GRAVITATIONAL STABILITY OF THE EARTH. 197 



25. Again, when v = \, equation (80) can be written 



_8?JLL_ ./!_*+__. Uo (82) 



3z*-23*+l I 3 + 3.5 



If we put 3? = 4, the left-hand member becomes 



41 \ 3 3.5 

 Now 



_ia_l!_ 645461 4' /' 4 \ 



3 3.5~ = 3.5...15 8.5...17V 19/ 



and 



Hence 1 -+ 7 ...>--, and the sign of the left-hand member of (82) is 

 3 3.5 41 



minus when x 2 = 4. When we put a? 3, the left-hand member of (82) becomes 



__^1._ _ + __. 

 but 



-3 + JL. = 3__?_ _?_ _9__/!_A. \ 

 3 3.5 5 5.75.7 5.7. 11 V 13 / 



7 5.7.11\ 13 '/' 

 and 



or the sign of the left-hand member of (82) is plus when 3? = 3. It follows that the 

 root of the equation (82) for x 3 lies between 3 and 4. 



Instability in respect of Displacements specified by Harmonics of the First Degree. 



26. When n > 0, we have to calculate expressions for A,, B,, C,, D, from the 

 formulae of 17. If n = 1, we have 



J Q' 1 ). (83) 



Now if we put h* = and I J = 0, we find 



f _ A T 7V 9V . v.^je+5)jj*-o fc 1 



L 275 + 2T4T5~ ' 2.4...2 K .5-J' 



44 



.s- /_ W 



; 



