9 2 Mr. Lax’s Method of finding the Latitude of a Place , 
consequently, dLJi. — (rf being neglected) will express 
the part of BG, or BG, (when they are supposed to be very small,) 
by which bg exceeds bg. Let this be multiplied into and it 
will equal — J=L== — — ==== = the part of bg itself by which 
it is greater than bg. But our method of equalizing the areas 
will take from bg a portion of this excess bearing to the whole 
the ratio of t : t -f- t ; and, consequently, bg will be made too 
small by — x ■■■ 1 = — - ■ * nearly. Hence - m r 
J T.sy-r *+ T 2 .sy — r J i.sy—r 
will express the minutes contained in the error arising from 
this cause. 
The same conclusion may be deduced from the formula 
— = i — . -V = the area gb, if the increment of the 
y sy X 1 ° 
time be equal to ge. For the same reasons, = l 
= the area gb, if the increment of the time be repre- 
sented by ge. Hence gb — gb = f = ^rxy , 
an d g b ~ [ g - x — 1 — = — r j - — x tt — = that part of the whole 
area gb by which it is made to exceed its proper magnitude; 
and y~ the minutes contained in the error which we 
2 sy—r 
are investigating. If, for instance, the latitude be 52 0 12', and 
the declination 2 0 , both of the same kind, and one of the alti- 
tudes be taken at the distance of 5 0 , the other at the distance of 
io°, from the meridian, this error will amount to Y^^th part 
of the whole difference betwixt the real and the assumed 
