1836.] 



Three Points in Surveying, 



323 



D = the tabular difference of the logarithmic sine of x. 

 8 = Ditto of (R—cc) 



0' = the correction to be applied to x in decimals of a minute. Where 

 x and (R— x) are both greater or both less than 90 ° : otherwise, 



L ~ \ 



L -f D, 0' = X +o. 0' and 0' = 



— — D 8 



the sign being changed. 



If Galbraith's tables are made use of, 



L+ . 0"= X + or ± 0" 

 ~ 100 ^ - 100 



L — X L ~ S 



where 0" = p + ^ 100 or = p ^ - 100 



The mode of deriving their correction must be apparent, and it is 

 not therefore necessary to investigate it. This method is very conve- 

 nient and handy in practice, and the only objection to it is, that the dif- 

 ferences are not great enough when both the angles are near 90° . To 

 give an application of these methods : — 



Let a = 3 miles 

 6 = 2 — 

 L 7T = 22o 30' 0" 

 — - P = 33 o 45' 0" 

 — C = 104o 28 39" 

 then because as in fig I. D is exterior 



R = 360° — (P -f- # + C) 

 V = 33° 45' 0" 

 w = 22° 30' 0" 

 C = 104° 28' 39" 



160° 43' 39" 

 360° 



R = 199° 16' 21" 



thus a = 3. log = + 0,477121 



y = 2 C. log = + 9,698970 



7T = 22° 30' sin = -f 9,582840 



P = 33o 45^ cosee = + 0,255261 



11 =199° 16' 21" see = — 0,025046 



— 1.094556 



= — 0,039238 



