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



the under surface (a right-angled parallelogram) and parallel 

 to the (longitudinal) sides of the bar or frame *. 



If we mark the vertex (or most elevated point) of the arc of 

 any segment of a circle previous to its revolution about an in- 

 scribed vertical line touching the arc in any point, then will 

 the true vertex and the initial mark coincide during the revo- 

 lution ; and tlie chord of the (vertical) segment (or a plane 

 cutting it at right angles), if perpendicular to the vertical line, 

 will continue horizontal throughout, and describe a perfectly 

 horizontal plane. Now as the middle point of the bubble of 

 a spirit-level will always come to rest at the vertex of the cir- 

 cular arch of its tube, represented by the arc of the segment; 

 and as the intersection (at right angles) of the under surface 

 of the level by the vertical plane of the circle of curvature is 

 equivalent to the chord of the segment, (and that under sur- 

 face to the plane cutting it at right angles,) we may be certain 

 that the surface on which the level may be moved about in 

 exact contact, without displacing the bubble, is a plane paral- 

 lel to the horizon. Or, as the ends of the bubble do not de- 

 viate from their marks on the tube, or divisions on the scale, 

 the under surface of the level preserves during the revolution 

 its parallelism to the surface of the liquid (or base of the 

 bubble), which is always horizontal, and must therefore move 

 parallel to a horizontal plane. 



When the level rests on a horizontal plane, with the ends of 

 the bubble coinciding with the two marks drawn on the tube, 

 or with each end at the same distance from the zero of the 

 scale, it is said to be adjusted ; in which case the middle of 

 the bubble is at the point of bisection of that arc of the circle 



* If the circle C move with its centre on the circumference of the 

 larger circle B, its plane being always per- 

 pendicular to that of the latter, and in 

 the direction of the line joining their 

 centres, then will its circumference gene- 

 rate a ring similar to the curved tube. 

 The circle described by that point v, of 

 the circumference of the smaller circle C, 

 which lies in the direction of the plane 

 of the great circle B (and of the straight 

 line connecting iheir centres) will there- 

 fore represent the circle of curvature of 

 the tube. 



Having placed the tube with its axis 

 parallel to the sides of the frame, bring 



the mark indicating the situation of some point of the circle of curvature 

 to its greatest elevation above the under surface of the frame, when it will 

 lie in the plane passing through the axis of the tube perpendicular to that 

 under surface. 



of 



