698 



VI. THE LENGTH OF A DEGREE OF THE MERIDIAN AND OF THE PARALLEL. 



THE formulae from which the following tables have been computed are as follows : 

 1 degree of the meridian = lll,132.0'9 m 566.05 m cos 2 $ -f 1.20 m cos 4 $ 

 0. 003 m cos 6<j>, etc., in which $ is the latitude. 1 degree of the parallel = lll,415.10 m 

 cos $ 94.54 m cos 3 $ -|- 0.12 m cos 5 <j>, in which $ is the middle latitude. For 

 example, the number given for 40 in the meridian table gives the length from 

 39.30 to 40.30. The dimensions of the earth used in the formulae are those of 

 Clarke's spheroid of revolution of 1866, and are the same as those now (1884) used 

 in the U. S. Coast and Geodetic Survey. They are as follows : 



, semi-axis major = 6,378,206.4 metres, log a = 6.80469857. 

 b, semUaxis minor = 6,356,583.8 metres, log b = 6.80322378. 

 ^ __ q2_ b 2 = aoo67686580 log 2 _ 7.83050257. 



=0.003390075 log = = 7.53020934. 



a 



= 7.22991612. 



a-\-b 



The numbers used in reduction to the different measures are as follows : 



German mile = T ^ equatorial degree = 7421.3802 metres, log 3.87048468 



Nautical league = gV equatorial degree = 5566.0351 metres, log 3.74554594 

 French league = ^ equatorial degree = 4452.8281 metres, log 3.64863593 

 Naut. or geog. mile = ^ equatorial degree = 1855.3450 metres, log 3.26842469 

 Statute mile = 1609.3296 metres, log 3.20664499 



Russian werst = 1066.781 metres, log 3.0280752 



G 



