S68 Messrs. du Bois and Eubens on Refraction 



I. Refraction. 



§ 6. Measurements of the deviation on oblique transmission 

 of light through the prisms would have possessed but little 

 intrinsic interest. We had therefore first to find a legitimate 

 way of developing, from our measurements, the relation 

 which must needs exist between the inclinations of the wave- 

 fronts in metal and air respectively to the surface separating 

 both media. In doing so we wished to avoid all auxiliary 

 hypotheses, and to base our inferences on none of the optical 

 theories at present in vogue. The following treatment of the 

 problem before us will show how far we have reached the end 

 in view on the lines thus prescribed. 



§ 7. Notation. — Accurately " parallel " light having been 

 always used, we have to consider plane wave-fronts, and in 

 particular the direction of their normals. Let the angles of 

 these directions with the normals to the prisms'' surfaces be 

 denoted by i m in the metal, i in the air. These are evidently 

 also the inclinations of the wave-fronts on either side of the 

 bounding surface metal | air. For the refractive index we 

 write the usual symbol n ; it has to be borne in mind that the 

 index has a strictly physical meaning only when Snellius's 

 sine law* holds absolutely or infinitely nearly (see § 12). 



' The angle between the normals Ni and N 2 to the two surfaces 

 of the biprism, as directly measured by Gauss's eyepiece, will 

 be called the " refracting angle" /3 ; it is the sum of the angles 

 of the two prisms. The angle between two pencils of light, 

 originally parallel, then each transmitted through a different 

 prism, is the deviation a. /3 as well as a may be considered 

 infinitely small for our present purpose ; the mathematical 

 treatment of the subject is thereby reduced to great simplicity. 



§ 8. Mode of Calmlation. — Fig. 1 represents a horizontal 

 cross-section of our biprisms, of course not drawn to scale. 

 The two surfaces are numbered 1 and 2, these numbers being 

 also used as suffixes to distinguish quantities related to one or 

 the other surface. Now consider two infinitely thin pencils 

 of light, 1 and 2, parallel to one another ; evidently these 

 will continue parallel in the metal M up to points A l and A 2 

 infinitely near the surfaces 1 and 2. This is still the case if 

 the glass plate or the film of platinum or both be wedge- 

 shaped (as indeed they always are more or less). The paral- 



* The ordinary law of refraction still often goes by the name of 

 Descartes ; however, there can be no doubt but that the Dutch mathema- 

 tician Willebrord Snell was the first to enunciate it. 



