234 



Radius of the Earth. 



"at once the value of b, corresponding to a latitude not expressed in 

 column A of the table. 



Radius of the Earth. 



1. Knowing the Reduction of Latitude, we can readily obtain the 

 Radius of the Earth, corresponding to any given latitude -L. Thus — ■ 

 let the radius Cvi be designated by p ; and we shall have, from the 

 triangle PCm, 3/" =:p-sin.^PCm, and a?=^ =p"cos.-PCm; but PC7n=-- 

 ■^ — 6, hence, y~ =p^s'm." (^ — 6), and x" =p^cos.^{^~i) = p^ X 

 [1— sin. = (4. — (5)] ; these values of y" and x- being placed in equa- 

 tion (1) will give the relation 

 P' s\n.^ (^ — d) = {l ~ ay [a" -p^[l—sm.-{-^ — 8)]), whence we ob- 



a 1 



tain p = -f niTniT/i"2 ' ^1 which, by substituting gQ| 



1 + 



i-{i-ay 



■Xsin.-(-^^-o) 



a)- 



for a, reduces to P = i+o.006678sin.^(4.-i) ' 



2. Formula (7) can be easily reduced to numbers, for we shall 

 have the value of 6, given by the table for the reduction of latitude, 

 when 4. is assigned : Regarding a, the earth's equatorial radius, 

 unity, we have calculated from formula (7) the table below, in which 

 columns A contain the given latitudes differing by 1°, and columns 

 B, the corresponding values of the terrestrial radius. 



Values of the Earth's radius — the eqtiatorial radius being l.COOOOO. 



Al 



100. 

 110. 

 12I0. 

 130. 

 140. 

 150, 

 16 0. 

 17iO, 

 ISO 

 1910 



2o;a 



B 



999900 

 999880 

 999857 

 999833 

 999807 

 999780 

 ,999750 

 ,999718 

 ,999685 

 ,999650 

 .999614 



B 



0.999614 

 0.999577 

 0,999537 

 0.999496 

 0.9994.54 

 0.999411 

 0.999366 

 999319 

 0.999272 

 0.999224 



300. 

 310. 

 320. 

 330. 

 34 0. 

 350. 

 36 0, 



B 



999175 

 999124 

 999073 

 ,999020 

 998967 

 998913 

 ,998859 

 ,998803 

 ,998747 

 ,998691 

 ,998634 



400. 

 41 0. 

 420. 

 43 0. 



440. 

 50. 

 46i0. 

 470. 

 48 0, 

 490, 

 50l0, 



B 



998634 

 998577 

 998519 

 998462 

 998404 

 998346 

 998288 

 998230 

 998172 

 9981 14 

 998057 



.50 0. 



51 0, 



52 0, 



53 0, 



54 0. 

 55 



998057 

 998000 

 997944 

 997888 

 997832 

 997777 

 997722 

 997669 

 997616 

 ,997564 

 ,99751 



B 



997513 

 997464 

 997415 

 997367 

 997320 

 997275 

 997231 

 997189 

 997147 

 997107 



0.997069 80,0, 



0. 

 

 0, 

 0. 

 0. 

 0, 

 0, 

 79|0, 



B 



997069 

 997032 

 996997 

 996964 

 996932 

 996902 

 996874 

 996848 

 996825 

 996800 

 .996779 



B 



0.996779 

 0.996760 

 0.996742 

 0.996728 

 0.996714 

 0.996703 

 13 996694 

 0.996687 

 0,996679 

 0.996678 

 0.996677 



When it is required to find the length of the radius, by means of 

 the table, for a place whose latitude falls between any two consecu- 

 tive ones of the table, we proceed in a manner entirely similar to 

 that explained for the reduction of latitude. 



3. Since a is equal to 3963 English miles, we have only to mul- 

 tiply this number by the decimal given by the table, and the product 

 will be the number of miles in the terrestrial radius, at the place 

 whose latitude is in column A, on the left of the decimal used. 



