[33] The evidence is much stronger now than when the lectures were delivered.

[34] The energy is required because on cooling down the matter must regain a more normal density and this involves a great expansion of volume of the star. In the expansion work has to be done against the force of gravity.

[35] Each orbit or state of the atom requires three (or, for later refinements, four) quantum numbers to define it. The first two quantum numbers are correctly represented in the Bohr model; but the third number which discriminates the different lines forming a doublet or multiplet spectrum is represented wrongly—a much more serious failure than if it were not represented at all.

[36] The probability is often stated to be proportional to instead of , as assumed above. The whole interpretation is very obscure, but it seems to depend on whether you are considering the probability after you know what has happened or the probability for the purposes of prediction. The is obtained by introducing two symmetrical systems of -waves travelling in opposite directions in time; one of these must presumably correspond to probable inference from what is known (or is stated) to have been the condition at a later time. Probability necessarily means “probability in the light of certain given information”, so that the probability cannot possibly be represented by the same function in different classes of problems with different initial data.