358 Light dispersed from Lines or transmitted by Slits. 



My own observations are in essential agreement with 

 Fizeau. At first accidental scratches upon silver surfaces 

 which had been worked in one direction were employed. 

 Afterwards I had the opportunity of observing specially fine 

 lines ruled with a diamond by a dividing-engine, for which 

 I am indebted to Lord Blythswood. In the latter case the 

 plate was of speculum-metal. 



It will be seen that the theory agrees with observation 

 well in some respects, but fails in others. When a and <£> 

 are both less than 90° and of the same sign, the polarization 

 expressed by (35) sufficiently represents the facts. But there 

 is little in the observations to confirm the strongly reversed 

 polarization which should occur when the denominator in (35) 

 becomes small. One defect of correspondence in the con- 

 ditions of theory and experiment is obvious. The former 

 relates to semi-cylindrical excrescences, while the observations 

 are made upon light dispersed from scratches which are 

 mainly depressions. In order to examine the question thus 

 arising, a glass plate provided with suitable scratches was 

 coated chemically with silver upon which copper was after- 

 wards deposited by electrolysis. When the coating thus 

 obtained was stripped from the glass, a highly reflecting 

 surface was obtained in which the original scratches are 

 represented by precisely fitting protuberances. But even 

 with this I was unable to find the strongly reversed polarization 

 to be expected according to (35) when (36) is nearly satisfied. 



If we trace back the denominator in (35), we find that it is 

 derived from the factor (^--f cos#) in (26), and that its 

 evanescence depends upon the antagonistic effects of the 

 terms which are symmetrical and proportional to cos 6. The 

 precise form of this factor is doubtless connected with the 

 assumption of a circular cross-section, but the discrepancy 

 from observation seems almost too complete to be attributed 

 to such departures from the theoretical shape. As other 

 possible sources of discrepancy we may note the assumption 

 of reflecting power which is absolutely complete, and again 

 that the dimensions of the line are small in comparison with 

 the wave-length. It may be that lines sufficiently fine to 

 justify (35) in its integrity would not reflect enough light 

 to be visible. At the same time the evanescence of II with 

 a. or cj) does not demand such a high degree of fineness. 



In the memoir already cited Fizeau treats also the polari- 

 zation impressed upon light which traverses fine slits. Thus 

 (p. 401): " Une lame d'ar gent tres-mince, depose chimique- 

 ment sur le verre, a ete rayee en ligne droite, avec de l'emeri 

 tres-fin ; c'etait un fragment de la lame designee precedem- 

 ment par la lettre (A), et dont l'epaisseur a ete trouvee de 



