622 ON THE FIGURE, DIMENSIONS, AND MEAN SPECIFIC GRAVITY OF THE EARTH, 
where r is the number of observed latitudes in any arc, the symbol 2 signifying 
summation with respect to the different arcs. 
Bessel adopts the approximate elements o-i=57008 toises the equations 
for the different arcs are then as follows, putting I0000?'=j9 and \(ih=.q. 
1, Peruvian Arc. 
a:W-a;,= + l'966+l-1225p+5:60.‘j9 9. 
2. First East Indian Arc. 
4*)— 4-0'937+0“5697 jo+2-5835 q. 
3. Second East Indian Arc. 
— ^3=+ 5-346+3'5628/?+ 15-9269 q. 
a-®— + 4-801 +5-7458 jo+24-0257 q. 
xf~x^= + 12-440+7-6875 p+29-798] q. 
4. French Arc. 
+3-991 +0-97l3;?+0-8601 q. 
xf-x,— +0-646+0-9772 jo+0-8642 q. 
xf - x^-= +0-026+1-6378 j0+ 1-1889 q. 
5-035+2-7041 J0+ 1-2671 q. 
a;f_X4= + 1-191 +3-6655 j»+0-8659 q. 
xf—x^= +5- 1 7 1 +4-4537 p+0-205 1 q. 
5. English Arc. 
+» -X,— + 3-772+0- 1 064;?- 0- 1 038 q. 
xf —X, — + 3-735 +0-3095 jo— 0-3 1 76 q. 
+^>—^ 3 =+ 4-302 + 0-5784^9 — 0-6308 9 . 
^ 3 =+ 1-258+1-0224^—1-2226 q. 
xf—x,= -\- 7-874+2-0272 p — 2-8959 9. 
xf—x,= -\- 7- 127+2-4649 p- 3-7683^. 
.rf)_^^=4.10-883+3-6763p— 6-6163 q. 
6. Hanoverian Arc. 
.r[j'>-X6= +5-679+0-7263 p— 0-9224 q. 
