Chase.] J-^ [March 7, 



to the times of actual or virtual fall, rotary and orbital velocities can be 



compared by a simple and natural hypothesis. Let 



p = modulus of rotation, or distance from Sun through which a planet 



would fall in T ^ . p f cc \/~ 2 X ~ 

 r* — time of fall which will satisfy the proportion. 



z f : r r : : V :-v 

 z. = length of day. 

 V = orbital velocity. 



2 - r. 

 u = equatorial velocity of rotation = ~ 



d -* 



8 VJ 

 Substituting for v its value, in the above proportion, and reducing, we 

 obtain the equation »... , 



r I ? ~ _ 

 r — * [ y ^ 



The Earth being the controlling planet of the intra-asteroidal system, it 

 is not surprising that- its radius vector and the factor of equilibrium, _> 



-' - 4 



both enter into the values of ,,. 2 4 = — , and — X Earth's mean 



' - 32 32 



radius vector = major axis of Mars, which in its turn = mean radius 

 vector -j- modulus of rotation of Mercury ; Earth's p = its perihelion 

 distance ; the moduli of rotation for Venus and Mars are, respectively, 

 and __- X Earth's modulus; Sun's modulus = mean distance of 

 Uranus ==-■ distance of Neptune's radial centre of oscillation. The ac- 

 cordance of these theoretical values with the actual values,, is shown in 

 the following table : 



Moduli and Times of Rotation. 



j> Theoretical ~ . Observed t . 



Mercury.. 2.653 24.321 24.091 



Venus 1.093 23.342 23.357 



Earth.... 983 23.972 23.934 



Mars 1.213 24.537 24.622 



Sun 19.183 003.138 604.007 



The solar modulus serves to connect the synchronism of light-oscilla- 

 tion at Neptune and ^planetary oscillation at Sun with the light-velocity 

 which would be communicated by the action of solar-superficial gravity 

 in a half-rotation. 



The modulus of rotation for Mercury (2.653 ; cfr. Juno, 2.671 ; \ Jupi 



ter, 2.G01 ; | Earth, 2.667), may, perhaps, indicate a fall from the middle 



of the asteroidal belt, since the time when Mars and Venus were thrown 



off from the nebulous earth. Or, inasmuch as _ / is the aphelion distance 



* See foregoing note on the ' ' Estimation of Solar Mass and Distance. ' ' 



