760 ANNUAL EEPOET SMITHSONIAN INSTITUTION, 1912. 



longs that line, extending it into a region not yet observed where the co- 

 ordinates of his curve indicate to liim new phenomena. Then by further 

 experiments he may test these prechcted phenomena to see whether or 

 not he has truly prechcted. If truly, then his extrapolation was justi- 

 fied and expresses real relationsliips; if not, then he must try again. 



Unless I have been deceived, the picture just sketched inchoates 

 just exactly the purpose of mathematical physics and the part it 

 plays both in synthesis and in prechction. The mathematical 

 expressions of physical theory are algebraic translations of the 

 curves such as I have just described and which the physicist mentally 

 draws. The better a physical theory expresses the real relationships 

 between the phenomena, the better will it prechct hidden relations veri- 

 fiable by trial and the more useful it will be, the more fit, the more true. 



But the truth of a theory must not be misunderstood. No theory 

 could be more useful than Fresnel's in attributing hght to move- 

 ments of the ether. To-day we prefer that of Maxwell, which sup- 

 poses hght is due to oscillating electric currents. Does that mean 

 that the theory of Fresnel was erroneous? No, for the object of 

 Fresnel was not to prove the existence of the ether or whether or not 

 it is formed of atoms, whether these atoms move tliis or that way; 

 liis object was to precUct optical phenomena. For that the theory of 

 Fresnel serves to-day as well as it chd before Maxwell. Wliat 

 changes is only the picture by wliich we represent the objects between 

 which the physicist has chscovered and proved relationsliips. Various 

 reasons make us from time to time change these pictures which other- 

 wise are unimportant. But it is these pictures alone wliich change; 

 the relationships always remain true provided they rest upon well- 

 observed facts. 



It is because of this common foundation upon truth that the most 

 ephemeral theories do not che in every part; but hke the torch wliich 

 the couriers of ancient times passed on from hand to hand, each 

 theory transmits to its successor that which is the only accessible 

 reahty, namely, the group of laws wliich expresses the relationships 

 existing between things. These conclusions reached by Poincar6 

 relative to physics hold as well for the other branches of science, 

 chemistry, the biological sciences, even for those sciences wliich are 

 yet young and classed as moral or social, since they all branch out 

 from physics, and accorchng to their nature, have for their final 

 object the foundation of their more or less complex laws upon those 

 of physics; accordingly, upon the latter ^vill be based all of our 

 knowledge of the world. 



It is clear that the conclusions of Poincar6 reduce to its proper value, 

 which is a minumum, a certain common materiahsm which dreams of 

 attaining the absolute and inclosing it in several differential equations. 

 There is not, there can not, be a metaphysical conception of science. 



