map may be the humblest part of the teacher's equipment, but it is a necessary one. The spade does not make a gardener, yet he must

use one.

In fact, it is the educational nature of such maps that must be especially urged. From this educational standpoint a chronological sequence of production maps has quite special value. To take an actual and simple example, let us for the moment regard man himself as a commodity. The U.S.A. census shows a decennial sequence of population maps from 1790 onwards. These not merely state the gradual expansion from coast settlement to the Middle West, to the High Plains, and ultimately to the Pacific; they show it in such a way as to be a constant challenge to the historian. They ask questions, the answers to which rest largely in the physical environments encountered. They define the line of enquiry, and save much actual time.

Or again, a quinquennial series of maps for some great agricultural commodity, wheat or cotton, say, would show not merely the development of new lands, but the changes in distribution consequent upon new types of agriculture; the invasion of areas at one time considered unsuitable for the particular crop considered, by means of irrigation, dry farming, seed selection and adaptation, or a more scientific use of fertilizers.

One cannot too much emphasize the thought compelling quality of such maps, quite apart from the actual information they present. A word as to some technical difficulties involved in quantitative map production. Three main methods appear. Each has its special uses and its limitations.

The first is the method of pure reduction and is only partially quantitative. One may take an aeroplane photograph as an example. If such a photograph distinguishes between arable and grass land, or between certain crops (as it does in some lights), then it resolves itself into an excellent detailed commodity map. The writer is not suggesting that aeroplane photographs should be used for this purpose -though their important place in general map making is common knowledge-but is merely giving an illustration of the type of pure reduction maps. Each field is shown in its relative position, occupies its proportional area, and may be marked with its appropriate crop symbol. Such maps are only partially quantitative because of the variation in yield per acre. For small areas, however, this is not very important, and the map is too elaborate for construction over big areas.

For very small areas, however, such a field survey provides a most stimulating school exercise. In our country, of course, its cadre would be the 6 in. ordnance map. For the uninitiated, we must state that this map is contoured and shows field boundaries. It is difficult to conceive of a more useful instrument in the hands of a capable teacher. It adds a new joy to trespassing! With its straight-sided fields the science of arithmetic becomes an outdoor

game. It is an invaluable aid to the initial study of contours and of typical land forms. In addition to all this-and returning to our subject the actual fields may be traversed map in hand, and each marked with an appropriate crop symbol. The relation between the nature of the soil and the use made of the land can be studied. If the local schools of adjacent districts were to undertake such work in a systematic way, useful combined maps of very considerable areas could be easily produced and reduced. County education authorities might well father such a scheme, stipulating such uniformity of technique as would make combination possible, limiting their jurisdiction to the mapping of certain major crops, but otherwise entirely avoiding any encroachment upon that liberty of initiative as precious to every good teacher as to every child of nature.

An example of a very simplified field survey appears in Fig. 1. The map was constructed to show the influence of geological structure (and consequent outcrop soils) upon agriculture, in a small selected area. The map is reduced from the 6 in. The fields are grouped only into arable, permanent grass, woodland, and wooded down. It will be seen that in this instance there happens to be a complete correlation between the outcrop and the use made of the land.

From the point of view of map technique all such maps are reduction maps simply. They represent directly an actual state of affairs without the intervention of calculation based on production and unit area figures.

For very large areas very different methods must be employed. These all involve crop density figures for each administrative

FIG. 1.-SIMPLIFIED FIELD SURVEY BY STUDENTS OF THE GEOGRAPHY
DEPARTMENT, LONDON SCHOOL OF ECONOMICS.

division considered, the quantitative grouping of these figures, and the marking in some way of each administrative area on a map to indicate the density group to which it belongs. The method is one which every school child would follow for himself, and needs no further explanation. As we have already pointed out, the significance of such maps is in inverse ratio to the general size of the units for which figures are available.

A form of this production map much in vogue, and one to be guarded against, is that showing by colour grading for each administrative division, the area under a certain crop considered as a percentage of the total cropped area of that division. Such maps may be very useful as showing environments specially favourable to certain crops, or again, as indicating sometimes too great a dependence upon one type of culture; but obviously they cannot be substituted for production maps pure and simple, otherwise hundreds of square miles of desert might simulate a maximum of productivity on the strength of a single irrigated acre of some one crop! The official mind is peculiarly attached to this type of map. It is frequently the only one available.

A noteworthy variation on the grading (by colour tint, or shading) of the administrative area, is to place on the map within the boundaries of each such area an appropriate number of dots each representing a definite unit of production. This method has some distinct advantages. These partly arise from our psychological deficiencies. If an area is covered with some even tint representing a certain crop density, it requires almost a mental effort to prevent a conception of the crop as covering the whole area--however thinly! A small matter perhaps, and one avoided in a moment's thought, yet the Unit Dot system overcomes the difficulty, and, further, it is not difficult to choose the average size of the dot so that it approximately does represent (upon the scale of the map) the actual crop area concerned. There is the further advantage that if the map-maker has, say, 100 dots to insert in some one (too large) area which he knows to exhibit very varying physical conditions, he can, if he be sufficiently informed, so place them within this area as to give really a truer picture of the actual state of affairs than that conveyed by an even distribution throughout the whole area.

The Unit Dot method is used successfully for very large areas in the agricultural maps of the last U.S.A. Census. An example of a very large area so treated appears in Fig. 2. It is not at all the purpose of this article to go into the physical and historical reasons for the distribution there shown, but the writer has added to the map three simple lines which indicate the nature of some of the chief controlling factors, and has left the correlation to the reader. These lines are:

An

(i) (See Fig. 2.) Limit of Laurentian Archæan Shield.
area of old crystal'ine, glacier-stripped country occupying

the N.E. quadrant of North America. Naturally forested, rugged, difficult and expensive to clear, and of soils generally inferior to those of the prairie lands.

(ii) Approximate line of average of 130 days above 60° F. for a year.

(iii) Line of 10 in. precipitation.

The western limit is formed by the foothills of the Rocky Mountains.

There remains the case of mineral production. At present almost the only maps available are those based upon the geological outcrop maps, and we have already noted that the usual coal-field map is little guide to reserves and none to production. The case of iron is worse. The normal iron ore maps of the U.S.A. and Sweden would suggest that the Lake Superior and Lapland ores are the least important in their respective countries.

For minerals we have a new difficulty in map technique in that we are dealing with a point production rather than an area production. In the case of a crop it is possible to mark the map area which actually represents the area covered by a particular crop. Obviously this cannot be done for mineral production, though if the administrative areas for which figures are available are sufficiently small, one may imagine the production spread over the whole area and adopt the same methods as for crops with significant results. Thus in the U.S.A., official figures for counties exist, and in the eastern coal-fields these counties are small enough to indicate very clearly (when tinted for production density) the eastern edge production of the Appalachian field, and the basin rim production of the Illinois field.