S62 Mr. Nixon's Theory oj' the Spirit-Level. 



equal to that of the inclined plane, when the chord, then in 

 the direction of the horizontal line described on the inclined 

 plane, will be horizontal, and the vertex be situated at the point 

 of bisection of the total arc, and of that portion of it compre- 

 hended between the initial mark and the vertex at its greatest 

 elongation from it. Or conceive an adjusted level to be placed 

 so as to coincide in the first instance with any horizontal line 

 di'awn on the inclined plane, and subsequently with one at 

 right angles to it, or in the direction of the line on which the 

 inclination of the plane is measured; and it will be evident 

 that the bubble must have advanced I'rom zero towards the 

 elevated end of the level, by a distance on the scale equal to 

 the inclination of the plane. But on reversing the level, the 

 same end, (repassing the horizontal line with the bubble re- 

 verted to zero,) will be depressed equal to its previous eleva- 

 tion, and the bubble must consecjuently come to rest at the 

 same distance from zero as before, but on that side of it the 

 nearest to the other (now elevated) end of the level; so that 

 the arc of distance passed over by the bubble will equal tivice 

 the inclination of the plane. 



To find the angular inclination of a plane, move the level 

 about on its surface until the bubble has made its maximum 

 approach to the (elevated) end of the tube. Having registered 

 the divisions on the scale giving the middle point of tlie bub- 

 ble, proceed with the rotatory movement of the level until its 

 direction is reversed, which will occur when the bubble has 

 made its greatest approach to the other end of the tube, and 

 ascertain the middle point of the bubble as before. Half' the 

 sum of these two middle points when the signs are unlike, or 

 half their difference when the signs are like, will be equal to 

 the angle of inclination of the plane*. When the level is placed 

 on the inclined plane in such a direction that the bubble set- 

 tles at that point of the scale answering to the half-difference 

 of these two middle points, the longitudinal lines of the under 

 surface of the level are horizontal, and its corresponding sides 

 inclined at an angle equal to that of the planef. 



• When the level is furnished with a transverse tuhe properly ailjiistecl, 

 wc are enabled to place it at once on the inclined plane, in the direction of its 

 greatest inclination, which will be, when the sides of the level are vertical, 

 known by the bubble of the transverse tube coming to rest between its marks. 



f On this account the bubble wonld deviate (at right angles) from the 

 equally inclined circle of curvature, and horizontal lines cannot be safely 

 drawn by a similar level on the inclined plane with which its under surface 

 is in contact. To draw them correctly, tlie sides of the level must be pre- 

 served vertical by means of the transverse tube, whilst one of the longitu- 

 dinal lines of the under surface rests on the inclined plane with the bubble 

 of the principal tube at the proper divisions. 



The 



