Chase.] ->-& [April 4, 



paraboloid, the focal ordinate would be equal to radius. I then found (Laws 

 6, 7, 11, 12), that by comparing the vis viva of satellite revolution al Earth's 



surface (oc y 8 = gr), with the vis viva of rotation at the primitive focal 

 abscissa (oc u* = | of the square of the velocity of equatorial superficial 

 rotation), we may obtain the equation : 



\V y 



(i; 



in which y represents the distance traversed by a ray of light (compare 

 Laws 13, 15), while a body, at the equator, would fall through the "fun- 

 damental increment" of the foregoing tabular comparison (^|^ of 4215.8 

 ten millionths of a millimetre). For, 



_ . 1385 3963 



% = vgr = \-jg x ^280 = 4 - 90 ~ m - 



v 1 = 7! x 3963 -=- 86165 = .1445 m. 



y = r ( V[ \ = 3.436 m. 

 W 



t = •TOOOOOOOO 16468 -*- 4.8894 = .000018353 sec. 



Light traverses Earth's mean radius-vector in 497.825 sec. Therefore!, 



according to this estimate, Sun's mean distance is 



497.82.1m 



t ff = 93,203,000 miles (2) 



A second approximation may be made by remembering that the basic 

 lines are the reciprocals of harmonic lines, and comparing the eethereal 

 volumes, or the reciprocals of the ratio of variability in tidal influence, 



( ) at the points where the disturbing forces are greatest (the surfaces 

 \d /' 



of the disturbing bodies). By the laws of elasticity, the sethereal undula- 

 tions that are set up at any point, are propagated with uniform velocity. If 

 we take the theoretical fundamental wave length as our fundamental unit, 

 and if we call the mean orbital distance which Earth traverses in the time 

 (t z= .000018353 sec.) of falling through the fundamental increment, the 

 "orbital unit," we find that 



Orbital unit /Sun's radius 



Fundamental unit 



For, representing Earth's mean radius-vector by x ; 



Orbital unit = 2- x X .000018353 sec. -=- 1 year. 



„ , , . 4215.R X .0000000039371 



Fundamental unit = — .. ,,„,. — — m. 



odobO 



Sun's radius — x -=- 214.524. 



Earth's radius = 3963 m. 



Substituting these values in equation (3), we get 



2 t: x X .000018353 X 63360 _ / x \ 3 



365.256 x 86400 X 4215.8 X .0000000039371 ~ V.2 14 -524 X 3963,) 



.-. x — 92,579,000 miles (4) 



_ /Sun's radius \ 3 



~ VEarth's radius / (d) 



