by Means of two Altitudes of the Sun. 1 lg 
each other by a point. The first quantity expresses the log. 
area in the latter, the second expresses it in the former case. 
Thus, for instance, in the fifth column we have 136.108, and 
we are to understand that the log. of the area gb is equal to 
136, when the computed time is too small; and equal to 108, 
when the computed time is too great. 
The argument at the top is carried to every twelve seconds 
of time, or every three minutes of a great circle ; and should be 
continued as far as four or five minutes of time for the first 
twelve or fourteen degrees from the meridian ; as far as three 
minutes for the next ten degrees; two minutes for the next 
ten degrees; and so on, (the time being diminished as the 
tangent of the hour-angle increases,) as far as sixty or sixty- 
five degrees, beyond which the table need not be extended. 
The argument in the first column should be carried to every 
eight seconds of time for the first twelve or fourteen degrees ; 
and to every twenty seconds for the rest of the table. 
Tab. II. This table consists of two columns. The first 
contains the differences betwixt the logs, of the area gb and 
gc, when the latit. is varied one minute in calculating the in- 
cremental area. These differences are negative as far as the 
fourteenth, because so far the area gc exceeds the area g b. In 
the second column are exhibited the errors in the assumed latit. 
corresponding to these differences. 
Tab. III. This table is composed of four columns. The 
first contains the computed distance in time from noon ; the 
second the altitude of the sun ; the third the log. sine of the 
hour-angle, or the log. cosine of the altitude, expressed in the 
first column ; and the fourth twice the logarithm in the former 
