398 Intelligence and Miscellaneous Articles. 



the point where the Luminous ray strikes the retina. Such is the 

 polar equation of the sole-curved fringe (f range en semelle). 



This fringe has two axes of symmetry of unequal length. The 

 shorter axis is given, in orientation and in length, by the two for- 

 mulae : — 1 



tan<3=-_ — , 



tan 2 a cos 6 



, 9 sin 2rr sin $ 



tanz7rp" = 



V 1 — sin 2 2<r sin 2 1 



Hence the following consequences : — 



1. If 2>0 (that is, if the mirror is positive), the minor axis is 

 oriented in the upper right-hand quadrant. 



2. If 2<0 (that is, if the mirror is negative), the same axis is 

 oriented in the upper left-hand quadrant. 



3. If £ = (that is, if the mirror is neutral), the minor axis 

 vanishes. 



4. If S= + - (that is to say, under the principal incidence), the 



minor axis remains oriented at 45°, whatever may be the orienta- 

 tion of the initial vibration. 



5. Under this incidence, wdien the polarizer is rotated, Airy's 

 fringes become transformed into Dove's rings. Let a be the azi- 

 muth obtained; it is that of the restored polarization, connected 

 with the factors of alteration of the amplitudes by the formula 



h 

 tana= -. 



k 



This method is convenient for the study of reflection in general 

 and also of the laws of Cauchy and Jamin ; moreover it is delicate. 

 Indeed, if you employ ordinary glass as the mirror, and observe 

 under an incidence near the polarization-angle, you will recognize 

 that the extremities of the minor axis have an appreciable devia- 

 tion ; and yet the elliptical polarization is so little evident that it 

 escaped Fresnel. 



An interesting experiment consists in arranging in succession 

 three mirrors — of steel, of alum, and of fluorine. The first and the 

 third, being one positive, the other negative, present two contrast- 

 ing positions of the fringe en semelle ; the second, being neutral, 

 offers the transitory phenomenon of conserved rectilineal polariza- 

 tion. — Comjptes Rendus de V Academic des Sciences, March 26, 1877, 

 tome lxxxiv. pp. 604-606. 



NOTE ON MOLECULAR VOLUMES. BY F. W. CLARKE, S.B., 

 PROFESSOR OF PHYSICS AND CHEMISTRY. 



Several years ago, in a series of papers upon atomic or molecu- 

 lar volumes, I pointed out some curious multiple relations connecting 

 both elements and compounds*. For example, I found that a simple 

 relation of this kind connected the alkaline metals with each other; 



* Silliman's American Journal, March and May, 1869 ; September, 1870. 



