The first quantum condition is very much the same as in the case of circular orbits. Take the mass of the electron, its velocity at (where it is nearest to the nucleus ), and the circumference of the circle whose radius is , and multiply these three together; the result must be an exact multiple of , say . The second quantum condition determines how much the ellipse departs from a circle; it states that there is a second whole number (the second quantum number), such that is the amount of flattening in the sense defined a moment ago. The second number ′ may be zero; we then obtain Bohr’s case of circular orbits. If it is not zero, the electron moves in a more or less eccentric orbit. It turns out that, apart from niceties, the energy of an electron in its orbit, and therefore the spectral lines corresponding to jumps from one orbit to another, do not depend upon the separate numbers and ′, but only upon their sum '. The result is that the lines to be expected, apart from niceties, are the same as on Bohr’s original theory of circular orbits. If the matter were to end here, we might seem to have had a lot of trouble for nothing. Even [Pg 79] then, however, we could have drawn a useful lesson from the theory of elliptic orbits. There are, as we shall see, certain facts which are explained by elliptic orbits and not by circular orbits, but these facts are mostly recent discoveries, and might easily have remained unknown for some time longer. In that case, Bohr’s original theory would have accounted admirably for all the known facts, and there would have seemed to be very strong grounds for accepting it. Yet the theory of elliptic orbits would have accounted for the facts just as well, so that there would have been no way of deciding between them. This illustrates what is sometimes forgotten, that a theory which explains all the known relevant facts down to the minutest particular may nevertheless be wrong. There may be other theories, which no one has yet thought of, which account equally well for all that is known. We cannot accept a theory with any confidence merely because it explains what is known. If we are to feel any security, we must be able to show that no other theory would account for the facts. Sometimes this is possible, but very often it is not. Poincaré advanced a proof that the facts of temperature radiation cannot be explained if we assume that radiation is a continuous process, and that any possible explanation [Pg 80] must involve sudden jumps such as we have in the quantum theory. His argument is difficult, and it is possible that it may not ultimately prove wholly cogent. But it affords an instance of that further step without which scientific hypothesis must remain hypothetical. In our case, fortunately, there is evidence that elliptic orbits actually do occur when an electron moves round a hydrogen nucleus. That is to say, there is evidence that this hypothesis explains certain facts which