206 
have given so unscientific a description of 
it. “The key-stone should be about 3, 
‘or 7; of the span, and the rest should in- 
crease in size ali the way down to the 
‘impost; the more they increase the bet- 
ter.” In the propositions, he considers 
the whole thickness at the vertex as so 
much wall standing upon a mathematical 
curve, in the same manner as Mr. Emer- 
son does. Even in speaking of the arch 
of Blackfriars-bridge, he considers the 
whole thickness at the vertex as wall, and 
the arch, as he above defines it. 
Tke leading proposition of Emerson’s 
theory, is thus: ** The nature of a curve 
forming an arch being given, to find the 
nature of the curve, bounding the top of 
the wall supported by that arch, by the 
pressure or weight of which wall, all the 
parts of the arch are kept in equilibrio 
without falling.” Here the arch is con- 
sidered as something given, not some- 
thing to, be discovered; it is true, if the 
arch is to be considered as of infinite 
thinness, it would be absurd for any 
useful purposes to attempt to determine 
its shape; but it would be mathematically 
proper to discover the infinitesimal in- 
crements from the vertex. If it is of 
some thickness, as practice requires, 
jt is anomalous to set about determining 
what it shall bear, unul it is itself deter- 
mined; for its extrados is the curve upon 
which the Emerson theory proceeds to 
determine the wall to be placed upon it. 
As by this, or, ratner as it may be sig- 
nificantly termed, the wali theory, the 
arch cau have but an imaginary exis- 
tence, it follows that in proportion as the 
arch is practically secure and stable by 
the increase, in consequence of the depth 
of the vousgoirs, in that proportion it is 
insecure and unstable by the theory. 
What the wall is, as applied to bridges, 
which js to stand upon the arch, an ar- 
chitect would be at a loss to guess; but 
it is consistent that an imaginary wall 
should stand upon an imaginary arch. 
Were the wall theory the true theory, 
the propositions could have no applica- 
tien in respect of bridyes among scien- 
ufic yen. The practice of arch-building 
from Michael Angelo at the Rialto, 
through the most enlightened architects 
on the Continent, to Mr, Labelye and 
Mr. Mylne, have been to increase each 
voussoir in depth, from the vertex to the 
springing; pyr has there been wanting 
eminent mathematicians to confirm this 
principle, and the relative increase has 
not been.a matter of guess; hence, if the 
arch, have substance, the propositions of 
On the Emerson Theory of Arches. 
[April 1, 
the wall theory must be framed anew to 
a novel series of curves; if the arch be 
spiritual, then the infinite ascension of 
the two points of the forked extradoses 
of the semicircular, elliptical, and cy- 
cloidal, arches, have properly intercourse 
with the aérial regions; or these, and the 
unicorn of the cissoid, might serve at 
Balniberbi, to prevent the descent of the 
flying island of Laputa. 
It is not dificult to conceive, that the 
mathematician who, in a mathematical 
work, could seriously give an account of 
an automaton which could play at chess, 
might have his risible faculties so orga- 
nised as to be unsusceptible of the ab- 
surdities merely exemplified in the dia- 
grams of this theory. But it is difficule 
to conceive that an enlightened philoso- 
pher should thus slander “ most innocent 
Nature.” ‘She, good cateress, means 
her provisions” for the uses of mankind ; 
in the contemplation of a bridge, she 
could not have prescribed a form which 
would render it impassable; the bounty 
of Nature, in respect of bridges, has ex- 
ceeded any other instance of her provi- 
dence. What in other cases are impedi- 
ments to perfection, in this instance are 
auxiliaries; what in other cases oppose 
the artist, and increase his errors, in this 
instance assist him, and are antidotes to 
his mistakes: could a semicireular or 
elliptical arch be built after the wall the- 
ory, cohesion and friction might prevent 
for a minute the ruin which} without 
their aid, must instantly ensue. 
The first proposition on which the 
whole of this theory depends, most cer- 
tainly does not apply to the question of 
the equilibration of arches, and is not 
true in itself, as stated in the tracts.in 
the support of this theory; it is still fur- 
ther from the truth than the proposition 
of the funicular polygon, acted upon ina 
vertical plane by weights in different 
points of the cord, when the weight of 
the cord itself is not taken into the ac- 
count. In the question of an arch, it is 
all cord—all voussoirs. When the vous- 
svirs balance each other, there is no wall 
but the parapet or fence-wall, which, it 
is hardly possible to believe, has been 
thought to be in the thickness the depth 
of the vault. The filling-in of the span- 
drels, is but another mode of balancing 
the voussoirs, or giving them the same 
perpendicular action, when from eco- 
nomy, or other causes, it has been judged 
expedient to give the arch-stones on the 
face the same depth. In this primary 
proposition, the tangential forces are 
uP neithey 
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