In the case of a body of any shape which can vibrate round any centre or axis, the moment of inertia round this axis of rotation is the sum of the products of each element of its mass and the square of their respective distances from this axis. The periodic time T of any small vibration of this body is then obtained by the following rule:— T = 2π√((moment of inertia round the axis of rotation) × (displacement per unit of torque, or pliability)) or T = 2π√(IP). In the case of an electric circuit the inductance corresponds to the moment of inertia of a body in mechanical vibration; and the capacity to its pliability as above defined. Hence the time of vibration, or the electrical time-period of an electric circuit, is given by the equation— T = 2π√(LC) where L is the inductance, and C is the capacity. It can be shown easily that the frequency _n_, or number of electrical vibrations per second, is given by the rule— _n_ = 5000000/(√((capacity in microfarads) × (inductance in centimetres))) For instance, if we discharge a Leyden jar having a capacity of ¹⁄₃₀₀ of a microfarad through a stout piece of copper wire about 4 feet in length and one-sixth of an inch in diameter, having an inductance of about 1200 centimetres, the electrical oscillations ensuing would be at the rate of 2¹⁄₂ millions per second. Any two electrical circuits which have the same time-period are said to be “in tune” with each other, and the process of adjusting the inductance and capacity of the circuits to bring about this result is called electrical tuning. In the case of a vertical aerial wire as used in wireless telegraphy, in which the oscillations are created by the inductive action of an oscillation-transformer as shown in Fig. 82, page 271, the capacity of the Leyden jar in the condenser circuit must be adjusted so that the time-period of the nearly closed or primary oscillation P agrees with that of the open or secondary circuit S. When this is the case, the electrical oscillations set up in the closed circuit have a far greater effect in producing others in the open circuit than if the two circuits were not in tune. The length of the wave given off from the open circuit is approximately equal to four times the length of the aerial wire, including the length of the coil forming the secondary circuit of the oscillation-transformer in series with it. FOOTNOTES [1] The wave-velocity in the case of waves on deep water varies as √(_g_λ/2π), where λ is the wave-length. The rule in the text is deduced from this formula. [2] If V is the velocity of the wave in feet per minute, and V′ is the velocity in miles per hour, then (V′ × 5280)/60 = V. But V′ = √(2¹⁄₄λ), and V = _n_λ, where λ is the wave-length in feet and _n_ the frequency per minute; from which we have V′ = 198/_n_, or the rule given in the text.