70 



by precluding the necessity or reducing the labour of com- 

 puting proportional parts, which is the great inconvenience 

 of" methods of this class. 



Notwithstanding, however, the inconvenience arising from 

 the distinction of cases, some very eminent mathematicians 

 have exerted themselves in investigating the correction of 

 the distance. The first method by Dr. Maskelyne, the 

 methods by Mr. Lyons, Mr. Witchell, and Mr. Cavendish, 

 are of this class, as are also several investigated with his 

 usual ingenuity by M. Delambre, * one lately given by M. 

 Legendre, -f- and one by M. Bowditch, of which an account 

 is given by M. Delambre. X 



The practical conveniences in none of these methods seem 

 to counterbalance the inconveniences, and comparing them 

 with the solutions in which the connected distance is ob- 

 tained, several of the latter appear better adapted for 

 general use. 



An improvement of Mr. Dunthorne's solution, given in the 

 •second edition of the requisite tables, seems to have been 

 the first in which the distinction of cases was avoided, and 

 Avhich was at the same time sufficiently concise to be pre- 

 ferred to the solutions of the other class : yet, in this method, 

 the computation of the parts for seconds was very trouble- 

 some. This rule Avas farther improved by Dr. Maskelyne, 

 in his most useful preface to Taylor's Logarithmic Tables, 

 and those tables, extending to seconds, obviated the incon- 

 venience 



• Conn.de Temps, Ann. 12 & I*. f Mem. Nat. Inst. 



I Conn, des Temps, 1808. 



