Chase.] ^^^ [April 21, 



Laplace's two laws of constant sums, viz : — The sum of all the instantane- 

 ous virtual areas in a system will always remain invariable. 



From Alexander's harmony (Note 156, p. 605) it follows, that the ratio 

 between the virtual areas of Jupiter and Saturn is nearly the reciprocal 

 of the ratio of their direct areas. The harmonic influence of the repeated 

 nodal action of this ratio, upon subordinate planetary aggregation, is 

 shown in the following table : 



Harmonic Areas. 

 a 40.256 



The greatest proportionate difference is that of Uranus, li per cent. 

 The harmonic change from the outer to the inner belt of planets, ()-=-£ 

 = 16.983, represents the orbital retardation at the chief centre of conden- 

 sation, Earth. If Earth were rotating with the speed which it would have 

 if Laplace's limit coincided with its equatorial surface, its time of rotation 



I'r 

 Avould be 2 - ^'— = 5073.6 seconds ; 86164.1 -- 5073.6 = 16.983. The 



synchronous virtual area of Mars differs by less than 4i per cent, from | 

 of J ^. This is less than 18 per cent, of the probable error. 



100. Laplace's First Late of Stability. 



The first of the two laws in which the author of Mecanique Celeste em- 

 bodied his discoveries in relation to the stability of the solar system, is 

 thus stated ; "If the mass of each planet be multiplied by the product of 

 the square of the eccentricity and square root of the mean distance, the 

 sum of all these products will always retain the same magnitude." By 

 combining the first and third of these factors, m V r, we get the quotient 

 of mass by orbital velocity, together with the following suggestions of 

 nodal influence: 



Jupiter's exponent represents the variable ratio of subsidence-accelera- 

 tion to orbital velocity ; Saturn's the product of orbital time by mean 

 distance; Neptune's, the variable ratio of Laplace's limit to uucleal radius. 



