-MK. J. H. JEANS ON THE VIBEATIONS AND 
1 HO 
except the one with wliich this paper is specially concerned. The question is not 
whether we observe the state just described, hut whether we can detect any approach 
to this state, and this, I believe, can he done. Professor Darwin writes* :— 
“ It is well known that tlie earth niav he divided into two hemispheres, one of 
which consists almost entirely of land and the other of sea. If the south of England 
he taken as the pole of a hemisphere, it will be found that almost the whole of the 
land, excepting Australia, lies in that hemisphere, whilst the antipodal hemisphere 
consists almost entirely of sea. This proves that the centre of gravity of the earth’s 
mass is more remote from England than the centre of figure of the solid globe. A 
deformation of this kind is expressed hy a surface harmonic of the first order.” 
§ 37. We can carry our calculations a step further. The divergence from the 
initial configuration is only represented hy a first harmonic so long as squares of this 
divergence may he neglected. If these squares are taken into account, we must 
Fig. 1. 
include a term proportional to the second liarmonic as well as tluit proportional to 
tlie first. This ]jrocess of successive ajiproximation might he continued to anv extent, 
so that a complete series of unsymmetrical configuintions might he calculated in the 
manner explained in my former paper, t We may, however, he content to stop at 
the second harmonic The free surface will now he of the form 
G. H. Dauwix, ‘ Phil. Tuxns.,’ vol. 173, 1882, jj. 230. 
t ‘Phil, Truns.,’ A, vol. 199, p. 41. 
