f°: 8g 
wall over 2 and N, when the arches are in equilibrium, be equal 
to d; if Hv be to Hv +d, as HK to KE, Hv will be equal 
to Er-d. Then a being the altitude of the building over the 
crown of both arches, and Ng the height over the point # in 
the femicircle, when truly balanced, the defect of equilibrium in the 
Gothic arch will be Ng + d-a-Ef, and in the femicircle it will be 
Ng-a-Hv=Ng+d4-a-Er; but E p is greater than Ev, and 
therefore the defe€t of equilibrium in the Gothic arch is lefs than 
in the femicircle. If Er be too fmall, produce EK tillEr-Hv 
= d, which is greater than 4, the difference of heights when EK 
is fo produced: then, @ fortiori, the deviation from a perfe& 
balance will be lefs in the Gothic arch, as before. In all cafes 
the aberration will be lefs when the altitude over the crown of the 
arch is lefs; becaufe, when quantities are in a given ratio, the 
lefs the quantities themfelves are, the lefs will be their difference. 
And therefore, when the height of the building above the {pring 
of the arch is given, the higher the arch the more it approaches to 
a perfect balance. 
Hence we may obferve, that this arch was peculiarly adapted 
to the ftyle of thofe religious buildings, which were in fafhion 
in. the middle ages, where the roof was to be raifed to 
an extraordinary height, and no great weight immediately 
incumbent on the. point of the arch, or where one tier of 
arches was to be raifed over another. But when a very high 
building is to be ere@ed upon a Gothic arch, the quantity of 
matter over the crown or vertex muft be very much lightened 
_ by windows or other perforations, as was the practice with the 
Gothic architeds. 
M 2 22. IF 
