64 C. S. Hastings — Double Refraction in Iceland Sjyar. 



from it and each other by quadrants, which are subdivided to 

 tenths of a degree. The observing telescope may be moved 

 independently or clamped to the circle; it is checked in its 

 rotation only by the collimating telescope. It is obvious that 

 by this construction it is always possible to measure an angle so 

 that one end of the arc shall be at a degree mark and the other 

 end fall within a subdivided degree ; hence both ends of the 

 arc are within the range of the reading microscopes. The 

 great and manifest advantage of this construction is that every 

 angle can be accurately measured after determining the abso- 

 lute place of only 396 lines or 198 diameters. 



The reading microscopes have micrometer screws of .80 

 threads to the inch, with heads divided into 100 parts, one rev- 

 olution of the screw being equal to one minute of arc. The 

 magnifying power is 220 diameters, doubtless unnecessarily 

 high, but not found inconvenient, and a much lower power 

 would have necessitated a notable change in the design, either 

 finer micrometer screws or longer microscopes with correspond- 

 ingly higher table and telescope carrier. The probable error 

 of a single setting of the microscope was found to be less than 

 0"'3, or less than half a division of the micrometer head. 



The errors of the circle were determined by means of two 

 auxiliary microscopes clamped to the base-plate of the instru- 

 ment at opposite sides. By bisections and trisections the ab- 

 solute position was determined of each diameter at multiples of 

 5° from the initial diameter, to within a probable error of less 

 than 1". As practically every such interval was involved in 

 the observations several times, equations of condition were 

 formed as checks upon the results ; if a discrepancy as great as 

 V was found the intervals were re-measured. A determination 

 of any angle was thus reduced to a maximum of five repeti- 

 tions, whence the true angle could be found, and, incidentally, 

 the corrections of four other arcs. As an illustration of the 

 precision of the method, I may state that in the only case where 

 a suspicion of the accepted value led to a complete redetermi- 

 nation of all the constants involved, the correction deduced 

 differed only 0"'\ from the former one. The origin of the 

 suspicion was afterwards found to be a false temperature cor- 

 rection. This determination of the errors of the circle was the 

 most laborious part of the whole investigation. 



(4) Angles of prism. 



The angles measured were those between the normals to the 

 faces P and Q, Q and R, R and P, which were made with all 

 attainable accuracy ; those between the normal to P, and the 

 normals to its three adjacent cleavage faces ; the normal angle 



