PREFACE. 7 



as large as several degrees come naturally within the scope of the method. 

 Similar remarks may be made with respect to the ratio of angular displace- 

 ment and micrometer displacement. Given, therefore, an apparatus which 

 measures very small angles without constraint or forced approximations, the 

 measurement of long distances is the next result in order; for it is merely 

 necessary to place the angle to be measured at the apex of the distance triangle 

 on the length of the ray parallelogram as a base. This may be done in a 

 variety of ways, some of which are shown in the chapter. The sensitiveness 

 may again be made remarkably large. 



The fringes here in question are preferably the very luminous achromatic 

 fringes. They have been identified as ultimately colors of thin plates, but 

 they look like Fresnel's fringes. In connection with this work, however, 

 another type of fringes was detected obtainable with a fine slit, white light, 

 and in case of centered spectrum fringes when the ocular of the telescope 

 (or the eye) is out of focus. These are actually Fresnellian interferences, 

 but being made up of broad concentric hyperbolic areas, brilliantly comple- 

 mentary in color, they resemble the lemniscates of biaxial crystals without 

 the shadows. 



My thanks are due Miss Lena F. Uhlig, who has assisted me efficiently in 

 the preparation of this volume for the press. 



CARL BARUS. 

 BROWN UNIVERSITY, 

 Providence, Rhode Island, June 1917. 



