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.