Status of the Theory of Isostasy. 321 



On a lowering of the datnm surface by 9,000 feet, the 

 mass of every column above the datum becomes 8 (h + 

 9,000), instead of Bh. Substituting h + 9,000 for h in the 

 equation giving the defect of density below sea level 

 gives, 



S — — * h + 9,0 00 



For convenience place j- = m, and write 



8 1= =(fe + 9,000) m 



For columns A, B, C, D the relative defects of density 

 for change of datum may then be tabulated as follows : 



Relative defects of density for change in datum by 9,000 feet. 



Columns, iig. 3. 



Datum A B C D 



Sea level +9,000 m —1,000 m —6,000 m 



—9,000 feet ... —9,000 m —10,000 m —15,000 m 



MacMillan points out that for the sea level datum the 

 defect of density is six times as great for column D with 

 elevation of 6,000 feet as it is for C with elevation of 1,000 

 feet; whereas for the datum at — 9,000 feet the defect 

 under D is only 1-5 times as much as under C He gives, 

 further, a table to show how enormously the ratios are 

 changed by selecting other reference surfaces. So far as 

 the writer can see, this argument involves a sophistry in 

 that it dwells on the ratio of these defects as compared 

 to a column whose surface is at sea level. In the deter- 

 mination of the deflections of the vertical it is not, how- 

 ever, the ratios, but the differences of the defects in the 

 different columns which measure the deflections of the 

 vertical. It will be observed that the difference of defect 

 between C and D is 5,000 m irrespective of datum, and 

 that between A and D is 15,000 m, corresponding to 

 the differences in elevation. MacMillan also raises the 

 objection that variations in the datum, by changing the 

 absolute values of the defects of density, change the re- 

 sulting specific gravities, and calls this a reductio ad 

 absurdum. Here again the argument is to one side and 

 sophistical, since the hypothesis of isostasy postulates 

 nothing in regard to the density of any shell below the 

 sea bottom, as indicated by the insertion of x in figure 2. 



