Distance traced on the Surface of an oblate Spheroid. $51 
of the multiples of the arc, we shall get with sufficient exact- 
ness, 
4 6 
GL cos a(S aE ts a ) 
4 6 
+ cos 7! sin 272! SAoich a an &c. ) 
15e& 
128 &c. ) 
3 e sin *7’ cos 7’ 
RIG dzcos2z. 
+ cos7’ sin *7! x ( 
d _ cost dx 
—Cxdz+ 
idx. : é 
Now Ch oe = is the arc 9’, or the difference of longitude of 
the two extremities of the arc z; and hence, by integrating 
between the limits 2° and z + z, we get, 
4 + os oF 
Ss ee cos (2 z° + 2) sin z. 
Now in the foregoing example, we have 
e* cos 7! = ‘0040917 
e* cos 2! = '0000266°4 
& cos z' = :0000001°7 
e* cos 7’ sin? z! = 0000161°2 
@=a?—-Cxz- 
and hence we get, 
C = 0:0020389, _ 
and the log. of the coefficient of the remaining term, multiplied 
by the seconds in the arc equal to radius, is 9°791. Where- 
fore, the arc z being 5° 15! 52"-77 = 18952"-77, we get, 
= 9! — 38-64 — 0-06. 
The arc ¢! is readily computed by this formula, 
; ) ___ cos?’ sin z | 
aa lies cos 7 cos u* 
O.= 87:2) a7 076 
— 38°7 
g = 8°21! 19!-06 
which is the difference of longitude between Seeberg and Dun- 
kirk, the latter place being west of the former. 
In such calculations, the defect is not in the algebraic for- 
mulze, but in the tables in ordinary use, which are not suffi- 
cient to ensure exactness in the fractions of a second. 
The editor of the Journal of Science greatly approves of 
M. Bessel’s researches, and he comments upon them with all 
that complacency which is so natural to him when he thinks 
he has got things in a right train. He concludes his remarks 
with announcing in set phrase, a simple rectification of the geo- 
delitic curve. It is an expression of the length of an elliptic 
arc 
