44 



SCIENCE 



[N. S. Vol. XXXIX. No. 993 



planation of the phenomena by means of 

 simpler and more familiar phenomena, or 

 what is more likely to be possible, a theory 

 which is the mere description of the 

 phenomena mathematically in quantitative 

 terms. For example, perhaps the first 

 natural phenomena to be observed were 

 those connected with the recurrence of day 

 and night, the seasons, and the weather. 

 But how long was it before the simple 

 hypothesis was formed of the rotation of 

 the earth, to say nothing of its orbital mo- 

 tion around the sun! And until clocks 

 were invented no very profound conclu- 

 sions as to the constancy of the length of 

 the day or year were possible. That the 

 properties of space and time might be dis- 

 cussed by philosophers was to be sure 

 possible, but their results would not carry 

 great weight with the new school of natural 

 philosophers. When Galileo deduced by 

 experiment, and described with mathemati- 

 cal precision, the acceleration of a falling 

 body, he probably contributed more to the 

 physical sciences than all the philosophers 

 who had preceded him. 



The investigation of physical phenomena 

 has been a most fertile source of improve- 

 ment of mathematical methods, but this to 

 me most alluring subject I have no time to 

 develop, having treated it at length else- 

 where.^ Of this the most notable example 

 is Newton's invention of the differential 

 and integral calculus, which has given us 

 probably the most powerful instrument de- 

 vised by man for making discoveries. 

 Without it no progress could have been 

 made in the examination of continuously 

 varying phenomena. Is nature continuous 

 or not, that is, in the neighborhood of every 

 point of space within a distance no matter 

 how small, are there as many other points 

 as we please, and may a similar statement 

 be made for time? Is matter continuous, 



1 Presidential address, American Physical So- 

 ciety, Physical Review, 1904. 



and do all varying quantities vary con- 

 tinuously? This I do not intend to dis- 

 cuss, referring you to Sir Oliver Lodge, 

 who took that for his subject. But whether 

 nature is continuous or not, it is extremely 

 convenient to postulate that it is so. We 

 are thus enabled to describe phenomena by 

 means of differential equations, explaining 

 or describing what happens at any point 

 of space and time in terms of what is hap- 

 pening at the infinitely near ones. This has 

 been then the most important of our ways 

 of thinking about physical phenomena. 

 For upon this we have based the method 

 of dynamics, so auspiciously begun by 

 Galileo and perfected by Newton. Galileo 

 gave us the notion of acceleration, very 

 important for a single body, but Newton 

 completed it by that of force, which enables 

 us to describe the actions of one body on 

 another. Let me point out to you that 

 what Newton did in connection with gravi- 

 tation was not to explain it in the sense of 

 telling what its cause is, but, as I have 

 stated above, to describe it in exact mathe- 

 matical terms. But, much more than this, 

 Newton, by his succinct statement of the 

 laws of motion, gave us the possibility of 

 the explanation of a vast number of recon- 

 dite phenomena in terms of the more famil- 

 iar ones of djmamics. 



The dynamical method then became the 

 most important of physical methods of ex- 

 planation. Here mathematics, by some 

 thinkers considered, as Huxley said, to be 

 "that science which knows nothing of ob- 

 servation, nothing of experiment, nothing 

 of induction, nothing of causation," has 

 rendered invaluable services. It is true 

 that mathematics can not turn out more 

 than is put in, but it can transform the 

 data in a wonderful manner. Thus pro- 

 ceeding from Newton's definition of force, 

 it led to the notion of energy, and eventu- 

 ally to the conception of the conservation 



