A wave-like curve, as shown in fig. 168, is used to represent these several changes, in which the horizontal distances represent time, and the vertical distances, the varying values of the electromotive force. It is called the sine curve because a perpendicular at any point to its axis is proportional to the sine of the angle corresponding to that point. =Ques. Describe the construction and application of the sine curve.= Ans. In fig. 168, at the left, is shown an elementary armature in the horizontal position, but at right angles to the magnetic field. The dotted circle indicates the circular path described by A B or C D during the revolution of the loop. 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_. Hence, on the horizontal line which passes through the center of the dotted circle, take any length, as 08, and divide it into any number of parts representing fractions of a revolution, as 0°, 90°, 180°, etc. Erect perpendiculars at these points, and from the corresponding points on the dotted circle project lines parallel to 08; the intersections with the perpendiculars give points on the sine curve. Thus the loop passes through 2 at the 90° point of its revolution, hence, projecting over to the corresponding perpendicular gives 2 2′, a point whose elevation from the axis is proportional to the electromotive force at that point. In like manner other points are obtained, and the curved line through them will represent the variation in the electromotive force for all points of the revolution. At 90°, the electromotive force is at a maximum; hence, by using a pressure scale such that the length of the perpendicular 2 2′ for 90° will measure the maximum voltage the length of the perpendicular at any other point will represent the actual pressure at that point. The 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. The application of the sine curve to represent the alternating cycle, is further illustrated in figs. 169 to 173, which show the position of the armature at each quarter of the revolution. [Illustration: FIGS. 169 to 173.--The sine curve with view of armature for each 90° of the revolution, showing progressively the application of the sine curve to the alternating current cycle.] In fig. 179, the loop A B C D is in the vertical position at the beginning of the revolution. At this instant the electromotive force is zero, hence the sine curve as shown begins at E, the zero point--that is, on the axis or line of no pressure.