All of this work was done in the most careful manner, every step in progress was checked, and no superfluous steps were taken. The beautiful simplicity of de Saussure's account of all this work entitled "Recherches Chimiques Sur la Vegetation" and published in Paris in 1804 cannot be overemphasized. In a small duodecimo volume of 327 pages and a few plates, he sets forth with clearness and brilliance all the essentials of the vital subject of plant nutrition in much the same form as we accept them today. To a student of de Saussure's clear, concise, and experimentally supported statements, the work appeals as would a Velasquez or a Titian to an art lover. One can see in it the bold and effective stroke of the master hand impelled by the master mind, and the color of the artist finds its analogy in the penetrating logic and ingenious experiment of the scientist. De Saussure painted with a large brush on a gigantic canvas.

The remarkably lucid and amply supported statements of de Saussure were, however, largely disregarded in Europe and particularly on the continent. The old humus theory was still in vogue and was, partly or wholly, supported by such eminent scientists as Sir Humphry Davy and Berzelius, the former writing it into his textbook on agricultural chemistry nearly a decade after the appearance of de Saussure's little volume. So far from adding to de Saussure's splendid contribution, many of the writers of the day, then, denied the truth of some of the most fundamental ideas so carefully and laboriously established and so clearly and simply propounded by de Saussure. In the decade between 1830 and 1840, considerable work of interest was being done, for example, the work of Sprengel on the ash constituents of plants, the work of Schübler on soil physics, the excellent quantitative work of Boussignault in field experiments, and the work of Liebig in agricultural chemistry. Only the last named deserves attention in connection with soil theory, however, since none of the others changed fundamentally de Saussure's conceptions with regard to the soil as a medium for plant growth and particularly on the subject of plant nutrition. The work of Liebig, however, deserves special consideration, not because he added much that was new, for he actually added little that was fundamentally different from de Saussure's teaching and in fact attempted to change some of the latter to their detriment, but because of the position which history has accorded him and because he succeeded in elaborating and making men generally accept the discoveries of de Saussure.

At the request of the British Association, Liebig made a report on the state of organic chemistry. This celebrated document was published in 1840, under the title "Chemistry in its Application to Agriculture and Physiology." In this book, which quickly went through several editions, Liebig took to task the chemists and physiologists of the day for the crudity of their ideas in the light of de Saussure's discoveries over a generation before. He attacked and completely demolished the humus theory, though it appears to me that his claims as to the general acceptance of that theory in those days were much exaggerated, to judge particularly from the literature of British scientists of the day. He defined more sharply than de Saussure had done some of the more detailed phases of the functions of the mineral elements in plant growth. He gave a detailed account of the respiration process in plants and of his ideas on the fixation of carbon and hydrogen. He put forward the hypothesis that roots of plants excrete acetic acid, which serves to dissolve the minerals of the soil and thus to render available elements essential to plant growth. He set forth the unequal solubilities of the compounds in soils. He believed that plants will absorb all constituents of solutions readily and will excrete such as are not necessary in their growth, and that they obtained their nitrogen from the ammonia of the air.

As can readily be seen, these were, more strictly speaking, amplifications and elaborations of the earlier ideas than new ideas in themselves. Indeed, a number of them have since been proved to be partially or wholly incorrect, but these will be considered later. It is most striking in Liebig's work to note the poignant sarcasm by which he awakened the scientific world to a realization of its backwardness, by which he forced it to examine existing ideas critically and to accept only such as were in accord with outstanding facts and the soundest theories. As characteristic, it may be interesting to quote Liebig's manner of accounting for the non-acceptance in full of the theories and experiments of de Saussure and his supporters. He says:

"All this is due to two causes which we shall now consider. "One is that in botany the talent and labor of inquirers has been wholly spent in the examination of form and structure: chemistry and physics have not been allowed to sit in council upon the explanation of the most simple processes; their experiences and their laws have not been employed through the most powerful means of help in the acquirement of true knowledge. They have not been used because their study has been neglected.

"All discoveries in physics and in chemistry, all explanations of chemists, must remain without fruit and useless because even to the great leaders in physiology"—and he might have added in chemistry-"carbonic acid, ammonia, acids, and bases are sounds without meaning, words without sense, terms of an unknown language, which awaken no thoughts and no associations. They treat these sciences like the vulgar who despise a foreign literature in exact proportion to their ignorance of it, since even when they have had some acquaintance with them, they have not understood their spirit and application.

