[ 318 ] 
another line on the bafe, reprefenting the meridional parts ; it is 
engraved on a cylinder contained within a groove in the bafe, 
and any part of this line neceflary may be eafily had by revolving 
the cylinder until it appears through the aperture prepared for 
that purpofe. 
Tur method of working every cafe which occurs in navi- 
gation is to make the inftrument fimilar to that ideal triangle 
which is compofed of the difference of latitude, departure and 
diftance failed ; or to that compofed of the meridional difference 
of latitude, difference of longitude, and enlarged diftance ; or to 
that compofed of the difference of longitude, departure, and 
fine of the middle latitude, which is done by means of the data 
procured from the compafs, log-line and quadrant; whence it 
follows, from the nature of fimilar triangles, or from the rela- 
tion which exifts between the fides, triangles, and the fines of 
their oppofite angles, that the parts of the inftrument become 
proportional to thefe which they reprefent, and will afcertain the 
length of thé lines, or the extent of the angles fought, by its 
graduations. 
a 
To make this general rule more eafily underftood, it is here 
particularly applied to each of the cafes of navigation. : 
CASE 
