1921 .] 
Reviews and Abstracts. 
271 
two preceding terms, which, for integral numbers is expressed by the 
Fibonacci series of Leonardo da Pisa thus : 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 
144, &c. The ratio between successive terms of this series becomes in 
the limit 
s/ 5 + 1 
_ or 1-618. 
The reciprocal of this number is 0-618... and 
its square is 2-618. Furthermore, when a line is cut in extreme and mean 
ratio (Euclid II: 11, and VI: 30) (the “ golden ” or “ divine ” section of the 
geometers) the parts are in the proportion of 1 : 1-618... 
The artists responsible for the superb creations of Greek pottery un¬ 
doubtedly were familiar with the work of the Greek geometers, and found 
that the application of “ science to industry ” simplified and schematized 
their design enormously. The standardized shapes of Amphorae, Kylikes, 
Hydriae, Skyphoi, Oinochoi, and Lekythoi were all arrived at by taking the 
full height of the vase as the length of a suitable root-rectangle, and fixing 
the other salient dimensions from the natural subdivisions of the figure. 
The Brygos Kantharos. 
The subdivisions were always obtained from using the similar and reciprocal 
rectangles obtained by drawing parallels through the intersections of the 
diagonals and perpendiculars drawn from opposite corners. Very many 
beautiful examples are illustrated, with their analyses into the formulating 
rectangles, and that of the strikingly beautiful Brygos Kantharos is repro¬ 
duced here. 
[This book is the record of a series of lectures given by the author at 
the School of Fine Arts of Yale University, and is the first volume published 
from the Rutherford Trowbridge Memorial Publication Fund. Similar 
analyses are being made of the works of art comprised in Greek architecture, 
statuary, and painting, and it is already clear that dynamic symmetry is 
the principle of their design also. The importance of this rediscovery can 
hardly be exaggerated ; indeed, one of the most prominent art masters of 
London has declared that “ the rapid spread of the system of dynamic 
symmetry will lay the foundation of our artistic salvation.” The deplorable 
position of architecture at the present day from the aesthetic point of view 
appears hopeless but for the promise contained in this principle; and its 
application to bridges and engineering structures generally is simple and 
obvious, but of prime necessity.] S. H. J. 
