g 6 Mr. Lax's Method of finding the Latitude of a Place , 
But the ratio of gb to gc will itself exceed the ratio of GB to 
GC, its proper value, by m . — -j f - ■■ . - s +^_ r r s . L ; and, by the me- 
thod of equalizing the ratios, it is suffered to retain a portion of 
this difference expressed by j-L— ; and, therefore, it will be 
made too great by m . 
these quantities, m . — 
_r 2L±_iii.L. The sum of 
t + r s y — r 
_L 2 9 i tT+ 2 r st , r y + zrsT 
iooooo t -f r sT — r *■ s y — r * 
will determine, in minutes of a degree, the amount of the whole 
error, when the incremental area gc represents one minute of 
latitude. But if, in our second hypothesis, the latitude be varied 
n minutes, instead of one, and p be the correction required, the 
above expression becomes p . 
~s + ' —r T m ^ nutes * Hence, in the lat. of Cambridge, when 
2 9 1 
I OOOOO ’ t + T 
tT + 2r st 
the declination is 2° north, and the sun’s distance from the me- 
ridian at one observation is 5 0 , and at the other 45 0 , p being 
equal to 10, and n equal to unity, the error will amount to little 
more than half a second. 
But, whenever it is judged necessary to guard against this 
species of error, we need only diminish the value of in the 
last expression; and this will readily be effected by dividing 
the difference betwixt the real and computed intervals of time, 
in such a manner that the portions belonging to the two obser- 
vations may be to each other inversely as the quantities taken 
out of the fourth table, according to the instructions before deli- 
vered. When the portion belonging to the greatest altitude is 
thus obtained, we can immediately deduce the correction to be 
made in the first assumed latitude, and then proceed to calculate 
