104 



Table 84. ACCELERATION OF GRAVITY. 



For Sea Level and Different Latitudes. 



This table has been calculated from the formula g-^ =^45 [i — .002662 cos 2<^],* where <f> is the latitude. 



• The constant .002662 is based on Harkness' data (Solar Parallax and Related Constants, Washington, i8gi). 

 The acceleration of gravity for any latitude <t> and elevation above sea level A is very nearly expressed by the equation 



g^=i:i5 ( I— .002662 cos 2<|>) ['— }f ('~^)J> 



where R is the earth's radius, 5 the density of the surface strata, and A the mean density of the earth. When S=o 



we get the formula for elevation in air. For ordinary elevations on land — is nearly J, which gives for the correction 



at latitude 45° for elevated portions of the earth's surface 



^«.^=98o.6X — = ia25.7s— cm. per sec. per sec. 

 4^? ^R R 



_i £ 



=386.o62X 511=482.562— in. per sec. x>tt sec 

 4^ R 



=32.i7i9X^ =40.2149 — feet per sec. per sec. 



4-^ R 



This gives per 100 feet elevation a correction of 



.005S8 cm. per sec. per sec. 



.00232 in. per sec. per sec. J diminution. 



.000193 feet per sec. per sec. 

 Smithsonian Tables. 



