270 
The N.Z. Journal of Science and Technology. 
[Nov. 
In conclusion, Dr. Taylor’s illuminating comparison of modern with 
ancient migrations may be quoted : “ The characteristics of a migration 
have always been much the same throughout the ages. A modern 
‘ migration,’ such as that of a city crowd to a football match, presents some 
useful analogies. First come the lowest classes and pariahs, who wander 
freely over the ground long before the general public arrives. They have 
arrived there by the usual roads and tracks, but ultimately are found perched 
in tree-tops and in the least attractive positions in the ground. Then the 
proletariat advances along the same roads and corridors. They are driven 
out of the best seats, which are reserved for the last comers.” This com¬ 
parison is stimulating as well as amusing. It forms no substitute, however, 
for the accurate and laborious work of orthodox ethnological research. 
H. D. Skinner. 
Dynamic Symmetry—the Greek Vase, by Jay Hambidge. Yale University 
Press, 1920. 
The artistic miracle involved in the shape or form of the Greek vase 
of the classic period, which is the greatest design-fabric ever created, made 
its analytical inspection of supreme importance ; but as long as the 
problem was attacked along the lines of linear (static) proportion the basis 
of design defied discovery. It has long been understood that design in 
decorative and pictorial art is dependent upon a fundamental schematic 
plan permeating the entire production, thus producing a basic symmetry 
and proportional relationship between parts and whole ; but the discovery 
that areal, or two-dimensional, proportionality governs all understanding 
of the true significance of structural form is a modern rediscovery of the 
basic principle which made possible that Grecian perfection in sculpture, 
architecture, and pottery which is at once the delight and the despair of 
the modern artist. 
This book shows conclusively that all the finer examples of Greek vases 
were designed to have the salient dimensions commensurate in area and 
incommensurate in line, or, to translate it into the machinery of the 
designing-draftsman, that the shape was sketched out by the aid of a few 
rectangular figures whose sides were in the ratio of 1 : a/2, 1 : V3, 1: Vo, 
and 1 : 
V 5 ± 1 
" 1 
respectively. 
The author considers there is no ground 
for the assumption that any one of these rectangles is in itself a more 
beautiful shape than any of the others, although Plato considered that the 
root-three rectangle held that pre-eminence; but the root-five rectangle, 
with its companion or derivative the rectangle of the whirling squares 
/— 
(the rectangle whose sides are in the ratio 1 : _U=_), is the base of dynamic 
symmetry. These last two are the only rectangles used in formulating 
the Parthenon and such other examples of Greek architecture and statuary 
as have yet been analysed. 
The peculiar properties of the rectangle of the whirling squares are 
well brought out; and its connection with the logarithmic spiral of 
vegetable and cell growth and with the summation series of phyllotaxis, 
or leaf-distribution, is carefully noted. Construction of form in the plant 
(and probably animal) world is associated with the summation series—so 
called because any term of the series is obtained by adding together the 
