352 



Mr. G-. Forbes. 



[Feb. 22, 



either of the two screws first referred to be turned, the plane of the 

 prism will be turned about a horizontal axis inclined at 45° to the 

 base. A tilt of one prism about its axis of symmetry gives rotation to 

 the picture about the optical axis. A tilt about an axis at right 

 angles to the axis of symmetry raises or lowers the picture seen by the 

 half-base under consideration. 



(10.) Errors of the Base and Hinge. — The errors of the hinge and base 

 may best be considered with reference to the half-base. The error is 

 the angular deviation, measured in the plane of the binocular, of the 

 ray entering the binocular from the direction in which it entered the 

 outer end of the base. This error depends upon three things — 

 (1) the inclination of the axis of the two prisms to each other, (2) the 

 position of the plane which is parallel to these two axes relatively to 

 the line of vision, and (3) the part of the field of view in which the 

 observation of the distant object is made. 



Let OZ be parallel to the axis of the first prism and OP parallel to 

 the axis of the second prism. Let OPZ be the plane of XZ. Let OS 

 be parallel to the direction of the object viewed. Let xyz, x'y'z' be the 

 co-ordinates of the point S according as OZ or OP is taken as axis 

 of Z. 



Fig. 2. 



LetZS = 8, and PS = 



7T - PZS = <f>, and ZPS = $ . 



PZ = i, which is a very small quantity. 



8' = 8 + 88, <f> = cf> + 8<f>; then 88 and S(f> are very small. 



\tt - 8 = a, then in practice a is small. 



OZ = unity. Then we have 



x = sin 8 . cos<£ x' = sin#'. eos</>' 



y = sin 8 . sin <b y' = sin 8' . sin <j> 



z = cos 8 z' = cos 8' 



sin cos c/>' = x' = a;cos& + 2sin& = sin #cos </>cos^ + cos 8&mi... (1) 



sin#'. sin <j>' = if = y = sin 8 sin <f> (2) 



cos 8' = z' = z cos % - x sin i = cos 8 cos i - sin 8 cos <f> sin i ... (3). 



