332 Mr. J. Nixon on the Measurement of the 



inner surface BS of the bar must be elevated by the arc BA 

 before the bubble of the level attached to it can attain its mark. 

 This arc being in defect of double the elevation of ES (or arc 

 A'A) by the arc BA, equal to the angle formed by the sur- 

 faces of the bar, whilst the previous measurement exceeded it by 

 the same quantity, half their sum will be the correct elevation. 

 The elevation of a distant object, measured on this plan by 

 a 30-inch telescope carrying a divided arch (of 18 inches ra- 

 dius), of which the moveable index was furnished with a double 

 level, exceeded by 30"- 5 the angle obtained by the correspond- 

 ing observation with the sector. 



When a double level is affixed to the face of a divided cir- 

 cle, move the latter until the bubble of the level uppermost 

 settles with its extremities equidistant from the zero of its 

 scale ; then turn the circle exactly half round, and alter the 

 adjustments of the other level (at present uppermost) until the 

 ends of its bubble lie also equidistant from the zero of its 

 scale. The two levels must now be parallel to each other, 

 and the reversing of the connecting bar not requisite. The 

 parallelism might be similarly effected with the bar fixed to 

 the telescope of the circle. 



By the Eighth Method. 



Having secured the bar lengthwise to the tube (cylinder) 

 of which the axis is considered to be horizontal, note the po- 

 sition of the bubble of the uppermost level of the bar, before, 

 and that of the bubble of the other level, after inverting the 

 tube within its Ys. Then take off the double level, and re- 

 place it, reversed in direction, with the bubble of the level 

 which may be uppermost at the previous points of its scale. 

 In the event of the tube being perfectly cylindrical (and in- 

 flexible), it will be found on inverting it that the other level 

 (of the bar) will come up with its bubble in its original po- 

 sition. Were the tube conical, the bubble would be situated 

 nearer the wider end of it by quadruple the constant error or 

 inclination of the axis of the tube. 



Some years ago two reserve levels of the sector were glued 

 to a bar of wood, with the design of ascertaining the error in 

 question ; but the levels were repeatedly so much changed in 

 inclination by the setting of the glue, as to render the apparatus 

 unserviceable. 



By the Sixth Method. 



When the ring (or collar) of a telescopic-level nearest the 

 object-glass exceeds the other in diameter, elevations are 



