440 Astronomical'and Nautical Collections. 



the literature of astronomy. I imagine also, that every at- 

 tentive reader will infer, from the form of my second essay, 

 that I must have been already in possession of the mate- 

 rials of the third when I wrote it. So much for my personal 

 explanation : but I have a few more remarks to make in an- 

 swer to some further criticisms of Mr. Ivory. 



The object of my third essay was to give a method, by 

 which the Longitudes and Latitudes might be computed, not 

 as far as the second or fourth powers only of the eccentri- 

 city, but as near as it was possible to compute them with any 

 trigonometrical tables whatever : and this was to be done, 

 not for short distances only, but generally to every possible 

 extent of measurement : and I apprehend that I have ef- 

 fected this by a computation, which is not materially more 

 laborious than if the figure of the earth were spherical. 

 This computation requires the assistance of a table of four 

 octavo pages, and which contains the coefficients, computed 

 once for all, that it would without it have been necessary to 

 determine in each particular case. How far Mr. Ivory is 

 right in calling these four pages '* bulki/ tables,'' and whe- 

 ther he is correct in saying that my expression for the por- 

 tion of the geodetical line requires " the calculation of many 

 subsidiary arcs ;" I must beg every reader, who understands 

 my Essay, to determine for himself. The truth is, that my 

 tables require the computation of no subsidiary arc what- 

 ever, but merely the formation of two arguments, which 

 are obtained by adding to the logarithm of cos m, which is 

 always of necessity to be found in such computations, two 

 other logarithms depending only on the eccentricity, and 

 which are therefore always the same for the same spheroid. 

 Whoever attempts to apply Mr. Ivory's formulas to a deter- 

 mination, equally accurate with that which is obtained from 

 my tables, will very soon find on which side the advantage 

 lies. Mr. Ivory appears therefore to have gone too far when 

 he calls my method " complicated :" and I am the more dis- 

 posed to think, since I have read Mr. Ivory's Essays, that it 

 contains nothing whatever that is superfluous, upon the sup- 

 position that we wish to obtain perfect accuracy both for 

 small and for great distances. 



