Since I have not been able to give here the details of the calculation, I should make it plain that the curve in Fig. 7 is traced by pure theory or terrestrial experiment except for the one constant determined by making it pass through Capella. We can imagine physicists working on a cloud-bound planet such as Jupiter who have never seen the stars. They should be able to deduce by the method explained on p. 25 that if there is a universe existing beyond the clouds it is likely to aggregate primarily into masses of the order a thousand quadrillion tons. They could then predict that these aggregations will be globes pouring out light and heat and that their brightness will depend on the mass in the way given by the curve in Fig. 7. All the information that we have used for the calculations would be accessible to them beneath the clouds, except that we have stolen one advantage over them in utilizing the bright component of Capella. Even without this forbidden peep, present-day physical theory would enable them to assign a brightness to the invisible stellar host which would not be absurdly wrong. Unless they were wiser than us they would probably ascribe to all the stars a brilliance about ten times too great [Note: For this prediction it is unnecessary to know the chemical composition of the stars, provided that extreme cases (e. g. an excessive proportion of hydrogen) are excluded. For example, consider the hypotheses that Capella is made respectively of (a) iron, (b) gold. According to theory the opacity of a star made of the heavier element would be 2 1/2 times the opacity of a star made of iron. This by itself would make the golden star a magnitude ( = 2 1/2 times) fainter. But the temperature is raised by the substitution; and although, as explained on p. 23, the change is not very great, it increases the outflow of heat approximately 2 1/2 times. The resultant effect on the brightness is practically no change. Whilst this independence of chemical constitution is satisfactory in regard to definiteness of the results, it makes the discrepant factor 10 particularly difficult to explain.]

-- not a bad error for a first attempt at so transcendent a problem. We hope to clear up the discrepant factor 10 with further knowledge of atomic processes; meanwhile we shelve it by fixing the doubtful constant by astronomical observation.

Dense Stars

We must recall that the theory was developed for stars in the condition of a perfect gas. In the right half of Fig. 7 the stars represented are all diffuse stars; Capella with a mean density about equal to that of the air in this room may be taken as typical. Material of this tenuity is evidently a true gas, and in so far as these stars agree with the curve the theory is confirmed. But in the left half of the diagram we have the Sun whose material is denser than water, Krueger 60 denser than iron, and many other stars of the density usually associated with solid or liquid matter. What business have they on the curve reserved for a perfect gas? When these stars were put into the diagram it was not with any expectation that they would agree with the curve; in fact, the agreement was most annoying. Something very different was being sought for. The idea was that the theory might perhaps be trusted on its own merits with such confirmation as the diffuse stars had already afforded; then by measuring how far these dense stars fell below the curve we should have definite information as to how great a deviation from a perfect gas occurred at any given density. According to current ideas it was expected that the sun would fall three or four magnitudes below the curve, and the still denser Krueger 60 should be nearly ten magnitudes below. [Note: Observation shows that the sun is about 4 magnitudes fainter than the average diffuse star of the same spectral class, and Krueger 60 is 10 magnitudes fainter than diffuse stars of its class. The whole drop was generally assumed to be due to deviation from a perfect gas; but this made no allowance for a possible difference of mass. The comparison with the curve enables the dense star to be compared with a gaseous star of its own mass, and we see that the difference then disappears. So that (if there has been no mistake) the dense star is a gaseous star, and the differences above mentioned were due wholly to differences of mass.]