620 ON THE FIGURE, DIMENSIONS, AND MEAN SPECIFIC GRAVITY OF THE EARTH 
7. Danish Arc. 
Latitude. 
Amplitude. 
Distance between 
the parallels. 
Lauenburg 
Lyssabbel 
53 22 17*046 
54 54 10-352 
1 31 53-306 
toise. 
87436-538 
8. Prussian Arc. 
Trunz 
54 13 11-466 
toise. 
28211-629 
86176*975 
Kbnigsberg 
Memel 
54 42 50-500 
55 43 40-446 
0 29 39-034 
1 30 28-980 
9. Russian Arc. 
Belin 
52 2 40-864 
54 39 4-519 
56 30 4-562 
56 34 51-550 
58 22 47-280 
60 5 9*771 
2 36 23-655 
4 27 23-698 
4 32 10-686 
6 20 6*416 
8 2 28*907 
toise. 
148811*418 
254543*454 
259110-085 
361824-461 
459363-008 
Neniesch 
Jacobstadt 
Bristen 
Dorpat 
Hochland 
10. Swedish Arc. 
Maldrn 
Pahtawara 
65 31 30-265 
67 8 49-830 
1 37 19*565 
toise. 
92777*981 
If f be the radius of curvature of the meridian at a point whose latitude is X, 
a{\—e^) 
^ (1— e^sin^X)® 
or if we make 
a—b 2 
a + b ^ (1 
«(1 — w)(l — n^) 
P= 5, 
(1 + 2n cos 2A + n^Y 
which being expanded becomes 
gi=a(l — n)(l — w®)N{ I — 2o5 cos 2X+2a' cos 4X— } 
N =1 + (|)V+(||)V+.... 
IVT ^ I ^ ^ ^ 3 I 
Na 
, 3 . 52 , 3 . 5 . 73 ,, 
— o “ho A «"o^“h 
’2.4"' ‘ 2.4.6 2 
If s be the meridian distance between the points whose latitudes are XjXj 
.5=1 ^.dX; 
and putting Xa— A, = 2 X=X,+X 2 , 
— 2a sin <p cos 2X4-a^ sin 2(p cos 4X— — 
