British Association,, Edinhurgh Meeting — Lcqnoorth. 233 
that the anticline or arch never occurred without the syncline or trough 
—in other words, that there was never a rise without a corresponding 
fall of the stratum— yet it is only of late years that the stratigraphical 
geologist has come clearly to recognize the fact that the anticline and 
sj'ncline must be considered together, and must be united as a single 
crust-wave. For the arch is never present without its complementary 
trough, and the two together constitute the tectonic, strxictural, or oro- 
(jraphic unit, namely, The Fold, the study of which, so brilliantly in- 
augurated by Heim in his "Mechanismus der Gebirgsbildung," is des- 
tined, I believe, in time, to give us the clue to the laws which rule in 
the local elevation and depression of the earth-crust, and furnish us with 
the means of discovery of the occult causes which lie at the source of 
those superficial irregularities which give to the face of our globe its 
variety, its beauty, and its habitability. 
We have said already that this wave or fold of the geologist resembles 
that of the wave of the physicist. Now we may regard such a wave as 
formed of two parts, the arch-like part above and the trough-like part 
below. The length of the wave is naturally the length of the axial line 
joining the outer extremities of the arch and trough, and passing 
through the centre, node, or point of origin of the wave itself, which bi- 
sects the line of contrary curvature. The amplitude of the wave is the 
hight of the arch added to the depth of the trough. The arch part of 
such a wave, if perfectly symmetrical, may clearly be regarded as be- 
longing either to a wave traveling to the right, in which case the com- 
plementary trough is the one in that direction, or it may be regarded as 
belonging to a wave traveling to the left, in which case its trough must 
be the one in that direction. But as in the case of the shore wave, the 
advancing slope of the wave is always the steeper, and the real centre of 
the wave must lie half-way down this steeper slope; so there is no diffi- 
culty in recognizing the centre of a geological fold and fixing the real 
direction of movement. 
The fold of the geologist differs from the ordinary wave of the physi- 
cist essentially in the fact that even in its most elementary conception, 
as that of a plate bent by a pressure applied from opposite sides, it nec- 
essarily includes the element of thickness. And this being the case, 
the rock sheet which is being folded and curved has different layers of 
its thickness affected differently. In the arch of the fold the upper 
layers of the rock sheet are extended, while its lower layers are com- 
pressed. On the contrary in the trough of the fold the upper layers are 
compressed and the lower layers are extended. But in arch and trough 
alike there exists a central layer, which, beyond taking up tlie common 
wave-like form, remains practically unaffected. 
But the geological fold has in addition to length and thickness, the 
further element of breadth, and this fact greatly complicates the phe- 
nomena. 
Many of the movements which take place in a rock sheet which is 
being folded, or in other words those produced by the bending of a 
compound sheet composed of many leaves, can be fairly well studied in 
