A. — MATHEMATICS AND PHYSICS. 47 



what is perhaps a still wildei- guess. Eathei- we should admit that the 

 source is not certainly known, and seek for any possible astronomical 

 evidence which may help to define its necessary character. One piece 

 of evidence of this kind may be worth mentioning. It seems clear that 

 it must be the high temperature inside the stars which determines the 

 liberation of energy, as H. N. Russell has pointed out.^ If so the 

 supply may come mainly from the hottest region at the centre. I have 

 already stated that t-lie general uniformity of the opacity of the stars 

 is much more easily intelligible if it depends on scattering rather than 

 on true absorption ; but it did not seem possible to reconcile the deduced 

 stellar opacity with the theoretical scattering coefficient. Within 

 reasonable limits it makes no great difference in our calculations at what 

 parts of the star the heat energy is supplied, and it was assumed that 

 it comes more or less evenly from all parts, as would be the case on 

 the contraction theory. The possibility was scarcely contemplated that 

 the energy is supplied entirely in a restricted region round the centre. 

 Now, the more concentrated the supply, the lower is the opacity requisite 

 to account for the observed radiation. I have not made any detailed 

 calculations, but it seems possible that for a sufficiently concentrated 

 source the deduced and the theoretical coefficients could be made to 

 agree, and there does not seem to be any other way of accomplishing 

 this. Conversely, we inight perhaps argue that the present discrepancy 

 of the coefficients shows that the energy supply is not spread out in the 

 way required by the contraction hypothesis, but belongs to some new 

 source only available at the hottest, central part of the star. 



I should not be surprised if it is whispered that this address has at 

 times verged on being a little bit speculative ; perhaps some outspoken 

 friend may bluntly say that it has been highly speculative from 

 beginning to end. I wonder what is the touchstone by which we may 

 test the legitimate development of scientific theory and reject the idly 

 speculative. We all know of theories which the scientific mind in- 

 stinctively rejects as fruitless guesses; but it is difficult to specify their 

 exact defect or to supply a rule which will show us when we ourselves 

 do err. It is often supposed that to speculate and to make hypotheses 

 are the same thing; but more often they are opposed. It is when we 

 let our thoughts stray outside venerable, but sometimes insecure, 

 hypotheses that we are said to speculate. Hypothesis limits speculation. 

 Moreover, distrust of speculation often serves as a cover for loose 

 thinking ; wild ideas take anchorage in our minds and influence our out- 

 look; whilst it is considered too speculative to subject them to the 

 scientific scrutiny which would exorcise them. 



If we are not content with the dull accumulation of experimental 

 facts, if we make any deductions or generalisations, if we seek for any 

 theory to guide us, some degree of speculation cannot be avoided. Some 

 will prefer to take the interpretation which seems to be most imme- 

 diately indicated and at once adopt that as an hypothesis ; others wiU 

 rather seek to explore and classify the widest possibilities which are 

 not definitely inconsistent with the facts. Either choice has its dangers ;, 



» Pub. Act. Soe. Pacific. August 1919. 



