DOI Page / Citation link:
https://doi.org/10.11588/diglit.4423#0080
THE APPABENT PBOPOBTIONS.
55
1st. The given heights of the Porticoes traced upon the plane HOZ, Fig. 1.
given Tiagkts.
plcaw H.O.Z.
In Kg. 1.—The apparent heights,
measured by the visual angles, of the
Steps = S, the Columns = C, and the
Entablature = E, are calculated by the
Eorm 1, Log. tan. A = log. r + log. a
+ log. b., then comparing the calculated
apparent heights of the several members
of the Portico (S,0,E) with the given
apparent height = the arc Ii, the visual
angles are generally found to be incom-
mensurable one with another.
Thus, comparing the apparent height of Column C with the whole height H, the ratio is generally \ Substitute the
Again, comparing the apparent height of the Entablature E with the apparent height of Column C, ^ j,. 2
' the ratio is generally irrational J &'
2nd. The corrected heights of the Porticoes traced upon the plane HOZ, Fig. 2.
Substituting in Eig. 2—The nearest
apparent commensurable ratios, the whole
apparent height = arc H, will be divided
into some given number of aliquot parts,
then, taking one of these parts as a modu-
lus, the apparent heights of the Steps,
the Columns, and the Entablatures will
be multiples of this modulus, and the
true executed heights are calculated by
the
print
sigh
0
nearest
alios as
Eorm 2, Log. a
A —10.
log. b. + log. tan.
In every example this double calculation has to be made: 1st. To determine the visual angles the heights being
the given quantities ; 2nd. To determine the true executed heights, when the visual angles have been made commensurable
with each other, and with the whole apparent height.
The actual calculations for determining these plus and minus quantities in the Parthenon and in other designs will
render the subject clearer than any further explanation.
TO DETERMINE THE APPARENT HEIGHT = ANGLE fcOfc-H.
When tabulating the observed facts in Part I., Plate III., we noticed in some cases,
in the whole height of the Portico, a difference between the first given quantity and the
executed dimension; thus, in the Parthenon, the difference amounts to + 4"85 inches, and
in the Temple of Theseus to-6'75 inches. In other examples, as in the East Portico of
the Erechtheium, in the Central Portico and in the north wing of the Propylaea, the
whole executed height of each Portico exactly agrees with the first given quantity, in fact
there is no correction, and the whole height is taken as one of the given quantities.
Therefore, in all cases in which it was considered requisite to correct the whole
apparent height of the Portico, before we can determine correctly the heights of the Steps,
the Columns, and the Entablatures, the true apparent height, = H, must be accurately
ascertained at the angle of the design nearest to the point of sight 0.
This was always considered necessary whenever, from the angular point of sight 0,
tl front and the return side of the design were seen together without any interruption in the
1 <Tn the Parthenon, the Theseium, and in the North Portico of the Erechtheium, then the
55
1st. The given heights of the Porticoes traced upon the plane HOZ, Fig. 1.
given Tiagkts.
plcaw H.O.Z.
In Kg. 1.—The apparent heights,
measured by the visual angles, of the
Steps = S, the Columns = C, and the
Entablature = E, are calculated by the
Eorm 1, Log. tan. A = log. r + log. a
+ log. b., then comparing the calculated
apparent heights of the several members
of the Portico (S,0,E) with the given
apparent height = the arc Ii, the visual
angles are generally found to be incom-
mensurable one with another.
Thus, comparing the apparent height of Column C with the whole height H, the ratio is generally \ Substitute the
Again, comparing the apparent height of the Entablature E with the apparent height of Column C, ^ j,. 2
' the ratio is generally irrational J &'
2nd. The corrected heights of the Porticoes traced upon the plane HOZ, Fig. 2.
Substituting in Eig. 2—The nearest
apparent commensurable ratios, the whole
apparent height = arc H, will be divided
into some given number of aliquot parts,
then, taking one of these parts as a modu-
lus, the apparent heights of the Steps,
the Columns, and the Entablatures will
be multiples of this modulus, and the
true executed heights are calculated by
the
sigh
0
nearest
alios as
Eorm 2, Log. a
A —10.
log. b. + log. tan.
In every example this double calculation has to be made: 1st. To determine the visual angles the heights being
the given quantities ; 2nd. To determine the true executed heights, when the visual angles have been made commensurable
with each other, and with the whole apparent height.
The actual calculations for determining these plus and minus quantities in the Parthenon and in other designs will
render the subject clearer than any further explanation.
TO DETERMINE THE APPARENT HEIGHT = ANGLE fcOfc-H.
When tabulating the observed facts in Part I., Plate III., we noticed in some cases,
in the whole height of the Portico, a difference between the first given quantity and the
executed dimension; thus, in the Parthenon, the difference amounts to + 4"85 inches, and
in the Temple of Theseus to-6'75 inches. In other examples, as in the East Portico of
the Erechtheium, in the Central Portico and in the north wing of the Propylaea, the
whole executed height of each Portico exactly agrees with the first given quantity, in fact
there is no correction, and the whole height is taken as one of the given quantities.
Therefore, in all cases in which it was considered requisite to correct the whole
apparent height of the Portico, before we can determine correctly the heights of the Steps,
the Columns, and the Entablatures, the true apparent height, = H, must be accurately
ascertained at the angle of the design nearest to the point of sight 0.
This was always considered necessary whenever, from the angular point of sight 0,
tl front and the return side of the design were seen together without any interruption in the
1 <Tn the Parthenon, the Theseium, and in the North Portico of the Erechtheium, then the