FROM THE ORDNANCE TRIGONOMETRICAL SURVEY. 
621 
where g is the length of a mean degree of the meridian determined by the relation 
Hence if s be the meridian distance of two points whose latitudes are X,+.ri and 
^2~1"'^25 we must substitute in this equation ^+‘^ 2 — foi' neglecting the influence 
of the small quantities x on the mean latitude of the arc ; after this substitution we 
obtain 
(p 4 * 2 a sin (p cos 'Jk — a! sin 2^5 cos 
|W/= 1 d- 2 a cos p cos 2 X. 
Now let gi «! be approximate values of g and a, so that 
I 1 +* 7 
Then substituting in the preceding equation, we have finally 
rseoo. , „ i„i 
-s — <P d- Pi — I 
where x^ x^ and p are expressed in seconds, and 
2 a, . ^ 
P,= - - - , 7 , Sin p COS 2k 
‘ sin 1'' ^ 
5«2 
P„=-^ — sin 2ffl COS 4X. 
® sm 1" ^ 
This equation contains the relation between the corrections to the terminal latitudes 
of a measured line s required to bring them into accordance with the measured 
distance, the elements of the spheroid of reference being as expressed above ing, a, i k. 
An arc in which there are n observed latitudes will therefore afford n— 1 equations 
of the form 
x^—x^=.ni-Yai-\-hk ; 
the quantities ik must then be determined so as to make the function 
x^^-\-xl-]rxl-Y .... 
a minimum. 
The final equations thus deduced are 
0=:M d-A/+B^ 
0=M'+Bi+B'^ 
