2'Iie Second I.tikc AhjfUKin i u . — Tinjlov. 169 
feet, and the greater hight of tlie fall is taken to aecf)unt 
for liie narrowness of the gorge. The depth of the river is 
assumed to be as great as in the parts above. A little consid- 
eration shows, liowever. that neither of these ideas is defens- 
ible on sound i)rinciples. 
On the depth of the gorge of the rapids Dr. Spencer's con- 
clusion seems to me to lie contrary to conclusive facts. I re- 
gard it as a matter of simi)le demonstration that tlie river is 
much shallower there th;in in the wider gorge above the rail- 
road bridges. If we know the volume of a river from meas- 
urement at some place where its velocit}^ is moderate we may 
readil}' calculate its mean depth in ;iny other place if we know 
its width and velocity. For its velocity is inversely propor- 
tional to the area of its cross section, and if we know the 
width and velocity then we can easily find the mean depth. I 
regret that I have no accurate data on this point. l>ut after 
standing beside the rushing, roaring torrent of the narrow 
Whirl|)ool rapids and then being rowed in a skifl' across the 
river at the American fall, one is fully convinced that the ve- 
locity of the water in the Whirlpool rapids can hardly be less 
than five or six times that in the wider gorge al)ove. But ac- 
cording to Dr. Spencer's idea of a substantially uniform depth 
for the whole gorge, the water cross-section of the Erigan 
gorge is al)out half of that at Johnson's ridge. This allows 
for a velocity onl}' twice as great. In order to find a cross- 
section to suit the observed velocity we must reduce the 
mean depth of the Erigan gorge to 75, GO, or i)erhaps only 50 
feet. It is impossible to supply the conditions of high veloc- 
ity for the rapids in any other way. 
In support of the first point Dr. Spencer a])peals to the law 
of erosion, viz., the steeper the declivity of a stremn the more 
it cuts vertically and the less horizontal. This law is true 
for streams flowing without cataracts, but it iloes jiot apply 
to cataracts or vertical falls of ditl'erent bights, and the ex- 
ception is still more pronounced where the strata are horizon- 
tal and the weaker layers below are capped by a luiriler ledge 
above, as is the case with Niagara. The magnitude of the 
gorge in such a case depends mainly upon the stream's power 
of excavation at the hottoni of the cataract where the water 
falls with greatest force u])on the softer, lower rocks, under- 
