722 



SCIENCE 



[N. S. Vol. XL. No. 1038 



can. be indefinitely manifolded, like truth) 

 while our failures are still-born, we are known 

 not for what we are or actually do, but by the 

 occasional incident, by the happy accident. 

 And it is this incident that wills it that the 

 results of the mathematician are much more 

 glorious, soaring unfettered and free even into 

 transcendental space, whereas the results of 

 the physicist, as a rule, must be of the 

 earth, earthy. While the mathematician in- 

 dulges an oriental dream — "Nein, Wir sind 

 Dichter!" cries Kroneker — the physicist must 

 tread the straight and narrow path, guided by 

 the arithmetic of the fathers. We are the 

 Puritans, you the unmitigated voluptuaries. 



Judge, therefore, the astonishment of the 

 world that it was left to our brother of the 

 soil to detect the four-dimensional world 

 among the inadequacies, or shall I say the 

 debris, of the three-dimensional. It is the 

 journeyman of science that clamors for a 

 wider scope. It is rule of thumb evidence 

 that cries exultingly " we are living in a 

 Copernican era." Things believed to be at 

 rest are asserted to be moving and so un- 

 cannily moving, that if there were an In- 

 quisition in power to-day, we should all, like 

 Galileo, be put to the torture. Need we then 

 blame the physicist if in his intoxication he 

 suspects that the mathematicians may not, 

 after all, be the only experts, that the laws of 

 h's undoing may have been, in a measure, of 

 his own making? 



H.'iwever, I am digressing too far. I will, 

 therefore, reconsign the experimental skeptic 

 to the allurements of his workshop and there 

 he myy grumble as he chooses. 



I implied that it is suspected that the 

 mathematician makes our laws for us. It Is 

 thus necessary to indicate, however superfi- 

 cially, what I mean. When I began my work 

 in Germany in 1876 the theory of Weber, 

 " Das electrodynamische Grundgesetz " of 

 1846, was rife in that country and had even 

 invaded France (c/. Briot, ThermodjTiamique) 

 and the other countries of continental Eu- 

 rope. Electrodynamics through the genius of 

 Ampere (1821-22), had already definitely cap- 

 tured magnetism. Weber embraced the whole 



of electromagnetics in a single equation, con- 

 sistent with the law of the conservation of 

 energy. It was a beautiful theory; but it was 

 action at a distance gone mad. Such indeed 

 was the rage of these theories at the time that 

 even Gauss and Riemann did not escape 

 temptation, while Clausius revised and modi- 

 fied the argument throughout, bringing out a 

 new theory of his own. I doubt whether any 

 one here has read that theory. I have never 

 seen it referred to and yet it is a superb piece 

 of vigorous mathematical reasoning, quite 

 worthy of Clausius. 



I am induced to pause for a moment to 

 speak of Weber himself, a singularly lovable 

 child-like man, to all appearances hopelessly 

 unpractical, so much so, that many of his inti- 

 mates were wont to poke fun at him. But 

 Weber, like his friend Gauss, was a profound 

 mathematical thinker and in that capacity 

 introduced two of the most practical things 

 which the practical world has inherited; for 

 the electric telegraph is a Gauss- Weber in- 

 vention (1833) ; and what we now call our 

 C.G.S. system of units is fundamentally the 

 creation of Weber (1852) again following 

 Gauss (1832). A man may, therefore, be 

 practical even if he sometimes fails to drive 

 a nail straight. 



To resume: what these men did was to pos- 

 tulate a force which depended upon the states 

 or motion of the point where force originates; 

 but any phase of the force hammers away at 

 any distant point co-temporaneously with the 

 time of its origin. These electrical forces, in 

 other words, did what gravitational forces stUl 

 persist in doing. If we glance back at such 

 theories from our present point of van- 

 tage, we can not but marvel how perilously 

 near they came to the state of the case as we 

 know it to-day. If they had only retarded 

 their potentials! It is all the more curious 

 that they suspected nothing, as the 3 X 10^° 

 velocity which characterizes the relation of 

 Weber's electrostatic to his electromagnetic 

 system of units, measured by Weber and 

 Kohlrausch in 1856, is the velocity of light. 



The respite accorded to any of these theories 

 was brief. In England they were vigorously 



