The same law of deflection is shown, in smaller angles, in Fig. 2. In this figure, also, you observe in each of the angles A O B and A O C that the deflection, from the tangential direction toward the center, of a body moving in the arc A C is represented by the versed sine of the angle. The tangent to the arc at A, from which this deflection is measured, is omitted in this figure to avoid confusion. It is shown sufficiently in Fig. 1. The angles in Fig. 2 are still pretty large angles, being 12° and 24° respectively. These large angles are used for convenience of illustration; but it should be explained that this law does not really hold in them, as is evident, because the arc is longer than the tangent to which it would be connected by a line parallel with the versed sine. The law is absolutely true only when the tangent and arc coincide, and approximately so for exceedingly small angles. [Illustration: Fig. 2] In reality, however, we have only to do with the case in which the arc and the tangent do coincide, and in which the law that the deflection is _equal to_ the versed sine of the angle is absolutely true. Here, in observing this most familiar thing, we are, at a single step, taken to that which is utterly beyond our comprehension. The angles we have to consider disappear, not only from our sight, but even from our conception. As in every other case when we push a physical investigation to its limit, so here also, we find our power of thought transcended, and ourselves in the presence of the infinite. We can discuss very small angles. We talk familiarly about the angle which is subtended by 1" of arc. On Fig. 2, a short line is drawn near to the radius O A'. The distance between O A' and this short line is 1° of the arc A' B'. If we divide this distance by 3,600, we get 1" of arc. The upper line of the Table of versed sines given below is the versed sine of 1" of arc. It takes 1,296,000 of these angles to fill a circular space. These are a great many angles, but they do not make a circle. They make a polygon. If the radius of the circumscribed circle of this polygon is 1,296,000 feet, which is nearly 213 geographical miles, each one of its sides will be a straight line, 6.283 feet long. On the surface of the earth, at the equator, each side of this polygon would be one-sixtieth of a geographical mile, or 101.46 feet. On the orbit of the moon, at its mean distance from the earth, each of these straight sides would be about 6,000 feet long.