244 On finding the Longitude 



Those which Mr. M. imagines he has detected are merely con- 

 sequences of his own misconception. 



But after all his affectation of superior precision, it will not 

 perhaps be expected that the improved method which he proposes 

 for finding the true altitude is founded on the same principles, 

 and must always produce exactly the same result, as that of which 

 he has endeavoured to prove the fallacy. — Yet that this is the 

 case will be easily made appear. 



From the apparent altitude of the limb FAD (see last figure) 

 he deducts the corresponding refraction, which is DA B ; to the 

 remainder he adds the true semidiameter B A C, and the sum is 

 obviously the angle FA C, the true altitude of the centre above 

 the sensible horizon, and of the same magnitude as we have be- 

 fore determined it to be. 



If further elucidation be necessary, the truth of the matter, in 

 any given case, may be put to the vulgar test of arithmetical com- 

 putation. Let us take an extreme case, and suppose the alti- 

 tude of the lower limb to be 5°, and the semidiameter parallel to 

 the horizon 16'. — The computation for the true altitudes above 

 the sensible horizon by both methods will stand as under : 



By the common Method. 

 Observed altitude, lower limb . . 5° 0' 0" 

 Reduced semidiameter . . . . 1 5 35 



Apparent altitude centre . . . , 

 Refraction to 5° 15^' .. 



True alt. above sensible horizon , . 



By Mr. Meikle's Method. 



5° 0' 0'' 

 Refraction to 5° 9 53 



True alt. lower limb above sens. hor. 4 50 7 

 Horizontal semidiameter .. ,. 16 



5 6 7 



This I hope will be satisfactory. 

 On this part of the subject it appears then, that if Mr. M. has 

 produced nothing new, he has proposed nothing which will lead 

 to error. But when to the angle FAD he directs the " aug- 

 mented" semidiameter, that is the angle BAG, to be applied, 

 and considers the result as the apparent altitude; he immediately 

 gets perplexed in what he calls the angular point of the triangle, 



and 



