1811.) " 
will endeavour to split the arch with 
equal forces, and willbe in perfect eyti- 
librium with each other.” » Here. the 
theorist does not consider, as Lapicida 
pretends, “(an imaginary wall upon an 
imaginary arch,” but a load upon vous- 
soir; and yet the proposition corre- 
sponds accurately in its results with those 
of Dr. Hutton, inhis book on Bridges, 
a8 Dr. Gregory proves immediately after. 
Secondly. Though Emerson left the 
theory imperfect, as he found it, Dr. 
Hutton does not. He gives a general 
proposition to determine the intrados 
from a proposed extrados, and illustrates 
it by some of the most useful examples, 
Thirdly and fourthly, the results of a 
“theory differing “ from that of the sim- 
ple catenaria,” are no proofs of its  in- 
accuracy. Here both Lapicida’s autho- 
Tities are against him, though he is so 
Jamentably ignorant of the subject as 
not to be aware of it; as I shewed at 
page 362 of your valuable Magazine for 
November, 1809; to which I now refer, 
in order to avoid repetition. But I must 
be permitted to remark, that if Lapi- 
cida’s malady had not been of the most 
desperate kind, the wholesome dose I 
then administered, would have produced 
a perfect cure. » 
| Fifthly. The instances ef failure ad- 
duced by Dr. Robison, have nothing to 
do with the question, as I shewed in the 
Magazine, and ai the page just referred 
to. But it is, on the contrary, perfectly 
in point to remark, that in semicircular 
arches with rectilinear extradosses, ei. 
ther horizontal. or sloping on both sides 
to meet over the vertex, it is constantly 
found that, after the centring of such 
arches is struck and removed, they settle 
‘at the crown and rise up at the flanks: 
for this js exactly what the true theory of 
equilibration, against which Lapicida so 
absurdly cavils, would lead us to expect. 
Sicthly. Dr. Robison, another of 
Lapicida’s authorities, gives evidence 
directly in his teeth, on the subject of 
Domes. For, inthe article Arcn, (Sup. 
Ency. Britan:) he applies exactly the 
same theory of equilibration, to inves- 
tigate the properties of Domes ; I say the 
same theory, though a few additional 
principles are called in: he shews to 
what extent a deviation from true equi- 
libration may be allowed, and why; and 
illustrates his positions by references to 
gome remarkable structures, such as the 
dome of St, Paul’s, the [lulle du Bled at 
Paris, &e, 
~ Seventhly, The theory of piers bas 
to the Theory of Arches. 
427 
been stated accurately by at least four 
authors; namely, Drs. Hutton and Gre- 
gory, M. M. Bossut and Prony. T will 
assert farther, thawithe most candid, skil- 
ful, and experienced of those who have 
been “ nursed in the practice,” are ready 
ta acknowledge, that in general they 
give to the piers full twice the substance 
they apprehend may be necessary, be- 
cause of their uncertainty as to what is 
actually required for stability. 
Eighthly. Whatever, in Lapicida’s 
estimation, “ the methods by analysis and 
geometry” may resemble; the fact is, 
that the principles of equilibration are 
always deduced from a simple and very . 
elementary application of geometry, to 
the composition and resolution of forces; 
and that the fluxionary processes only 
arise in the solutions of problems which 
cannot be touched in any other way, 
except by a gross approximation. 
Ninthly.. With regard to “ mathe 
matical hermits,” to whom “the com- 
mon practices of mankind are myste- 
rious,” few of them seem to have med- 
died with the theory of arches, Dr. 
Hutton, the author against whom La- 
picida levels his ill-directed fire, is no- 
torious, for his having, for a series of 
years, united theory with practice, to an 
extent never exceeded, and perhaps 
never equalled by any other man since 
the time of Archimedes.’ We owe to 
him, to his judiciously blending theory 
with experiment, all extant that is worth 
knowing on the subject of gunnery: and 
he has done more, both as a man of 
science, an engineer, and an architect, 
to improve and confirm the only tenable 
theory of arches and piers, than any 
other philosopher. Whence then ori« 
ginates this incessant tendency on the 
part of men who are not able to read 
(and of course not to estimate) a tenth 
of his writings, to depreciate and de. 
spise them?’ fis Essay on Bridges, 
though published as a hasty imperfect 
attempt, contains more valuable and 
correct propositions on the subject, than 
ean be collected from the aelohiiiee 
of all the mathematicians who have at- 
tended to it. I hope and trust he will 
extend his researches on this interesting 
branch of enquiry, in the edition of his 
Tracts now announced, (I perceive) as 
publishing ; for I doubt not, the result of 
his enquiries for so many years, will place 
the subject in a flood of light, will shew 
in what points all various theories, supe 
posed by infants in science to differ, yxy 
fact agree, in what points authors sup- 
posed 
