J 
~ 
» the errors almost always arise from the 
i. 
1811.].. On the Emerson 
neither opposite, nor are they equal; and 
those forces are assumed which are to be 
discovered, and that is to be found out 
which is given.* In the question of the 
equilibration of arches, justly considered, 
some one force is given (generally that at 
the vertex, as there the perpendicular 
action is equal to its whole absolute gra- 
vity,) to find the two adjoining forces, or 
any others in the system, which is pre- 
cisely the question of the simple catenary, 
where there are no weights but those in- 
_ corporated in the chain. The wall theory 
isa plagiary, garbled and misunderstood, 
from the familiar mechanical method of 
suspending from a chain bits of chain, 
their lower extremities forming a given 
Jine of roadway to determine the curve. 
This method is untrue, and could only 
be made to approximate to truth, as Dr. 
Robison has observed, by making the 
voussoirs bear the same proportion to the 
weight as the chain does to that of the 
bits of chain. The result from this ope- 
ration is untrue, inasmuch as it differs 
from that of the simple catenaria. 
In the investigation of the catenaria, 
the powers considered were the absolute 
gravity of the particle, or link, ‘“ abso- 
lutam gravitatem particule Dd ;” and 
that part of the gravity which acts per- 
pendicalarly, “gravitatis partem eam 
que normaliter in Dd agit:” now it is 
‘admitted by all, that the actions of the 
Voussoirs of an arch are similar to the 
links in a chain, and that the conclusion 
elicited from the one, that the action of 
gravity, perpendicularly exerted on the 
correspondent parts of the chain Dd, 
will be every where the same, “ gra- 
Vitatis actio in partes correspondeutes 
catene Dd normaliter exerta etiam 
constans erit, sive ubique eadam,” ap- 
‘plies egually to the other. To produce 
an arch of equilibration, each voussoir, 
or the weight incorporated in each vous- 
“soir, requires to be increased, so that the 
| * Dr. Milner, in his answer to the Select 
Committee of the House of Commons, to 
‘questions submitted to him on this subject, 
most justly observes: ‘¢It is not from any 
. error of computation, that erroneous practical 
inferences are apt to be made by the theorists ; 
assumptions made at the setting out of the 
Solution of the problem. Dr. Milner thinks 
he is within bounds in believing, that for one 
* €rror in the fluxionary and algebraical part of 
Calculations, a hundred have been made by 
discordant and unnatural hypotheses, respecte 
~ ing powers, forces, and modes of action.” 
3 
» 
Theory of Arches. 227 
force exerted perpendicularly, may be 
every where the same; or that the same 
adjustment should be obtained by art in 
an arch which, in a chain suspended at 
its extremities, naturally appertains to it. 
The distinction between the weight and 
the chain is not real. A catenary may 
be formed of links of unequal weights, 
as well as of equal weights; though the 
curve would be different, the operation 
to discover that curve would be the same. 
Whatever the weight is, or wherever it 
is, it must be incorporated in the chain ; 
and the perpendicular action of each 
force, in a system of forces in equilibra- 
tion solicited by gravity, whether an arch 
or chain, must be constant, or every- 
where the same; and it is the constant 
force which must determine the other 
forces. 
Architects well acquainted with the 
facility to be derived on some occasions 
by the methods of investigation by al- 
gebra and fluxions, affect generally to 
disregard them as marks in their pro- 
fession rather of speculative than real 
knowledge ; but there would be no af+ 
fectation in asserting, that they would as 
soon apply a theodolite to measure a 
cornice, as their knowledge of fluxions to 
the simple and plane theory of equilt 
bration, and the easy proposition of de- 
scribing the extrados of an arch of equi- 
libration, There are mathematical her- 
mits, as well as religious hermits; the 
common practices of mankind are mys- 
teries to the one as well as to the other. 
There is also a superior order of learned 
men, who condescend to try their the- 
oretical knowledge by the practice of 
the workmen, or their own experiments ; 
in the praise of such men, the skilful 
builder will become an enthusiast; and 
from such men, he will be proud to ac- 
knowledge himself indebted for the best 
acquirements in his art. 
Mr. Thomas Simpson, in his answer to 
the three questions proposed by the Com- 
mittee for building a bridge at Black. 
friars, seems to reason on the subject nog 
like a theorist, but an architect, not~ 
withstanding that Emerson’s notions 
had been published some time: indeed, 
throughout the papers published previ- 
ously to the erection of Bilacktriars- 
bridge, although Emerson volunteered 
his opinions to the public, they seem 
to have been wholly neglected;, and 
they would have remained so to the 
present time, among other proposi- 
tions, as the curious wanderings of a 
mathematician, had it not been for the 
doubly 
