Methods of correcting Lunar Observations. 365 



nature of a graphical construction. But these scales must ob- 

 viously be liable to the errors which seem to be inherent in the 

 tables ; and their application can scarcely be more simple or 

 commodious, than the method by the scale and sector already 

 explained. 



XII. Varions Formulas. 



Many other devices have been suggested for facilitating the 

 solution of this important problem ; and some of them, though 

 they do not possess equal advantages with those which have 

 been already explained, may deserve to be simply enumerated 

 here. 



A. Mr, KrafTt's formula, which seems to have been the foun- 

 dation of Mendoza's, is vs D — vs {d + b) + vs (d /w 6) — vs 

 ([w ~ s] + 6) - vs ( [tm ~ s] ~ 6) + vs (M-f- S), D, M, and S 

 being the true distance and the true altitudes, and b the auxiliary 

 angle, of which the cosine is =: ^ cos. M cos. S sec. m sec. s. 



B. Dr. Maskelyne's formula, published in the Introduction to 

 Taylor's Logarithms, is equivalent to this ; tang, b zz cosec. J 

 (M /*» S) v/ (sin. I (rf + [m — s] sin. | (d — [ m ~ s] ) cos. M 

 cos. S sec. m sec. s) ; and then sin. | D =: sin. ^ (M ;>» S) sec. b. 



C. Several other methods of computation may be found in 

 the Connaissance des T'cjws for 1775, 1785, 1796, 1806, 1807 

 and 1808. But it is of more importance to attend to such cor- 

 rections, as are equally applicable to all modes of computation , 

 and without which complete accuracy can never be attained 

 even in ordinary cases. 



XIII. Tables of Minute Corrections. 

 Whatever method may be preferred for the accurate calcula- 

 tion of the correction of the distance, there are some precau^ 

 tions, not universally understood, which will require attention 

 when great precision is required. 



A. Of the Vertical Semidiameters. 

 Since the actual refraction affects the observation in its pri- 

 mitive state only, it is obvious that the correction, which it 

 requires, must depend on the altityde of the observed limb of 



