262 Mr. Nixon's Theory of the Spirit-Lcvel. 



vertex of the sphere, then will the centres of the bubble of the 

 rino- and that of the sphere also coincide, or be in the same 

 vertical ; yet it will be found after any partial revolution of 

 the sphere, that although the bubble of the ring will always 

 come to rest at the most elevated point of the ring, or that 

 part of it the nearest to the vertex of the sphere (or centre of 

 its bubble), its distance from its initial mark, as measured on 

 its o-raduated scale will, however, fall short of the correct 

 zenith-distance of that mark or arc of revolution; — the dis- 

 crepancy augmenting with the inclination of the ring to the 

 circle described by the bubble of the sphere. When the in- 

 clination equals 90°, in which case (the plane of) the ring 

 passes through (the centre of) the sphere in the direction of 

 its axis, the arc of revolution may amount to 90°, without dis- 

 placing the (unserviceable) bubble of the ring from between 

 its marks *. 



Let a U a!b be the great circle of the sphere parallel to the 

 horizon; bV the ver- 

 tical circle perpendi- ^ 

 cular to the axis of 

 rotation a a', descri- 

 bed by the bubble of 

 the sphere now at 

 rest at the vertex v : 

 and let if be the bub- 

 ble of the (oblique 

 circle, or) ring r;-', 

 inclined to bb at an 

 angle equal to vin ~J, m 

 being their point of 

 intei-section or initial 

 mark where the bub- 

 bles of the ring and 

 sphere coincided when 

 in the same vertical. Then as the bubble of the ring will be 

 stationary at that point of the ring the most elevated above 

 the horizontal circle, ti' will be equidistant, or 90°, from r and 

 7-', and also touch the nearest of the small circles of equal al- 

 titude described round u as a centre, so that m^Jv must be 

 rio-ht-anded at -J. We shall, therefore, have given in the 

 ri^ht-angled spherical triangle v m r/ the leg t/ m (or zenith 

 distance of m as given by the bubble and graduations of the 

 rino-) and the angle (of inclination of the ring to the vertical 



• The bubble will neveitlieless pass over an arc of 90° of the minute 

 circle on which we measure the interior diameter of the ring. 



circle) 



