Mathematical and Philosophical State of the Physical Sciences. 493 



expansion being transmitted to a very delicate indicator. I hope 

 hereafter to communicate the results of such experiments as may 

 show how far the other metals differ in their behaviour from 

 mercury. 



LXVI. The Mathematical and Philosophical State of the Phy- 

 sical Sciences. By Professor Joseph Lovering*. 



'T'HE luminiferous aether and the undulatory theory of light 

 have always troubled what is supposed to be the imperturb- 

 able character of the mathematics. The proof of a theory is 

 indisputable when it can predict consequences, and call success- 

 fully upon the observer to fulfil 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 dis- 

 covered 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 firm 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 aether affected by the gross matter which it invests 

 and permeates ? Does it move when they move ? If not, does 

 the relative motion between the sether and other matter change 

 the length of the undulation or the time of oscillation ? These 

 queries cannot be satisfactorily answered by analogy ; for analogy 

 is in some respects wanting between the aether and any other 

 substance. Astronomy says that aberration cannot be explained 

 unless the aether is at rest. Optics replies that refraction cannot 

 be explained unless the aether moves. Fresnel produced a recon- 

 ciliation by a compromise : — the aether moves with a fractional 

 velocity large enough to satisfy refraction, but too small to dis- 

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

 ported to Fresnel that he found no sensible difference in the 

 prismatic refraction of light, whether the earth was moving with 

 full speed toward a star or in the opposite direction, and asked 

 for an explanation. Fresnel submitted the question to mathe- 

 matical analysis, and demonstrated that, whatever change was 

 produced by the motion of the prism in the relative velocity of 



* From the Presidential Address of Professor Lovering before the 

 American Association at Hartford, August, 1874 (Silliman's American 

 Journal, October, 1874, p. 297). 



