ORIGINAL COMMUNICATIONS. 



Some Considerations Concerning Symmetry. 



By Professor 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. Eadial 

 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 



