Methods of correcting Lunar Observations. 361 



instead of the logarithmic difference ; and by entering another 

 table with this angle, and first with the distance, and secondly 

 with the sum of the apparent altitudes, he takes out at once the 

 sums of the respective pairs of verse sines, so that he requires, 

 after the auxiliary angle is found, only four references to tables, 

 though two of them involve double entries. 



VI. By Dr. Brinkleys Tables. Naut. Aim. 1820, 1821. 



Dr. Brinkley has published two new methods of computing 

 the corrections of Lunar distances in a compendious manner. 

 The principal peculiarity of the first method is to obtain, from 

 some very short tables, an equivalent to Duuthorne's logarith- 

 mic difference, the rest of the computation resembling that of 

 the Appendix to the Requisite Tables. The second method is 

 a very good approximation, not requiring the natural verse 

 sines ; in which, however, there are about 20 references to short 

 tables of a few figures, so that the whole process does not ap- 

 pear quite so compendious as that which has been explained in 

 Section IV., though it may be a little more accurate in some 

 extreme cases, and may therefore be occasioneJly employed 

 with advantage in the absence of tables carried to seconds, if 

 Dr. Brinkley's happen to be at hand. 



VII. By Logarithms carried to Seconds. 



The methods of Borda, published in the Connaissarice des 

 Terns for 1775, and elsewhere, seem to be the most convenient 

 of the direct methods, when we have logarithms of sines carried 

 to seconds : they are somewhat shorter than Dunthorne's, but 

 they may be rendered still more compendious by employing 

 Dunthorne's table. 



Example. 



Supposing still d = 59° 25' 34 ", /« = 27° 2' 30", s =. 59° 

 1 r 52", p = 59' 27", the corrections of the altitudes -f 51' 33" 

 and — 30", and Dunthorne's difference 9.996719, we find 

 i{m + s + d)zz h = 72° 49' 58", h^d = 13° 24' 24", and 

 the half sum of the corrected altitudes 43" 32' 42i" : or, 



