of the Obliquity of Planets to their Orbits. 191 



dulum of length equal to the present mean radius of the planet, 

 swinging under mean pure gravity. Then 



p = ? 2 Q 



2tt/xD 6 ' 



and the equation becomes 



, tan KP 2 Q 



loo- 



& tan I p 



This equation shows that as p diminishes 6 diminishes, and 

 when p is infinitely small 6 is zero. That is to say, if a nebu- 

 lous mass is rotating about an axis nearly perpendicular to the 

 plane of its orbit, its equator tends to become oblique to its 

 orbit as it contracts. 



In the case of the earth, P 2 Q = — =-^g- ; and taking the pre- 

 sent obliquity of the ecliptic as 23° 28', the equation may be 

 written 



Log 10 tan #=9'63761 — ^ — — 



On the hypothesis of homogeneity, 1*76 12 must be replaced 

 by 2-3229. 



The extreme smallness of the coefficient of — shows that the 



,P 

 earth must have had nearly the same obliquity even when its 

 matter was rare enough to extend to the moon. But if it can 

 be supposed that the moon parted from the earth without any 

 abrupt change in the obliquity of the planet to the ecliptic, 

 then from that epoch backwards the function Q would have 



1 2*5750 



had only one term, viz. ^, and P 2 Q would be — t?w~' The 



coefficient of — in the above equation would be reduced to 

 P 



-ztt^t, or -TTTQ-i according to whichever value of K is taken. 



10 9 ' 10 y 7 ° 



This being granted, it follows that when the diameter of the 

 earth was 1000 times as large as at present, the obliquity to 

 the ecliptic was only a few minutes. 



This somewhat wild speculation can hardly be said to receive 

 much support from the cases of. the other planets ; but it is not 

 thereby decisively condemned. In all the planets up to and 

 inclusive of Jupiter, the expression Q will have to be reduced 



to its first term 7™, because the satellites are rather near their 



