188 Mr. G. H. Darwin on a suggested Explanation 



of the discharge, a change occurs in the heating of the elec- 

 trodes. Such a phenomenon has been observed by Gassiot * 

 at the discharge of a Grove battery of 400 pairs between 

 metal or coke balls. 



XXV. On a suggested Explanation of the Obliquity of Planets 

 to their Orbits. By George H. Darwin, M.A., Fellow of 

 Trinity College, Cambridge^. 



IN a former paper J I have shown that if 6 be the obliquity 

 to its ecliptic of a planet which is slowly changing its 

 shape, so that its principal moments of inertia at the time t 

 are A + at, A + ht, C + ct, then, so long as at, bt, ct remain 

 small compared with C— A, 



dd __ IT a + b-2c 

 dt " 2n ~C-A ' 



n cosec 9 being the precession of the equinoxes, and — n the 

 rotation of the planet. This equation will hold true for long- 

 periods, if all the quantities on the right hand are treated as 

 functions of the time ; and if a = b it may be written 



dt n C— A 



In the case of the earth, 



Gtt 2 /^ 1 l-4sin 2 ^| C-A _ n _pC-A 



— \ T 2 + T / 2 -ytji v f Q ~ S i n COS e - n "C ? su PP ose ' 



where T, T f are the year and month, v is the ratio of the earth's 

 mass to the moon's, and i is the inclination of the lunar orbit 

 to the ecliptic. In the corresponding function for any other 

 planet there will be a term for each satellite, and l—^sm 2 i 

 will be replaced by a certain function called X by Laplace. 

 The equation may now be written 



t7 log tan 0= r, (C— A). 



p dt & n dt v J 



The object of the present note is to apply this equation to the 

 supposition that the planets were originally nebulous masses, 

 and contracted symmetrically under the influence of the 



* Golvanismus (2), Bd. ii. S. 1044. 

 t Communicated by the Author. 



X " On the Influence of Geological Changes on the Earth's Axis of 

 Rotation," Abstract, Proc. Roy. Soc. No. 175 (1876). 



