548 TF. Gibson — Age of the Rand Beds. 



have moved to some position in A' B'. It is also a point in the line 

 C D, and therefore it must have moved to some position in C T)'. 

 Consequently the new position of the point must lie both in A' B' 

 and in C D', and it must therefore lie at their intersection 0' : the 

 effect of the fault has been to move the point to the position 0', 

 and every point in A B and in C D has moved along a line parallel 

 and equal to 0'. 



It may be remarked here that it is impossible to say whether 

 A B or A' B' was the original position of the bed, and it is therefore 

 impossible to determine whether the movement took place from 

 to 0' or from 0' to 0. 



If the movement has been uniform throughout the area considered, 

 then the solution is perfectly general. A B and C D may or may 

 not be the same bed. The line A C need not be horizontal or even 

 straight. The positions of A and C with respect to each other may 

 be chosen quite ai'bitrarily. The only conditions to be satisfied are 

 that A A', A B, A' B', C C, C D. and C D' make the proper angles 

 ■with the horizontal ; and that A A' and C C be drawn according 

 to the particular scale selected. If this be done, then O' will also 

 make the proper angle with the horizontal and will be on the same 

 scale as A A' and C C. It must be noted, however, that the angles 

 "which A B, C D, etc., make with the horizontal, are not the angles 

 of the true dips of the beds in question, but the angles of the apparent 

 dij^s in the "plane of the fault. 



Although the solution is general, there are many faults to which 

 it cannot be applied, even theoretically. If the lines A' B' and C D' 

 are not parallel respectively to A B and C D, the problem is in- 

 soluble, because the movement has not been uniform. All that 

 we can do is to determine the direction of motion at some 

 particular spot. 



As the displacement due to a fault is pi'obably never the same 

 throughout its whole length, it is advisable to take beds A B and 

 C D, which are in actual fact near to each other; and as a general 

 rule there are no cases more favourable for the application of the 

 method than unconformities, where beds of different dips are found 

 one above another. 



1 



V. — The Age or the Band Beds. 



By W. Gibson, F.G.S. 



N several parts of South Africa, thick sedimentary and un- 

 fossiliferous deposits are found resting on gneisses or highly 

 altered rocks. They are well developed in the Southern Transvaal 

 around the towns of Johannesburg and Potchefstroom ; in the 

 Northern Transvaal in the districts of Lydenburg and De Kaap, and 

 possibly Zoutspansberg; in Matebeleland, Bechuaualand, Griqualand 

 West, Damaraland, and Zululand. These widely distributed sedi- 

 ments have been generally taken as representing the whole or 

 portions of the sedimentary series typically developed in the 

 Southern Transvaal. 



