February,’18] hartzell: graphic illustration 33 
indicate the average amount of injury in each square by a number. 
However, there is apt to result a mass of data which is more or less 
confusing unless the work is carried farther. If, in addition, we use 
orthographic projection, representing the amount of injury as an eleva¬ 
tion, and interpolate sufficient points having the same elevation, it 
will be easy to connect these points by means of smooth curves or 
contours. Each contour is numbered to show its elevation. In other 
words, we have a topographic map in which the contour lines represent 
places having equal amounts of injury. The work can be carried to 
the degree of refinement desired. Unless the detail is too intricate, 
a slight effort of the imagination will give a good idea of the undu¬ 
lating surface which such contours represent. The weather map is a 
familiar example of such a chart. The terms isotherm, isobar, and 
isohyetal lines, as applied to the contour lines in meteorology, are cur¬ 
rent. Since the chief injury by an insect is generally produced by its 
feeding, we have designated the line showing equal amounts of injury 
an isofag (’ Laos , equal +<£<*7 euv, to eat). In certain instances, similar 
lines may be used to show the distribution of equal numbers of insects 
but here the term isopleth (’to-oxX^s, of the same number) might 
be used, although it should be stated that isopleth is used in another 
sense in mathematics. 
Theoretical Considerations 
We will assume vast numbers of a migratory species located in a 
very restricted area in the center of an extensive field having a uniform 
crop so the pest is at liberty to move with equal ease in any direction. 
We will further assume that every environmental influence is exerted 
equally in all directions. Now, as the insects continue to feed it will 
be necessary for them to migrate and in this movement each insect will 
fly a short distance. In this general movement usually all food will 
not be destroyed in the path of the infestation. Since the insects can 
move in any direction with equal ease—except perhaps toward the 
center of infestation owing to conditions brought about by their own 
feeding—it is probable that points equally distant from the center of 
infestation will sustain an equal amount of feeding. If we map this 
area and represent the inj ury by isofagal lines, we would find them to 
be concentric about the original area of infestation. These are shown 
by the lighter concentric circles in Figure 1. On the other hand, if all 
these conditions exist except that one influence, as for example, the 
wind, tends to carry the insects farther in one direction than any other, 
on mapping such an area, it will be found that the isofags would be 
oval and eccentric about the original area of infestation. These are 
also shown in Figure 1. Under conditions where the results approach 
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