of Middle Latitude Sailing. 181 



of this problem does not, in a practical point of view, confer ma- 

 terial accuracy on the results, even supposing the earth to be a 

 sphere. Besides, from the use of the log as generally construct- 

 ed, and the instability of the compass in an irregular sea, it is 

 not possible to steer with great nicety, seldom' to so much as 

 within a quarter of a point of the tenth. The errors, therefore, 

 to which a ship's place is liable by these causes are much great- 

 er than by any small inaccuracy in ordinary cases, arising from 

 the common method of computing the course and distance. In 

 addition to these, however, the earth is not a sphere but a sphe- 

 roid, of about yjy of compression, and since this is the case, it 

 appears to me to be an unnecessary refinement to take into ac- 

 count corrections which proceed on the spherical hypothesis. 

 On this account I think it needless to encumber a process with 

 any additional complexity, intended for the use of ordinary sea- 

 men. 



Instead of entering upon any lengthened discussion on this 

 subject here, I shall merely refer to the third volume of De- 

 lambre's Astronomy, chapter xxxvi, for a demonstration of the 

 methods to determine the meridional parts on the spheroid, and 

 to Mendoza Rios' tables for the proper table. It is shewn by 

 the celebrated astronomer first named, that the meridian parts, 

 answering to the reduced latitude for a given ellipticity, are 

 those on the spheroid. Strictly speaking, then, the meridian 

 difference of latitude found in this manner ought to be employed 

 in determining the course and distance by Mercator's sailing, 

 and to the results from these, those by Middle Latitude sailing 

 ought to be made conformable. Suppose, for example, that the 

 middle latitude is 55°, and the difference of latitude 6° ; then, 

 on the spheroidal or true hypothesis to yj^ compression, the 

 correction of the middle latitude is — 7'. But by Workman's 

 Table this correction on the spherical hypothesis will be -f 6'. 

 The results would therefore have been more accurate in this 

 case, by omitting the correction than by applying it. 



It may, consequently, be remarked, that, in Mercator's sailing, 

 the meridional parts should strictly be taken for the reduced or 

 geocentric latitudes, which are always smaller than the observed 

 or apparent latitudes. The reduction of the latitude is greatest 



