478 Intelligence and Miscellaneous Articles. 



3. The azimuth of the incident vibration can thus be brought to 

 be such that the two principal components of the reflected vibration 

 will be equal. This azimuth is again determined by pairs of obser- 

 vations whose only inferiority to the preceding is their not having 

 a constant sum (the source being so), but which, like them, have 

 the advantage of being swift, grouped in pairs independent of one 

 another, and terminated by two equal values of the galvanometric 

 deflections. 



4. If we designate by <u the azimuth of the bisectrices of the axes 

 of the ellipse (the incident ray vibrating at 45°), by a the azimuth 

 of the incident vibration which renders the two principal reflected 

 components equal, by 8 the difference of phase produced by the 

 reflection, and, lastly, by I and J the absolute numbers by which 

 the reflection multiplies the amplitude of the principal components, 

 we have the two relations 



cos c= — and - = tana to determine - aud S*. 



tan 2a J J 



If the Tables (p. 479) be compared with that given by M. Jamint for 

 the red, the analogy is remarkable. In each of them the rate is seen 



to increase with the incidence, pass through -r at 76° with the red, 



at 79° with \ v at 82° with \ 2 , and at 83°-5 with \ 3 . To these in- 

 cidences always corresponds a minimum value of the amplitude - 

 ratio. 



Let us now turn our attention to the two quantities which " enter 

 as constants into the formulae of metallic reflection, viz. (1) the 

 incidence of the polarization restored after two reflections from 

 parallel mirrors, (2) the polarization-azimuth of the reflected ray 

 under this incidence when the initial azimuth is equal to 45° "J. 

 The first is the incidence for which the difference of rate is a 

 quarter of an undulation ; it is therefore 79° for \, 82° for X 2 , 

 83°'5 for X 3 . As to the second, if we designate it by (1, we have 



I 2 



tnn(3=-r-, whence tan (3= tan 2 a; we then find for /3 the values 

 J 



15° 40' for \, 14°-5 for \, and 13° 20' for X 3 . And, on comparing 



these results with the Table § in which M. Jamin has given the 



values of these two principal quantities, proceeding from the violet 



to the red, we see that the azimuths of the restored polarization, 



which diminish for steel from the violet to the red (from 21° to 



10° 20'), continue to do so beyond, while the principal incidences, 



which increase from the violet to the red (from 73° to 77° 52'), 



continue the series of their increasing values in proportion as we 



advance into the obscure radiations. 



Permit me, in conclusion, to express my acknowledgements to 

 M. Desains : his assistance and daily counsels have been a great 

 help to me in carrying out this investigation. — Comptes Rendus de 

 VAcademie des Sciences, April 2, 1877, tome lxxxiv. pp. 650-653. 



* See M. Jamin's "Discussion theorique," Ann. de Chim. et de Phys. 

 3 e serie, t. xix. p. 276. t Ibid. t. xix. p. 317. 



X Ibid. t. xxii. p. 313. § Ibid. p. 316. 



