lii ^ GEODESY. 



Numerical examples. — i°. Suppose c^i = 0.^0 = 9°° and AX = 360°. Then 

 (7) should give the area of a hemispheroid. The calculation runs thus : 



log. log. log. 



^1 5-7375398 C2 2.79173 ^3 9.976 — 10 



cos ^ 9.8494850 — 10 cos 3 9.84948,, — 10 cos 5 <^ 9.849,, — 10 



sin \ A<^ 9.8494850 — 10 sin | A<^ 9.84949 — 10 sin -g A^ 9-848,, — 10 



360 2.5563025 360 2.55630 360 2.556 



Sum 7.9928123 5.o47oo„ 2.229 



Hence — 



ist term = -|- 9835S591 

 2d term = -j- 11 1429 

 3d term = -j- 169 



(2= sum = 98470189 



Twice this is the area of the spheroidal surface of the earth ; /, e., 196 940378 

 square miles. 



2°. The last result may be checked by (4). Thus, 



(e^ e^ \ 



Y + 7^- + • • . j = 0.00225928 



Jog (i - y - • . • j = 9-9990177 

 log a^ = 7.1961072 



log 4 TT = 1.0992099 



log (196940407) = 8.2943348 



This number agrees with the number derived above as closely as 7-place 

 logarithms will permit, the discrepancy between the two values being about 

 TTTTiriTrtTTj P^^'t of the area. Hence, with a precision somewhat greater than the 

 precision of the elements of the adopted spheroid warrants, 



Area earth's surface = 196 940 400 square miles. 



The areas of quadrilaterals of the earth's surface bounded by meridians and 

 parallels of 1°, 30', 15', and 10' extent respectively, in latitude and longitude, are 

 given in Tables 25 to 29. 



10. Spheres of Equal Volume and Equal Surface with 



Earth's Spheroid. 



ri = radius of sphere having same volume as the earth's spheroid, 

 ^2 = radius of sphere having same surface as that spheroid. 



= a(i - ^e^- y\ c' - xiiff e' -. . .). 



