to describe the orbits which Sommerfeld admits as possible, in addition to Bohr’s circles. If there is any reader who does not know what an ellipse looks like, he can construct one for himself by the following simple device. Tie [Pg 74] a piece of string to two pins, and stick them into a piece of paper at two points , ′ near enough together for the string to remain loose. Then take a pencil, and with its point draw the string taut. Any place that the pencil will reach is on a certain ellipse, and by moving the pencil round, the whole ellipse can be drawn. The points , ′ are called “foci.” An ellipse may be defined as a curve such that, if and ′ are any two points on it the sum of the distance of from and ′ (the foci) is equal to the sum of the distances of ′ from and ′. In our construction, both are equal to the length of the string that we tied to the two pins. The ratio of the distance between the pins to the length of the string is called the “eccentricity” of the ellipse. It is obvious that if we were to stick the two pins into the same place we should get a circle, so that a circle is a particular case of an ellipse, namely an ellipse which has zero eccentricity. All the planets move in ellipses which are very nearly circles, whereas the comets move in ellipses which are very far removed from circles. In each case the sun is in one of the foci, and there is nothing particular in the other focus. An ellipse which is very far from being a circle can be drawn by making the distance ′ between the two pins not very much shorter than [Pg 75] the length of the string.