176 BELL SYSTEM TECHNICAL JUURXAL 



ference between velocity of groups and velocity of wave-crests; they 

 both have the same universal constant value c. However this cannot 

 be true for light in transparent material media such as glass, water, 

 or carbon bisulphide; for the refractive index of all these media varies 

 from one wave-length to another — they are said to be dispersive. 



Now Michelson measured the time taken by a flash of light to cover 

 a measured distance, first through air (very nearly the same as vacuum) 

 then partly through air and partly through carbon bisulphide. The 

 source of light shines continuously, and an incessant beam falls on a 

 revolving mirror and is reflected in a continuously-changing direction; 

 a second, stationary mirror receives this reflected beam during a very 

 small fraction of each complete revolution and sends it back, so that 

 the twice-reflected beam is a series of segments cut from the primary 

 beam. It was the time taken by the segments to travel a known dis- 

 tance which Michelson measured.^ Reasoning back from the data, 

 he computed that they took (1.76 ± 0.02) times as long to go a given 

 distance in carbon bisulphide as in air. But the refractive index of 

 carbon bisulphide, in the range of the spectrum where Michelson's 

 source of light was brightest, is about 1.63; so that the primitive wave- 

 front-theory gives 1.63 for the ratio of the speeds in air and CS^, 

 and the corpuscle-theory gives (1.63)~^ 



Foucault and Fizeau, be it remembered, had done the experiment 



with water. It happens that for water the derivative dvld\ is much 



smaller, and the group-speed therefore much closer to the wave-speed, 



than for carbon bisulphide. Also their experiments, though performed 



by the same method as Michelson was later to adopt and adapt, were 



less accurate than his. But if they had performed the Michelson 



experiment in 1850, the result would have been astounding. For 



Arago had asked, in effect: is it the speed of the wave-fronts in the 



wave-theory, or the speed of the corpuscles in the corpuscular theory, 



which agrees with the measured speed of a piece of light? Arago had 



said: "These experiments . . . will permit no further hesitation as 



between the rival theories. They will settle mathematically (I employ 



this word on purpose) they will settle mathematically oneof the greatest 



and most disputed questions of natural philosophy." He had proposed 



a question to Nature, and had written down two and only two answers. 



Everyone thought that Nature must reply by ratifying one of the 



9 When the segments returned from the second to the first mirror they found that 

 the latter had revolved a little further beyond the oiientation which it had when 

 they left it, so that it reflected them onward not quite along the path to the source of 

 light, but along another path inclined to that one at an angle twice as great as that 

 through which it had revolved. Michelson measured the angle, and knowing the 

 rate of revolution of the revolving mirror he then knew how long the light had taken 

 to go from it to the stationary mirror and back. 



