(a) Commutators and collectors, being liable to be heated through imperfect contact, and liable to be corroded by sparking, should be made of very substantial pieces of copper.

(b) In the case of a collector made of parallel bars of copper, ranged upon the periphery of a cylinder, the separate bars should be removable singly, to admit of repairs and examination.

(c) The brushes should touch the commutator or collector at the 2 points, the potentials of which are respectively the highest and the lowest of all the circumference. In a properly and symmetrically built dynamo, these points will be at opposite ends of a diameter.

(d) In consequence of the armature itself, when traversed by the currents, acting as a magnet, the magnetic lines of force of the field will not run straight across from pole to pole of the field - magnets, but will take, on the whole, an angular position, being twisted a considerable number of degrees in the direction of the rotation. Hence the diameter of commutation (which is at right angles to the resultant lines of force in machines of the Siemens and Gramme type, and parallel to the resultant lines of force in machines of the Brush type), will be shifted forward. In other words, the brushes will have a certain angular lead. The amount of this lead depends upon the relation between the intensity of the magnetic field and the strength of the current in the armature. This relation varies in the 4 different types of field - magnets. In the series dynamo, where the one depends directly on the other, the angle of lead is nearly constant, whatever the external resistance. In other forms of dynamo, the lead will not be the same, because the variations of resistance in the external circuit do not produce a proportionate variation between the 2 variables which determine the angle of lead.

(e) Hence in all dynamos it is advisable to have an adjustment enabling the brushes to be rotated round the commutator or collector, to the position of the diameter of commutation for the time being. Otherwise there will be sparking at the brushes, and in part of the coils at least the current will be wasting itself by running against an opposing electromotive force.

(/) The arrangements of the collector or commutator should be such that, as the brushes slip from one part to the next, no coil or section in which there is an electromotive force should be short - circuited, otherwise work will be lost in heating that coil. For this reason, it is well so to arrange the pole - pieces that the several sections or coils on either side of the neutral position should differ but very slightly in potential from one another.

(g) The contact points between the brushes and the collector, or commutator, should be as numerous as possible, for, by increasing the number of contacts, the energy wasted in sparks will be diminished inversely as the square of that number. The brushes might with advantage be laminated, or made of parallel loose strips of copper, each bearing edgeways on the collector.

## Relation Of Size To Efficiency

The efficiency of a dynamo is the ratio of the useful electrical work done by the machine to the total mechanical work applied in driving it. Every circumstance which contributes to wasting the energy of the current reduces the efficiency of the machine. It has been shown what the chief electric sources of waste are, and how they may be avoided. Mechanical friction of the moving parts can be minimized also by due mechanical arrangements. But even the best conductors have a certain resistance, and it is impossible to prevent the heating of the conducting coils; the more powerful the current generated by the machine, the more important does this source of waste become. The one way to reduce this is by increasing the size of the machines. For some years, Prof. Thompson has advocated large dynamo machines, because the larger machines may be made more efficient than the small, in proportion to their cost. In discussing the relation of size to efficiency, he assumes, for the sake of argument, that the size of any machine can be increased n times in every dimension, and that, though the dimensions are increased, the velocity of rotation remains the same, and that the intensity of the magnetic field per square centimetre remains also constant.

If the linear dimensions be n times as great in the larger as in the smaller, the area it stands on will be increased n2 times, and its volume and weight n3 times. The cost will be less than n8 times, but greater than n times. If the same increase of dimensions in the coils be observed (the number of layers and of turns remaining the same as before), there will be in the armature coils a length n times as great, and the area of cross - section of the wire will be n2 times as great as before. The resistance of these coils will therefore be but - 1/n part of the original resistance of the smaller machine. If the field - magnet coils are increased similarly, they will offer only 1/n of the resistance of those of the smaller machine. Moreover, seeing that while the speed of the machine is the same, the area cut through by the rotating coils is increased n2 times, these coils will in the same time cut n2 times as many lines of force, or the electromotive force will be increased n2 times. Supposing the whole of the circuit to be similarly magnified, its resistance will also be but l/n of the pre vious value.

If the machine is a "series - wound" dynamo, an electromotive force n3, working through l/n resistance, will give a current n3 times as great as before. Such a current will, as a matter of fact, much more than suffice to bring up the magnetic field to the required strength, viz., n 2 times the area of surface magnetized to the same average intensity per square centimetre, as stipulated; for the mass of iron being n3 times as great, it need not be so much saturated as before to give the required field. Here an economy may be effected, therefore, by further reducing the number of coils, and therefore the wasteful resistance of the field - magnet coils, in the proportion of n2 to n2, or to 1/n of its already diminished value. Even if this were not done, by the formula given above for the electrical efficiency of a " series " dynamo, the waste, when working through a constant external resistance, will be n - fold less than with the smaller machine. Now, if the current be increased n3 times, and the electromotive force n2 times, the total electric work which is the product of these will be n5 times greater than in the small machine, and it will consume n5 times as much power to drive it.

It is clearly an important economy, if a machine costing less than n3 times as much, will do n5 times as much work (to say nothing of the increased ratio of efficiency). A machine doubled in all its linear dimensions will not cost 8 times as much, and will be electrically 32 times as powerful.

Suppose the machine to be " shunt " wound, then to produce the field of force of n2 times as many square centimetres area, will require (if the electromotive force be n2 times as great) that the absolute strength of the current remain the same as before in the field - magnet coils. This can be done by using the same sized wire as before, and increasing its length n2 times, to allow for n times as many turns, of n times as great a diameter each, in the same number of layers of coils as before. In this case the work done in the shunt, being equal to the product of the n2 - fold electromotive force into the unaltered current, will be only n3 times as great, while the whole work of the machine is augmented n. times. If, while augmenting the total work n. times, the waste work is increased only n2 times, it is clear that the ratio of waste to the total effect is diminished n3 - fold. There is, therefore, every reason to construct large machines, from the advantage of economy both in relative prime cost and relative efficiency.