Mr. Nixon's TJieory of the Spirit-Level. 359 



equal to 15 feet. But as the levity of the water near the ex- 

 tremities of the arc is greater than under the vertex, it must 

 stand higher there than in the latter place, or an equili- 

 brium cannot be effected. From this cause the length of the 

 bubble becomes reduced from 15 feet to little more than as 

 many tenths of an inch : however, as the reduction will be the 

 same at each end, provided the tube be a perfect ring, the 

 middle of the bubble will still coincide with the vertex of the 

 arc. For reasons already assigned, it is nevertheless requisite 

 that the bubble should be of a proper length and depth. 



When a vertical plane describes any arc of revolution about 

 a horizontal line or axis, a straight Une, as the radius or chord 

 of a circle, previously drawn anywhere on that plane, will have 

 its inclination to the horizon varied by an angular quantity 

 equal to that arc of revolution. This will be as obvious for 

 an excentric line as it is for one intersecting the axis, when 

 we consider that their parallelism or angle of inclination to 

 each other remains constant. If we therefore describe with 

 the same radius two circles on the vertical plane, one concen- 

 tric and the other excentric to its axis, and mark their vertex 

 points before, and also after any partial revolution of the plane, 

 the lineal distance of the two points on the one circle will be 

 exactly equal to that of the corresponding points on the other. 

 Were we to fix anywhere on (but parallel to) either vertical 

 side of our circular vessel * the tube of a spirit-level having 

 an equal radius of curvature, then, as the vessel revolved, its 

 bubble would pass over the same lineal space as that of the 

 tube. Should the radius of curvature of the tube exceed that 

 of the vessel, the arc of revolution (or variation of inclination), 

 as measured by the graduations on the rim of the latter, would 

 nevertheless correspond with the indications of the scale of 

 the level. With this explanation we may now comprehend 

 how a spirit-level, having a radius of curvature of several hun- 

 dred feet, although fixed (parallel) to a vertical plane (such 

 as that of an astronomical circle) within a few inches of the 

 axis of rotation, should have its bubble displaced by the same 

 (sensibly) lineal space as though that axis coincided with the 

 centre of its circular curve. 



To construct an instrument called a level, capable of deter- 

 mining the horizontal incUnation of straight lines, planes, &c. 

 the curved tube of a spirit-level furnished with a scale is fixed 

 with its convex side upwards to the upper surface of a straight 

 bar of brass, wood, &c. in such a manner that the plane of 

 the circle of curvature of the tube shall be perpendicular to 



, * See above, page 257. 



the 



