Status of the Theory of Isostasy. 319 



Let h be the elevation of a topographic feature above 

 sea level and 8 the mean density of the outer few miles 

 of the crust. Then, disregarding local variations of 

 density in the surface rocks, the mass of the unit column 

 above sea level is §h, as shown in C, figure 2. 



Let h x be the depth of compensation measured below 

 sea level. As it extends downward 100 kilometers, more 

 or less, and as density increases toward the center of 

 the earth, its mean density will be presumably some- 

 what greater than S. For the column such as B, whose 

 surface is at sea level, let this mean density be 8 + as- 

 Then in column C, to maintain the equality of mass 

 with B, there must be a defect of density below sea level 

 represented by B l9 so that S^ == -$h, a constant. 



Therefore 8,= — 8-^. 

 a. 



The mean density of column C is, then, 8 (lj-J 



i-)-i-x 



For convenience in computations, the defect is taken 

 as extending from the surface through a uniform depth 

 instead of from sea level. This gives the surface at the 

 bottom of compensation the form of the upper surface 

 of the crust, the difference between the two assumptions 

 being found immaterial in the results. This is as it 

 should be, for neither the regular or irregular form of 

 the bottom surface can be regarded as representing the 

 conditions of nature. 



The sea level, however, is a wholly arbitrary surface, 

 so far as isostasy is concerned. It is merely a con- 

 venient datum from which positive (land) and negative 

 (sea) elevations may be measured. What, then, would 

 be the influence on the results if another datum surface 

 were selected? This is a subject not discussed by Hay- 

 ford or Bowie. MacMillan enlarges upon the fact that 

 Hayford chose as his datum surface the sea level, in- 

 stead of a datum representing the mean surface of the 

 earth, which would be 9,000 feet below sea level. To 

 show the sophistry of this reasoning, in so far as the 

 geodetic computations are concerned, the following figure 

 is drawn for the present article, MacMillan giving no 

 diagram or detailed analysis : 



Let A, B, C, D be four unit columns of the crust. The 

 top levels of the columns are taken at — 9,000, 0, +1,000, 



