Mr. Nixon's Theory of the Telescopic Level. 429 



a revolution of the tube within its Ys) will be constantly ele- 

 vated at an angle of which the tangent is the (calculated) in- 

 crease of perpendicular height divided by the distance between 

 theYs. 



When the instrument is set up ready for taking levels, the 

 upper surface of the tube * at the object end is at a greater 

 elevation than at the eye end, by the difference of the semi- 

 diameters of the tube (measured over each Y), added to the 

 corresponding augmentation of height of the axis. As the 

 angles are minute, the horizontal inclination of the surface of 

 the tube will be to that of its axis, (or to the error of collima- 

 tion,) as the augmented perpendicular height of the former is to 

 that of the latter. When the Ys open at 90 degrees, the ratio 

 will be as 2-4-14 to 1-414. 



In the case of the Ys being unequal, the error will be the 

 mean of its value calculated for each Y. Supposing one of 

 them (X) to open at 90, and the other (Z) at 88; and that 

 the radius of the eye end (A) of the tube is I'O, and that of 

 the object end (B) 1-2. When A rests within Z, the height 

 of the axis is 1-440, and 1'697 with B within X; so that it is 

 more elevated over X than over Z by 0*257. On reversing 

 the tube, A rests within X at a height of 1'414, and B within 

 Z at a height of 1 '728; the axis being higher over Z than over X 

 by 0-314. But if we lower the narrower Y by 0-0285 (or half 

 the difference), then will the elevation of the axis, before and 

 after reversing, be equal to 0*2855, or to the tangent of the 

 constant error of collimation. 



The following methods of ascertaining the instrumental 

 error are the most feasible of those that have occurred to me. 

 The result of each, on its application to determine the error of 

 the horizon-sector, will be given hereafter. 



I. Find by a spirit-level, placed on the surface of the tube, 

 its inclination to the horizon. 



II. Place a vessel filled with quicksilver between the object- 

 glass of the instrument and that of another telescope f, and 

 observe through the latter the intersection of the cross-wires 

 of the former direct and by reflection. 



III. By Captain Kater's horizontal floating Collimator. 



IV. Make the lines of collimation of two telescopes parallel 

 to that of the instrument, and afterwards point the telescopes 

 at each other with the bubbles of their levels at their marks. 



V. Or measure by the instrument the minute inclination of 



* Or, more correctly, of the line formed by the intersection of the upper 

 surface of the tube by a vertical plane passing in the direction of its axis. 



f In every case the telescopes are understood to be adjusted to the side- 

 ral focus. 



the 



