Mr. Nixon's Theory of the Spirit-Level. 261 



angles at A, B, C, D will be constant, and the upper side AB 

 preserve its parallelism to the horizon*. 



When the temperature of the level is not uniform, the bub- 

 ble (as in the parallel case of the circular vessel) vi'ill be dis- 

 placed and move towards the warmer end of the tube. Its 

 ground arch, as well as the divisions of the scale being dis- 

 torted, the half-sum of the divisions at each end of the bubble 

 cannot correspond with the true vertex of the level. 



The tube of the level is generally mounted in a thin case of 

 brass, a metal which expands in a greater ratio than glass. 

 When the bottom of the case and that side of the tube in con- 

 tact with it are not strictly parallel, it may occur in great va- 

 riations of temperature that the tube will rest on some dif- 

 ferent part of the case, and cause a sensible variation in its in- 

 clination to the horizon. The difference of expansion may 

 also affect the radius of curvature, or alter the perfectly cir- 

 cular figure of the arch of the tube. 



In our circular vessel, as the graduated rim is perpendicu- 

 lar to its horizontal axis, either end of the bubble (or hori- 

 zontal line L/) must describe, as the vessel revolves, arcs of a 

 circle lying in a vertical plane: and were a hollow (glass) 

 sphere, nearly filled with any liquid, made to complete a re- 

 volution about a horizontal line (or axis) passing through its 

 centre, then would the centre of the surface of the liquid (or 

 bubble) have described a great circle, also lying in a vertical 

 plane perpendicular to the axis, and on which, when gradu- 

 ated, zenith-distances, &c. might be measured, precisely the 

 same as on the rim of the circular vessel. And if we divide 

 the interior of the sphere into two unequal parts by means of 

 a circular plane (inferior in diameter to the sphere) also placed 

 at right angles to the axis of rotation, and nearly fill the two 

 divisions with any liquid, then will a vertical plane passing in 

 the direction of the axis of the sphere, divide at any period of 

 its revolution the semicircular bubble of the lesser division, and 

 the circular one of the larger division (moving parallel to each 

 other) into two equal parts. Hence differences of inclination, 

 &c. measured on the great circle, or on the similarly graduated 

 rim of the parallel circular plane would always be equal. 



Let a graduated hollow glass ring, nearly filled with any 

 liquid, be made to closely incircle the sphere (the partition 

 being withdrawn) in the direction of any one of its great cir- 

 cles except the one perpendicular to its axis. When tlie point 

 of intersection of these two circles is made to coincide with the 



• It is nevertheless certain tliat cliangc of temperature alters the vertex, 

 or reversing point of most spirit-levels; which the artists attribute to the 

 tubes not being perfectly cylindrical. 



vertex 



