GRAVITATIONAL STABILITY OF THE EARTH. 183 



It will be convenient presently to have observed that the equation derived from 

 this one by differentiating the left-hand member with respect to r can be written 



10. Tljp forms of v,, w t and u^, v a , w 3 have been put down and it remains to 

 determine u t , v lt >,. We have a system of three equations of the type 



We express x<a H in the form 



(42) 



and then the above equation becomes 



2n+ 1 8* y LW / rfr A" r 



We seek solutions of the system of three equations of this type in the forms of 

 the type 



in which P, and Q, are functions of r. We find 



Hence the assumed forms can be adjusted to satisfy the equations if P, and Q. 

 satisfy the linear equations 



2ndP 

 " 



