88 Mr. Lax’s Method of finding the Latitude of a Place , 
y 1 ^— Py 1 r + 2 dlylx-<P>? 
y$ X l y'S — d X 
zdlyoX — 
== [d' x* 
yZxlyZ-dx. V 
being rejected, as incomparably less than the sum of the 
other terms,) x . and, consequently, we 
have m . 
*T t 
. L = 
sy 
in — 
29 
7+2 rs 
nutes. Hence it appears that, in the latitude of Cambridge, 
when the sun’s declination is 2 0 north, and his distance from 
the meridian f, this error will be equal to in . — — — . — — mi- 
- 1 2 43 12 
nutes of a degree. Let the assumed differ from the true lati- 
tude ten minutes, i. e. let m = 10, then will the error amount 
to half a second ; and, if we suppose m = 30, the error will 
not exceed four seconds. 
If, instead of varying the assumed latitude one minute, we 
vary it n minutes, in calculating the area gc, the above ex- 
pression will be transformed into m . — — . - 2 ? . 2 ± 1 LL 
r 2 100000 sy — r 7 
the increment of the latitude being, in this case, n L. The 
error will consequently vary as m . -—g— • n, when the declina- 
tion, latitude, and time of observation are given; and, if we 
suppose the real to differ from the assumed latitude p minutes, 
tliis last expression will become — .n—p. p 
which varies as - ~ ” , when p remains constant; and, of course, 
the error may be diminished in any proportion by diminishing 
this quantity . Now, the increment of the latitude is al- 
ways = xT z; and, therefore, since z is determined by the 
process explained above, we have only to ascertain the value of 
T, in order to approximate nearly to p. But the sine of the 
t 
