( 104 ) 



to Vioooo ^^s long- as the volumes of the mercury menisci are known 

 with sufficient accuracy. 



§ 3. IT. Detennlnations of the optical constants. 



1^'. Owing to the prismatical sliape of the windows in the jacket 

 through which the volumenometer was observed, and 2"*^ to the 

 circumstance that their surfaces were not accurately vertical, an 

 optical correction had to be applied to the height readings in the 

 volumenometer. The latter correction may be regarded as composed 

 of two distinct parts, 1''^ . a correction in consequence of the deviation 

 from 90° of the inclination to the horizon of llie long axis of the 

 apparatus in the plane of incidence, and 2"*^. a correction in conse- 

 quence of the angle ai made at any point i by the outer surface 

 witii the long axis of the apparatus. 



Of these the first was determined every time from the deviations 

 of a plumb line arranged so that when pointing at the corresponding 

 mark it is parallel to tlie long axis of the apparatus, or from the 

 deviations of a spirit level laid on a plane perpendicular to the long 

 axis. Both this perpendicular jilane and the plumb line mark were 

 firmly attached to the apparatus. With a sufficiently careful observation 

 with the plumb line an accuracy of 0.01 mm in the height readings 

 can be attained. By reading the spirit level during this operation one 

 can substitute the simpler level reading for the plumb line. When 

 it is not desired to read to more than 0.05 mm. a simple reading 

 with the plumb line is sufficient. 



The angles between the front surfaces of the windows at any point 

 i and the long axis of the apparatus are constants of the apparatus, 

 and need to be re-determined only in the event of the windows being 

 removed. The correction resulting from this angle may be evaluated 

 in either of two ways. 



:1«' Method. If the long axis of the apparatus is perfectly vertical 

 the correction to be applied to a reading for a perfectly horizontal 

 beam of light is, for small angles of incidence, 



in which A is the length of the path traversed by tiie light in water 

 from the i)oint on which the telescope is focussed to the front of 

 the windows (in the apparatus used this distance was 8 cm.), 6 is 

 the angle ^) between the normal- to the windows and the horizontal 



1) One can easily see that a difïeience of 1' in the horizontal position of the 

 telescope (when the distance between the objective and the focussed mark is 

 + 45 era.) can liave no effect upon an accuracy of 0,01 mm. nor can the deviation 

 of light caused by the glass of the connecüng necks when these are carefully 

 constructed. 



