[ 9i8 ] 
been 29 0 13', and the greater 40° j in 9 degrees of 
north latitude the interval between the obfcrvations 
would have been nearly the fame, as before. But if 
this latitude be fought by any latitude affumed near 
it, the latitude computed according to the method 
above, will fall more remote from the truth, than 
that a domed, and err the fame way. 
In general, the error in the latitude affumed will 
bear to the error in the latitude computed, nearly 
the ratio compounded of that of the reCtangle under 
the radius and the coline of the diftance from noon 
of the middle point of time between the two obfer- 
vations to twice fin. ~ ABC x fin. ~ ABD, and 
the ratio of rad. x fin. AF to fin. BC x cof. AB; 
infomuch that the difiance of the middle point of 
time between the two obfervations from noon is 
to be confidered, as the limit, where thefe com- 
putations fhall ceafe to converge, when the rect- 
angle under the radius, and the coline of this 
difiance from noon fhall be to twice fin. I ABC 
x fin. 7 ABD, (or the cofine of this diftance to the 
difference between the verfed fine of this diftance 
from the verfed fine of half CBD) as fin. BF x cof. AB 
to rad. x fin. A F. And the errors in the alfumed 
and computed latitudes fall on different fides of the 
true latitude, when both the obfervations are on the 
fame fide of noon, and the zenith lies between the 
meridian fun and the elevated pole ; or when the ob- 
ervations are one before, and the other after noon, 
if the meridian fun paffes between the zenith and 
the elevated pole : otherwife, they fall on the fame 
fide of the true latitude. 
However * 
