EXACT ASTRONOMY. 25 



We remain ignorant of the sun's actual distance till this ratio 

 is multiplied by the ascertained length of the earth's equa- 

 torial radius. 



The so-called wonderful difficulty and complexity of the 

 problem of the sun's distance have been enlarged upon by 

 all the astronomers, but I have shown most conclusively 

 that the problem is an extremely simple one and is easily 

 solved by elementary mathematics. 



Since the astronomers are themselves lost in the fog 

 raised by their conception of solar parallax, which, rightly con- 

 ceived, is the key to the exact determination of all astro- 

 nomical magnitudes, whether of distance, mass or volume, I 

 will endeavor to make the thing so styled clear to the minds 

 of my non-mathematical readers, by detaching it from all 

 ideas of parallax. The earth's orbit is an ellipse of small 

 eccentricity, but is exactly equal to a circle the radius of 

 which is the earth's distance from the center of her motion 

 when she is at the vernal or autumnal equinox ; she is then 

 at her mean distance. 



At those times, the plane of her equator exactly coin- 

 cides with the plane of her orbit, and her equatorial semi- 

 diameter is concentric and coterminous with a very small 

 segment of the aforesaid great circle, since so small an arc 

 is .not sensibly different from its chord. This minute arc 

 containing the unknown number x seconds, being taken as 

 the unit of the radial arc is made thereby to measure the 

 whole circumference, and therefore to measure the time of 

 its description, or the sidereal year, containing 3 1558 149.3 

 time seconds, equal to 129600c" x 24.3504238425926. It is 

 now self-evident that these arcs of the said great circle are 

 in the same ratio as the earth's mean-orbital and equatorial 

 radii. The sesquiplicate ratio of the time and distance units 

 must be the same as that of the wholes ; whence, and from 



