[ 914 ] 
Radfl : cof. lat. x cof. decl. O 
fin. 
ABD -f ABC 
2 
fin. 
ABD- ABC 
lin 
AD+AC r AD-AC 
. ! x an. } 
2 2 
now requiring the common logarithmic fines only. 
Again, the fquare of the radius being, as above, 
to cof. lat. x cof. decl. O, as the verf. f. ABC to 
verf. f . A C — verf. f. A F, or as verf. f. ABD to 
verf. f. A D — verf. f. AF, thefe analogies exprefs the 
fecond operation, which, in this treatife, is unnecef- 
farily confined to the leffer angle ABC. The co- 
lumn in the table intituled Riling confifts of loga- 
rithmic verfed fines, which may be applied to either 
of the angles ABC or ABD promilcuoufly ; for 
here A F being equal to the excels of B C or B D 
above the arch BA, aflumed for the complement of 
the latitude, the arches A C and A D, in the pre- 
ceding analogies, will be the complements of the alti- 
tudes obferved, if the latitude were truly aflumed, 
otherwife not ; but the difference of their verfed fines. 
will however be equal to the difference of the verfed 
fines of the complements of the true latitudes $ for 
this is fuppofed in the firfl operation. Therefore, if 
one of the fourth terms of thefe analogies be de- 
ducted from the verfed fine of the complement of 
the greater altitude, or the other from the verfed fine 
of the complement of the leffer, the remainder will 
be the fame, and exhibit a verfed fine for the com- 
plement of the funs altitude different from AF, 
when B A is aflumed different from the true latitude, 
and nearer to the truth, if the times for the obferva- 
tions are properly chofen. 
But farther, the two preceding analogies may be 
reduced to thefe j 
Rad. 
