3o8 THE POPULAR SCIENOE MONTHLY 



ADDRESS BEFORE THE AMERICAN ASSOCIATION. 1 



By Prof. JOSEPH LOVEPJNG. 



II. 

 Mathematical Investigations in Physics. 



I AM thus suddenly brought face to face with the second head of 

 my subject : the mathematical and philosophical state of the 

 physical sciences. 



The luminiferous ether and the undulatory theory of light have 

 always troubled what is supposed to be the imperturbable character 

 of the mathematics. The proof of a theory is indisputable when it 

 can predict consequences, and call successfully upon the observer to 

 fulfill its prophecies. It is the boast of astronomers that the law of 

 gravitation thus vindicates itself. The undulatory theory of light has 

 shown a wonderful facility of adaptation to each new exigency in 

 optics, and has opened the eye of observation to see what might 

 never have been discovered without the promptings of theory. But 

 this doctrine, and that of gravitation also, have more than once been 

 arrested in their swift march and obliged to show their credentials. 

 After Fresnel and Young had secured a tirni foothold for Huyghens's 

 theory of light in mechanics and experiment, questions arose which 

 have perplexed, if not baffled, the best mathematical skill. How is 

 the ether affected by the gross matter which it invests and permeates? 

 Does it move when they move ? If not, does the relative motion be- 

 tween the ether and other matter change the length of the undulation 

 or the time of oscillation ? These queries cannot be satisfactorily an- 

 swered by analogy, for analogy is in some respects wanting between 

 the ether and any other substance. Astronomy says that aberration 

 cannot be explained unless the ether is at rest. Optics replies that 

 refraction cannot be explained unless the ether moves. Fresnel pro- 

 duced a reconciliation by a compromise. The ether moves with a 

 fractional velocity large enough to satisfy refraction, but too small 

 to disturb sensibly the astronomer's aberration. In 1814, Arago re- 

 ported to Fresnel that he found no sensible difference in the prismatic 

 refraction of light, w r hether the earth was moving with full speed 

 toward a star or in the opposite direction, and asked for an explana- 

 tion. Fresnel submitted the question to mathematical analysis, and 

 demonstrated that, whatever change was produced by the motion of 

 the prism in the relative velocity of light, the wave-length in the 

 prism, and the refraction, was compensated by the physiological aber- 

 ration when the rays emerged. Very recently, Ketteler, of Bonn, has 



1 Retiring Address before the American Association for the Advancement of Science 

 at the Hartford meeting, August 14, 18*74, by the ex-Preeident. 



