9 5 SEVENTEENTH CENTURY. PT. in. 



lions Kepler calculated where it ought to arrive at other 

 fixed times if it moved in a circle, as the earlier astronomers 

 had supposed. But he found that it did not arrive there 

 as computed, and he was so sure that Tycho's observations 

 were exact that he said boldly, ' All the theories must be 

 wrong if they do not agree with what Tycho saw.' So he 

 puzzled on, trying one explanation after another, until at 

 last he discovered three remarkable laws, by which the 

 movements not only of Mars, but of all the other planets, 

 are explained. 



The first of these laws is that planets move round the 

 sun in ellipses or ovals, and not in circles. You know that 

 to draw a circle you put one leg of the compasses into a 

 spot and draw the other leg round it, and the middle spot 

 is called the centre or focus. But to draw an ellipse you 

 must have two focuses or foci. To understand this, stick 

 two pins a little distance apart in a piece of paper, and 

 fasten a string to them by its two ends. Place a pencil 

 upright in the string, so as to keep it tightly stretched, and 

 draw the pencil round first on one side then on the other. 

 You will then have an ellipse, and the two pin-holes will be 

 the two foci Draw the sun in one of the foci and a round 

 globe on some part of the ellipse, and you will have a figure 

 of the path of our earth or any of the planets round the sun. 

 You will find that the farther you put the pins apart the 

 flatter the ellipse will be. The path or orbit of the planet 

 Mercury is much more elliptical than the orbit of the Earth. 

 Another difference in the orbits of the planets is that they 

 do not all lie in the same direction, though they all have the 

 sun as one of their foci. For instance, in Fig. 10 the orbit 

 of the planet A has the sun for one focus and the dot c for 

 the other, while the orbit of the planet B has the sun for one 

 focus and the dot d for the other, and this makes the two 



