Pupil. I have, Sir; and am so well convinced of what you told me, that nothing farther need be said on the subject.
Tutor. As that is the case, I shall proceed.—I dare say you do not forget what the plane of the ecliptic is.
Pupil. I do not, Sir; but have a perfect recollection of it.
Tutor. Now, remember, that the axis of the earth is not upright or perpendicular to the plane of the ecliptic, but inclines to, or leans towards it, 23-1/2 degrees, and makes an angle with it of 66-1/2 degrees.
Pupil. An angle signifies a corner; but that cannot be the meaning here.
Tutor. That is what is generally understood by an angle: but, in geometry, it means the meeting of any two lines which incline to one another, in a certain point. Now, if you conceive the axis of the earth to be one line, and the plane of the ecliptic the other, the point where they meet or cross each other will form an angle.
Pupil. I think I understand it; but how can it contain 23-1/2 or 66-1/2 degrees?
Tutor. You know what a degree is.
Pupil. If I remember right it is the 360th part of a circle.
Tutor. It is so: and the measure of an angle is an arc or part of the circumference of a circle, whose angular point is the center: and so many 360th parts as any arc contains, so many degrees the measure of the angle is said to be; thus, Z C P (Plate III. fig. 1.) makes an angle of 23-1/2 degrees, because the arc Z P contains 23-1/2 360th parts of the whole circle. Then if A B represent the plane of the ecliptic, and N C S the axis of the earth, as D N contains the same number of degrees as Z P, will not its inclination from a perpendicular be 23-1/2 degrees?