What had been taken to be the approach and recession of the star as a whole was really the approach and recession of the surface as it heaved up and down with the pulsation. The stars which vary like Cephei are diffuse stars enormously larger than the sun, and the total displacement measured amounts to only a fraction of the star's radius. There is therefore no need to assume a bodily displacement of the star (orbital motion); the measures follow the oscillation of that part of the star's surface presented towards us. - The decision that Cephei is a single star and not double has one immediate consequence. It means that the period of 5 1/3 days is intrinsic in the star and is therefore one of the clues to its physical condition. It is a free period, not a forced period. It is important to appreciate the significance of this. The number of sunspots fluctuates from a maximum to minimum and back to maximum in a period of about 11 1/2 years; although we do not yet understand the reason for this fluctuation, we realize that this period is something characteristic of the sun in its present state and would change if any notable change happened to the sun. At one time, however, there was some speculation as to whether the fluctuation of the sun spots might not be caused by the revolution of the planet Jupiter, which has a period not so very different; if that explanation had been tenable the 11 1/2 year period would have been something forced on the sun from without and would teach us nothing as to the properties of the sun itself. Having convinced ourselves that the light-period of Cephei is a free period of a single star, belonging to it in the same way that a particular note belongs to a tuning-fork, we can accept it as a valuable indicator of the constancy (or otherwise) of the star's physical condition.

In stellar astronomy we usually feel very happy if we can determine our data -- parallax, radius, mass, absolute brightness, &c. -- to within 5 per cent.; but the measurement of a period offers chances of far superior accuracy. I believe that the most accurately known quantity in the whole of science (excluding pure mathematics) is the moon's mean period, which is commonly given to twelve significant figures. The period of Cephei can be found to six significant figures at least. By fastening an observable period to the intrinsic conditions of a star we have secured an indicator sensitive enough to show extremely small changes. You will now guess why I am approaching 'the age of the stars' through the Cepheid variables. Up to the present they are the only stars known to carry a sensitive indicator, by which we might hope to test the rate of evolutionary change. We believe that Cephei like other stars has condensed out of a nebula, and that the condensation and contraction are still continuing. No one would expect to detect the contraction by our rough determinations of the radius even if continued for a hundred years; but the evolution must indeed be slow if an intrinsic period measurable to 1 part in 10,000,000 shows no change in a century. It does not greatly matter whether or not we understand the nature of this intrinsic period. If a star contracts, the period of pulsation, the period of rotation, or any other free period associated with it, will alter. If you prefer to follow any of the rival interpretations of the message of Cephei, you can make the necessary alterations in the wording of my argument, but the general verdict as to the rate of progress of evolution will be unchanged. Only if you detach the period from the star itself by going back to the old double star interpretation will the argument collapse; but I do not think any of the rival interpreters propose to do that.

It is not surprising that these pulsating stars should be regarded with special interest. Ordinary stars must be viewed respectfully like the objects in glass cases in museums; our fingers are itching to pinch them and test their resilience. Pulsating stars are like those fascinating models in the Science Museum provided with a button which can be pressed to set the machinery in motion. To be able to see the machinery of a star throbbing with activity is most instructive for the development of our knowledge.

The theory of a steady star, which was described in the first lecture, can be extended to pulsating stars; and we can calculate the free period of pulsation for a star of assigned mass and density. You will remember that we have already calculated the heat emission or brightness and compared it with observation, obtaining one satisfactory test of the truth of the theory; now we can calculate the period of pulsation and by comparing it with observation obtain another test. Owing to lack of information as to a certain constant of stellar material there is an uncertainty in the calculation represented by a factor of about 2; that is to say, we calculate two periods, one double the other, between which with any reasonable luck the true period ought to lie. The observational confirmation is very good. There are sixteen Cepheid variables on which the test can be made; their periods range from 13 hours to 35 days, and they all agree with the calculated