71 



venience from proportional parts. But Taylor's tables can- 

 not be very generally diffused, and besides they require too 

 particular attention in using them, to be held in that estima- 

 tion with seamen which is their due. 



Mr, Mendoza, to whose exertions nautical astronomy is 

 much indebted, has given, in a valuable paper in the Phil. 

 Transactions for 1797, forty different formulas fop computing 

 directly the true distance. Of these, that which he selected 

 as best adapted to practice, affords a very concise and 

 plain method of computation, requiring only the addition 

 of five versed sines. It may be doubted, however,^ whe- 

 ther it is preferable to Mr. Dunthorne's first method, im- 

 proved by the substitution of versed sines for co-sines, as 

 was done by Dr. Mackay. * Mr. Mendoza's method re- 

 quires an extensive table for an auxiliary angle (equivalent 

 to the auxiliary table in Mr. Dunthorne's method, and in 

 those derived from it,) and the formation of five different 

 arguments, and also to practise it with convenience, a com- 

 plete table of versed sines, for at least the semircircle.. Mn 

 Mendoza, anxious to improve still farther the solution of 

 the problem, published his very extensive tables, -j- by which 

 he reduced the method to be equivalent to taking out and 

 adding together three numbers, and not requiring the forma- 

 tion of arguments. His ingenuity and perseverance in form- 

 ing, computing, and publishing his tables, are deserving of 

 the greatest praise. But on several accounts those tables will 



L 2 • not 



* A Treatise on the Longitude, &c. 



\ Tab. II, CollectioQ of tablet for Navigation and Nautical Astronomy. 



