GRAVITATIONAL STABILITY OF THE EARTH. 



213 



increase slightly the stability of the body in respect of disturbances specified by 

 harmonics of the first degree, and to increase it enormously in respect of disturbances 

 specified by harmonics of higher degrees. 



.\l>i'l'"''ili'>i' I" '/<' I'l'olil' in <>f lln- Hi-'iril'ili<,,,>il St'ili,/,'i/ <>f tli- /.'"/'/'. 



39. For a body of the same size and mass as the Earth, the values of a and p u in 

 C.G.8. units are 6'37xl0 8 and 5'53 ; the value of y being 6'65xlO~ 8 , the value of 

 Jjry/JoV is 3'46x 10". In the following table the first column gives a value of .iV, 

 the second column gives the corresponding value of \ + 2/x (the body being of the same 

 size and mass as the Earth), the third and fourth columns give the values of the 

 corresponding moduluses of compression in the cases where v = and v = , irrelevant 

 entries being omitted. These moduluses are denoted by and A-,. The quantities 

 given in the fifth, sixth, and seventh columns are the moduluses of compression of 

 steel, glass, and mercury (denoted by k,, k g , k m ). 



According to these results, a homogeneous solid body of the same size and mass as 

 the Earth, with a modulus of compression as great as that of steel, would have 

 complete gravitational stability. If the modulus of compression were equal to, or less 

 than that of glass, the planet would be unstable as regards radial disturbances, and a 

 concentration of density towards the centre would take place. If the critical value of 



