intensity approaches the truth. There is a famous Correspondence Principle enunciated by Bohr which asserts that for states of very high number the new quantum laws merge into the old classical laws. If we never have to consider states of low number it is indifferent whether we calculate the radiation or statistics according to the old laws or the new.

In high-numbered states the electron is for most of the time far distant from the nucleus. Continuous proximity to the nucleus indicates a low-numbered state. Must we not expect, then, that in extremely dense matter the continuous proximity of the particles will give rise to phenomena characteristic of low- numbered states? There is no real discontinuity between the organization of the atom and the organization of the star; the ties which bind the particles in the atom, bind also more extended groups of particles and eventually the whole star. So long as these ties are of high quantum number, the alternative conception is sufficiently nearly valid which represents the interactions by forces after the classical fashion and takes no cognizance of 'states'. For very high density there is no alternative conception, and we must think not in terms of force, velocity, and distribution of independent particles, but in terms of states.

The effect of this breakdown of the classical conception can best be seen by passing at once to the final limit when the star becomes a single system or molecule in state No. 1. Like an excited atom collapsing with discontinuous jumps such as those which give the Balmer Series, the star with a few last gasps of radiation will reach the limiting state which has no state beyond. This does not mean that further contraction is barred by the ultimate particles jamming in contact, any more than collapse of the hydrogen atom is barred by the electron jamming against the proton; progress is stopped because the star has got back to the first of an integral series of possible conditions of a material system. A hydrogen atom in state No. I cannot radiate; nevertheless its electron is moving with high kinetic energy. Similarly a star when it has reached state No. 1 no longer radiates; nevertheless its particles are moving with extremely great energy. What is its temperature? If you measure temperature by radiating power its temperature is absolute zero, since the radiation is nil; if you measure temperature by the average speed of molecules its temperature is the highest attainable by matter. The final fate of the white dwarf is to become at the same time the hottest and the coldest matter in the universe. Our difficulty is doubly solved. Because the star is intensely hot it has enough energy to cool down if it wants to; because it is so intensely cold it has stopped radiating and no longer wants to grow any colder.

We have described what is believed to be the final state of the white dwarf and perhaps therefore of every star. The Companion of Sirius has not yet reached this state, but it is so far on the way that the classical treatment is already inadmissible. If any stars have reached state No. 1 they are invisible; like atoms in the normal (lowest) state they give no light. The binding of the atom which defies the classical conception of forces has extended to cover the star. I little imagined when this survey of Stars and Atoms was begun that it would end with a glimpse of a Star-Atom.