In choosing signs suitable for kinematic form-symbols we are struck by the existence of a certain insufficiency, for our purposes that is, in some very usual geometrical ideas or methods. In geometry the name given to a body of a certain form is that of a portion of space limited by the same figure. In general it is the portion of space inclosed with in this figure which is considered to be the form of the body having the same name. Evidently there is here a certain indefiniteness ; because the two portions of space, the one outside and the other inside the figure, cannot both be meant at the same time.
For our purposes, however, it is necessary to distinguish between these two, the portion of space inclosed by the figure, and the portion inclosing it. If between two parallel planes, for instance, there be a circular cylinder, its axis at right angles to them, then the space inclosed between the planes and inside the cylinder must be distinguished from that which is between the planes but outside the cylinder ; in other words we must know upon which side of the cylindrical surface the material forming our element is placed. We call the body inclosed by the cylinder a full cylinder, and that in which it is inclosed an open cylinder. We shall use for the form-symbols of full and open* bodies respectively the ordinary signs for plus and minus.
The plane limitation of a solid of revolution requires also a sign. It lies equally between the limits + and , and there- fore may suitably be indicated by zero.
For curved profiles, that is profiles which are neither rectilinear nor circular, we may use the circumflex ; we therefore have
+ for full bodies for plane bodies
"for open bodies "" for bodies having curved profiles.
These form-symbols will be placed above and to the right of the class-symbols (excepting the circumflex, which will be placed over the letter to which it refers), and in a smaller type. Thus
- I use these words as being at the same time shorter and more expressive than the
commoner ones solid and hollow.