186 Mr, William Galbraith^ on some 



of the level and rod, what was the value of the whole arc 

 A" passed over by the bubble, and the length L, of a division 

 of a" (10") on the scale of the level? 



_ R" X 6/ 206264"-8 x 2 ^__, 

 By formula (1) A" = — g — = gQQQ = 137 bl 



, ^, Dx«"xr 3000x10x1-5 ^ ^^f, . 

 By formula (2) L= ^ ^ ^ = 2062648x2 ^^'^^^ ^"^ 



From this last formula, a scale may be readily adapted to 



a level. 



2. Let the length L of one of the divisions of the scale 



of a level be one-twentieth of an inch, the run of the bubble 



two inches, the distance c?one inch and a fifth, and D five 



hundred feet, required a", the value of one division of the 



scale in seconds? 



-D r 1 /ox '/ R"xLx6? 206264"-8x 0-05x1-2 ,..^o 

 Byformula(3)a=-3^^ = q^^^^^ =1 ^^ 



3. At the distance D = 90*6 feet, the vane of a levelling 



rod passed over 0*06 of a foot in a run of 25 divisions of 



the level, what was the value a' of one division of the 



scale, and the radius of curvature of the level, L being 



one-tenth of an inch ? 



^ „ . rAs " R" X ^ 206264"- 8 x 0-06 .. ^ 



By formula (4) a =^=r = — — — — = 5 -5 



^ D X n 90-6 x 25 



By formula (5) , = -— ^ = ^^-- = ^.^^^0x12 " 



206264"-8 oio^^ . 

 — ^^- — = 312-5 feet. 

 660 



This result &''b is nearly the value of one division of a 

 level attached to a six-inch travelling circle of Captain 

 Kater's construction, made by Robinson. It is obvious, that 

 the same method may be applied to determine the value 

 of the divisions of a level belonging to larger instruments 

 when required, and it is susceptible of very considerable 

 accuracy when sufficient care is taken in performing the 

 necessary operations. 



II. After having determined the value of the divisions 

 of the scale of a level, it is next proper to adopt a simple 

 and ready method of applying its effects to observations. 



Let e be the eye end of the telescope next the observer, 

 the object end, a the value of one division of the level in 



