selves. It was necessary that the dimensions should be so small that it was possible to get near to all of the charge at once and so realize forces much larger than would be possible were the charge spread over the whole atom. This view was consistent moreover with requirements from another angle. For since experimental evidence led to the conclusion. that the number of electrons in an atom was far too small to account for the atomic mass, it was necessary to look to the positive electricity for an explanation of that mass. Now, strange as it may seem, electrodynamic theory required that in order to get a large mass out of an assigned charge, it was necessary to concentrate it into exceedingly small dimensions, so from this consideration also we were driven to assume the positive charge in the atom to be a thing very small in size. But with the positive electricity concentrated into a minute thing or into a number of minute things, and the negative electricity concentrated into a number of minute things, there seemed no way in which to provide for a stable and permanent structure to be made out of these things unless they should be allowed to seek equilibrium against their attractions by revolving around each other; and so thought centered once more on the planetary idea of the atom with a determination to do the best that might be done with it in making it fit the optical results. And so there arose Bohr's great theory of atomic structure in which it is true. the electrons are required to do things which they ought not to do according to their strict traditions but in which they pay for this privilege many fold in the achievements made.

Bohr's theory is founded upon the model of the atom suggested by Sir Ernest Rutherford. In this model we have for the center of the atom a heavy nucleus, containing all of the positive charge of the atom and in general some electrons as well. Around this nucleus we have electrons revolving in orbits as planets revolve around the sun. Suppose we take the lightest atom, the atom of hydrogen. This contains nothing but a single proton with an electron revolving around it. In order to picture to you the relative magnitudes

it will suffice to say that the hydrogen atom would look like what the earth and sun would look like if, leaving them at their present distance apart, we should squeeze the sun until it was two miles in radius. You see we cannot draw a true diagram of the hydrogen atom; for, if we should draw the nucleus sufficiently large to be seen, we should have to draw the electron bigger than the blackboard and place it on a circle 300 miles away.

This characteristic of relative emptiness is shared by all the atoms. It explains why we can fire things like electrons through relatively thick pieces of metal. The metal is very compact as regards its resistance to the passage of a big thing but very empty to the passage of small things. The problem of walking through a brick wall is not so miraculous as it seems. I will tell you how to do it. If you should consider any plane section through your body you would find that in any area only about one millionth of the one thousand millionth of it would be covered with the sections of electrons, all the rest would be emptiness, and very much the same thing may be said about the brick wall. Therefore you see that there is plenty of room for you to walk through the brick wall. All you have to do is to make your electrons dodge those of the brick wall.

If we arrange the atoms in a row, in order of their atomic weight, then (with certain slight reservations which need not delay us here) the number which represents the position in the row is called the atomic number. On the Bohr-Sommerfeld theory of atomic structure, the net number of unbalanced protons in the nucleus of an atom is equal to the atomic number, and around the nucleus there revolve in minute planetary orbits as many electrons as there are unbalanced protons in the nucleus. Thus, helium, the atom next to hydrogen in weight, has a nucleus containing two unbalanced protons, and two electrons revolving in orbits around them. If there were nothing more than two protons and two electrons in the helium atom, we should expect the atom to be just twice as heavy as the hydrogen atom, whereas it is four times

as heavy. This necessitates the supposition that, in addition to the two unbalanced protons in the nucleus, there shall be two more protons and two more electrons. This principle of half of the total number of protons in the nucleus being neutralized as regards their external action by electrons in the nucleus is one which holds for all the atoms, hydrogen being the only exception.

In order to avoid the difficulties of which I have spoken, and concerned with the fact that on a strict application of electromagnetic principles the electrons of an atom would eventually fall into the nucleus, and in order to provide for the known facts as regards the light which atoms may emit, Bohr introduced a few extra assumptions. These assumptions are rather drastic in type but they are simple in form and few in number. I can best illustrate them by considering the case of the hydrogen atom-the case of a single electron revolving around a single proton.

Now the first assumption made by Bohr is that, although we might be able to knock the electron out of the ring in which it found itself, by bombarding it with some other electron, or by some other means, we could not cause it to revolve in any ring we chose. There are only certain orbits in the atom which the electron may be permitted to have, and these are related to each other in a manner which is quite simple of expression, even though it may be rather artificial in statement. Suppose we draw a line from the nucleus to the electron, and measure the area which the line sweeps out per second. The area will, of course, increase with the size of the orbit. Now Bohr's first Now Bohr's first assumption amounts to supposing that the orbits must be such that these areas are integer multiples of the area for the smallest. We can have an orbit which makes this area twice, three times or four times the area for the smallest orbit, but we cannot have an orbit for which the area is two and a half times that unit. Moreover, the smallest orbit is such that the area described by the radius vector per second, when multiplied by 27 times the mass of the electron, gives a certain number h, which

first made its appearance in the theory of heat radiation and has since invaded first one branch of physics and then another until it has finally assumed a status comparable with those of the electronic charge and mass.

In each of the possible orbits the electron possesses a perfectly definite energy, calculable in terms of the radius. of the orbit according to exactly the same principles available for the calculation of the energy associated with the rotation of a planet around the sun. The greater the size of the orbit the greater the energy. We can only persuade an electron to leave the orbit in which it happens to be revolving at the time and go into some larger orbit by giving it energy; and, if it should go from a larger orbit to a smaller one, it would have to part with energy. Now the second assumption which Bohr makes is that, so long as the electron remains in any one orbit, it does not radiate any energy at all. The laws of classical electrodynamics would call for such radiation, but Bohr assumes that, for some reason or other, radiation does not take place. On the other hand he assumes that if one of these electrons, after having been thrown into one of the outer orbits, returns to the orbit from which it was thrown, or to some intermediate orbit, it gives out the whole of its surplus energy in the form of vibrations of definite wave length, determined entirely by the amount of energy which has been radiated. He assumes in fact that the number of vibrations emitted per second is just proportional to the energy change, the factor by which we must multiply that frequency (or number of vibrations per second) in order to obtain the energy change being the same mysterious constant, h, which had already been used in specifying the possible orbits, and which, as I have already pointed out, had previously made its appearance in other branches of physics.

The passage of an electron from any one orbit to a smaller orbit thus gives rise to a perfectly definite wave length radiated; and, in the ideal case, by properly stimulating the electron by throwing it out to the various orbits it should be

possible to cause the atom to emit as many frequencies as there are possibilities of this kind of passing from one orbit to a smaller one. Thus we see how it may come about that this very simple structure, consisting of no more than a positive nucleus and an electron, may give rise to a large number of different frequencies.

Of course, it is to be distinctly understood that Bohr's theory makes no attempt to give what, in the ordinary use of words, we might call a reason for the performances which are postulated, and it does not describe any mechanism by which the radiation is emitted during the passage from one orbit to another.

Even a superficial examination of the light emitted by glowing hydrogen will show that there are orderly relations between the wave lengths of the various colors emitted. These relations have been studied very carefully by the spectroscopist; and, long before he had any theoretical reason for it, he knew that he could calculate the wave lengths actually found by substituting, successively, the numbers 3, 4, 5, etc., for n in the formula

Now the different wave lengths which Bohr's theory predicts as corresponding to the passage of an electron between the various orbits are just those which would be obtained by substituting the numbers 1, 2, 3, etc., for nɩ and në in a formula of the type

A special case of this is the formula (1), where n1 = 2. This is the Balmer series. But Bohr's theory predicted not only this possibility but also the possibilities to be obtained by putting n1 = 1, and constructing a series on this basis, and the possibilities by putting n1 = 3 and constructing a series. on this basis, and so on. Some of the lines and series predicted