24 EXACT ASTRONOMV. 



expanded 200,000 miles thereby, is a very clumsy device 

 for masking the fraud. 



The sums expended by the different civilized govern- 

 ments in futile efforts to exactly determine the sun's distance 

 by triangulation to the celestial bodies and by geodetical 

 measurements, aggregate many millions of dollars. The 

 problems of the solar parallax and of the dimensions and 

 figure of the earth, are exhaustively solved by these few 

 equations. 



I have now arrived at the conviction that the solar hori- 

 zontal parallax, as defined by the astronomers, is not com- 

 prehended by the average reader. 



Its dynamical resolution is the key to the exact deter- 

 mination of all the numerical relations of the solar system 

 and is, in fact, the foundation-stone of the entire structure of 

 mathematical astronomy. The name discourages the non- 

 mathematical reader, but the subject itself is simple and 

 within his mental reach, when accurately described in simple 

 terms. 



Although the earth's orbit is not exactly a circle, it is 

 exactly equal to the circumference of a circle whose radius 

 equals the earth's mean distance from the center of her mo- 

 tion. Now, the circumference of every circle contains 1,- 

 296,000", and the segment thereof which is equal to its ra- 

 dius contains 2o6264".8o6247 102477. ^ ne plane of the 

 earth's equator is always nearly coincident with the plane of 

 her orbit — exactly so when she is at the vernal or autumnal 

 equinox. At those times her equatorial radius occupies a 

 small segment of the above described great circle that con- 

 tains an unknown number x of seconds. Said arc is the 

 thing named by the astronomers solar horizontal parallax. 

 It is now obvious that the ratio 2o626 4;" 8 + i s the ratio of 

 the mean orbital radius and equatorial radius of the earth. 



