260 Mr. Galbraith on the Determination of the Latitude 



- 23° 5'' 28" = 45° 58' 54" = BLC. But BLC + PLB = PLC 

 = 167° 2' 46". 



6. It is now necessary to compute the sides LC, MC, and 

 BC, which will be found to be LC = 1 7' 57"-46, MC = 24' 56"-84, 

 and BC = 16' 29"-70. Hence LC = 20-66 English miles, 

 MC = 28-71, and BC = 18-98. 



7. In the triangle PLM are given the sides PL, PM, and 

 LM, to find the anglesPLM = 97° 58' 24", PML = 81° 24' 48". 

 If Napier's analogies be applied to the triangle LPM, these 

 will be found to be 97° 58' 34", and 81° 24' 38" respectively. 

 Also PLM + BLM + CLB = PLC = 167° 2' 46", as before. 

 In like manner PML + LMC = PMC = 123° 39' 40". 



8. In the triangle LBC are given the sides to find the an- 

 gle LBC = 51° 31' 32"; and consequently, LBC + PBL = 

 109° 58' 42". 



9. In the triangle PLC are given the two sides PL, LC, 

 and the contained angle PLC, to determine PC the co-latitude 

 = 34° 2' 32"-6, and the latitude = 55° 57' 27"-4 N. deduced 

 from the West Lomond. 



10. In the triangle PMC are given the sides PM, MC, and 

 the contained angle PMC, to deduce PC the co-latitude, and 

 thence the latitude = 55° 57' 26"-8 obtained from the Isle of 

 May. 



11. In the triangle PBC are given the sides PB, BC, and 

 the contained angle PBC, to find PC the co-latitude, and thence 

 the latitude 55° 51' 28" deduced from North Berwick Law. 

 The mean of these three is 55° 57' 27"-4 N. 



12. In the triangle PLC there are given the three sides to 

 find the angle PLC, the difference of longitude between the 

 West Lomond and the Calton Hill =7' 16"-5. 



Hence 3° 17' 4"-7' 16"-5 = 3° 9' 47"-5 W. by West Lo- 

 mond. 



13. Again, in the triangle PMC there are given all the sides 

 to find the angle MPC, the difference of longitude between 

 the Isle of May and the Calton Hill =37' 5"-6 W. 



Hence 2° 32' 47" + 37' 5"-6 = 3° 9' 52"-6 W. the longitude 

 of the Calton Hill deduced from the Isle of May. 



14. Lastly, in the triangle PCB, the sides are given to find 

 the angle CPB, the difference of longitude between North 

 Berwick Law and the Calton Hill =27' 42" '4 W. Whence 

 2° 42' 11" + 27' 42"-4 = 3° 9' 53"-4 W. The mean of these 

 three gives 3° 9' 5l"-2 = 12"' 39^-5 W. 



In order to verify the latitude thus determined, I measured 

 a base line on the road along the north side of the Calton Hill, 

 with a hundred-feet chain constructed by Mr. Adie, in order 



to 



