April 2S, 1916] 



SCIENCE 



585 



magnet acts upon another; and a current 

 closed or broken in one circuit occasions a 

 current in another closed circuit. Experi- 

 mental studies of these phenomena by Fara- 

 day and Weber revealed quantitative laws, 

 but seemed to show instantaneous effects — 

 forces acting at a distance with no delay in 

 time. The marvellous intuition of Faraday, 

 not himself an analyst, but certainly a pro- 

 found inventor of geometric motions, 

 created an ideal structure of tubes of force, 

 with something flowing through them under 

 hydrodynamical laws. This bold concept 

 served as basis for the calculations of three 

 mathematical minds that took up his great 

 problem. Sir William Thomson, later 

 known as Lord Kelvin, Heknholtz and 

 James Clerk-jMaswell, each in his own way 

 set forth, in precise notations, equations de- 

 scribing the amount and direction of the 

 transmitted forces. Thomson and Helm- 

 lioltz ventured hypotheses upon the nature 

 of the transmitting medium and its mo- 

 tions, culminating in those vortex-rings and 

 vortex-sheets which were studied eagerly 

 two decades ago. 



A closed vortex-filament in a perfect 

 fluid was shown to be indestructible, and 

 ardent was the hope that properties and 

 differences of vortices would be found 

 analogous to those of the indestructible 

 atoms of chemistry. But the third. Max- 

 well, penetrated in another direction, and 

 showed "what ought to be the rate of trans- 

 mission of electrical impulses or waves, 

 through an ether such as carries waves of 

 light. The result, that electrical effects 

 travel with the speed of light waves, shows 

 logic outrunning even imagination. Hertz, 

 almost the equal of these three as a mathe- 

 matician, still greater as an experimenter, 

 actually sent out and collected again such 

 waves, a hundred thousand times longer 

 than waves of light, reflecting and refract- 

 ing them like light, and so confirmed the 



speculative conclusions of Clerk-Maxwell. 

 In this exciting race to show the analogy, 

 resemblance, or even identity of things ap- 

 parently unlike, the study of vortex-rings 

 was suffered to lapse. Or was it because 

 physicists perceived that atoms were not so 

 simple as had been supposed ; that it would 

 require, for the explanation of a single 

 atom, more than one ring, however intri- 

 cately self -involved 1 At any rate, there re- 

 mains that one fragment of theory to be 

 revalued and completed by some genius of 

 a future generation. 



Certain passages in the preface of Max- 

 well's "Electricity and Magnetism" show 

 so clearly the relation of mathematical to 

 experimental science that I can not refrain 

 from extracting them verbatim; but first 

 I will quote a general remark from Samuel 

 Beidler upon accuracy. 



The appreeiation of the value of accuracy is a 

 thing of modern date only — a thing which ve owe 

 mainly to the chemical and mechanical sciences, 

 wherein the inestimable difference between pre- 

 cision and inaccuracy became most speedily ap- 

 parent. 



Maxwell's idea of the way in which de- 

 ductive methods come to be applied to phe- 

 nomena is compressed into these two pas- 

 sages. Observe that measurement is funda- 

 mental. 



I propose to describe the most important of 

 these phenomena [electromagnetic], to show how 

 they may be subjected to measurement and to 

 trace the mathematical connections of the quanti- 

 ties measured. Having thus obtained the data for 

 a mathematical theory of electromagnetism, and 

 having shown how this theory may be applied to 

 the calculation of phenomena, I shall endeavor to 

 place in as clear a light as I can the relations be- 

 tween the mathematical form of this theory and 

 that of the fundamental science of dynamics, etc. 



There are several treatises in which electrical 

 and magnetic phenomena are described in a popu- 

 lar way. These, however, are not what is wanted 

 by those who have been brought face to face with 

 quantities to be measured, and whose minds do not 

 rest satisfied with lecture-room experiments. 



