Structure of the Earth's Crust. 35 



ous nucleus, e and e^ being respectively the inner and outer ellip- 

 ticities of the shell. If, with M. Plana, we regard ei-e=0, or 

 if, in conformity with my conclusions, we consider it even possi- 

 ble that e, - e > 0, this equation cannot assist in detennming 



the fraction ^^ , which is a function of the radius of the 



nucleus, and from which the thickness of the shell is estimated. 

 Although I am far from regarding the numerical results which 

 I have myself obtained relative to the thickness of the earth's 

 crust as perfectly accurate, I believe that the mechanical and 

 physical principles to which I have appealed are those from which 

 the complete solution of this problem will arise. If the problem 

 were simply mathematical and mechanical, I should be induced 

 to concur with Professor Haughton* as to its insolubility, not 

 only from studying that gentleman's researches, but also from the 

 previously pubhshed investigations of Professor Stokes f relative 

 to Clairaut's theorem. If the surface of the solidified shell were 

 identical or similar to what may be called the astronomical sur- 

 face of the earth, namely that of its oceanic coating, all the sta- 

 tical and dynamical results depending on the internal constitu- 

 tion of the globe might be the same whether the crust were 

 merely a thin pellicle, or whether the earth were always sohd to its 

 centre 



But although the surface of the ocean is necessarily perpendi- 

 cular to gravity, we have no reason to conclude that the surface 

 of the shell, stripped of all its fluid and sedimentary coatings, 

 would possess the same property. Whatever knowledge we pos- 

 sess respecting the configuration of the bed of the ocean and ot 

 the great islands which rise above its surface so as to form the 

 continents of the eastern and western hemispheres, tends to show 

 that the surface of the soHdified shell is not similar to the sur- 

 face of equilibrium assumed by its liquid covering. 



Here I may be allowed to refer to Archdeacon Pratt s attempt 

 at confirming Mr. Hopkins's conclusion relative to the supposed 

 very great thickness of the earth's crust. He proposes to ascertain 

 the conditions of equilibrium of that portion of the crust occupied 

 by the great peninsula of India stretching from beyond the Hima- 

 layan Mountains to Cape Comorin. The meridional section 

 thus studied comprises an arc of about 24°, and the curvature ot 

 this segment of the shell is a very important element in the con- 

 sideration of Its stability; yet it has been totally neglected. 

 Moreover, the Himalayan Mountains and plateau ot Central in- 



* Trans. Royal Irish Acaaeiny, 18ij2. 



t Cambridge Mathematical Journal, May 1H4.>. 



