the hypothesis of circular orbits cannot explain. But although the agreement between theory and observation is astonishingly close, it cannot be said that we have yet reached the stage where we can be quite certain that no other theory would account for the facts. All the broad facts in the spectrum depend upon the sum of the two quantum-numbers, , not on either separately. We therefore classify orbits by this sum. We thus arrive at the following possible orbits: 1st case. . Since cannot be zero (because if it were the electron would fall into the nucleus), this gives only one possibility, namely , . When , there is no flattening, and the orbit is a circle. Thus this first case is that of Bohr’s minimum circle. 2nd case. . Here there are two possibilities, namely [Pg 81] , and , The first of these gives Bohr’s second circle; the second gives an ellipse in which there is a unit amount of flattening, that is to say, the ellipse is half as high as it is broad. 3rd case. . Here there are three possibilities, namely: (a) , ; this gives Bohr’s third circle (b) , ; this gives an ellipse in which the amount of flattening is a half, that is to say, the ellipse is two-thirds as high as it is broad, (c) , ; this gives an ellipse in which the amount of flattening is two, that is to say, the ellipse is a third as high as it is broad. In the fourth case, , there are four possibilities; and so on. The breadth of the ellipse depends only upon , so that all the possible ellipses under one head have the same breadth. The energy also, apart from niceties, depends only upon .[6] Of the three sets of facts which show that elliptical orbits must occur, we shall pass by the Zeeman effect (which shows how magnetism splits one line into three, or sometimes more) and the Stark effect (which shows the influence of an electric field). The third, however, [Pg 82] is so interesting that it cannot be omitted, since it shows that the electron, in so far as it obeys ordinary dynamical laws, follows the principles of Einstein in preference to those of Newton. Very careful observation shows that the lines in the spectrum which we have hitherto treated as single really consist of two (and in other cases three or more) separate lines very close together. This suggests that two different orbits which give the same value of do not produce exactly the same line in the spectrum when an electron jumps to or from them. The phenomenon is more noticeable in the case of other elements than in that of hydrogen, for reasons which the theory explains. Fortunately on this point our theory is able to tell us a good deal about other atoms; but in what follows we shall confine ourselves to hydrogen.