THE THEORY OF ISOSTASY 619 



from the resulting expression for the reduction factor. Taking 

 the value of D c given in (8) the reduction factor is 



D+Dc , 1 ^(H+hJ , r*+V (rQ'+Qg+ft,)' 



F M = -p- = i+— - — 84— log —77 -r^—T . 



log- 



, 8,(A-H), r*+V(r*Y+(h-Hy 

 + — a7, — lo § 



From (4) 



8h r.+yrf+Qi-Hy 



8x Mh 



Substituting (10) in (9) 



8 h+h 



r I +l/(r I ) 2 +(^+Ai) a 



(10) 



log 



_, MjH+h) ° y I + 1 / fl «+(g+/ Cl )2 



log - ' 



, r I +T/(r I ) 2 +(A-fl') 2 



log , 



M(h-H) n+VrS+Qi-HY 



ht+h r 1 



log - 



(11) 



This reduces to Hayford's factor if M be put equal to 1 and # 

 and h be put equal to zero. These are the three approximations on 

 which Hayford's factor is obtained. If h x is large, it is legitimate 

 to neglect H and h; but if hj. were to be taken as 12 miles h and H 

 would certainly have to be considered. This fact would increase 

 the length of the computations since for a complete solution of the 

 problem a different factor would be necessary for each compartment 

 whereas, before, the same factor was used for an entire ring. Doubt- 

 less, however, devices could be employed which would facilitate 

 the calculations. 



The necessity of having to use the reduction factor given in 

 (n) serves to make the depth and degree of completeness of com- 

 pensation more open to question than ever. 



SUMMARY 



On the basis of Hayford's work it may be considered settled 

 that there is some sort of isostatic compensation, but so far as 

 Hayford's investigation has yet gone there are many possibilities 



