It has been indicated that the differential equation does not represent oscillatory motion if the value of R is too great. The exact condition depends on the roots of the quadratic equation Lx² + Rx + 1⧸C = 0, obtained by writing 1 for Q, and x for d⧸dt, and then treating x as a quantity. These roots are －R⧸2L ± √(R²⧸4L² － 1⧸CL), and are therefore real or imaginary according as 4L⧸C is less or greater than R². If the roots are real, that is, if R² be greater than 4L⧸C, the discharge will not be oscillatory; the Faraday tubes referred to above will be absorbed in the wire without any return to the condenser. The corresponding result happens with the vibrator when R is sufficiently great, or L⧸C sufficiently small (a weak spring and a small mass, or both), to enable the condition to be fulfilled. If, however, the roots of the quadratic are imaginary, that is, if 4L⧸C be greater than R² (a condition which will be fulfilled in the spring analogue, by making the spring sufficiently stiff and the mass large enough to prevent the friction from controlling the motion) the motion is one in which Q disappears by oscillations about zero, of continually diminishing amplitude. A complete discussion gives for the period of oscillation 4πL⧸√(4L⧸C － R²), or if R be comparatively small, 2π√(LC). The charge Q falls off by the fraction e^{－RT⧸2L} (where e is the number 2.71828...) in each period T, and so gradually disappears. Thus electric oscillations are produced, that is to say, the charged state of the condenser subsides by oscillations, in which the charged state undergoes successive reversals, with dissipation of energy in the wire; and both the period and the rate of dissipation can be calculated if L, C, and R are known, or can be found, for the system. These quantities can be calculated and adjusted in certain definite cases, and as the electric oscillations can be experimentally observed, the theory can be verified. This has been done by various experimenters. Returning to the pendulum illustration, it will be seen that the pendulum held deflected is analogous to the charged jar, letting the pendulum go corresponds to connecting the discharging coil to the coatings, the motion of the pendulum is the analogue of that motion of the medium in which consists the magnetic field, the friction of the air answers to the resistance of the wire which finally damps out the current. The inertia or mass of the bob is the analogue of what Thomson called the electromagnetic inertia of the coil and connections; what is now generally called the self-inductance of the conducting system. The component of gravity along the path towards the lowest point, answers to the reciprocal, 1⧸C, of the capacity of the condenser.