U9 

 - 1 [Feb. 7, 



ESTIMATION OF SOLAR MASS AND DISTANCE, FROM THE 

 EQUILIBRIUM OF ELASTIC AND GRAVITATING FORCES. 



By Pliny Earle Chase. 



[Read before the American Philosophical Society, Feb. 1th, 1873.) 



The lightest and most elastic gas must be kept in mean position, under 

 conditions of equilibrium between the forces of gaseous expansion and 

 of virtual fall towards the centres of the Sun and the Earth. In cases of 

 explosive disturbance, the character and range of the resulting oscillations 

 must depend on those conditions of equilibrium. 



In order to ascertain the approximate ratio of terrestrial to solar 

 gravity, let us suppose the mass of the Earth concentrated in a single 

 point, c, at its centre of gravity. 



Let x = distance from c at which the satellite and planetary velocities 

 would be equal. 



£ = 2 a; ; d = 2 £ ; r = Earth's radius. 



S, <7°> 9 l = force of gravity at ff, r, and x, respectively. 



v = orbital velocity of earth, or satellite velocity at x. 



r, = distance of Sun from Earth. 



,, = mass (Sun -s- Earth). 



T = time of actual fall through a diameter d, or time of orbital rev- 

 olution at the mean distance x. 



r° — time of actuai fall through a diameter °, or time of virtual fall 

 through a distance = d at %. 



t. = time of virtual fall through a distance *=■ d, at r. 

 Then by the laws of gravitation, we have the proportion 



T* : / : : ** : ** : : ?V— ^~ 



" 9 9 



if 



. 8 



The six most recent experimenters upon the explosive force of hydro- 

 gen, have obtained results with a limiting variation of about 3^ per cent, 

 from the mean. Four of the experimenters agree within an extreme differ- 

 ence of less than two-fifths of one per cent., the mean of their results 

 differing from the general mean by less than one-fifth of one per cent. 

 This agreement is much closer than any hitherto obtained by astronomical 

 observations. 



According to the experiments referred to, the explosive force of H 2 

 may be represented by a virtual fall through a mean d of 1017.01 miles, 



in a t, = \ - = 578.5 seconds. The best approximate values of d 



are those of 



