the drawing be as accurate as possible. We therefore
class diagrams as diagrams of illustration, which merely suggest certain
relations to the mind of the spectator, and diagrams drawn to scale,
from which measurements are intended to be made. There are some diagrams
or schemes, however, in which the form of the parts is of no importance,
provided their connexions are properly shown. Of this kind are the
diagrams of electrical connexions, and those belonging to that
department of geometry which treats of the degrees of cyclosis,
periphraxy, linkedness and knottedness.

_Diagrams purely Graphic and mixed Symbolic and Graphic._--Diagrams may
also be classed either as purely graphical diagrams, in which no symbols
are employed except letters or other marks to distinguish particular
points of the diagrams, and mixed diagrams, in which certain magnitudes
are represented, not by the magnitudes of parts of the diagram, but by
symbols, such as numbers written on the diagram. Thus in a map the
height of places above the level of the sea is often indicated by
marking the number of feet above the sea at the corresponding places on
the map. There is another method in which a line called a contour line
is drawn through all the places in the map whose height above the sea is
a certain number of feet, and the number of feet is written at some
point or points of this line. By the use of a series of contour lines,
the height of a great number of places can be indicated on a map by
means of a small number of written symbols. Still this method is not a
purely graphical method, but a partly symbolical method of expressing
the third dimension of objects on a diagram in two dimensions.

In order to express completely by a purely graphical method the
relations of magnitudes involving more than two variables, we must use
more than one diagram. Thus in the arts of construction we use plans and
elevations and sections through different planes, to specify the form of
objects having three dimensions. In such systems of diagrams we have to
indicate that a point in one diagram corresponds to a point in another
diagram. This is generally done by marking the corresponding points in
the different diagrams with the same letter. If the diagrams are drawn
on the same piece of paper we may indicate corresponding points by
drawing a line from one to the other, taking care that this line of
correspondence is so drawn that it cannot be mistaken for a real lin