3 IS DESCRIPTION OF GARNETT'S NAVIGATION CHART, &C. 



: IV Terence of longitude 910' log. 2959041 



: . Cos. of mean parallel 44° 35' log. cos. 9.852620 



: Tan. of Course 3"° 4' log. tang. 9.878174 1. cos. B 9 901967 



A— B=distance - - 1074,6 miles log. 3.031520 



which agrees with the solution by Meridional Parts, or logarithmic tangents ; bxit by the 

 middle latitude not corrected, the course would have been 37° 16' and distance 1078 miles. 



EXAMPLE II. 



A ship from the latitude of 5 1° 1 8' N. in longitude 22° 6 

 W. sailing on acourse between theS. and E. has made 564- mile* 

 of departure, and 786 mdes difference of longitude. Required 

 the latitude of the place arrived at? (See Robertson's Navigation, 

 prob. X. page 170.) 



As difference of longitude , 786' log 2.895423 



: Departure - - 564' log. 2.751279 



: : Radius ... . 10-000000 



Cos. Mean Parallel 44° 9' log. cos. 9.855856 



Mean par. X 2 = 88 IS 



Subtract given lat. 51 18 



Lesser lat. (nearly) 37 



Did', of lat- (nearly) 14 18 



A9 the approximate lesser latitude must be diminished by twice the correction in Ta- 

 ble I to obtain the true lesser latitude, assume it 36° 10', and difference of latitude 15° 8', 

 the correction from Table I will then be 30' ; — this subtracted 



from 44° 9' the mean parallel, leaves - 43° 39' for the Middle Latitude. 



From the double of which - - - 87 18 



Subtract the greater latitude - - - 51 18 



Leaves the true lesser latitude - 36 differing a whole degree from 



the latitude found by the common method. 



These examples sufficiently shew the great use of Table I, to correct the errors of mid- 

 dle latitude sailing ; which by this means is made equally correct, and is more simple thar 

 Mercator's sailing by the table of meridional parts. 



Table II is intended to make the Loxodromic Chart strictly accurate, although this 

 correction in practice will be found insensible. It also shews the error of taking half the 

 sum of the natural cosines for the cosine of the mean parallel, which has been recommend- 

 ed in middle latitude sailing. 



This small correction of the Loxodromic Chart, by means of table II, will be easily un- 

 derstood from the following 



EXAMPLE. 



Suppose a ship to sail from the latitude»of 20° N. to the lati- 

 tude of 45° N. on a course between the N. and E. and make 

 40° difference of longitude; required the course and distance. 

 (See the Loxodromic Chart.) 



By table II, the correction for 20° lesser latitude and 25° diff. of latitudes is — 75',% 

 which measure off to the parallel of 45° from the meridian of 20° (the half diff. of longitude) 

 from a to A perpendicular to the parallel, so that a b =■ 75',9 ; then draw the line c b from 

 the parallel of 20° latitude to the parallel of 45°, making the half difference of longitude 20° 

 on each side the central meridian (which is essential to the principle of the chart,) and it 

 will be the correct course and distance. The line c d represents the course and distance 

 un the chart, without the tabular correction, which correction in all practical cases will be 

 insensible. " 



