Distance traced on the Surface of an oblate Spheroid. 345 
has computed the angles at the extremity of a length equal to 
400,000 metres, supposing the oblateness equal to =! and 
the results of his calculation, given in pp. 221, 222, expressed 
by the symbols we have and are as follows: ; 
‘ s = 400,000 
bri 452 
“u = 44° 53! 14!-73 
g = 5° 4! 3!-78 
f 86° 25! 8-46: 
i 
also, taking the proportion of the axes of the spheroid, we 
have f/1+e2= a and hence 
E vat OLGi 
Mittra 0°0065045 
log. —3'8131838. 
We may now compare the values of z computed in the dif- 
ferent ways we have investigated. In the first place, by the 
formula, sin u = sin / cos 2, we get 
== Bo Bo SOF 
As uw is here the result of an exact calculation and not affected 
with errors of observation, the value of z now found must be 
accurate as far as the tables usually employed will allow. But 
if u were determined by observation, we may reasonably sup- 
pose an error of 1" in defect; then 
p= ge Sn baths; 
so that an error of 1" in w has produced one of near 16” in z. 
Next computing by the difference of longitude, we have 
tan ¢ cos/ = tan 2, 
RR AOE LEN 
then, by the formula (D), 
z= 2 X 1:001631 = 3° 35! 38"-20. 
Lastly, to determine z by means of the variation in azimuth, 
we have 
w = 90° — yu! = 3° 34) 5154 
tan w 
tan / 4 
8° 35! 16"°78: 
sin y = 
J 
then, by the formula (E) 
z= y xX 1001625 + OTT ="8° Sols7ss. 
The values of z deduced from the difference of longitude 
and the variation of azimuth are not exactly equal, the former 
exceeding the latter by 0-32, which seems to arise from small 
errors in the calculated longitude and azimuth. For ac- 
Vol. 67. No. 337, May 1826. 2 cording 
