382 



NATURE 



YAtigust 25, 1 88 1 



look like the so-called supplementary eyes along the belly 

 and tail, the rare Macrurus sclerorhyncus, Hoplostctlius 

 Mediterrancus, and Hatoporpiiyrus li-pidion, from depths 

 of 508, 656. 860, and 1125 metres. We have at least two 

 species ol Tercbratula from depths varying from 600 to 

 1 200 metres. Several most interesting Crustaceans 

 besides those mentioned, and even a non-swimming 

 Brachyurous Decapod, from 1125 metres! But what is 

 still more interesting is the capture of several specimens 

 of a Hya/oiic-i/ia, very probably H. Lusitanica, but without 

 any spiral twist in its long spicute ; we got them off the 

 south and east coasts of Sardinia, in depths from 1600 

 to 623 metres ; we have, besides, several other forms of 

 Sponges, all siliceous, and several of a curious agaric-hke 

 form. We have a Brisinga from depths of 2145 to 2300 

 metres, but very few other Echinoderms ; I do not yet 

 give up the hope of seeing a Pentacrinus before our 

 cruise is ended. We have, as I mentioned, various 

 Annelids and Gephyreans, and some fine species of 

 Madreporia of the deep-sea forms. 



We have an interesting set of serial thermometric obser- 

 vations, which show that there is a slight difference in the 

 bottom temperature between the basins east and west of 

 Sardinia, the latter being slightly colder. Negretti and 

 Zambra's new deep-sea thermometers have answered 

 admirably, suspended in the peculiar frame devised by 

 Capt. Magnaghi. Henry Hillyer Giglioli 



Naples, August 20 



ON THE VELOCITY OF LIGHT 

 'T'HE result announced by Young and Forbes (Roy. 

 J- Soc. Proc, May 17, iSSi) that blue light travels in 

 vacuo about rS per cent, faster than red light, raises an 

 interesting question as to what it is that is really deter- 

 mined by observations of this character. If the crest of 

 an ordinary water wave were observed to travel at the 

 rate of a foot per second, we should feel no hesitation in 

 asserting that this was the velocity of the wave ; and I 

 suppose th.it in the ordinary language of undulationists 

 the velocity of light means in the same way the velocity 

 with which an individual wave travels. It is evident 

 however that in the case of light, or even of sound, we 

 have no means of identifying a particular wave so as to 

 determine its rate of progress. What we really do in 

 most cases is to impress some peculiarity, it may be of 

 intensity, or of wave-length, or of polarisation, upon a 

 part of an otherwise continuous train of waves, and de- 

 termine the velocity at which this peculiarity travels. 

 Thus in the experiments of Fizeau and Cornu, as well as 

 in those of Young and Forbes, the light is rendered inter- 

 mittent by the action of a toothed wheel ; and the result is 

 the velocity of the group of waves, and not necessarily 

 the velocity of an individual wave. In a paper on Pro- 

 gressive Waves i^Ptoc. Math. Soc. vol. ix.), reprinted as 

 an appendix to vol. ii. of my book on the " Theory of 

 Sound," I have investigated the general relation between 

 the group-velocity U and the wave-velocity V. It appears 

 that if /• be inversely proportional to the wave-length, 

 TT-d{kV) 

 dk ' 

 and is identical with V only when V is independent of /', 

 as has hitherto been supposed to be the case for light in 

 vacuum. If however, as Young and Forbes believe, V 

 varies with k, then 1/ and V are different. The truth is 

 however that these experiments tell us nothing in the first 

 instance about the value of V. They relate to Uy and if 

 ris to be deduced from them it must be by the aid of 

 the above-given relation. 



When we come to examine more closely the form of 

 this relation, we see that a complete knowledge of V (as 

 a function /!•) leads to a complete knowledge of W, but that 

 a complete knowledge of 6^— all that experiments of this 



kind can ever give us — does not determine V, without the 

 aid of some auxiliary assumption. The usual assumption 

 is that V is independent of k, in which case i/ is also 

 independent of k. If we have reason to conclude from 

 observation that i/ is not independent of k, this assump- 

 tion is disproved ; but we can make no progress in 

 determining F until we have introduced some other. 



It is not easy to see how the missing link is to be 

 supplied ; but in order to have an idea of the probable 

 magnitude of the difference in question I have assumed 

 the ordinary dispersion formula F= A + B k- to be 

 applicable. Taking the ratio of wave-lengths of the 

 orange-red and green-blue lights employed as 6 : 5, I find 

 that for red light K= L/ (1 - -0273), so that the velo- 

 city of the wave would be nearly 3 per cent, less than 

 that given by Young and Forbes as the result of the 

 experiment. 



Under these circumstances it becomes a matter of 

 interest to examine the bearing of other evidence on the 

 question of the velocity of light. Independently of the 

 method of the toothed wheel, the velocity of light has 

 been determined by Foucault and Michelson using the 

 revolving mirror. It is not very obvious at first sight 

 whether the value thus arrived at is the group-velocity 

 or the wave-velocity, but on examination it will be found 

 o be the former. The successive wave-fronts of the 

 light after the first reflection are not parallel, with the 

 consequence that (unless V be constant) an individual 

 wave-front rotates in the air between the two reflections. 



The evidence of the terrestrial methods relating ex- 

 clusively to U, we turn to consider the astronomical 

 methods Of these there are two, depending respectively 

 upon aberration and upon the eclipses of Jupiter's satel- 

 lites. The latter evidently gives U. The former does 

 not depend upon observing the propagation of a pecu- 

 Harity impressed upon a train of waves, and therefore has 

 no relation to U. If we accept the usual theory of 

 aberration as satisfactory, the result of a comparison 

 between the coefficient found by observation and the 

 solar parallax is V —the wave-velocity. 



The question now arises whether the velocity found 

 from aberration agrees with the results of the other 

 methods. A comparison of the two astronomical deter- 

 minations should give the ratio U : V, independently of 

 the solar parallax. Ths following data are taken from 

 Mr. Gill's " Determination of the Solar Parallax from 

 observations of Mars made at the Island of Ascension in 

 1877." 



The time k, required by light to travel a mean radius 

 of the earth's orbit, has been determined by two astro- 

 nomers from the eclipses of Jupiter's satellites. Delambre 

 found, from observations made in the last century, 

 k = 493'2s., but recently Glasenapp has obtained from 

 modern observations the considerably higher value, 

 X- = 500-S5. ± I-02. With regard to the constant of 

 aberration, Bradley's value is 2o""25, and Struve's value 

 is 2o"'445. Mr. Gill calculates as the mean of the best 

 modern determinations (nine in number), 2o"'496. 



If we combine Glasenapp's value of /• with Michel- 

 son's value of the velocity of light, we get for the solar 

 parallax 8"76. Struve's constant of aberration in con- 

 junction with the same value of the velocity of light gives 

 8 "-Si. From these statements it follows that if we regard 

 the solar parallax as known, we get almost the same velo- 

 city of light from the eclipses of Jupiter's satellites as 

 from aberration, although the first result relates to the 

 group velocity, and the second to the wave velocity. If 

 instead of Struve's value of the constant of aberration 

 we take the mean above spoken of, we get for the solar 

 parallax 8"78, allowing still less room for a difference 

 between U and V. 



Again, we may obtain a comparison without the aid of 

 the eclipses of Jupiter's satellites by introducing, as other- 

 wise known, the value of the solar parallax. Mr. Gill's 



