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APPENDIX
If you add a line of 5 inches to one of 8 inches you produce one
13 inches long, and if you proceed by always adding the last two
you arrive at a series of lengths, 5, 8, 13, 21, 34, 55 inches,
&c. Mr. William Schooling tells me that any two of these lines
adjoining one another are practically in the same proportion to
each other; that is to say, one 8 inches is 1.600 times the size
of one 5 inches, and the 13-inch line is 1.625 the size of the 8-inch,
and the 21-inch line being 1.615 times the 13-inch line, and so
on. With the mathematician's love of accuracy, Mr. Schooling has
worked out the exact proportion that should exist between a series
of quantities for them to be in the same proportion to their neighbours,
and in which any two added together would produce the next. There
is only one proportion that will do this, and although very formidable,
stated exactly, for practical purposes, it is that between 5 and
a fraction over 8. Stated accurately to eleven places of decimals
it is (1 + sqrt(5))/2 = 1.61803398875 (nearly).
We have evidently here a very unique proportion. Mr. Schooling
has called this the Phi proportion, and it will be convenient to
refer to it by this name.
290Testing this proportion on the reproductions of pictures in
this book in the order of their appearing, we find the following
remarkable results:
"Los Meninas," Velazquez, page 60 [Transcribers Note: Plate IX].—The right-hand side of light
opening of door at the end of the room is exactly Phi proportion
with the two sides of picture; and further, the bottom of this opening
is exactly Phi proportion with the top and bottom of canvas.
It will be noticed that this is a very important point in the "placing"
of the composition.
"Fête Champêtre," Giorgione, page 151 [Transcribers
Note: Plate XXXIII].—Lower
end of flute held by seated female figure exactly Phi proportion
with sides of picture, and lower side of hand holding it (a point
slightly above the end of flute) exactly Phi proportion with top
and bottom of canvas. This is also an important centre in the construction
of the composition.
"Bacchus and Ariadne," Titian, page 154 [Transcribers Note: Plate
XXXIV].—The proportion in this picture both with top and
bottom and sides of canvas comes in the shadow under chin of Bacchus;
the most important point in the composition being the placing of
this head.
"Love and Death," by Watts, page 158 [Transcribers Note: Plate
XXXV].—Point from which drapery radiates on figure of
Death exactly Phi proportion with top and bottom of picture.
Point where right-hand side of right leg of Love cuts dark edge
of steps exactly Phi proportion with sides of picture.
"Surrender of Breda," by Velazquez, page 161 [Transcribers Note:
Plate XXXVI].—First
spear in upright row on the right top of picture, exactly Phi proportion
with sides of canvas. Height of gun carried horizontally by man
in middle distance above central group, exactly Phi proportion with top and bottom of picture. This line gives height
of group of figures on left, and is the most important horizontal
line in the picture.
"Birth of Venus," Botticelli, page 166 [Transcribers Note: Plate
XXXVII].—Height of horizon line Phi proportion with top
and bottom of picture. Height of shell on which Venus stands Phi
proportion with top and bottom of picture, the smaller quantity
being below this time. Laterally the extreme edge of dark drapery
held by figure on right that blows towards Venus is Phi proportion
with sides of picture.
"The Rape of Europa," by Paolo Veronese, page 168 [Transcribers
Note: Plate XXXVIII].—Top
of head of Europa exactly Phi proportion with top and bottom of
picture. Right-hand side of same head slightly to left of Phi proportion
with sides of picture (unless in the reproduction a part of the
picture on the left has been trimmed away, as is likely, in which
case it would be exactly Phi proportion).
I have taken the first seven pictures reproduced in this book that
were not selected with any idea of illustrating this point, and
I think you will admit that in each some very important quantity
has been placed in this proportion. One could go on through all
the illustrations were it not for the fear of becoming wearisome;
and also, one could go on through some of the minor relationships,
and point out how often this proportion turns up in compositions.
But enough has been said to show that the eye evidently takes some
especial pleasure in it, whatever may eventually be found to be
the physiological reason underlying it.
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