374 F. L. 0. Wadsworth — Method of Determining the 



perpendicular to the plane of the circle in any convenient way, 

 say by adjusting it until the image of any distant object as 

 seen by reflection from the silvered surface occupies the same 

 position in the field of the observing telescope when the mirror 

 is either in the position shown, or is turned through 180° as 

 shown by the dotted lines. 



The telescope is then set with its axis perpendicular to the 

 mirror by making the image of the cross wires coincide with 

 the wires themselves, the wires being illuminated for this pur- 

 pose by placing a small piece of unsilvered glass, 5, in front of 

 the eyepiece at an angle of about 45° so as to throw the light 

 from a gas flame or window into the field of the telescope. 

 There is no difficulty in seeing the image by placing the eye 

 behind and close to &.* 



The single vernier attached to the telescope is then read, 

 and either the circle, carrying with it the mirror, or the tele- 

 scope is turned through 180° or until the image of the vertical 

 cross wire as seen by reflection from the other side of the 

 silver coat (this time through the glass), is again in exact coin- 

 cidence with the wire itself and a second reading of the vernier 

 taken. If the unsilvered face of the mirror is parallel to the 

 silvered face the angle through which the telescope or circle is 

 turned between these two settings will be just 180°, if they 

 are not parallel it will be 180 db %<p, where \y is the deviation 

 due to the prismatic form ; equal approximately to \ the angle 

 <p between the faces .... Usually however the error of paral- 

 lelism in a good sextant glass is not more than 5" and the 

 resulting error in angle consequently only 2" to 3", a quantity 

 smaller than the venier will ordinarily indicate. If larger 

 however the effect may be readily eliminated by reversing the 

 glass on the spectrometer table, repeating the settings and tak- 

 ing the mean of the readings. Then if £ be the eccentricity 

 of the circle and d the angle between the of graduation and 

 the line of centers of rotation and graduation, a the circle 

 reading for the first setting, /3 that for the second setting . . . 

 then evidently 



m = true angular reading for ] st setting = a + € sin (a + 6) 

 n= " " " " 2d " = /3 + es'm(180 + a + d) 



m-n = 180° = a— /?+2«sin (a + 6) 



/l 1 =180° — (a — /3) = 2ssin(a + d) (1) 



If now we take a second set in which the first reading is y and 

 the second o we have 



* The setting of the mirror perpendicular to the plane of the circle and of the 

 telescope at right angles to the mirror is readily accomplishad at one and the 

 same operation, for the telescope can first be set perpendicular to the mirror face, 

 the latter then turned through 180° and the vertical difference between image 

 and cross wires, corrected, half by adjustment of the mirror, half by the adjust- 

 ment of the telescope. 



