Methods of- correcting Lunar Observations. 363 



Dunthorne's own Method. 



Log. Diff. 9.996719 Half diff. tr. a. 15° 38'39i" 



Sin. h — m 9.855400 Angle found 24 10 28 ' 



Sin. h — s 9.372426 



Difference 8 31 48| 



Sum 39 49 7^ 



2) [1] 9.224545 

 Sin. 24° 10' 28" 9.612272 



Log. COS. diflF. found 9.995169 

 -1- Sum 9.885403 



2)19.880572 



Cos. 29° 21' 44" 9.940286, half the true distance. 

 In Borda's processes there are five references to the table of 

 logarithms, instead of the four references to the tables of verse 

 sines, and two to that of logarithms, employed in Section VL ; 

 and the advantage of simplicity seems to turn the scale in favour 

 of Borda's method, when tables of logarithms to seconds are 

 at hand. In Dunthorne's own method there are six references 

 to tables, and some further addition and subtraction. 



IX. By Mendoza's Tables. 



See Section VI. The only objection to Mendoza's very inge- 

 nious arrangement seems to be the double entry that is required 

 at the principal steps, and perhaps the bulk of the volume of 

 tables. Indeed the whole process is so much altered from the 

 original steps of the demonstration, that it must be considered 

 as an operation equally mechanical with the motion of a ma- 

 chine, or the reference to a single table of corrections, which is 

 the next method to be considered. 



X. By Shepherd's Tables. 



The great Tables of Corrections, published, at no small ex- 

 pense, by the Board of Longitude, have been so little in request, 

 that the greater part of the impression is said to have been con- 

 demned to be sold (or waste paper. It is true that the labour 

 required for taking out all the corrections and their differences, 



