Status of the Theory of Isostasy. 



323 



becomes h + c, in which h as before is variable, positive 

 or negative, and c is a constant. The total mass to be 

 compensated with the new datnm becomes 8 (h -\- c) = 

 $h + §c, the new or added mass is 8c, which is indepen- 

 dent of h. It is compensated by an equal deficiency of 

 mass, -$c, assumed to be spread over the whole depth of 

 compensation. Consider this effect in a cylinder of the 



Fig. 4. 



Fig. 4. Diagram to illustrate influence of change of datum on composition 

 of gravity. 



crust of limited radius, whose axis is the vertical passing 

 through the station, as shown in figure 4. It is seen that 

 the center of gravity of the added shell is near the sta- 

 tion, that of the compensation lies far deeper, at half 

 the depth of compensation. Since their gravitative ef- 

 fects vary inversely with the square of the distance of 

 each unit particle, the added mass below the station in- 

 creases gravity more than the equivalent compensation 

 decreases it. For a small cylinder, the lowering of the 

 datum consequently increases the computed value of 

 gravity. For a cylinder of larger radius, the outlying 



