10 Rev. 0. Fisher on Variations of Gravity and their 



tional swings of the pendulum per diem to what would produce 

 so few as 2*26 only. 



Let us now revert to the hypothesis of elevated masses of 

 the Earth, produced by lateral compression, being accompanied 

 by downward protuberances projecting into a denser sub- 

 stratum, and supported in a position of hydrostatic equilibrium; 

 and let us inquire how the variation of gravity at the surface 

 would be affected by such an arrangement of the masses. I 

 call the downward protuberances the " roots " of the moun- 

 tains. In my ' Physics of the Earth's Crust,' I have assumed 

 the density of the mountain, of the crust, and of the root to 

 be the same throughout ; for since the density of more basic 

 eruptive rocks is not much greater than that of acid rocks, 

 there is no great margin left for supposing a gradation. It 

 may be objected that the root could not remain protuberant, 

 but would be melted off owing to the high temperature of the 

 substratum. A probable answer to this is, that the root con- 

 sisting of acid rocks is less fusible than the basic rocks of the 

 substratum. Another is, that there has not been time ; and 

 this reason has more to be said in favour of it than appears at 

 first sight, because we know that the upper mountain, although 

 continuously degraded by atmospheric causes, is not at present 

 levelled down. There may therefore equally well not have 

 been time for the much larger root to have been melted off. 



Professor Darwin has proved that the material of which 

 the Earth is composed must be exceptionally rigid to support 

 mountains, if (as I understand him) they are supported by 

 rigidity alone. And since, with sufficient time given, every 

 known substance yields more or less freely to stress, this is of 

 itself an argument in favour of the hydrostatic theory. It is 

 not necessary for the purpose that the substratum should be 

 what would be called fluid ; although I myself believe that it 

 is so. 



In discussing the effect upon the local variation of gravity 

 arising from the supposed constitution of the crust, the first 

 question which presents itself is, to what extent the sea-level 

 will be affected. Pratt has an article (200) upon this ; but 

 the following proof is suggested. 



Suppose generally that there is a mass, whose volume is M 

 and density p, situated exterior to the Earth, and a mass, whose 

 volume is R and density //,, within the Earth ; and suppose 

 that R is enveloped by the stratum whose density is <r. 



Let ^r- and ~- be the potentials of the masses M and R 

 D D E 



at a point on the surface of the disturbed sea-level ; — the 



