Mr. Nixon's Theory of the Spirit- Level. 259 



subsequent to any degree of revolution of the vessel. The 

 zenith-distance of t/, equal to its change of inclination, may 

 BOW be ascertained at once, by observing on the graduated 

 rim, &c. the angular distance of the two marks. To guard 

 against any change of temperature in the interval of the ope- 

 ration, it will be advisable to mark the rim at both ends of the 

 bubble (L and I) and to consider the half-sum of the degrees, 

 &c. on the rim corresponding to each mark as the zenith-point 

 of V (or v'). The difference of these two half-sums, granting 

 the change of temperature to have been uniform, will give the 

 zenith-distance of i/. When the graduations are sufficiently 

 large to admit of being read off without vernier, &c. we may 

 dispense with the marks by noting the degrees, &c. exactly 

 over the ends of the bubble. 



In order to graduate in a similar manner the upper or con- 

 vex surface of a spirit-level, we must ascertain in the first place 

 the linear space passed over by its bubble, corresponding to 

 a certain angular change of inclination, as one minute, one se- 

 cond, &c. This may be effected after various methods * ; as by 

 fixing the level to a long straight bar of a known length, and 

 having elevated either end a quantity equal to the given angle, 

 to note the inches, &c. passed over by the bubble ; generally 

 termed its displacement. The tube or the ivory scale laterally 

 attached to it, may now be divided into equal spaces f, each 

 equivalent to a change of inclination of one second, &c. ; and 

 so nimibered as to give, without risk of mistake, the middle 

 point of the bubble, i-egardless of its varying length, and con- 

 sequently minute differences of vertical angles |. 



* The French verify the scale of the great level of their repeating-circle, 

 by measuring on its graduated vertical circle a sufficient multiple of the 

 minute angle subtended by two well-defined fixed objects situated in the 

 same vertical plane, and comparing the result with the corresponding mea- 

 surement by the divided scale of" the level. 



In lieu of the repeating-circle we might have recourse to the microme- 

 ter of a telescope. 



t When the bubble does not pass over equal spaces for equal angles of 

 inclination throughout the length of the tube, it proves that the arch is not 

 perfectly circular. 



t In general the middle division is considered as zero, whence the 

 numeration, alike for the divisions on each side of it, is carried on pro- 

 gressively to each end of the scale. — The divisions on the one side of zero 

 being considered as positive, and those on the other side as negative, the 

 distance of each end of the bubble from zero, with the proper signs pre- 

 fixed, are registered ; and half their sum, when the signs are alike, or half 

 their diHercncc (with the sign of the greater quantity), when the signs are 

 unlike, is considered the middle point of the bubble, or vertex of the level. 

 Hence the difference or sum, as their signs arc like or unlike, of two simi- 

 lar middle points, of which one was noted before, and the other after an al- 

 teration oi inclination of the level, indicate its angular value. 



2 L 2 The 



