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



The radius of curvature of a spirit-level is found by multi- 

 plying the linear displacement of the bubble, answering to a 

 change of inclination of one second, by 200,000 ; and vertical 

 angles are measured on the divided scale of a spirit-level as 

 correctly as by a plumb-line of the length of the radius of 

 curvature of its tube *. ( Had the cylindrical tube of the level 

 been without curvature, and closed at the ends with (circular) 

 planes perpendicular to the axis of the cylinder, the bubble, 



if we may designate the hori- __^ 



zontal surface of the liquid I^ \l 



as such, would extend from 

 one end of the tube to the 

 other, and small angles of in- 

 clination, measured on a divided vertical line or scale passing 

 through the centre of each end, would possess a degree of 

 accui'acy equal only to similar observations made with a plumb- 

 line of the length of the cylinder.) 



The circular vessel W, is represented in the figure as fixed 

 to a pedestal (P) of a triangular shape; and we might ima- 

 gine, that increased temperature, inasmuch as it would elevate 

 T without affecting the height of U, would produce a greater 

 inclination of the plane TU, and consequently throw v C out 

 of perpendicular. But as the sides of the triangle will elon- 

 gate in one and the same ratio, the angles they subtend, and 

 therefore the horizontal inclination of TU, must be constant. 

 Hence the exterior sides of the tube, instead of being parallel, 

 might be incUned to the cylindrical interior without disturbing, 

 during variations of uniform temperature, the position of the 

 bubble. Supposing even the interior of the tube to be coni- 

 cal, it does not follow, as might at first be conjectured, that 

 change of temperature would affect the inclination of the 

 level. 



Let ABCD represent ^ ^ 



the vertical section of a y -^.v,:;;^—-— ----■, -, 



conical tube resting on ^"~(r~~^~-^.^^^ / 



the plane E, which forms ^^~~~~---~X.^^^ 



an angle with the hori- "''^ * 



zon equal to the inclina- 

 tion of the sides of the cone (or B/D), so that the upper side 

 of the cone AB will be horizontal. Then if the four sides of 

 the section augment (from expansion) in the same ratio, the 



* The linear displacement per second of the bubble of a spirit-level sel- 

 dom exceeds the one-twentieth part of an inch ; but occasionally, especially 

 on the continent, they have been constructed with a much greater radius 

 of curvature. In a level by Reichenbach it amounted to 200 miles ! 



angles 



