

Instrumental Error of his Horizon-Sector. 331 



about the middle of the tube, must be horizontal. On invert- 

 ing the telescope, without varying its direction, the level-tube, 

 also inverted, will have its axis, now raised above the line of 

 collimation, inclined to the latter at the same angle as when 

 lying below it; MAS being equal to SAL. When the level 

 is depressed until its bubble fixes about the middle of the 

 (opposite) side of the tube, its axis must have described the 

 arc ML (of the angle MAL), half of which is the elevation of 

 the line of collimation ES. 



As a perfectly cylindrical level may be considered imprac- 

 ticable, it will be necessary to substitute two levels of the usual 

 construction, one (a) (fig. 3.) secured, as in the figure, to the 

 upper, and the other (b) to the lower surface of an inflexible 

 bar (c). This double level being fixed to the moveable index 

 (bar) of a graduated arch attached to a telescope, which now 

 points at an elevated star, alter the inclination of the index 

 until the bubble of the level (a) comes to rest anywhere within 

 the limits of its scale. — Having inverted the telescope, and 

 bisected the star, depress the index until the bubble of the 

 other level (b), now uppermost, settles wholly in view. Were 

 the levels, with their bubbles at those points of their respective 

 scales at which they became stationary, strictly parallel to each 

 other, then would half the arc, passed over in depressing the 

 index, be equal to the elevation of the star. Ignorant of the 

 inclination of one level to the other, we have, however, but to 

 repeat the observations with the double level reversed in di- 

 rection, and the average of the two measurements will give 

 the correct altitude of the star, and half their difference the 

 inclination of the levels to each other. The demonstration 

 will be greatly facilitated if we suppose the interior of each 

 level a cylinder to which the exterior is parallel; in which case 

 that surface of the wedge-shaped bar to which the level is 

 soldered will become horizontal whenever the bubble remains 

 in view. 



Fig. 5. The inner surface AE of the bar C, as indicated by 

 the level attached to it, is to be considered horizontal. On 

 inverting the telescope, its present inclination to the elevated 

 line of collimation ES will not be varied. The bar, moveable 

 about E, being now depressed until the bubble of the other 

 level, now uppermost, comes to rest at its mark, it is evident 

 that the exterior surface BE, to which that level is attached, 

 must have passed over the arc B'A, which exceeds A' A 

 ( = double elevation of ES) by the inclination of the surfaces 

 of the bar to each other, or to the arc A'B r (= AB). The 

 bar is represented in Fig. 4. reversed in direction, its outer 

 surface AS being horizontal. On inverting the telescope, the 



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