78 Mr. Lax's Method of finding the Latitude of a Place , 
their respective increments in the next interval of time, and sub- 
tract or add the part assigned to each, according as it is 
greater or less than the other. The table, however, might 
easily be carried to such an extent, that exactness in this division 
could never be required ; but, on the contrary, it would be quite 
sufficient, when the hour-angles were nearly equal, to add the 
areas together, and take half the sum for the value of each. 
From these principles may be deduced the following practical 
rule for determining the latitude of a place. When the sun 
comes within fifteen degrees of the meridian, in the morning, let 
his altitude be taken, and the time of the observation be accurately 
marked ; and let another altitude be taken after he has passed 
the meridian, whilst his distance from it is less than fifteen de- 
grees; and let the time of this observation likewise be noted. 
Then, with the supposed latitude of the place, compute the times 
corres ponding to each of the altitudes in terms of the log. cosine 
of the hour-angle, and take the difference of the intervals, as 
shewn by the clock, and determined by calculation, and divide 
it betwixt the observations in the manner explained above. 
Compute the log. cosine of the hour-angle a second time, with 
the greatest altitude and the latitude increased or diminished by 
a minute, according as it appears, from a comparison of the 
intervals, to have been too little or too great ; and take the dif- 
ference betwixt this log. cosine and that which resulted from the 
first operation, when the same altitude was employed. Having 
thus obtained the two areas gb and gc, we must subtract their 
logarithms from each other, and with their difference entering 
the second table we shall find the degrees, minutes, and seconds, 
by which the assumed latitude is to be increased or diminished. 
It will be needless, perhaps, to suggest that, in the higher 
