Mr. Nixon o?j the Curvature of Spirit- Levels. 175 



tubes were about six inches long, nearly half an inch in dia- 

 meter, slightly conical, and their bubbles were estimated to 

 move the one-fortieth part of an inch for a variation of inclina- 

 tion equal to one second. 



Conceiving that the reversing points of the levels of the 

 horizon-sector might be more immediately and correctly ascer- 

 tained from scales of equal parts attached to the tubes, than 

 by determining from measurements on the graduated arcs the 

 situation of these points relative to the fixed marks drawn on 

 the surface of the tubes, it became necessary to verify the esti- 

 mated curvature of the levels. In the accomplishment of this 

 object, the sector'afforded singular facilities ; but as the mani- 

 pulation of the instrument may not be generally understood, 

 I prefer pointing out the method by which the level of the 

 telescope of a good theodolite may be mounted with a scale, 

 and the angular value of its divisions obtained. 



For the scale, cut a piece of moderately stiff paper into the 

 form of a parallelogram of the proper length, and about a 

 quarter of an inch wide, and press it evenly upon the glass 

 tube, previously spread over with liquid glue, with either of 

 its longitudinal edges laid exactly upon the line of curvature 

 or straight line passing (in the direction of the axis of the tube) 

 through the middle points of the two bubble-marks. When the 

 scale is quite dry, divide this edge into minute equal parts, 

 and number them from zero, placed at that end of the scale 

 the nearest to the eye-piece of the telescope, progressively to 

 the other extremity. 



To find the angular value of the divisions, set up and fix 

 the theodolite in a situation inaccessible to the direct rays of 

 the sun, and adjust the instrument for observation with the 

 divided edge of the scale perpendicular to the optical axis of 

 the telescope, and with the zero of the vertical arch in a line 

 with that of its vernier. Having clamped the horizontal cir- 

 cles with the telescope exactly over two (opposite) screws of 

 the parallel plates, make use of these screws to force the bub- 

 ble of its level to the zero extremity of the scale. When at 

 rest, register in one column, which designate, " telescope de- 

 pressed," the distance of each end of the bubble from the zero 

 of the scale. The bubble being moved, in the next place, by 

 the aid of the tangent-screw, or rack-work of the vertical arch 

 to the other extremity of the scale, note the distance from zero 

 of each of its ends, and enter them in a separate column to be 

 termed, " telescope elevated." Half the difference of the sura 

 of each column is evidently the space traversed by the bubble, 

 of which the corresponding angle (of elevation) will be given 

 on the vertical arch. To insure to the measurements tlie re- 

 quisite 



