[ I09 ] 



of a degree erroneous :* and as thefe accidents are likely to 

 happen to a perfon ufing that kind of level in travelling, fo 

 I am perfuaded the inftrument here defcribed would remain longer 

 ferviceable to a traveller, than any other for this purpofe that 

 1 am acquainted with : and. it is as being the mofl fafely por- 

 table of any, and alfo manageable abroad at night when others 

 are not fo, that it is chiefly recommended; though after many 

 comparative trials of the, fluid level with this one, I would, 

 without confcioufnefs of partiality, generally prefer the latter; 

 for it is in fad a plummet, and may be made and adjufted to 



have . - 



* If the radius of a circle be ten inches, each inch divided into a thoufand equal 

 parts, i. e. in the whole ten thoufand, the fine of the arch of one minute is (not quite) 

 three of thofe parts, or the yyVj P^"^* °^ ^'^ inch: if the radius be only the 

 ^ of this, or two inches, the fine of one minute will be only the f of y|,-j- of an 

 inch; i.e. the ,^ j^ -^ part: confequently if the refledling plate or mirror above- 

 mentioned were four inches in diameter, and it were accidentally tilted up at one edge, 

 and deprefled on the oppofite one, even fo little as the t-j-ts-t- P'"'* °f -"^ inch, it 

 would be one minute of a degree oblique to the horizon : but I have fliewn, that the 

 greateft error of obfervation by a reflefting level, is always double the error of the 

 fpeculum ; hence half the above angle of obliquity of the fpeculum' to the horizon, 

 or an elevation and depreffion of its oppofite edges from it, of the y-r^jj part of an 

 inch, (and how fmall a quantity this is, I leave to the conception of the reader) 

 will, if the diameter of greateft obliquity happen to be in the plane of vifion, 

 produce an error in the obfervation amounting to one minute: the fame is true of 

 the level here defcribed ; fo that the property of a fcrew in producing fmall motions . 

 is admirable, fince its adjufting fcrews, even at the fame diflance (two inches) 

 from the centre of motion, can. in reftifying the fpeculum, be made to advance 

 with precifion enough, through a fpace far lefs than this, even fo fmall as the one- 

 hundred-thoufandih part of an. inch. 



