426 
profuse liberality to Baxter, Calamy, 
and others of the Presbyterian party; 
but they were in return expected to 
sell themselves entire to the sect which 
had so basely defrauded them, by vio- 
lating engagements the most solemn. 
Their noble disinterest rejected -all hush-. 
hire. The purest atonement which 
can now be made for the perfidy, is to 
sepeal the act of uniformity, and to 
open the church to the defrauded sec- 
taries. 
The most important feature of the 
Enquirer’s plan is however not its eccle- 
siastic operation. An alert statesman 
would have pereeived in it the only 
practicable way of enabling government 
to avail itself of those revenues of the 
church, which are in the gift of the 
crown, for purposes of civil patronage. 
Without any infringement of private 
property, with new indulgence to pri- 
vate judgment, it would enable the mi- 
nister to give among Edinburgh and 
Quarterly Reviéwers, the prebendal stalls 
and sinecure preferments of the church, 
and thus render needless many an in- 
erease of the pension-list, 
me 
Zo the Editor of the Monthly Magazine. 
sIR, 
LAS! Mr. Editor, how melancholy it 
is to. trace the preguess of poor Lapi- 
cida’s disorder! A year and a half ago 
I .administered some medicines, and 
pointed out a regimen, that I hoped 
would have proved salutary, and ulti- 
mately have restored the patient. But 
the eguilibratio-phobia, under which he 
labours,-having not yet been introduced 
into any of our modern systems of no- 
sology, it is certainly diffeult. to know 
when to-form a favourable prognosis. 
The disorder, however, seems now ra- 
pidly hastening to a crisis; but the’ ca- 
coethes scribendi, with which’ the poor 
gentleman has been all along troubled, is 
4 most unfavourable symptom. Like 
Gratiano, he “ talks an infinite deal of 
nothing, more than any man in all Ve- 
nice. His reasons ere as two grains. of 
wheat, hid in two bushels of chaff; you 
shall seek all day ere you find them; and 
when you have them, they are not worth 
the search.” I have gone through his last 
paper, which you have indulged with in- 
sertion in your Magazine for this month, 
(April) in order to pick out this grain or 
two, which he sets against the genuine 
theory of equilibration, and heve they are. 
‘ 
Refutation of Lapicidu’s Opinions relative 
[June1, 
1. Theorists consider “the whole 
thickness at the vertex as so much wall 
standing upon a mathematical curve,” 
2, Emerson’s leading propositian is, to 
find the extrados from a yiven  intra- 
dos. : 
3. This proposition is not true, nor 
does it apply to the question, because its 
result “ differs from that of the simple 
catenaria.” 
-4. “The authority of the Woolwich 
Academy has imposed Emerson’s ‘The- 
ory of Arches,” but the true theory is 
that, which Lapicida “ attempts to detail 
from Dr. Gregory’s paper, and Dr. 
Hooke’s conclusion.” x 
5. Dr. Robison admitted the falla- 
ciousness of the theory, and adduced, as 
the “clearest proof of ity that arches 
very rarely fail where their load differs 
most remarkably from that which this 
theory allows.” 
6. The theory of domes, founded upon 
the same principles of equilibration, 
stands “like the full and perfect warning 
which a wreck offers to the heedless 
mariner.” 
7. The theory of piers “is a part on 
which little has been written, and still , 
less understood, except by those who 
have been nursed in the practice.” 
8. “Phe methods by analysis and 
geometry, resemble the progress of a 
young and old hound.” 
9: “ There are mathematical hermits,” 
to whom “the common practices of 
mankiud are mysteries,” 
Now, in replying as briefly as possible 
to these, allow me to say, 
First. . That in Gregory’s Mechanies, 
page 141, vol. 1, there may be seen a 
demonstration of this proposition: “ The 
force of a voussoir devending on the 
magnitude of the angle, formed by its 
sides, the impelling force, and the re- 
sistance to be overcome, is on the first 
accouit directly as the radius of curvae 
ture of the arch at that point; on the 
second, as the square of the sine of the 
angle, included between the tangent of 
the curve at the yiven point, and the ver- 
tical line passing through that point; and 
on the third, as the sine of the same 
angle,” From this proposition the ob- 
vious corollary is deduced, that “if the 
height of the wall incumbent on any 
point of the intrados, is directly as ‘the 
cube of the secant of the angle, formed 
by a.tangent to the voussure at the given 
peint with the horizon; and inversely as . 
the radius of curvature ; all the hpysc en 
Wd 
