THE AID OF THE ACHROMATIC FRINGES. 113 



also interesting; for here the ellipses are apt to be circles with each of the two 

 groups a and b seen after two reflections, one in each of the orthogonal faces. 

 The light should enter nearly normal to the oblique face of the prism. 



Reflection from the face of the observer, if in high light, is adequate, but it 

 is preferable to look through a horizontal slot in a well-illuminated piece of 

 white cardboard, held at a small distance parallel to the oblique face of P. 

 The vertical side of P is therefore toward the source of light. Totally reflected 

 rays are again to be avoided; but the circles about axes, such as a and b, open 

 out through flower- like forms, into the usual parallel fringes at the limit of 

 total reflection, when the angle is approached (successively) by the two faces. 

 After this, in a well-adjusted apparatus, the black spot is apt to stand out 

 with striking clearness on an intensely white surface. 



I may add a correlative observation : If a cylindrical lens (say i diopter) is 

 placed on a plate and illuminated with homogeneous light, the interference 

 pattern consists of a succession of equidistant arrowheads along the line of 

 contact, all pointing in its direction. Now, these are the very forms observed 

 in the interferences of reversed spectra along the line of coincidence of spectra, 

 except that the latter are apt to be far narrower than the former. It seems , there- 

 fore, as if the effect of color variation in one case and of the cylindric increase 

 of thickness of air-film in the other were formally capable of like treatment. 



85. Measurement of small angles by a half=silver plate. In case of the 

 rectangular interferometer the slit-images contain a second method of meas- 

 uring small angles, which, though naturally inferior to the fringe method, is 

 not insensitive and may often be used with advantage independently. I shall 

 indicate this briefly by the aid of figure 112. Here LL' or LiL/ represent the 

 directions of rays of parallel white light issuing from a collimator. If the latter 

 are used the mirror N is superfluous ; but it is an essential part of the inter- 

 ferometer. They pass through the half-silver N", are reflected from the auxili- 

 ary mirror m in two positions, respectively, G radians apart, and then enter 

 the telescope at T in parallel, T being the fixed line of sight. Let PP' be the 

 princ'pal plane of the objective of the collimator with the optical center at O 

 and a focal length/, and let a micrometer plate 55 replace the slit with its fine 

 linear scale running parallel to the diagram. Then it is obvious that if y is 

 the displacement of this scale seen in the telescope, 



Q = y/2/=x/h 



if an object at a distance h from the axle a moves over the distance x. 



For instance, let a centimeter divided into 100 parts be used at 55 and let 

 / be a meter. If T is a strong telescope (magnification 25), lo- 3 cm. may be 

 estimated at T, so that 9= io- 3 /2Xio 2 = 5Xio- 6 ; i.e., the limit of measure- 

 ment is a second of arc. Good instruments are needed if / is a meter. I have 

 more often worked with 7=25 to 50 cm. when ordinary facilities (common 

 plate) suffice and the results are still very sharp. A small gas-flame suf- 

 fices for illuminating ss. Ith=io cm., x is determined to about a wave-length. 

 8 



