242 On finding the Longitude 



FE + E C will differ from F C by an almost unappreciable frac- 

 tion of a second. If it were possible for F E C to be 175^, which 

 it never can be; and if F E were 15°, the difference between 

 FE + E C and FC would not exceed -J^^ part of a second. 

 It would, in fact, be too minute for computation with the best 

 tables in common use. In all cases, therefore, F E + E C may 

 be taken for F C, without sensible error. 



Now C E is necessarily less than A C, from the property of the 

 curve ; the theoretical existence of the correction is therefore ap- 

 parent, notwithstanding Mr. M.'s censure of those whom he af- 

 t^fjts to call the " learned authors" that have recommended it 

 to be applied. 



He has indeed charged those authors with a mistake which he 

 must be content to have attributed to himself. It is not, as he 

 says, the line DE (in his figure) which they "have been pleased 

 to consider as shortened by refraction ;" but the line drawn from 

 the centre to the point in the disk from which the distance is 

 measured. And it has just been shown that if the semidiameters 

 so reduced be applied to the observed distance, the result will 

 differ from the apparent central distance by a quantity indefinitely 

 small. I proceed, in the next place, to show that the method 

 which has hitherto been pursued by those computists whom 

 Mr. M. describes as " aiming at great exactness," will always 

 give correctly the true and apparent altitudes of the centres of the 

 objects. 



Setting aside the effect of refraction, the centre of the lumi- 

 nary will be in the line joining the observer and the centre of the 

 disk. And if, from the effect of refraction, the centre of the 

 disk be elevated, the centre of the luminary, having the same al- 

 titude, will be elevated in the same degree. The apparent place 

 of the centre, therefore, will still be in the line joining the ob- 

 server and the point to which the centre of the disk is elevated 

 by refraction. 



Let then B, C,be the true places 

 of the lower limb, and the centre 

 of the luminary; and D,E, the ap- 

 parent places of the same points. 

 B A C will represent the true or 

 augmented semidiameter, and 

 DAE the reduced or contracted 

 semidiameter corresponding to the 

 altitude FAD. _ 



If now to D A F there be added 

 the reduced semidiameter DAE, 

 the sum will be the angle FAE, obviously the apparent altitude 



of 



