If the arcs 0-1, 1-2, etc., of the dotted circle, which are intercepted by the magnetic lines and passed through by the wire, be rectified and laid down under each other, as lines 0-1, 1-2, etc., the time of passage of the wire between successive magnetic lines will vary as the length, since the speed is uniform. Thus the wire in passing from line 0 to line 1, takes much more time than in passing from 1 to 2, as indicated at the left of the figure by 0-1 and 1-2, and still less in passing from 2 to 3; that is, the rate of cutting the lines increases as C D rotates from 0 to 4 and decreases from 4 to 8. Since similar conditions prevail with respect to A B, for its corresponding movement, it is evident that the number of lines which thread through the loop are _decreased with increasing rapidity_ as the loop rotates through the first quarter of a revolution, and _increased with decreasing rapidity_ during the second quarter of the revolution. Moreover, it must be evident that the reverse conditions obtain for the third and fourth quarters of the revolution. =The Sine Curve.=--In the preceding paragraph it was shown that an alternating current is induced in the armature of either an alternator or dynamo; that is, the current: 1, begins with zero electromotive force, 2, rises to a maximum, 3, decreases again to zero, 4, increases to a maximum in the opposite direction, and 5, decreases to zero. [Illustration: FIG. 168.--Application and construction of the sine curve. The sine curve is a wave-like curve used to represent the changes in strength and direction of an alternating current. An elementary alternator is shown at the left to illustrate the application of the sine curve to the alternating current cycle. It consists of a loop of wire A B C D, whose ends are attached to the ring F and shaft G, being arranged to revolve in a uniform magnetic field indicated by the vertical arrows which represent magnetic lines at equidistances. The alternating current induced in the loop is carried to the external circuit through the brushes M and S. Now, as the loop rotates, the induced electromotive force will vary in such a manner that its _intensity at any point of the rotation is proportional to the sine of the angle corresponding to that point_, this is represented by the wave-like curve. The mean value of the sine curve, or _average electromotive force_ developed during the revolution, or _period_, is equal to 2 ÷ π, or .637 of that of the maximum ordinate, that is, average electromotive force = .637 × _amplitude_. The sine curve lies above the horizontal axis during the first half of the revolution and below it during the second half, which indicates that the current flows in one direction for a half revolution and in the opposite direction during the remainder of the revolution.]