DOI Page / Citation link:
https://doi.org/10.11588/diglit.4423#0087
THE APPARENT PROPORTIONS. 61
PLATES I. and II.
THE PARTHENON.—No. 1, THE NORTH-WEST ANGULAR DESIGN, AND No. 2,
THE SOUTH-EAST ANGULAR DESIGN, SHOWING THE TRUE HEIGHTS
TRIGONOMETRICALLY DETERMINED UPON THE PLANE H 0 Z.
The plan of the Parthenon, the first given elevations of the Porticoes, and the positions
of the points of sight with regard to the Upper Step, have heen already assumed as given
quantities.
Plate I., Pig. 1.—Shows the plan of the Parthenon, with the given elevations of the Porticoes and of the return sides traced
upon the rectangular planes XY, YZ, XZ, passing through the two given points of sight O, Xo. 1, and O, Xo. 2.
It is at once seen that there are two distinct designs to be arranged, namely: No. 1,
the north-west angular design, and No. % the south-east angular design.
The diagonal line AB, Xo. 1 = 26272 ft., and the point of sight 0 is given below the Upper Step 193 ft.
The diagonal line AB, Xo. 2 = 277-906 ft., and the point of sight O is given below the Upper Step 9-2 ft,
A difference of 10 feet exists between the levels of the points of sight of the two designs,
and, to compensate for this difference, the spectator, by means of a longer diagonal line, AB,
is thrown to a greater distance from the angle of the design of the East Portico than of the
West, and the effect of this arrangement is found to be, that the corrections made in the height
of the Columns and of the Entablature, are practically the same for both designs, the difference
in the levels being compensated for by the greater distance.
Plate I., Pig. 2.—The plan of the projections, traced upon the horizontal plane XY, at the north-west angle nearest to the
point of sight O, Xo. 1;
Plate II., Pig. 2.—The plan of the projections, traced upon the horizontal plane XY, at the south-east angle nearest to the
point of sight O, Xo. 2.
Let H be the angle of the frieze projected on the horizontal plane XY, and let the vertical
plane HOZ be conceived passing through H and the point of sight 0, then on this plane HOZ
the true heights of the Porticoes are trigonometrically calculated.
Calculating the distances OC and OH from the point of sight 0, the difference between
them OH — OC = HK, gives the whole dimension of the projections = HK on the plane
HOZ, then dividing this into the required number of aliquot parts, we at once obtain the
distances from the point of sight 0, to the several projections traced upon the plane XY,
without fresh calculations.
Plates I. and II., Pig. 3.—In the case of the Parthenon, as an uninterrupted view is obtained of the fronts and of the
return sides, the whole apparent height, = IT, must be made commensurable with the apparent length and
breadth of the Middle Step at the given height z above the horizontal plane XY; therefore, by calculation, the
angles MOM// + MOM = M have to be determined for both designs.
Xo. 1 Design.-MOM// + MOM/ = M = 157325// )
Xo. 2 Design.-MOM// + MOM/ = M = 144564// j ^ ^ °f Calcuktio» » S*en at page 56.
PLATES I. and II.
THE PARTHENON.—No. 1, THE NORTH-WEST ANGULAR DESIGN, AND No. 2,
THE SOUTH-EAST ANGULAR DESIGN, SHOWING THE TRUE HEIGHTS
TRIGONOMETRICALLY DETERMINED UPON THE PLANE H 0 Z.
The plan of the Parthenon, the first given elevations of the Porticoes, and the positions
of the points of sight with regard to the Upper Step, have heen already assumed as given
quantities.
Plate I., Pig. 1.—Shows the plan of the Parthenon, with the given elevations of the Porticoes and of the return sides traced
upon the rectangular planes XY, YZ, XZ, passing through the two given points of sight O, Xo. 1, and O, Xo. 2.
It is at once seen that there are two distinct designs to be arranged, namely: No. 1,
the north-west angular design, and No. % the south-east angular design.
The diagonal line AB, Xo. 1 = 26272 ft., and the point of sight 0 is given below the Upper Step 193 ft.
The diagonal line AB, Xo. 2 = 277-906 ft., and the point of sight O is given below the Upper Step 9-2 ft,
A difference of 10 feet exists between the levels of the points of sight of the two designs,
and, to compensate for this difference, the spectator, by means of a longer diagonal line, AB,
is thrown to a greater distance from the angle of the design of the East Portico than of the
West, and the effect of this arrangement is found to be, that the corrections made in the height
of the Columns and of the Entablature, are practically the same for both designs, the difference
in the levels being compensated for by the greater distance.
Plate I., Pig. 2.—The plan of the projections, traced upon the horizontal plane XY, at the north-west angle nearest to the
point of sight O, Xo. 1;
Plate II., Pig. 2.—The plan of the projections, traced upon the horizontal plane XY, at the south-east angle nearest to the
point of sight O, Xo. 2.
Let H be the angle of the frieze projected on the horizontal plane XY, and let the vertical
plane HOZ be conceived passing through H and the point of sight 0, then on this plane HOZ
the true heights of the Porticoes are trigonometrically calculated.
Calculating the distances OC and OH from the point of sight 0, the difference between
them OH — OC = HK, gives the whole dimension of the projections = HK on the plane
HOZ, then dividing this into the required number of aliquot parts, we at once obtain the
distances from the point of sight 0, to the several projections traced upon the plane XY,
without fresh calculations.
Plates I. and II., Pig. 3.—In the case of the Parthenon, as an uninterrupted view is obtained of the fronts and of the
return sides, the whole apparent height, = IT, must be made commensurable with the apparent length and
breadth of the Middle Step at the given height z above the horizontal plane XY; therefore, by calculation, the
angles MOM// + MOM = M have to be determined for both designs.
Xo. 1 Design.-MOM// + MOM/ = M = 157325// )
Xo. 2 Design.-MOM// + MOM/ = M = 144564// j ^ ^ °f Calcuktio» » S*en at page 56.