101 
by Means of two Altitudes of the Sun. 
former case, when the altitudes are taken on different sides of 
the meridian, are very easily accommodated to the present; 
and it would therefore be superfluous to bestow any farther 
consideration upon them. 
From a review of the inaccuracies to which this method, in 
particular cases, may be liable, it appears that none of them 
can ever be of sufficient importance to affect the mariner. 
If he only computes the time with each of the altitudes and 
the latitude by account, and an incremental area with the 
greatest altitude and the former latitude varied ten minutes, 
the correction will generally be deduced within much less 
than a second, and, in the most unfavourable circumstances, 
within a minute, of the truth. But the astronomer, in every 
instance, even when the latitude and declination are nearly 
equal and of the same kind, by adopting the precautions 
which have been recommended, may be assured of a result 
perfectly ex^ict. If, however, he should entertain any doubts 
upon this point, he might easily compute a second value of the 
incremental area with the latitude already determined; and 
this, it is evident, would necessarily produce a conclusion not 
less accurate than if it were obtained from the direct method. 
The most satisfactory way of proving the utility of this rule, 
will be to suppose a particular latitude and declination; with 
these to compute the altitudes, when the sun is at two given 
distances from the meridian ; and thence to deduce the latitude, 
by an application of our own principles. 
EXAMPLE i. 
Let the latitude be 54 0 27' 50" north, and the declin. when 
the first altit. is taken, 2 0 22' 32", and, when the second is taken, - 
