384 



SCIENCE 



[N. S. Vol. XXXVIII. No. 977 



The best method of abating this scepticism is 

 to become acquainted with the real scope and 

 modes of application of conceptions which, in the 

 popular language of superficial exposition — and 

 even in the unguarded and playful paradox of 

 their authors, intended only for the instructed eye 

 — often look bizarre enough. 



One thing is very notable, that it is 

 closer and more exact knowledge that has 

 led to the kind of scientific scepticism now 

 referred to; and that the simple laws on 

 which we used to be working were thus 

 simple and discoverable because the full 

 complexity of existence was tempered to 

 our ken by the roughness of our means of 

 observation. 



Kepler's laws are not accurately true, 

 and if he had had before him all the data 

 now available he could hardly have discov- 

 ered them. A planet does not really move 

 in an ellipse but in a kind of hypocycloid, 

 and not accurately in that either. 



So it is also with Boyle's law, and the 

 other simple laws in physical chemistry. 

 Even Van der Waals's generalization of 

 Boyle's law is only a further approxima- 

 tion. 



In most parts of physics simplicity has 

 sooner or later to give place to complexity : 

 though certainly I urge that the simple 

 laws were true, and are still true, as far as 

 they go, their inaccuracy being only de- 

 tected by further real discovery. The rea- 

 son they are departed from becomes known 

 to us; the law is not really disobeyed, but 

 is modified through the action of a known 

 additional cause. Hence it is all in the 

 direction of progress. 



It is only fair to quote Poincare again, 

 now that I am able in the main to agree 

 with him: 



Take for instance the laws of reflection. Fres- 

 nel established them by a simple and attractive 

 theory which experiment seemed to confirm. Sub- 

 sequently, more accurate researches have shown 

 that this verification was but approximate; traces 



of elliptic polarization were detected everywhere. 

 But it is owing to the first approximation that the 

 cause of these anomalies was found, ia the exist- 

 ence of a transition layer; and all the essentials 

 of Fresnel's theory have remained. We can not 

 help reflecting that all these relations would never 

 have been noted if there had been doubt in the 

 first place as to the complexity of the objects they 

 connect. Long ago it was said: If Tycho had had 

 instruments ten times as precise, we would never 

 have had a Kepler, or a Newton, or astronomy. 

 It is a misfortune for a science to be born too 

 late, when the means of observation have become 

 too perfect. That is what is happening at this 

 moment with respect to physical chemistry; the 

 founders are hampered in their general grasp by 

 third and fourth decimal places; happily they are 

 men of robust faith. As we get to know the 

 properties of matter better we see that continuity 

 reigns. ... It would be difficult to justify [the 

 belief in continuity] by apodeictic reasoning, but 

 without [it] all science would be impossible. 



Here he touches on my own theme, con- 

 tinuity; for, if we had to summarize the 

 main trend of physical controversy at pres- 

 ent, I feel inclined to urge that it largely 

 turns on the question as to which way ulti- 

 mate victory lies in the fight between con- 

 tinuity and discontinuity. 



On the surface of nature at first we see 

 discontinuity; objects detached and count- 

 able. Then we realize the air and other 

 media, and so emphasize continuity and 

 flowing quantities. Then we detect atoms 

 and numerical properties, and discontinu- 

 ity once more makes its appearance. Then 

 we invent the ether and are impressed 

 with continuity again. But this is not 

 likely to be the end ; and what the ultimate 

 end will be, or whether there is an ultimate 

 end, is a question difficult to answer. 



The modern tendency is to emphasize the 

 discontinuous or atomic character of every- 

 thing. Matter has long been atomic, in the 

 same sense as anthropology is atomic; the 

 unit of matter is the atom, as the unit of 

 humanity is the individual. Whether men 

 or women or children — they can be counted 



