We now proceed to the next illustration. Without entering into the details of the calculation you will see that with a pulsatory current the effect of transmitting musical signals simultaneously is nearly equivalent to a continuous current of minimum intensity—see A^2 + B^2, fig. 12; but when undulatory currents are employed the effect is different—see fig. 13. The current from the battery B is thrown into waves by the inductive action of iron or steel reeds M M´, vibrated in front of electro-magnets _e e´_, placed in circuit with the battery; A^2 and B^2 represent the undulations caused in the current by the vibration of the magnetised bodies, and it will be seen that there are four undulations of B^2 in the same time as five undulations of A^2. The resultant effect upon the main line is expressed by the curve A^2 + B^2, which is the algebraical sum of the sinusoidal curves A^2 and B^2. A similar effect is produced when reversed undulatory currents are employed as shown in fig. 14, where the current is produced by the vibration of permanent magnets M M´ in front of electro-magnets (_e e´_), united upon a circuit without a voltaic battery. It will be understood from figs. 13 and 14 that the effect of transmitting musical signals of different pitches simultaneously along a single wire is not to obliterate the vibratory character of the current as in the case of intermittent and pulsatory currents, but to change the shapes of the electrical undulations. In fact, the effect produced upon the current is precisely analogous to the effect produced in the air by the vibration of the inducing bodies M M´. Hence it should be possible to transmit as many musical tones simultaneously through a telegraph wire as through the air. The possibility of using undulatory currents for the purposes of multiple telegraphy enabled me to dispense entirely with the complicated arrangements of the circuit shown in figs. 3, 4, 5, and 8, 9, 10, and to employ a single battery for the whole circuit, retaining only the receiving instruments formerly shown. This arrangement is represented in figs. 15, 16, and 17. Upon vibrating the steel reed of a receiver R, R´, at any station by any mechanical means, the corresponding reeds at all the other stations are thrown into vibration, reproducing the signal. By attaching the steel reeds to the poles of a powerful permanent magnet, as shown in fig. 19, the signals can be produced without the aid of a battery. [Illustration: Fig. 15. Fig. 16. Fig. 17.] [Illustration: Fig. 18.[23]]