RESULTING FROM THE THEORY OF THE GYRO SCO PI). 3 



/> 



, being very great. In the phenomena of the gyroscope, the first condi- 

 I 2y AMyg 



tion obtains ; in the case of the earth, attracted by the sun or moon ( being small), 

 it is easy to show that the alternative condition is fulfilled. 1 



Putting ' equal to zero in equation (3) we get 6=u for the maximum of 0, and 



(I i 



for the minimum, the equation, 



cos 0= /P+^l+2/3 1 coso+0 4 



in which, if 3 is very great, the value of cos differs but slightly from that of cost). 

 Hence by introducing a new variable , equal to o 0, and deducing the values of 

 </,/ and (liy development) of sin a and cos (neglecting the higher powers of w) and 

 substituting in (tt) and (4), they become (omitting, as relatively small, cos o in the 

 factor cos u-}-^). 



G. =2 



at 



Kquution (5) gives by integration and putting 



7. M= _^ sin o sin 



^P 



which substituted in (6) gives 



8. *LJUa**< 



at p* 



9. 



If we make 6>=90, sin u=l, in equation (6), deduce the value of dt, and sub- 

 stitute in (5) we get, 



10. 3= 



/7i differential equation of the cycloid, generated by a circle of which the diameter 

 is ,, and having a 



1 For the earth the moments of inertia, A and C, with reference to principal axes through the centre, 



n I n 



differ very little. The value of ft may therefore be approximately written -gl. , and the denominator 



" 



is to be replaced (17) by . Z L. Substitute the value of L (19) and put, for the sun, -=!,' (25), 



sin $ r* 



and the yalne of ft becomes _!L \- , which is Terr large. 



2n,W3(C-A)ces9 



The Talue as depending on the moon's attraction is (28a), / "**' , of the same order 



2n t +J3(C-A) cos* 



of magnitude as before. 



