The Evolution of Beauty. 
383 
1878.] 
Reduce to their simplest form the four numbers 264, 330, 
396, 462, by dividing them by their greatest common mea- 
sure, viz., 66, and you have the series 4, 5, 6, 7, the relations 
of which are perceptible at once to the most ordinary mind. 
Place before a person ignorant of plants the little yellow 
celandine and a red pasony, and he would not recognise any 
family resemblance ; but fill up the gap between them with 
a buttercup, a globe-flower, and a Christmas rose, and he 
would perceive the gradation from one to the other and 
admit the relationship. 
The closer the relationship, the more easily is it recog- 
nised ; therefore the objects which appear beautiful to 
human minds must be those in which the parts are closely 
related, the proportions simple, the design obvious. Among 
mathematical figures the pentagon is one of the most ele- 
gant, because there is in its outline a sufficient variety with 
such simple proportions that the unity is easily grasped. 
The circle also is beautiful, so is the hexagon, the square, 
and the equilateral triangle ; but in each of these the variety 
is less than in the pentagon. The dodecahedron, of twelve 
pentagons, is scarcely beautiful, except to a mathematician, 
because the variety is so confusing that part of the unity is 
lost, and the figure appears almost chaotic. 
Divide a hexagon into six equilateral triangles, and let 
these be aCted upon by an accelerated repulsive force so 
that they are driven radially from the centre to distances 
represented by the numbers 1, 3, 6, 10, 15, 21. They will 
then stand in a spiral of such form that the majority of 
persons would not recognise any law of relationship binding 
them into one group. Let, now, the repulsive force be 
changed into an attractive one whose formula is precisely 
reversed, and, as the triangles are drawn gradually towards 
the centre, their relationship will become more and more 
easily discerned, till, as they close up into the original hex- 
agon, every human mind will perceive the unity of the 
group, and a sense of beauty will inevitably follow. 
It is the character of the centripetal organic wave to be 
continually simplifying the relationship of its component 
waves with each other, both by concentration and the filling 
up of gaps ; and it results from this that the nearer any 
organic wave approaches towards its climax, the closer are 
the relations of the component weaves, and the more readily 
will its beauty be perceived by the human mind. 
Beauty is thus shown to be an index of organic maturity, 
and not to depend upon any accidental or external influence, 
but to be inherent in every objeCt, and only unseen during 
its embryonic stages. 
