With respect to an annular eclipse, it must be remembered, that the paths of all bodies revolving round others are elliptical; i.e., they take place in the form of an ellipse, which is a figure easily demonstrated; and is, in fact, one of the conic sections.
If a slice be taken off a cone, parallel with the base, we have a circle thus—
Fig. 29.
If it be cut obliquely, or slanting, we see at once the figure spoken of, and have the ellipse as shown in this picture.
Fig. 30.
Now, the ellipse has two points within it, called "the foci," and these are easily indicated by drawing an ellipse on a diagram-board, in which two nails have been placed in a straight line, and about twelve inches apart. Having tied a string so as to make a loop, or endless cord, a circle may first be drawn by putting the cord round one of the nails, and holding a piece of chalk in the loop of the string, it may be extended to its full distance, and a circle described; here a figure is produced round one point, and to show the difference between a circle and an ellipse, the endless cord is now placed on the two nails, and the chalk being carried round inside the string, no longer produces the circle, but that familiar form called the oval. As a gardener would say, an oval has been struck; and the two points round which it has been described, are called the foci. This explanation enables us to understand the next diagram, showing the motion of the earth round the sun; the latter being placed in one of the foci of a very moderate ellipse, and the various points of the earth's orbit designated by the little round globes marked a, b, c, d, where it is evident that the earth is nearer to the sun at b than at d. In this diagram the ellipse is exaggerated, as it ought, in fact, to be very nearly a circle.
| Fig. 31. | Fig. 32. |
We are about three millions of miles nearer to the sun in the winter than we are in the summer; but from the more oblique or slanting direction of the rays of the sun during the winter season, we do not derive any increased heat from the greater proximity. The sun, therefore, apparently varies in size; but this seeming difference is so trifling that it is of no importance in the discussion: and here we may ask, why does the earth move round the sun? Because it is impelled by two forces, one of which has already been fully explained, and is called the centrifugal power, and the other, although termed the centripetal force, is only another name for the "attraction of gravitation."