PRESIDENTIAL ADDRESS SECTION A. 3/ 



matical result. The principle of the Conservation of Energy 

 means nothing more nor less than the equation of which it is a 

 happy translation : moreover, it establishes no reliable proposition 

 outside systems which are known to obey the elementary laws 

 of motion — i.e., the domain of the mechanical sciences. The 

 law seems often to be c|uoted by serious men as if it proved, " If 

 you do enough thinking (logically or illogically), you will reach 

 some \aluable result;" "if you talk persistently enough 

 you will get }Our way in the end." This question 

 of words suggests that the use of " logarithms " would 

 be much wider spread, and they woidd be much easier 

 to learn, if they had been called what they are, " in- 

 dices of ten." The choice of words makes, of course, little 

 difference to the ex])ert who has the idea safe : but the student 

 and the public suffer much from unnecessary technicality. Of 

 course, there is another point of view. If Galileo, in his tenta- 

 tive shots at the true laws of motion, had fixed his attention (as 

 ]>ossibly Huyghens did) on the velocity acquired after a certain 

 distance fallen, instead of after a certain time, he would have 

 obtained " velocity varies as square root of distance," instead of 

 " velocity varies as time," and our energy equation would not 

 have appeared as secondary. But there is a wider view — that 

 the entity which the historic development of the subject has hit 

 on more or less accidentally, and which it has called " energy," 

 is more "real," more fundamental, than the " mass " and 

 " acceleration " by which we have approached it. Thus, the whole 

 of dynamics in the case of one " degree of freedom " may be 

 foimded on what is, in the orthodox scheme, a derived proposi- 

 tion — viz., that in all motion a certain something, which we may 

 as well call " energy " (including now both ' kinetic " and 

 ** potential "j, is constant. This simple statement does not 

 suffice when there is more than one " degree of freedom " : but 

 the " energy " can in this case be made the foundation of the 

 treatment necessary for the solution. 



This use of energy represents, on the one hand, the modern 

 development of the Newtonian philosophy, and on the other a 

 certain desire to get beyond Newton. Newton's system has not 

 succeeded in explaining all the phenomena ; and recently the 

 conviction has grown that something more — or different — is 

 needed : a few accepted facts seem, after much patient work, 

 to be irreconcilable with the principles of that system. I will 

 venture to show shortly how Newton's scheme for two centuries 

 succeeded in explaining phenomenon after phenomenon, until 

 thinkers 'became confident that no new theory would be neces- 

 sary — that the Newtonian laws would ultimately explain every 

 fact in the universe. This confidence has only been shaken 

 within the last 40 years; it has at last seemed possible to prove 

 that one or two phenomena were distinctly contrary to those 

 laws. 



Isaac Nc7vto)i (1642 to 1727), Professor of Mathematics at 



