July 18, 1902.] 



SCIENCE. 



well as in the ether, we cannot be assured 

 that we are entitled to consider the deter- 

 mination by the group methods used here- 

 tofore as sufficient to give us the absolute 

 velocity of light. Even if we regard the 

 evidence from astronomical obsetvations of 

 the common velocity in space for all colors, 

 and from this conclude that the absolute 

 velocity is the group-velocity, as the equa- 

 tions of Lord Rayleigh show with the as- 

 sumptions he makes, we are still lacking 

 sufficient data for the relation in the case of 

 ponderable media. 



In the discussion of the results by the 

 toothed-wheel method and the rotating- 

 mirror method, considerable difference of 

 opinion has been expressed as to just what 

 we obtain by the latter method. There 

 seems to be no dissenting opinion that the 

 toothed-wheel method gives the group-ve- 

 locity directly, for here we have the time of 

 transit of an interrupted beam of light. In 

 the rotating-mirror method the ray is also 

 intermittent. Lord Rayleigh seems first to 

 have raised the interesting question as 

 to what is actually measured in these ex- 

 periments, and in his first note states that 

 the rotating-mirror method gives the group- 

 velocity U. In a later article he arrives at 

 a different result and gives the square of 

 the wave-velocity divided by the group- 

 velocity, V^/U. Evidently unless we know 

 the relation of the two we can find neither 

 if this be correct. Now this relation is not 

 certainly known as pointed out above. On 

 the other hand Gouy, however, dissents 

 from this second view and shows that the 

 group-velocity U is the quantity determined 

 by the rotating-mirror method. Schuster in 

 a later article dissents from Gouy's con- 

 elusion and corrects Lord Rayleigh 's second 

 result, and gives the square of the wave- 

 velocity divided by twice the wave-velocity 

 minus the group velocity, V^/(2'V—'V). 

 J. Willard Gibbs in a later article points out 

 an error in the derivation of this relation 



by Schuster and shows that the group- 

 velocity is after all what is determined by 

 the rotating-mirror method. He shows fur- 

 ther that the results of Michelson's observa- 

 tion on carbon disulphide give a closer 

 agreement with the refractive index with 

 this conclusion than with the conclusion ar- 

 rived at by Schuster. Lord Rayleigh sug- 

 gests in his second note that by placing a 

 lens in the path of the ray so that the fixed 

 mirror is at its focus the rotation of the 

 wave-front caused by the rotating mirror 

 would be corrected on the return and we 

 should thus find the absolute velocity V. 

 This is evidently in error, as Schuster show- 

 ed, as the rotations would be added. Even 

 if neutralized we should not obtain V, but 

 U. In a reply to a communication by the 

 writer to Lord Rayleigh in 1890 as to such a 

 method for the absolute velocity he has indi- 

 cated a misapprehension on this matter and 

 expressed his opinion as to the probable 

 correctness of Professor Gibbs 's conclusion 

 which agrees with his first position. With 

 the exception of Schuster the rotating- 

 mirror method seems to be accepted by all 

 as giving the group-velocity. The correc- 

 tion for the rotation between two successive 

 wave planes which is erroneously given by 

 Schuster would give the group-velocity and 

 thus an agreement with the results of the 

 rest. While the observations of Michelson 

 on carbon disulphide give the closest agree- 

 ment with this result, more exact data for 

 specific wave-lengths are desirable in order 

 to confirm the theoretical conclusion. 



In studying the question of group and 

 wave-velocities in connection with disper- 

 sion the following two methods occurred to 

 the writer : The first one was for increasing- 

 the sensibility of the old methods, and the- 

 second one for observing the wave-velocity 

 directly bj^ means of interference. In 1889' 

 he was invited by President Hall to Clark 

 University to conduct, among other things,, 

 an investigation on some special problem. 



