ground, or without any load at all. Ayrton and Perry have a motor weighing only 350 lb., which will give an effective power equal to 8 h.- p.; and without any mechanical governor, without anything, in fact, in the nature of a moving governor, it always goes at the same speed, whatever work it has to do.