20 EXACT ASTRONOMY. 



from Greenwich in lat. 51° 29': [ (239230 + 2990 — 2468)* 

 + (3 I °i) 9 ]* = 239,782 miles. 

 Her actual diameter : 



239782 x i854 // ~2o6264. // 8=:2i55.2 miles. 



A Crucial Test 



Of the foregoing determinations is applied by the observed 

 duration, 118 seconds, of the total phase of the solar eclipse 

 of Jan. 1 st, 1889, at Willows, California, in latitude 39^°. 

 It is obvious that the diameter of the moon and that of her 

 shadow parallel to its motion at intersection with the earth 

 are sections of an equilateral triangle standing on the sun's di- 

 ameter. It is equally obvious that the duration of the observ- 

 er's immersion in the moon's shadow, when she is on his me- 

 ridian, is the diameter, perpendicular to her direction, of the 

 shadow's intersection with the earth, divided by the rate of 

 its motion. Because of the great eccentricity of the moon's 

 orbit, her motion is far from uniform, and the velocity of the 

 earth's rotation is also greatest at the equator. But, in con- 

 sequence of the divergence from parallelism of the planes 

 of the two motions towards the east, and of the earth's con- 

 vexity, the velocity of the shadow's intersection therewith 

 is. the difference of the moon's mean velocity and the equa- 

 torial velocity of the earth's rotation : 



23923 o x 6.2831853 3963-2735X6.283X853 =0.348541 mile per second. 



23605915.5 864005 ^ ' ^^ j- 



Diameter of the shadow's intersection with the earth 

 perpendicular to the moon : 



118 x 0.348541 =41.127838 miles. 



Taking the apparent semi-diameters of the sun and 

 moon, computed for date of the eclipse, as given in the 

 Nautical Almanac, the observer's distance from the sun's 

 center.: 927741 17 x 962"— 9 76" 2 = 91,424,606 miles. 



