in it, so arranged that the pin F shall always move along the long diameter AB, and the pin G shall always move along the short diameter DE; then any point H of the bar describes an accurate ellipse. This is the principle used in carpenters' trammels and oval chucks. It describes an accurate ellipse exactly similar to that described by another method, of which I am going to speak, but it has no relation to the various parts of the ellipse upon which I am going to remark. _page_101_figure_30.png)
Fig. 30. In Figure 30, if we stick a pin in a board at S, and call that point a focus; and if we stick another pin in the board at H, and call that a focus; if we then fasten a string by its two ends to these two pins, keeping it always stretched by the point of a pencil as at P, and carry the pencil round, it will describe an ellipse. S and H are the two focusses of the ellipse; but in all the treatment of astronomical theory, we have only to do with one of them.
If the ellipse in Figure 30 be the orbit of a planet, S will be the place of the sun. The sun is at one focus of the ellipse described by every planet Every planet describes a different ellipse. The degree of flatness of every ellipse is different for every planet; the direction of the long diameter of the ellipse is different for every planet; there is every possible variety among them.
Now, one of the important things that Kepler made out was this: that the orbits of planets are
