Original and Actual Fluidity of the Earth and Planets. 269 



Solving these equations with respect to e, , and making A = 2p„ we find 



m + - e 

 5 



_ ( 7e — hm) 0' 



(32) 



(33) 



Ehminating e, and solving for <r, we find, 



i_(_3£+^io+M:M+i) fo,^ 



a~ (30= + ^)(0' + l) ' *'''*^ 



, • , , ., 5?» + 3e 



in which A = d . 



7e — bm 



But the nucleus being supposed fluid, the denominator of the right-hand mem- 

 ber of (34) is greater than its numerator; consequently we have the inequality 



bm -f 3e , , 



20' + 50- < 3 — . (35) 



^ ^ 7e - bm ^ ' 



The value = 1-2407 renders the left-hand member of (35) equal to the 

 right, and therefore must be less than 1-2407, and, consequently, the depth 

 to which the density of the surface extends is less than 768 miles. 



The results which have just been obtained are to be regarded merely as ex- 

 amples of the manner in whicli equations (14) and (15) should be used, if we 

 were acquainted with the laws of density and ellipticity of the fluid and solid 

 parts of the Earth. So long as we are ignorant of these laws, we cannot calcu- 

 late numerical values, and indeed the chief use of the investigation I have just 

 given appears to be, to enable us to estimate at their just value speculations 

 relating to the interior of the Earth, of whose real structure we are, and must 

 remain, hopelessly ignorant. 



2n2 



