The cars are first and third class, some open and some covered, and are constructed to hold twenty people, exclusive of the driver.  At present, only one is fitted with a dynamo, but four more machines are now being constructed by Messrs. Siemens Bros., so that before the beginning of the heavy summer traffic five cars will be ready; and since two of these will be fitted with machines capable of drawing a second car, there will be an available rolling stock of seven cars.  It is not intended at present to work electrically the portion of the line in the town at Portrush, though this will probably be done hereafter; and a portion, at least, of the mineral traffic will be left for the two steam-tramway engines which were obtained for the temporary working of the line pending the completion of the electrical arrangements.

Let us now put in a form suitable for calculation the principles with which Mr. Siemens has illustrated in a graphic form more convenient for the purposes of explanation, and then show how these principles have been applied in the present case.

Let L be the couple, measured in foot-pounds, which the dynamo must exert in order to drive the car, and w the necessary angular velocity.  Taking the tare of the car as 50 cwt., including the weight of the machinery it carries, and a load of twenty people as 30 cwt., we have a gross weight of 4 tons.  Assume that the maximum required is that the car should carry this load at a speed of seven miles an hour, on an incline of 1 in 40.  The resistance due to gravity may be taken as 56 lb. per ton, and the frictional resistance and that due to other causes, say, 14 lb. per ton, giving a total resistance of 280 lb., at a radius of 14 inches.  The angular velocity of the axle corresponding to a speed of seven miles an hour, is 84 revolutions per minute.  Hence L = 327 foot pounds, and w = (2[pi] x 84) / 60.

If the dynamo be wound directly on the axle, it must be designed to exert the couple, L, corresponding to the maximum load, when revolving at an angular velocity, w, the difference of potential between the terminals being the available E.M.F. of the conductor, and the current the maximum the armature will safely stand.  This will be the case in the Charing-cross Electrical Railway.  But when the dynamo is connected by intermediate gear to the driving wheels only, the product of L and w remains constant, and the two factors may be varied.  In the present case L is diminished in the ratio of 7 to 1, and w consequently increased in the same ratio.  Hence the dynamo, with its maximum load, must revolve at 588 revolutions per minute, and exert a couple of forty-seven foot-pounds.  Let E be the potential of the conductor from which the current is drawn, measured in volts, C the current in amperes, and E1 the E.M.F. of the dynamo.  Then E1 is proportional to the product of the angular velocity, and a certain function of the current.  For a velocity [omega], let this function be denoted by f(C).  If the characteristic of the dynamo can be drawn, then f(C) is known.