77 
by Means of two Altitudes of the Sun. 
little, when the azimuth is less than 90 degrees ; but the con- 
trary, when the azimuth exceeds a right angle. Tables of the 
above description shall be constructed, if this method be re- 
ceived with approbation ; and, in the mean time, it is proposed 
to subjoin a short specimen which is already completed. 
I have presumed that we are able to determine eg, the error 
in time arising from an error in the assumed latitude, at either of 
the observations ; and hence it becomes necessary, before we can 
avail ourselves of the principles which have been laid down, to 
point out the manner in which this may be accomplished. The 
clock gives us the whole interval betwixt the observations (sup- 
posed to be made on different sides of the meridian) equal to 
ae -f ae, and by computation we obtain ag -f- ag, and 
thence we deduce eg -f- eg the whole error in time. Now the 
area gb is equal to gb; and therefore, if we make a rough divi- 
sion of the whole error, without any regard to accuracy, in the 
inverse ratio of the hour-angles at the two observations, and, 
entering the first table with these times, mark the area corre- 
sponding to each at their respective distances from noon, and 
increase the one and diminish the other equally, till we get the 
areas of the same magnitude, this, we may conclude, is the pro- 
per value of each. 
If the table were constructed to every second of time, we 
might ascertain these logarithmic areas merely from inspection ; 
but, as it will be advisable to confine it within narrower limits, 
we shall sometimes find it necessary, as in other tables, to 
deduce their ultimate value by the rule of three. When we 
have increased one portion of time and diminished the other, till 
the difference of their corresponding areas becomes a minimum , 
we must divide this difference betwixt them, in the proportion of 
