In the above equation, the letter e stands for the number 2·71828, the base of the Napierian logarithms, and R is the resistance in series with the condenser, of which the capacity is C, to which the electromotive force is applied. This equation can easily be deduced from first principles,[9] and it shows that the potential difference v of the terminals of the condenser does not instantly attain a value equal to the impressed electromotive force V, but rises up gradually. Thus, for instance, suppose that a condenser of one microfarad is being charged through a resistance of one megohm by an impressed voltage of 100 volts, the equation shows that at the end of the first second after contact, the terminal potential difference of the condenser will be only 63 volts, at the end of the second second, 86 volts, and so on.

Since e-10 is an exceedingly small number, it follows that in 10 seconds the condenser would be practically charged with a voltage equal to 100 volts. The product CR in the above equation is called the time-constant of the condenser, and we may say that the condenser is practically charged after an interval of time equal to ten times the time-constant, counting from the moment of first contact between the condenser and the source of constant voltage. The time-constant is to be reckoned as the product of the capacity (C) in microfarads, by the resistance of the charging circuit (R) in megohms. To take another illustration. Supposing we are charging a condenser having a [capacity of one-hundreth of a microfarad,] through a resistance of ten thousand ohms. Since ten thousand ohms is equal to one-hundredth of a megohm, the time-constant would be equal to one-ten-thousandth of a second, and ten times this time-constant would be equal to a thousandth of a second. Hence, in order to charge the above capacity through the above resistance, it is necessary that the contact between the source of voltage and the condenser should be maintained for at least one-thousandth part of a second.

In discussing the methods of interrupting the circuit, we shall return to this matter, but, meanwhile, it may be said that in order to secure a small time-constant for the charging circuit, it is desirable that the secondary circuit of the induction coil should have as low a resistance as possible. This, of course, involves winding the secondary circuit with a rather thick wire. If, however, we employ a wire larger in size than No. 34, or at the most No. 32, the bulk and the cost of the induction coil began to rise very rapidly. Hence, as in all other departments of electrical construction, the details of the design are more or less a matter of compromise. Generally speaking, however, it may be said that the larger the capacity which is to be charged, the lower should be the resistance of the secondary circuit of the induction coil.

In the practical construction of induction coils for wireless telegraphy, manufacturers have departed from the stock designs. We are all familiar with the appearance of the instrument maker's induction coil; its polished mahogany base, its lacquered brass fittings, and its secondary bobbin constructed of and covered with ebonite. But such a coil, although it may look very pretty on the lecture table, is yet very unsuited to positions in which it may be used in connection with Hertzian wave telegraphy.

Three important adjuncts of the induction coil are the primary condenser, the interrupter and the primary key. The interrupter is the arrangement for intermitting the primary current. We have in some way or other to rapidly interrupt the primary current, and the torrent of sparks that then appears between the secondary terminals of the coil is due to the electromotive force set up in the secondary circuit at each break or interruption of the primary circuit. We may divide interrupters into five classes.

We have first the well-known hammer interrupter which Continental writers generally attribute to Neef or Wagner.[10] In this interrupter, the magnetisation of the iron core of the coil is caused to attract a soft-iron block fixed at the top of a brass spring, and by so doing to interrupt the primary circuit between two platinum contacts. Mr. Apps, of London, added an arrangement for pressing back the spring against the back contact, and the form of hammer that is now generally employed is therefore called an Apps break.

As the ten-inch coil takes a primary current of ten amperes at sixteen volts when in operation, it requires very substantial platinum contacts to withstand the interruption of this current continuously without damage. The small platinum contacts that are generally put on these coils by instrument makers are very soon worn out in practical wireless telegraph work. If a hammer break is used at all, it is essential to make the contacts of very stout pieces of platinum, and from time to time, as they get burnt away or roughened, they must be smoothed up with a fine file. It does not require much skill to keep the hammer contacts in good order and prevent them from sticking together and becoming damaged by the break spark.

By regulating the pressure of the spring against the back contact, by means of an adjusting screw, the rate at which the break vibrates can be regulated, but as a rule it is not possible, with a hammer break, to obtain more than about 800 interruptions per minute, or, say, twelve a second. The hammer break is usually operated by the magnetism of the iron core of the coil, but for some reasons it is better to separate the break from the coil altogether, and to work it by an independent electromagnet, which, however, may be excited by a current from the same battery supplying the induction coil. For coils up to the ten-inch size the hammer break can be used when very rapid interruptions are not required. It is not in general practicable to work coils larger than the ten-inch size with a platinum contact hammer break, as such a butt contact becomes overheated and sticks if more than ten amperes is passed through it. In the case of larger coils, we have to employ some form of interrupter in which mercury or a conducting liquid forms one of the contact surfaces.

The next class of interrupter is the vibrating or hand-worked mercury break, in which a platinum or steel pin is made to vibrate in and out of mercury. This movement may be effected by the attraction of an iron armature by an electromagnet, or by the varying magnetism of the core of the coil, or it may be effected more slowly by hand.