Chase.] ^CiO [Dec. 19, 



Astronomical Approximations. I. Apparent Semi-diameter of the Sun, 

 and Nebular Origin of the Terrestrial Day. By Pliny Earle Chase, 

 LL.D., Professor of Philosophy in Haverford College. 



(Read before the American Philosophical Society, Dec. 19, 1870.) 



The various mathematical deductions which I have drawn from the 

 nebular hypothesis, as modified by Herschel's theory of "subsidence," 

 furnish many independent tests for judging of the probable accuracy of 

 delicate and difficult astronomical observations. The consistency of the 

 tests may be shown by examples, one of which is given In the present note. 



The hypothesis that the solar system has been shaped by undulations, 

 moving with the velocity of light, leads to the following equation : 



(1 year\ 3 - 2 / Earth's distance \ 3 

 1 day/ 2 ' \ Sun's semi-diameter/ 



From this equation we find, for Earth's mean distance from Sun, 214.54 

 solar semi-diameters; and for Sun's apparent diameter, 32' 2". 85. The 

 accordance of this result with observations is as follows : 



Newcomb, 



Chase, 



Fuhg, 



British Naut. Almanac, 



American " " 



Lockyer, 



Dr. Fuhg's estimate, which approximates most closely to my own, is 

 deduced from 6827 measurements* Notwithstanding the vast labor which 

 is represented by those measurements and their subsequent discussion, I 

 cannot but believe that my own result is still more accurate. For it in- 

 volves no careful micrometry, no allowance for irradiation, and no other 

 elements of possible uncertainty than small fractions of a second, in the 

 estimated lengths of the sidereal year and of the mean solar day. 



This result may, perhaps, be rightly regarded as an experimentum cruris. 

 Therefore, to avoid the trouble of referring to the papers in which I have 

 established the data for my formula, I will repeat the fundamental con- 

 siderations on which it rests. 



Any body, revolving in a circular orbit, under the influence of a central 

 force g, which varies inversely as the square of the distance, would ac- 

 quire the velocity of revolution (^ gr), in the time of describing an arc 

 equivalent to radius. It would acquire a parabolic velocity / 2 gr, in 



1 7T 



- of a revolution, and it would acquire — - times the parabolic ve- 

 " 1 2 r /2 



locity in a half revolution, provided all the increments of the central 



*Asln,n. Nachriclilen, 2040, cited in Am. Joum.BcL for Aug. L875, p. 57. 



