304 PHYSIOGRAPHY OF CENTRAL-ASIAN DESERTS AND OASES. 
number of centuries since it was founded, times the difference between its rate of 
accumulation and the rate of surrounding aggradation. If, as has been with 
many excepting those of type I, it was away from aggradation, its height would 
be simply /G. 
Most of the oases that interest us have long since been abandoned and erosion 
enters the equation; then h=/G—[E(t—l)+At], or total thickness of culture, 
minus erosion since abandonment and amount the plain has arisen around it. 
But obviously the plain will in time rise to bury the eroding top. Let ¢,=time at 
which erosion will meet aggradation (time of total burial), then h=o and 1G= 
E(t,—1) + At, and poe and the first equation kh =I1G—[E (t—l) + Af] is true 
GEE 
only when ¢ is less than / - ALE 
Residual height 
=1G6-[t At(t-1)E] 

(t-1)E ZZLZLL2, 
7 






Fig. 470.—Diagram showing Relation between Erosion and Burial of Abandoned Kurgans. 
Cross-hatching represents wasted top of Kurgan. 
G+E 
A+E 
After that burial takes place, and the depth to which the top is buried at any time 
will be: 
(1) h=1G—[E (t—l) +At] when t<l 
G+E 
(2) d=A 15 7 te when t> he Gay 
or the rate of aggradation multiplied by the time since foundation minus the time 
that elapsed between then and the beginning of burial. 
Changing the equation of obliteration somewhat in form, we get our third 
and most important equation. 
(3) 1+ 2 when h=o 
which means that on aggrading areas any town, not occupied more than the ratio 
eee +e times the number of centuries since it was founded, has vanished from sight 
beneath the aggrading plain. The depth to which the eroded top of its accumula- 
tion has been buried can be found from equation (2). 
Assuming Professor Pumpelly’s values obtained at Anau, we have G=2 and 
A =o.8, and since it is from erosion the growth of plains is supplied and since the 
areas of erosion and aggradation seem to correspond in a general way and our cul- 
ture mounds probably erode as fast as anything, we may for experiment assume 
o ef. A+E 1.6 
E=A or E=o.8. Then Conese 
error than equation E = A, because E partly compensates itself by division. 
=0.57 as a conservative ratio of much less 
