ORIGINAL COMMUNICATIONS. 
Some Considerations Concerning Symmetry. 
By Proressor R. J. ANDERSON. 
SYMMETRY has so much to do with the order, form, and arrangement of 
parts in natural objects and figures geometric, that one becomes 
interested in its varieties, the causes of these latter, and the relation- 
ships that exist between them. There is involved also the question of 
asymmetry. Symmetry is the outward and visible sign of the 
resultant forces that fashion a body. There is no limit to the number 
of forms that may be assumed, but with certain kinds of symmetry 
one becomes more familiar than with others. Bilateral symmetry is 
one of these. Corresponding to a part on one side of a bilaterally 
symmetrical body there is a part on the other side, the parts thus 
appearing to balance one another like weights in scales. <A three- 
legged table, or other utensil of a tripod nature, seems to suggest more 
completeness because of the greater steadiness. The four -limbed 
symmetry of the vertebrate, and the six, eight, ten or more legged 
insects, spiders, crabs, etc., are instances of the bilateral. Radial 
symmetry is to be observed in numerous organisms, e.g. many plants, 
sea anemones, and star-fish, and is commonly distinguished from the 
bilateral. 
The sphere is the most generally symmetrical solid body. It is 
divided into two parts by any plane passing through its centre. The 
spheroid is divided into two symmetrical halves by every plane passing 
through its axis of rotation, and by the equatorial plane. The general 
ellipsoid can only be divided symmetrically by three planes. The 
right circular cylinder can be divided into two similar parts by any 
plane passing through the axis, The right elliptical cylinder can be 
divided into two equal halves by two planes only, passing through the 
axis, and the right circular and elliptic cones conform to this rule. 
If the cylinders and cones be oblique only one plane can divide those 
solids symmetrically. These are only special forms of the infinite 
number of possible cones and cylinders. The conceptions and practical 
investigation of complex figures gradually become impossible to all except 
7—NAT. sc.—VOL. xv. No. 90. 97 
