the Weight of Continents and Mountains. 269 



inequality on the earth's surface, because it depends essentially 

 on heterogeneity of density. 



It is well known that the earth may be divided into two 

 hemispheres, one of which consists almost entirely of land, and 

 the other of sea. If the south of England be 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 center of gravity of the earth's mass is more 

 remote from England than the center of figure of the solid 



A deformation of this kind is expressed by a surface har- 

 monic of the first order, for such an harmonic is equivalent to 

 a small displacement of the sphere as a whole, without true 

 deformation. 



Now if we consider the surface forces produced by such a 

 deformation in a homogeneous sphere, we find, of course, that 

 there is an unbalanced resultant force acting on the whole 

 sphere in the direction diametrically opposed to that of the 

 equivalent displacement of the whole sphere. 



The fact that in the homogeneous sphere such an unbal- 

 anced force exists shows that in this case the problem is 

 meaningless; it is. in fact, merely equivalent ton mischoice in 

 the origin for the coordinates. But in the case of the earth 

 such an inequality does exist, and the force referred to must of 

 course be counterbalanced somehow. The balance can only be 

 maintained by inequalities of density, which are necessarily 

 unknown. The problem therefore apparently eludes mathe- 

 matical treatment. 



It is certain that so wide-spreading an inequality, even if not 

 great in amount, must produce great stress within the -lube. 

 And just as the second harmonic produces a more even distri- 

 bution of stress than the fourth, so it. is likely that the first 

 would produce a more even distribution than the second. 



It is difficult to avoid the conclusion that the whole of the 

 solid portion of the earth is in a sensible state of stress. _ 



I would not, however, lay very much emphasis on this point 



which the e 



From this discussion it appears that if the earth be solid 

 throughout, then at a thousand miles from the surface the 

 material must be as strong as granite. If it be fluid or gaseous 

 inside, and the crust a thousand miles thick, that crust must 

 be stronger than granite, and if onlv two or three hundred 

 miles in thickness much stronger than granite. This conclu- 

 sion is obvious! v strongly confirmatory of Sir William Thom- 

 son's view that the earth is solid throughout. 



