EXACT ASTRONOMV. 1 9 



plicate ratio of the computed periodic times of the supposed 

 earth and satellite, both revolving at the distance i : 



/ x d 2 \2 __ d^ __ 33V76 _ 'yiOAOK 

 \x(i+m)%' (i + m)i 1.0041493 OO^^^D' 



The sun and earth both revolve in a year about their 

 common center of gravity; distant from the sun's center ; 

 92774117^330405 = 280.8 miles. 



The earth and moon both also revolve about the outer 

 end of the earth's radius-vector eccentric to her center : 

 239230-^80 = 2990 miles. But being always in the direc- 

 tion of the moon from the center, its mean position, with 

 reference to the sun's distance, is at the center. The sun's 

 mean apparent diameter, 1923^.6, as observed at Greenwich 

 Observatory in latitude 51 °29', depends on the observer's 

 distance from the sun's center, which is. less by the cosine of 

 the latitude than to the earth's center. 



Wherefore, the actual diameter of the sun : 



927 TJt!!r 8468 x i923".6 = 865,180 miles. 



200264 .806247 



His volume: ( 3 -g^) 3 = (109.15) 3 = 1,300,383 earths. 



Distance and Diameter of the Moon. 



60.0294004722 x 1.00553639x3963.2735 = 239230.11 

 miles is her mean distance from the center of her motion. 

 Since her mean position is in the plane of the equator, her 

 mean distance from the center of the earth is 2,990 miles 

 greater. By reason of proximity, her mean apparent diame- 

 ter, 1 85 4", measured at Greenwich, varies slightly with the 

 latitude of the observer's station. Consequently, her mean 

 distance from the earth's surface is the square root of the 

 the sum of the squares of the sine of the observer's latitude 

 and the distance from its intersection with the plane of the 

 equator to the moon's center. Hence, her mean distance 



