703 



VII. TABLES FOR COMPUTING TERRESTRTAL SURFACES. 



These tables replace a similar set in the earlier edition, which were published 

 first by Delcros in the Annuaire Meteor ologi que de la France pour 1850, p. 60 et 

 seq. In the following tables the dimensions assumed for the earth are those of 

 Clarke's spheroid of revolution of 186G (see table, p. G 14 et sec.) 



Tlie formula from which the tables have been computed reads as follows : 



sin ^ f cos (L + -^ ^) 



yo ' 



— etc. ; 

 in which a and b are the semi-axes, L and L' the latitudes of the upper and lower 

 limits of the quadrilateral surface respectively, f ^ L' — L. Substituting numerical 

 values, we have for surface of one degree 



224.996175 cos ( L + 0° 30') 



— 0.7G4620 cos (3L+ 1°30') 

 — i +0.001946 cos (5L -j- 2° 30') 



+ etc. 



As in the tables in the earlier edition the numbers are given in square miles the 



linear base of which is a mile equal to ^^^ of the mean degree of the meridian. 



r^. , ., . „ 10001888.2 



That mile is thus ^^ . = 7408.806 metres, log. 3.86974822. In order to 



convert these results into geographical miles, 60=1° equator, multiply by 15.945827, 

 log. 1.20264706 ; into French leagues, 25= 1° equator, multiply by 2.768371, log. 

 0.44222458; into nautical leagues, 20 = 1° equator, multiply by 1.771759, log. 

 0.24840456; into German miles, 15=1° equator, multiply by 0.996614, log. 

 9.99852708 ; into English statute miles, multiply by 21.193684, log. 1.32620646. 



Use of the Tables. 

 Table I., which gives the number of square miles contained in the quadrilateral 

 surfaces of one degree in latitude and longitude, successively ironi the equator to the 

 pole, will be more frequently used. Table II. has been computed for maps on a 

 smaller scale; and Tables III. and IV. for maps of very small scale, covering large 

 areas, in which surfaces of one degree could not be estimated with sufficient accuracy. 

 If the scale is large enough to have the minutes traced on, then Table V. is to be used. 

 For computing a surface by Table I., which may serve as an example for all the 

 others, find first the lowest parallel circle wliicli crosses, on the map, the surface to 

 be estimated ; suppose it is 40° lat. N., and the zone within 40'^ and 41° lat. N. 

 contains four integral degrees of longitude, that is, four surfaces of one degree each 

 way ; then in the first column of the table, on the line beginning with latitude 40°, 

 and in the vertical column headed 4, take the value ot these four surfaces, viz. 

 685.94. Then take likewise the value of the number of surfaces between 41° and 

 42° lat. N., and so on. The fractional parts left outside of the integral degrees are 

 best estimated, with the compass, in decimals, the values of which can be found in 

 the columns of the multiples, by properly moving the decimal point to the left. 

 Having taken them in that way, and summing them up with all the integral sur- 

 faces, we obtain the total surface required. 

 G 19 



