524 Mr. A. E. Oxley on an Apparatus for the 



If ^ = 54° 37', which is the angle of Fresnel's rhomb 

 (fi being 1/1*51) equation (6) gives 



dA =±0°-203, 



C— F 



and there being two reflexions the extreme phase-difference 

 for the C — F interval amounts to + 0°'406. Hence, the 

 variation of A with /j, is only half as great in the Bi-rhomb 

 as it is in Fresnel's rhomb, for a given wave-length. 



Ihe dimensions of the Bi-rhomb. — Owing to the large value 

 of yfr the Bi-rhomb for a given aperture is rather incon- 

 veniently long. If S denote the aperture, and % the angle 

 of the rhomb, the length in the direction of the incident 

 light when the full aperture is utilized will be 



{ 



S < tan % — 



tan 2^; -f cot^ 



and if A be 1*1 cms., and -^ = ^ = 74° 38', the length is 

 7*4 cms. This has to be doubled, and the total length of 

 the Bi-rhomb of aperture 1*1 cms. is approximately 15 cms. 

 Since, however, the value of dA for i|r = 42° 34'"8 for the 



c — ¥ 

 four reflexions amounts to ±3°*6, it is better to sacrifice 

 compactness for efficiency. 



In many experiments the length of the Bi-rhomb may be 

 no serious objection to its use, but by the following method 

 involving three reflexions an apparatus has been devised 

 which combines practically all the advantages of the form 

 just considered with compactness. ABODE in fig. 3, shows 



Fig. 3. 



the bi-trapezoidal form of the section. The faint lines show 

 the trace of a beam of light through the instrument, the 

 beam passing through symmetrically with respect to the line 

 EF. Thus the emergent beam, although it has suffered 

 lateral inversion, is not displaced as a whole from the 

 incident beam. 



If <f> be the angle of incidence on the face AE, <j> is the 

 angle of reflexion from the face ED. Let <f>' be the angle of 

 incidence on the face BO. Clearly <j>' must be greater than 



