One great advantage of electric motors is, that they can be so easily fixed directly on the spindle of the machine which they are to drive; an advantage not lightly to be thrown away.

## Application

When once we have electrical mains of sufficient capacity carried from central stations to our houses, how simple a matter it will be to combine lighting with domestic operations, and even the larger operations required for purposes of trade; for each motor of a series, placed in parallel circuit, performs the work required of it independently of all the others, and independently of the generating machine, provided only that the generator is capable of producing the power it is called upon to furnish.

Three conclusions are to be 'drawn, which are the fundamental principles of the theory of the electrical transmission of power.

I. The motor, as a machine, is entirely independent of the generator, and must be designed for the particular work it has to do without reference to the generator.

II. The current depends upon the load on the motor, and upon no other thing whatever.

III. The speed depends upon the E.M.F. of the generator, and the total resistance in the circuit of the machines. If the mains which supply the current to the motor be maintained at a constant potential, and the motor be separately excited, or have permanent magnets, the. speed is proportional to the potential of the main, less the loss of potential due to the resistance of the armature.

As a practical corollary, the generator must be designed to give the current required of it by the motor, and E.M.F. sufficient after allowing for fall of potential through the resistance of the mains, to give the requisite speed. Keeping these points in view, it is easy to design a combination of machines for performing any particular work, to calculate exactly the efficiency of the combination, and to account for the various losses that occur.

To put these considerations in a mathematical form: - The first problem is, given a main with a constant E.M.F., denoted by E, to construct a dynamo machine, drawing its current from the main, to work with a given load L, and at a given number of revolutions n per minute.

Take Ox Oy (Figs. 96,97) as axes of co ordinates; along Oy cut off OM, representing the E.M.F. of the main in volts. The makers of each type of dynamo machine know approximately the percentage of energy their machines absorb in producing the necessary magnetic field. Take a point N in OM, such that the ratio ON/OM is equal to this percentage.

Fig. 96. Again, it is known that a dynamo is not an absolutely perfect machine, but that a certain amount of energy is wasted in the friction of the bearings, of the brushes against the commutator, and in induced currents in the core of the armature. Take OR, such that OR/ON represents the efficiency of the machine. This, in the case of the Siemens machine, is at least 90 per cent. From Ox cut off OH, such that the rectangle OHR'R represents the power required from the motor expressed in watts. Then OH is the current passing through the motor, measured in amperes, and HP is the inverse E.M.F. The proper motor, therefore, is that dynamo which, when running at the given number of revolutions n per minute, has a characteristic curve passing through the point P. The total efficiency is evidently the ratio of the rectangle OHR'R to the rectangles OHM'M, which is equal to HR/HM ; the electrical efficiency is HP/HM,= E'/E'the ratio of the inverse E.M.F. of the motor to the E.M.F. of the main. The energy spent in magnetization is measured by PNMM', and the tangent of the angle PNM' represents the resistance of the armature and magnets.

Fig 91. The second problem is: - Given a motor requiring a certain current and E.M.F. for the work it has to do, to construct a suitable generator, the distance between the machines being represented by an electrical resistance R measured in ohms. Let OPP' be the characteristic curve of the motor, when running at the required speed; ON the E.M.F. in volts, and OH the current in amperes. Let R' be the sum of the resistances of the motor and conductor. Draw PN perpendicular to Oy, and make the angle PNM' having its tangent equal to R'; then M'H represents the difference of potential between the terminals of the generator. Produce QM' HM' to Q, so that qm/qh is the ratio of the energy expended in producing the magnetic field to the total energy of the machine; then the generator is that dynamo which, when running at its proper speed, has a characteristic curve passing through the point Q. The electrical efficiency of the combi nation is the ratio PH/QH, i.e. the ratio of the E.M.F. of the motor to the E.M.F. of the generator, which, if the machines are similar, is equal to the ratio of their speeds.

The energy converted into heat in the wires of the machine, and in the conductor, is NPQS; and the total efficiency of the combination is the ratio of the electromotive forces, multiplied by the product of the efficiencies of the 2 machines, considered separately. The conductor connecting the 2 machines has been assumed to be perfectly insulated, though this is not practically attained. (A. Siemens.)