1902.] Refractive Indices of Fhiorite, Quartz, and Calcite. 331 



and a condensing lens also of quartz, the whole of more than ordinarily 

 solid construction, was used for the work. On this instrument each 

 degree of the circle is subdivided into 12 parts (of 5' each), and the 

 wheel of the micrometer, one revolution of which corresponds with 

 one subdivision of the circle, is divided into 5 parts (of 1' each), and 

 subdivided into 300 parts (of 1" each), thus rendering the measurement 

 of seconds of arc, and with care fractions of seconds, possible. 

 Iieadings were always taken to 0*25", the quartz fibre of the micrometer 

 being brought into position by turning the screw in one direction only. 

 In dividing the circle, burrs are thrown up by the engraving tool on 

 each side of the cut, and reflections from either or both of these appear 

 as fine white lines in the reading microscope. The quartz fibre is made 

 to cover each of these reflections in turn, and the mean taken. Further- 

 details of the method are given in the list of indices. 



3. Temperature. — In order to reduce errors due to change of tem- 

 perature to a minimum, I have kept a standard thermometer on the 

 prism table, and have never attempted to regulate the temperature by 

 raising or lowering that of the room, without allowing at least 2 hours 

 to elapse before making observations, so as to ensure the prism attain- 

 ing the same temperature. In most cases times were chosen for 

 observation when the temperature was, without artificial means, found 

 to be that required. The temperature adopted for observation was 

 15° C. In the very few cases in which observations took place at 



and, substituting for 8, &c, this gives 



• D . D + 2A- 



sin _ sin 



/i = /x<; i + -,v(*r + + 



. 2 A 9 D + A 



sm A — cos- 



9 9 



Putting in the small term D = 40° and A = 60°, the value of the 

 trigonometrical expression is found to be 3 approximately. 

 Hence 



+ i(ai 2 + *2 2 + O}. 



If a, &c, be in minutes, since the circular measure of a minute is 

 1/3420, or 0-00029, 



ft = -p {1 + 0-00000001 (a x 2 + a 2 2 + a 3 2 )} . 



For fluorite, ol y = 1-J, a 2 = - 2 J, a 3 = J, so that 



f = /*{1 + 0-00000007}. 



The error is almost unity in the seventh figure, which is quite negli- 

 gible. For the other prisms it is less. 



