166 Mr Galbraith on Trigonometrical 



position was in latitude 55° 57' 22".5 N., longitude 3° 10' 52."5 W., from 

 ■which the summit of Benlomond was observed to have a zenith distance 

 of 89° 49' 30" ; required the latitude and longitude of Benlomond, and 

 the height of its summit above the sea, together with the azimuth or bear- 

 ing of Edinburgh from Benlomond, taking M, 0, and P from table V ? 



Distance or a =308304 feet log. 5.488979 5.488979 



Azimuth or m' =73° 12' 40" cos 9.460667 sin 9.981082 



Mid lat. !(?+?')= 56 4 26 log M 7.993736 x gives log P 7.992853 



m" = 14 37.9 log. 2.943382,/'= 48' 23".4 log. 3.462914 



V = 55 57 22.5 



m" + ?' = A =56 12 0.4 sin 9.919594 secant 0.254696 



p" = 48 23.4 cos 9.999957 tan 8.148516 



Benlomond,? =56 11 29.8 sin 9.919551 w=l° 26' 58".5 tan 8.403212, 

 Longitude of Edinburgh, =3 10 52 .5 W. 



Longitude of Benlomond =18in 31s.40= 4 37 51 .0 W. 



Mid. lat. |(Z+?') = 56"' 4' 26" sin 9.91895L 



Convergence c = + 1 12 10.4 tan 8.322163 



Benlomond N. 73 12 40.0 W. 



m = m' + c =S. 74 24 50.4 E., the bearing of Edin. from Benlomond. 



To 4 (? + V) = 56° 4'.5 and a=73| log. O is 7.992933 log a 5.488979. 



a= 308304 feet log 5.488979 log. A + 6 



^(2 7^-1)=— 0.42 log 9.623249 log. s + 8 



\ ^' —0° 21' 13.9 log —3.105161 



^ ..'^ - 89 49 30.0 



\ — 89 28 16.1 cot 7.965255^ 



A h = 2846.1 7 feet log. 3.454248 



h = 349.7 3 



H = 3195.8 feet, the height of Benlomond above the 



mean level of the sea. 



When h is small, as in almost all cases in this country, then m h and 

 pa'^ are nearly insensible. 



Example 2. The latitude of Benwyvis in Ross-shir^is 57" 40' 44".2 N., 

 longitude, 4° 34' 38".2 W., and the bearing of the station on Tarbetness 

 is N. 67' 14' 66".4 E., distant 162760 feet, required the latitude and longi- 

 tude of Tarbetness, and conversely, the bearing of Benwyvis from Tarbet- 

 ness ? 



