80 
BRITISH ASSOCIATION.— 1835 . 
To the dodecahedral throughout, Kalmias, Flax, Wood-sorrel, 
&c.— 
To the dodecahedral half-twisted, the branches departing from 
the stem, in Horse-tails ; varying divisions in the flowers of Jasmine 
and Clematis, quaternary and quinary, as noticed in others by Linne, 
and easily corroborated by many examples: 
To this altered structure in all the flowers, Centunculus , JRa- 
diola , Tormentilla. 
In general, to the icosahedral structure,—approximately, how¬ 
ever, as we cannot understand icosahedra thus to mould each other, 
—the Endogene races of plants. 
Dr. Allman briefly refers, as to a subsidiary solid capable of 
moulding, and of leaving within octahedral spaces, to the tetradeca- 
hedron, reciprocal of the rhombic, as the icosahedron is of the ordi¬ 
nate dodecahedron. The four plane angles which form the solid 
angle of this fourteen-sided solid, together measure 300°, as do the 
five plane angles which form the solid angle of the icosahedron. 
Four such quadrangular solid angles, with two quadrangular solid 
angles, each plane angle of 60°, as of the octahedron, accurately 
meet at a point. 
Notwithstanding, this solid seems admissible into the structure 
Exogene , of which the examples among plants are far more numer¬ 
ous than of the reciprocal Endogene. 
The author suggests its conformity to the square stems and four 
exterior distinct packets of fibres in the Calycanthi ; viewed in 
different positions, its indication of the ternary ovary, with the qua¬ 
ternary exterior, in Soap-trees, and in Tropceolum , varied still more? 
All the other above-named solids (except the ordinate dodecahe¬ 
dron and the icosahedron) may be derived from two tetrahedra. 
Those of equal mean diameter, placed reciprocally at a common 
centre, have their envelope the cube, their nucleus the octohedron. 
These last, of like dimension and position, have their envelope 
the rhombic dodecahedron, their nucleus the tetradecahedron. 
Between the squares of the diameters of circumscribed and in¬ 
scribed spheres, the square of the mean diameter is, in the tetrahe¬ 
dron a geometrical, in the cube an arithmetical, in the octohedron 
a harmonical mean. The continued proportions are, 9.3.1.; 3.2.1.; 
6. 3. 2. 
On the Formation of a Natural Arrangement of Plants for a Eotanic 
Garden. Eg Mr. Nivex. 
The principal object of this plan is to divide the exotic from the 
European plants by a serpentine walk, bringing the allied species in 
juxtaposition by the numerous curvatures. 
On Phcenogamous Plants and Ferns indigenous to Ireland which 
are not found in England or Scotland. Eg. Mr. Mack ay . 
Mr. Mackay having been requested to present a general report on 