"Physiologists reject the aid of chemistry in their inquiry into the secrets of vitality, although it alone could guide them in the true path; they reject chemistry, because in its pursuit of knowledge, it destroys the subjects of its investigation; but they forget that the knife of the anatomist must dismember the body, and destroy its organs, if an account is to be given of their form, structure, and functions.

"The second cause of the incredulity with which physiologists view the theory of nutrition of plants by carbonic acid of the atmosphere is that the art of experimenting is not known in physiology, it being an art which can be learned accurately only in the chemical laboratory.

It is not surprising that such statements aroused the slumbering spirits of the doubly conservative physiologists and chemists of Liebig's time. In later editions of his book he formulated two so-called laws: first, the Mineral Law-"the crops on a field diminish or increase in exact proportion to the diminution or increase of the mineral substances conveyed to it in manure"; and, second, the Law of the Minimum-"by the deficiency or absence of one necessary constituent, all the others being present, the soil is rendered barren for all these crops to the life of which that one constituent is indispensable."

As time went on, moreover, Liebig came to believe more and more firmly in two theories: first, that the needs of crops for minerals are indicated by the composition of the ash, and second, that plants can obtain from the air the nitrogen which they need. He believed that the latter idea was borne out by the longevity of certain Dutch, Hungarian, and American soils, and further that on the basis of these two ideas we should merely have to analyze the plant ash and the soil, and draw up certain tables for use by the average farmer with regard to the fertilizer needs of his crops and soils in the form of minerals only.

(Continued in December.)

BOLSHEVIK MULTIPLICATION.

BY H. J. R. TWIGG.

Certain South Russian peasants are able to multiply together figures no matter how large, and yet do so while unable to do anything more than double, halve, add, or subtract, and not understanding fractions; any such arising have to be ignored. The modus operandi is as shown in four examples:

No. 1. Multiply (say) 40×25:

(i) Put 40 at the top of the left-hand column (or vice versa).

(ii) Put 25 at the top of the right-hand column to match.

(iii) Go on halving the left hand.

(iv) Go on doubling the right hand.

Ignore left hand. Total up right hand (except where left-hand figures are even).

Can any readers of School Science and Mathematics explain the principle involved in these operations or throw any light upon its origin?-[School World.

LOAN $7,097,000,000 TO ALLIES.

Up to date the United States has loaned the allies $7,097,000,000, of which $6,377,787,895 has been expended in this country in purchasing their obligations for munitions, food, etc. The allies still have a large balance to their credit in the treasury.

A NEW METHOD OF MAPPING COMPLEX GEOGRAPHICAL FEATURES, ILLUSTRATED BY SOME MAPS OF GEORGIA.

BY ROLAND M. HARPER,
College Point, N. Y.

Ever since geography became a subject for scientific investigation it has been the aim of geographers to represent the various complex features of the earth's surface, such as topography, soil, climate, vegetation, population, agriculture, etc., on maps in as rational and obvious a manner as possible. When each of these features is resolved into its components it is a simple matter for anyone who has the necessary data to map one component at a time, in a manner which may require some skill but leaves little room for difference of opinion; and if they do not conflict too much two or more components may be put on the same map.

For example, altitude, the principal component of topography, is easily represented by contour lines. Soils may be mapped according to the percentage of some one physical or chemical constituent, such as fine sand or silt, or calcium or phosphorus. Innumerable climatic factors, such as temperature and rainfall (average, maximum, minimum, seasonal, departure from normal, etc.), length of growing season, and average date of arrival of spring, are easily mapped, singly or two or three together. (The daily weather maps with which we are all familiar show temperature, barometric pressure, and one or two other things.) In mapping vegetation we may indicate the distribution of one species at a time, by means of dots, boundary lines, or shading, or we may map several species at once if they do not overlap too much. We might also indicate the percentage of evergreens, or of plants belonging to a given family, in each state or county or natural region, by appropriate shading. Under the head of population we can indicate density by dots or otherwise, and rate of increase in a given period, proportion of negroes, foreigners, tenants, etc., by shading.

But routine work of the kinds mentioned is mere cartography, or chorology, rather than true geography, and can be undertaken just as well by topographers, climatologists, botanists, demographers, etc., as by geographers. Furthermore, if we - mapped only one thing at a time we would need innumerable maps to show all the geographical features of any region, and they would fail to give the user a good mental picture of the region. The geographer therefore seeks to put as many things