G.—ENGINEERING 117 
occasion endure any laborious stretch of thought or harass their minds 
with unaccustomed investigations. We shall therefore attempt to show 
the weaknesses of the elliptical arch, by arguments which appeal simply to 
common reason, and which will yet stand the test of geometrical examina- 
tion. Any weight laid upon the top of an arch, has a tendency to force 
that top into the vacuity below ; and the arch thus loaded on the top stands 
only because the stones that form it, being wider in the upper than in the 
lower parts, that part that fills a wider space cannot fall through a space 
less wide ; but the force which laid upon a flat would press directly down- 
wards, is dispersed each way in a lateral direction, as the parts of a beam 
are pushed out to the right and left by a wedge driven between them. In 
proportion as the stones are wider at the top than at the bottom, they can 
less easily be forced downwards, and as their lateral surfaces tend more 
from the centre to each side, to so much more is the pressure directed 
laterally towards the piers, and so much less perpendicularly towards the 
vacuity. 
‘Upon this plain principle the semi-circular arch may be demonstrated 
to excel in strength the elliptical arch, which approaching nearer to a straight 
line must be constructed with stones whose diminution downwards is very 
little, and of which the pressure is almost perpendicular. It has yet been 
sometimes asserted by hardy ignorance, that the elliptical arch is stronger 
than the semi-circular ; or in other terms, that any mass is more strongly 
supported the less it rests upon the supporters. If the elliptical arch be 
equally strong with the semi-circular, that is, if an arch, by approaching 
to a straight line, loses none of its stability, it will follow, that all arcuation 
is useless, and, that the bridge may at last, without any inconvenience, 
consist of stones laid in straight lines from pillar to pillar. But if a straight 
line will bear no weight, which is evident at the first view, it is plain likewise, 
that an ellipsis will bear very little ; and that as the arch is more curved its 
strength is increased. Having thus evinced the superior strength of the 
semi-circular arch, we have sufficiently proved, that it ought to be 
preferred... .’ 
Johnson goes on to state that ‘‘the elliptical arch must always want 
elevation and dignity,” and that the only bridge of the elliptical kind 
had ‘“‘ stood two hundred years without imitation.” 
A correspondent of the journal maintained that although an elliptical 
arch may not be as strong as a semi-circular one, ‘ the semi-ellipsis may 
yet have strength sufficient for the purposes of commerce’ ; also ‘ that 
the convexity of the semi-ellipsis may be increased at will to any degree.’ 
In the third letter, Johnson points out that the advocate of the elliptical 
arch does not promise that ‘ it will stand without cramps of iron, and 
melted lead and large stones and a very thick arch,’ and recommends all 
‘those who may still doubt which of the two arches is the stronger to 
press an egg first on the ends, and then upon the sides.’ 
Contemporary writers disclosed the fact that Johnson consulted Mr. 
Simpson and Mr. Miiller, both professors at Woolwich Academy. 
Neither favoured the semi-circular arch in preference to the elliptical, 
and he then procured ‘ from a person eminently skilled in mathematics 
and the principles of architecture, answers to a string of questions drawn 
up by himself, touching the comparative strength of semi-circular and 
elliptical arches.’ 
