112 



SCIENCE 



[N. S. Vol. XLI. No. 1047 



ence to the needs and the activities of 

 other institutions. Cooperation often 

 makes severe demands upon the individ- 

 ual; it means that he must be willing to 

 use his mental and his material equipment 

 in furthering an impersonal plan; it 

 means that he must sometimes subordi- 

 nate his own judgment to that of others; 

 it means that he must sometimes use 

 methods that he would to like to modify 

 in some particular if he were working 

 alone. 



I believe that it is true that the astron- 

 omer has broken more completely with an- 

 cient tradition than has the mathemati- 

 cian. Many of the latter are still inclined 

 to take what may be called the artistic view 

 of their work; they refuse to admit that 

 mathematics is a means to some other end, 

 and they frankly assert (half in jest and 

 half in earnest) that their science need 

 have no reference to material things. A 

 few years ago a prominent mathematician, 

 speaking I think from the very chair that 

 I am vacating to-day, quoted with sym- 

 pathy the sentiment that mathematics is 

 born and nourished out of the play in- 

 stinct of mankind. It is difficult for me to 

 see the difference between this view and 

 the view that a chess player takes of his 

 game. In the one we may start if we like 

 with a set of axioms and an arbitrary set 

 of postulates without inquiring whether 

 they apply to the world around us, and we 

 may then amuse ourselves by tracing the 

 consequences. The chess-player does this 

 very thing : he sets out with a set of axioms 

 that he calls rules and a set of postulates 

 that he calls openings, and after the ex- 

 penditure of much thought and ingenuity 

 he is able to trace the consequences. 



It is understood, I hope, that I have been 

 speaking in averages. By no means all 

 astronomers have gotten rid of the artistic 

 notion in their work, and by no means all 



mathematicians have severed their connec- 

 tion with the real world by applying the 

 square-root of minus unity. But there is 

 no denying that the idea of cooperation in 

 a broad sense has not yet taken a strong 

 hold in mathematics. Whether as great 

 advantage would flow from cooperation 

 between one mathematician and another, 

 as is the case in astronomy, it is not for me 

 to say. But when we come to speak of co- 

 operation between mathematics and the 

 other sciences, the benefits that would fol- 

 low are diificult to overestimate. Let me 

 spend a few minutes in pointing out how 

 greatly the help of the mathematician is 

 needed in a single astronomical subject, 

 namely, that which concerns spectroscopic 

 binaries. If in these remarks I emphasize 

 individual stars, Algol for example, you 

 will understand that these are types of a 

 large class, and that the problems they 

 present are of cosmieal importance. 



The first star to be recognized as vari- 

 able in its light was probably Algol. The 

 Arabs seem to have made this discovery, 

 for it is difficult to account otherwise for 

 the very apt name they gave the star, Algol 

 or El Ghoul, the changing spirit or 

 demon. The same discovery was inde- 

 pendently made by others, among them 

 Goodricke of England in 1782, when he 

 was eighteen years of age. Goodricke con- 

 tinued to observe the star until he had de- 

 termined the period and the nature of the 

 light changes, and he advanced what we 

 now know to be the true explanation of its 

 changing light, namely that Algol is peri- 

 odically eclipsed by a darker companion 

 of nearly the same size as itself. This 

 conjecture was a very bold one in that day, 

 for we must remember that binary stars 

 were then unknown. A great many double 

 stars had been detected, but it was sup- 

 posed that these were the result of per- 

 spective and chance. It was about this 



