Kirkwood.] l^Z [Nov. 21, 



/ The large planets : 



Primitive Density. 



Neptune 1.0000 



Uranus 3. 89.50 



Saturn 32.7073 



Jupiter 210.7440 



II. The planets interior to the zone of asteroids : 



Mars 7.446.4 



Earth 24,880.5 



Venus 70, 129.2 



Mercury 468,616.0 



III. The secondary planets, of which our moon and Jupiter's first 

 satellite may be taken as types : 



Jupiter's first satellite •. 2, 600,000 



The Moon 4, 820, 000 



There is, we may remark, an antecedent probability that the law truly 

 formulated will assign to Saturn a period of rotation somewhat less than 

 the period observed ; as it is sufficiently obvious that if the ring had re- 

 mained an integral part of the planet, the resulting time of rotation would 

 have been, in fact, sensibly shorter than the present. It is also to be re- 

 membered that the late observations of Denning and Schiaparelli make 

 Mercury's time of rotation nearly 25 hours. In the case of the satellites, 

 the equality between the periods of rotation and revolution was established 

 at an early epoch in their history. No further decrease in the time of 

 rotation was therefore possible. 



A comparison of the quantities used in equation (1) suggests that a 

 planet's time of rotation is a function of its mass, distance, and primitive 

 density. The form of this function — found by a tentative process — may 

 be expressed as follows : 



The square of the number of a planet's days in its year is to that of any 

 other of the same group, as the primitive density of the latter is to that of the 

 former ; that is, 



( is\y^ 



rO- : n' : : /\> : /\ ; or, n' =z n \-;r, ) (4). 



where 



/\=-— = the primitive density, and 



T orbital period ^, , ^ , ., •, • .^ 



n = — = . — -. — r = the number of a planet s days m its year. 



t rotation period 



Equation (4) may be reduced to 



''■■'"■■■'-i-u)'-'n' Q' • (5). 



where d, d' and R, R' are the respective distances and primitive radii. 



