1885.] of the Appalachian Mountains. 261 
In consequence of the condition of the strata it is exceedingly 
difficult to determine in the field the number of folds occurring in 
the valley. It is not probable, moreover, that they are regular or 
constant. The beds involved are, however, about a mile in thick- 
ness, so that there can scarcely be less than eight arches in the 
sixteen miles. If then for the south-eastern legs we adopt Pro- 
fessor Rogers’s lowest angle of dip, or 45°, and for the north- 
western sides his lowest estimate, or 60°, and plat these to scale, 
we have the following result : 
The Cumberland valley, sixteen miles wide, consists of at least 
eight overthrown anticlinal arches, the crest of each of which 
overlaps to some extent the base of that following it. This will 
be clear from an inspection of the diagram, where a single bed of 
rock is shown folded as required by the conditions above given. 
A B C, &c., are the successive crests of the arches formed by the 
stratum. X Y represents the present surface of the ground. 
a bc are the bases of the synclines corresponding to the arches. 
Taking into consideration the mid-layer of the stratum repre- 
sented by QOS TU V, &c., which will represent the actual 
length of the folded bed, a short mathematical calculation will 
prove that O Q is 3.3 times as long as R Q. R Q representing 
one mile, O NV will therefore represent 6.6 miles. All the eight 
south-eastern legs of the arches will consequently measure about - 
fifty-two miles. 
In like manner we find that the length of the line O R, com- 
pared with R Q, is 2.7. Consequently the length of the line O S 
represents 5.4 miles and the eight north-western sides of the arches 
amount to forty-three miles. 
Again, a reference to the figure will show that the north-west- 
ern side of each arch underlies its south-eastern side, so that its 
whole length must be added to the figures previously obtained. 
Summing up results, we find : 
Twenty-nine miles at 40° dip, 0 38 miles. 
Eight anticlinal arches in Pe valley— , 
astern sides. ss = 
No Aas sides.. 43 
Add twenty miles for flat strata, as previously deducted.,...20 
nee 
Total. 153 
In other terms this means that a tract of the earth’s surface 
measuring originally 153 miles from south-east to north-west has 
