TR 
difference of the ordinates, for the altitude can fearcely be conceived. 
to be fo fmall as the difference of the ordinates; confequently there 
will be a lefs deviation from a true balance in the elliptic arch than 
in the Gothic. 
24. Ir follows therefore, that an elliptic arch, whofe tranfverfe 
axis is perpendicular to the horizon, is to be preferred to the Gothic 
arch for ftrength; both becaufe its ftrength exceeds that of a 
Gothic arch of equal fpan and altitude, when both are in a 
ftate of equilibration ; and alfo becaufe a given altitude of build- 
ing raifed upon it and terminated by an horizontal line produces 
a lefs aberration from a perfect balance of the parts. It follows 
alfo that the Gothic arch, when carried up to a fufficient height, 
is to be preferred to a femicircular arch for the fame reafons. 
Ir feems unneceffary to compare the ftrength of the piers 
requifite to fuftain elliptic and Gothic arches with the ftrength 
of the piers of femicircular arches, as, from the great elevation of 
their vertexes, they are entirely unfit to be applied in bridges, where 
alone piers are introduced. 
