Mr. Nixon's Theory of the Spirit-Level. 361 



of curvature, of which the line of intersection of its plane by 

 the (horizontal) under surface of the level is the chord. 



As the sides of the level are perpendicular to its under sur- 

 face, if we fix a short tube to the frame at right angles to the 

 principal one, and mark the ends of its bubble when the level 

 rests on a plane found to be horizontal, we shall know in fu- 

 ture that the sides of the frame, and consequently the parallel 

 plane of the circleof curvature, will be vertical when the bub- 

 ble of the transverse tube comes to rest between its marks. 



It is also evident, that if we place the level with either of 

 its (perpendicular) sides in contact with a vertical plane so 

 that its under edge (or corresponding longitudinal line of 

 the under surface) lies exactly on, parallel to, or in the direc- 

 tion of a straight line described on that plane, and find on 

 reversing the level (that is, on making the opposite side of the 

 level to press against the vertical plane with its under edge 

 coinciding with the straight line) that the ends of the bubble 

 come to rest at the same marks, it proves that the line is hori- 

 zontal. 



If a segment of a circle be made to revolve about an inscribed 

 line inclined to the horizon, and touching its arc in any point, its 

 chord, if perpendicular to that line, will describe an inclined 

 plane. A horizontal line being drawn on this plane through 

 the point in which the line of revolution, if produced, would 

 touch it, another straight line lying in the same plane and 

 passing through that point at the greatest possible angular in- 

 clination to the horizon, also that of the plane, will intersect 

 that horizontal line at right angles *. Then, if we mark the 

 vertex of the arc when the segment is vertical, that is when in 

 the direction of the inclined line drawn on the generated plane, 

 the mark will attain its maximum distance from the true ver- 

 tex, varying as the segment revolves, at the completion of a 

 semi-revolution; at which period the reversed segment be- 

 comes vertical again, and coincides with the inclined line for 

 the second time ; and half this maximum distance, as mea- 

 sured on the graduated arc of the segment, will be equal to 

 the zenith distance of the line of revolution, and to the hori- 

 zontal inclination of the plane and generating chord. At one- 

 fourth, and again at three-fourths of the revolution, the plane 

 of the segment will be at its greatest inclination to the horizon, 



• The intersection of an inclined plane through any point on it by a 

 horizontiil plane, is a straight line parallel to the horizon; and the inter- 

 section of the same plane hy a vertical one passing through any point of it 

 per()endicular to its horizontal (parallel) lines, will be a straight line having 

 in comnion with lines parallel to it, an inclination to the horizon greater 

 than that of any other line that can be drawn on the same plane. 



New Series. Vol. 1. No. 5. Mai/ 1827. 'i A equal 



