Methods of correcting Lunar Observations. 369 



C. Dr. Maskelyne's method, explained in the Requisite 

 Tables, is considerably more complicated than this, and appears 

 to possess no particular advantage in any case. 



D. Mti Lyons's method is shorter than Dr. Maskelyne's, but 

 requires about seventeen references to tables, including two pe- 

 culiar tables occupying about four pages, which are printed in 

 the Requisite Tables and elsewhere, and which afford, by a 

 double entry, the correction for the obliquity. (A. Precept 5.) 



E. Mr. Witchell's method requires 25 references to tables, 

 including the determination of the correction for obliquity ; and 

 neither of these three methods is materially more accurate th^n 

 the rule here laid down with 11 or 12 references only, 



IV. By the Requisite Tables. 



The methods of Dr. Maskelyne and of Mr. Lyons compre- 

 hend the employment of some short tables, which are printed 

 m this work, as well as the method of Mr. Dunthorne, which is 

 more perfect, but in which the logarithms must be taken out to 

 seconds. 



\ . By the Requisite Tables with the Appendix. 



The Appendix to the Requisite Tables contains a very well- 

 contrived table for obtaining the natural verse sines to seconds, 

 which is rendered much more concise than a logarithmic table 

 could possibly be. By means of this table, together with 

 Mr. Dunthorne's very useful invention of logarithmic differences, 

 which form a table, showing the logarithm of the product of the 

 cosines of the corrected altitudes, divided by that of the cosines 

 of the apparent altitudes, the correct computation may be per- 

 formed more readily, than by any other method, depending on 

 these collections of tables alone. 



Mr. Dunthorne's table is also found, m an improved form, 

 with the addition of differences, in the Connaissance des Terns 

 for 1788, and in Norie's Navigation. 



A. Example from the Appendix. 



Given the distance d zz 59° 25' 34 ", the moon's altitude 

 m = 27" 2' 30', the sun's s — 59° 11' 52', and the horizontaJ 



