Suroeying and Levelling, 1 6T 



Constant log. page 162, 6.914630 



a = N. G7° 15' E. cos 9.587386 



a SB 162760, feet, log 6.211548 



4 {I— I') = 0» 6'.2 . log. in minutes . . , 0.713664 

 ... I' =s 57 40;.8 



4 («+?') = 57 46.0 log. M.tab.v. . 7.993621 x gives log. P 7-992817 



mf = 67" 14' 56".4 cos . 9.587405 sin . . 9.964823 



a = 162760 feet log . 5.211548 . . 5.211548 



m" =: + 0° 10' 20" .3 log. 2.792574, /'=:24' 36".3 log. 3.169188 



V = 57 40 44 .2 < 



Lat. X = 57 51 4 .5 sin 9.927714 sec . , 0.273991 



p" = 24 36. 3 cos 9.999989 u'-W W'A log. 3.443179 



? = 57 60 56. sin 9.927703 ( 



4 (« 4- 1') s= 57 45 50. sin 9.92729? 



c'=39' e^.B log. 3.370476 



u' ^ , . . . 46' 14".40 c' = . 39' 6.80 



Correction, (tab. III.) for tan m' — .15 for tan c' — 0.10 



M = . . . . — 46 14 .25 E. c = + 39 6.70 

 Longitude of Benwyvis, . 4 34 38 .20 W. N. 67 14 56.40E. 



Longitude of Tarbetness, . 3 48 23 .95 W. S. 67 54 3.10W. 



Hence, unless in cases of very great nicety, the logs, of the lengths of 

 the arcs less than one degree may be used in place of their tangents, since 

 the corrections are always less than two or three tenths of a second. As 

 a farther simplification, I would recommend a small table, VI, to reduce k 

 to /, and then the operation would be brought perhaps to the greatest pos- 

 sible simplicity, retaining the requisite accuracy.* 



Example 3. The perpendicular from the spire of the church of Notre 

 Dame at Calais on the meridian of Greenwich is 427611.43 feet, and the 

 arc of the meridian from the observatory of Greenwich to the point where 

 the preceding perpendicular cuts it is 184282.44 feet, required the lati- 

 tude and longitude of Notre Dame, the convergence of the meridians, and 

 the bearing of Greenwich from Calais, the latitude of Greenwich being 

 61" 28' 38".5 N. longitude 0° 0' 0", and the bearing of Calais from Green- 

 wich being S. 66* 40' 62".0 E. 



• When the Logarithmic Tables now printing by Shortrede, under the care 

 of Mr E. Sang, are published, they will enable computers to make these calcu- 

 lations very readily, since the log. sines and tangents are given to every second 

 of the circle, with proportional parts for decimal fractions. 



