40 o Theory of the Spirit Level. 



and contraEls the bnbble, this lad may occupy the fpace A B precifely in the middle of 

 the tube, and the inftrument being then retlified, wiH indicate the level. But when it 

 becomes cold, the liquor being condenfed, the bubble will occupy the fpace C D, which 

 is no longer in the middle of the tube. A good inftrument ought always to fhew the 

 level when the bubble is in the middle of the tube, which is the rule followed in prac- 

 tice ; 'it is therefore fubj eft to error when the tube is irregular. Irregularities, not dif- 

 cernable to the fight, are of much confequence to the ftation of the bubble. Thefe may 

 vary without limit and produce a correfpondent number of variations in the bubble itfelf. 

 which will in fome cafes be too fenfible, and in others not enough fo, will be much 

 affefted by the fame degrees of inclination in fome cafes, and not at all in others, or it 

 may ftand to the right or left end of the tube without being capable of fixing itfelf- in the 

 middle. 



(4.) The length of the radius of curvature of the infide of the tube depends on its 

 fenfibility, or rather this fenfibility is in proportion to the length of the radius. The ra- 

 dius of curvature of the furface of the earth is likewife of fome confequence when the 

 fenfibility is very great. 



The fenfibility of a level may be exprelTed by the fpace run over by the bubble in the 

 tube, divided by the degree of inclination which has occafioned the derangement ; or if 

 the degree of inclination be fuppofed to be a conftant quantity, as for example one fe- 

 cond, the fenfibility will be fimply as the fpace pafTed over. 



Let A B, fig. 2, plate xviii. reprefent this fpace ; A C the radius of the earth, and 

 A D the radius of curvature, A b, of the infide of the tube W when the tube is inclined 

 fo as to caufe the bubble to run over the fpace A B, its radius b D will apply itfelf upon 

 B C the fame as A D was before applied upon A C. The angle D B C (or D b C, be- 

 caufe the fpace b B may be confidered as nothing on account of the extreme minutenefs 

 of the angle b A B) will be the angle of the inclination of the tube, which we fuppofe to 

 be conftantly one fecond. The angle A C B will be known if the radius of the earth and 

 the fpace A B be known. The angle A D B is conftantly the fum of the two external 

 angles, and may alfo be known if A D and A B be afcertained. The angles A D B, 

 A C B, being fubtended by the fame arc, will be to each other inverfely as the two radii 

 AD, A C, Of three quantities, A C, A D, A B, two being known, the third may alio 

 be found. 



Let A B =fl, A D — r, A C = R, the angle C B D = -J, the angle A C B =,w, 

 and the angle AD B -zzin. If the value of r be fought, every thing elfc being known, 



we (hall have b-\r m : m : : R : r = - — ; — ■. If therefore a were one line m being nearly 



-\-tn 



TTTff'jr ^c ihall have r :=: 238 toifes nearly. 



If the value of a be fought, or, which is •the fame thing, the value of m, the reft 



being 



