( 106 ) 



case to the determination of the changes in the distances between 

 two successive central lines. 



In the sequel the glass windows, even when they exhibit some 

 curvature, are regarded as prisms, and it is assumed that each of 

 the portions through which the screens are seen — even in the same 

 piece of glass — has an individual angle of refraction. These angles 

 of refraction «j, «.^ etc., (projected upon the plane which during the 

 height measurements coincides with the vertical plane through the 

 axis of the telescope) were all measured beforehand. 



The next figure (in which the ray is projected upon the vertical 

 plane through the axis of the telescope) shows a window in which 



the prismatic character is strongly accentuated so as to add to the 

 clearness of the drawing. Let / be the incident ray which traverses 

 the axis of the cathetometer telescope supposed horizontal. The media 

 are represented by the indices 1, 2, and 3. Let /?„ represent the total 

 deviation which the ray undergoes at the mark ?«„ owing to refraction 

 at the surfaces 1.2 and 2.3; for the sake of simplicity this total 

 deviation will, in the sequel, be referred lo as i^ as long as tiiere 

 is only a single mark involved. 

 Since 



l3 = z\ -{- 2^ — a 

 we get 



/? = (wi.2 — 1) « + To (W3.2 n],<2). 



When there is no water in the volumenometer jacket it follows that 



^ = (^12 — !)«• 



Hence, calling the distance of the front surface of the windows 

 from the screens A, we get for the optical correction to be applied 

 to the reading for a line on the screens 



