The calculation of the orbits of planetary electrons, on Newtonian principles, is only possible in the two simplest cases: that of hydrogen, which consists (when unelectrified) of one proton and one electron; and that of positively electrified[Pg 26] helium, which has lost one, but not both, of its planetary electrons. In these two cases the mathematical theory is practically complete. In all other cases which actually occur, although the mathematics required is of a sort which has been investigated ever since the time of Newton, it is impossible to obtain exact solutions, or even good approximations. The case is still worse as regards nuclei. The nucleus of hydrogen is a single proton, but that of the next element, helium, is held to consist of four protons and two electrons. The combination must be extraordinarily stable, both because no known process disintegrates the helium nucleus, and because of the loss of mass involved. (If the mass of the helium atom is taken as 4, that of a hydrogen atom is not 1, but 1·008.) This latter argument depends upon considerations connected with relativity, and must therefore be discussed at a later stage. Various suggestions have been made as to the way in which the protons and electrons are arranged in the helium nucleus, but none, so far, has yielded the necessary stability. What we may call the geometry of nuclei is therefore still unknown. It may be that, at the very small distances involved, the law of force is not the inverse square, although this law is found perfectly satisfactory in dealing with the motions of the planetary electron in the two cases in which the mathematics is feasible. This, however, is merely a speculation; for the present we must be content with ignorance as regards the arrangement of protons and electrons in nuclei other than that of hydrogen (which contains no electron in the nucleus).