[ 921 ] 
one, as can be, the dead reckoning of the {hip need 
not be intirely relied on for that purpofe; for the 
inftrumental conftru&ion propofed by Mr. Collins (d) 
will very readily give the true latitude, as nearly as 
the inftruments ufed can exprefs : and his method 
may be defer ibed thus. 
Two ftraight lines AB, AC 
being drawn in an angle cor- 
relponding with the diftance 
in time between the obferva- 
tions, and in one of the lines, 
as AB, the lengths AD, AE 
being taken from any fcale of 
tangents, one equal to the 
tangent of half the fum, and 
the other equal to the tangent 
of half the difference of the 
diftance of the fun from the pole, and from the zenith 
of the firft obfervation, and alfo the points F, G, taken 
in the other line in the fame manner related to the 
other obfervation ; then circles being defcribed on the 
two diameters D E, F G, the diftance of A from one 
of the in ter ft dtions of thefe circles will be the tan- 
aent of half the complement of the latitude. . 
^ Moreover, as in the treatife, which has given oc- 
cafion to this difcourfe, it is propofed fometimes to 
take into confideration the (hip’s motion during the 
time, between the obfervations, but imperfectly, re- 
gard being had to the change made by the fhip in 
longitude onty ; but the change in latitude alfo may 
be taken into confideration in the foregoing con- 
( d ) In the i^lace above cited. 
ftru&ion. 
