i 



tr) 



EXACT ASTRONOMY, nir 2 1 



Now, let x equal the length of segment of the moons 

 shadow cut off by the earth, and we have from similar tri- 

 angles the proportion : 



x :41.12783s : : x + 91424606 : 865180. 

 865 1 38.872 i62x = 3760096384. 78 1 828. 

 x = 4346. 23 miles. 

 Also, 41.127838 : 4346.23 :: 2155.2 : moons shadow. 

 Total length of shadows 227,753 miles. 

 The observer's distance from the moon : 

 227753—4346 = 223407 miles. 

 Her mean distance from the center of her motion: 

 [(223407 + cosine 39^°, 3058) 2 - (sine 39^°, 252 1) 2 ]* x 



^i = 239,226 miles. 

 927" ^ 7 ' 



The deficiency of 4 miles may be credited to error of 

 observation. 



A Sophistical Assumption Refuted. 



Professor E. S. H olden, of the Lick Observatory, and 

 a number of College Professors of Mathematics have assert- 

 ed that my resolution of the solar parallax is fallacious, be- 

 cause time and distance cannot be measured by the same 

 unit; and that the expansion or contraction of the earth 

 would not alter its periodic time. The sophistry of the first 

 objection is apparent, since every astronomer assumes that 

 the only possible unit of the earth's mean distance is an arc 

 of a great circle of the celestial sphere, which must become 

 the unit of the time in which the whole circumference is de- 

 scribed, when taken as the unit of circumference. The 

 second objection is fallacious, puerile and absurd because, 

 although true of abstract time, the numerical expression of 

 the periodic time is the ratio of the periods of revolution and 

 rotation. The^subdivisions of the latter are arbitrary and 

 their number constant. By the laws of mechanics, expan- 



