432 Archdeacon Pratt on the Fluid Theory of the Earth. 



case the change would alter the force acting at the surface, which 

 would therefore cease to be a surface of equilibrium ; in the 

 second case the external surface retains its form only under the 

 condition that the arrangement of the mass is one of certain de- 

 finite arrangements determined by equations of condition. In 

 neither case, therefore, is the form of the external surface inde- 

 pendent of the internal arrangement of the mass. To arrive at 

 this conclusion was the object of my proposition. 



3. But though I have in the last paragraph changed the word- 

 ing of the proposition to meet the case I was considering, I have 

 no intention whatever of abandoning the proposition itself in its 

 bearing upon the question of the fluid-arrangement of the earth's 

 mass, further than that I would change the words " must neces- 

 sarily be arranged" into "is undoubtedly arranged;" for the 

 first words would seem to exclude the mathematical possibility of 

 any other arrangement ; but the second exclude only the physical 

 probability of a different distribution. I should be wrong to 

 assert that it is impossible for a pyramid to stand balancing on 

 its apex ; but I should be safe in saying that it would be physi- 

 cally impracticable. So in the case before us, as I hope now to 

 show, any other than the fluid-arrangement — whether or not the 

 earth is or ever was fluid, in whole or in part — appears to me to 

 be physically improbable in the highest degree ; so that I regard 

 the mass as being undoubtedly so arranged. My critic thinks that 

 I have very much over-estimated the force of the evidence for the 

 fluid- arrangement ; and he considers that it does not rise above a 

 slight probability. I am not conscious of being actuated by a 

 spirit of retaliation ; but I consider that he has very much under- 

 rated the evidence, and I am tempted to think that he has not 

 dwelt upon it sufficiently to see its full nature. Some of his ex- 

 pressions have led me to this conclusion. To this I now address 

 myself. 



4. The state of the case is this : — that (1) the fluid-arrange- 

 ment of the mass, whatever its past or present circumstances as 

 regards fluidity and solidity, precisely meets the condition that 

 the surface is a spheroid of equilibrium ; (2) any general or arbi- 

 trary change of the arrangement of the mass will lead to a viola- 

 tion of this condition ; and (3) only a class of precise changes in 

 the distribution of the mass, limited by the condition that the 

 external attraction shall remain unchanged by the redistribution 

 of the mass, will leave the form of the surface unaffected. 



For convenience we may represent any redistribution of the 

 mass of the earth, in the removal of materials from one part of 

 its volume to another, by the algebraical addition or superposi- 

 of an Imaginary Body, parts of which are of positive and other 

 parts of negative density, the total mass being zero. In the case 



