G' GEOGRAPHY IN THE GRADES. By CHARLES R. DRYER. IX.-The Crust of the Earth. EOGRAPHY is often defined as "a descrip- | deepest boring or cut ever made into it is only a tion of the earth's surface," and the majority of students are taught to think and say that we live upon the surface of the earth. A moment's thought will show the error of such a statement. The atmosphere is as much a part of the earth as the land or the water, and this outside gaseous shell extends far above the plane of human existence. In fact, we live about 200 miles inside the earth. The truth to be thought and taught is that we all have our legal and permanent residence upon the surface of the solid earth or lithosphere, from which some of us make occasional and temporary excursions upon the surface of the liquid earth or hydrosphere, and a few rarely into the gaseous earth or atmosphere. The surface of the earth has no inhabitants, and geography knows nothing of it. He who studies only the surface of the lithosphere and hydrosphere has but a superficial knowledge of the earth and, in fact, can know little of that surface itself. Nothing is more curious in educational custom than the traditional fear, on the part of the old-fashioned geographical teacher and text-book maker, of looking or thinking an inch below the surface of land and water. It is as if one should confine his attention to the external form and surface of the human body with the pores, lines, ridges, hairs, paint or dirt he might find there, while rigidly excluding any hint as to the structure of the parts within. Such a study is possible and would have some value, but would be more superficial than beauty, which is, at least, skin deep. Surely no one would advocate the introduction of such a whim into the schools. Why are we hampered by a similar whim in the study of geography? True, geography deals primarily with the surface features of land and water, but it has the right to go to any depth or height in the search for an explanation of those features. The crust of the earth is the foundation, the stage or arena upon which plants, animals and men play their most important parts. It forms the dry land and the bottom of the sea, but that part of it of which we have any direct knowledge forms but the thinnest skin or pellicle over the rock mass within. That mass may be practically solid or largely liquid. There is some evidence, and there are many theories, upon the subject, but of actual knowledge very little. The little over one mile. This crust or skin, except here and there in a volcanic pipe, is found to be solid, and penetrated everywhere in its pores and crevices by liquid water and by the gases of the air. Is there any good reason why every little child who comes to school should not be helped to get an idea from his own experience of the materials and structure of this crust in his own neighborhood? In most cases, before he comes to school at all, he has made some investigations upon this subject. He is more or less familiar with clay, sand, gravel and pebbles, the almost universal surface materials. It is an easy task for the teacher to lead him to make his knowledge more exact and systematic, which means more scientific. One of the first generalizations is that all these rocks (a sand bank is a rock as much as a granite ledge: see Dictionary) are made up of loose, incoherent grains, some very fine and soft as in clay, some larger, hard and sharp as in sand, some much larger, hard and rounded as in gravel. A post hole, cellar or trench shows that these materials are several feet deep. Then there are wells going down still deeper, perhaps 100 feet or more, and if they cannot be looked into, the owner or digger can probably tell what kind of material it passes through. Nothing creates so much general interest in the crust of the earth and knowledge of it as the necessity of going down into it for a water supply. If the country is at all uneven, railroads and highways have made cuts through the ridges where the materials are exposed in the banks on either side. Nature has done much for us also, for every stream is cutting a trench in which the materials of the earth's crust are shown, sometimes to great depths. Any hole in the ground, wells, railroad-cuts, and stream channels afford opportunities for this kind of study. There are many counties in Indiana where none of these pricks, scratches or cuts in the earth-skin show anything but loose material, and the student would conclude from observations made at home only, that the earth is nothing but sand, gravel and clay clear to the center. Let not such localities be despised or neglected. He who knows from his own observation sand, gravel and clay thoroughly and their arrangement in the crust of the earth has learned a very important chapter of earth-lore. Many localities are more fortunate in this respect. Somewhere within reach of walk or and is either shale, sandstone, limestone, conglomerate, a mixture of two or more of them, or an alternation of two or more in strata of varying order and thickness. If we go deep enough down through sand, gravel and clay (it may be 500 feet in some parts of Indiana) we shall always strike bed-rock of some kind, and since sand, gravel and clay always occur on top of bed-rock and never under it, they are collectively called mantle rock. On the west side of the Wabash river near Terre Haute a cut across the end of a bluff has been shale quarries, and it should not be used as a substitute for actual study in the field. Fig. 12 is from a photograph of the face of the quarry and shows a section of the hill from the top as far down as excavation has been made, forty-one feet. The picture shows it as it looks from a single standpoint plus some distortion due to the lens of the camera. Fig. 13 is a diagramatic section which shows the thickness and position of the strata as they really The limits of the strata shown in Fig. 13 are marked on the picture by heavy black lines. At are. tains. Iron is the almost universal coloring matter of rocks as well of green vegetation and red blood. When exposed to air or percolating water containing air it usually oxidizes or rusts to the familiar red color. This upper six feet of bedrock, by the action of such water, is weathering into mantle rock, and if it were not for the stratum of sand which separates them, it would be hard to tell where mantle rock ends and bed-rock begins. Thus, even down in the crust of the earth, bedrock is being changed into mantle rock. Under the feet of the man in the picture is about two feet of light gray, pasty shale, which naturally breaks up into irregular pieces which look like lumps of tallow dug out and smoothed over with a ladle Below this is thirteen feet of a darker gray shale in regular, even, horizontal layers two to four inches thick. This is the most nearly typical shale in the quarry. Below this is a two-foot band of very fine-grained, compact limestone. It is not continuous, but broken up into blocks two or three feet in diameter with more or less rounded corners and edges. The surface of these blocks is dark red, and the red color extends into the block from half an inch to an inch or more. The outer red portion is softer and partially decomposed. Inside the red shell the limestone is of a rich pinkish drab color. Here, again, is an example of the action of underground water carrying air down into the cracks or joints of a very compact rock and slowly rotting it. The limestone blocks are not used by the brick-makers, and are thrown aside, forming a pile in the foreground of the picture. The next seven feet is one single stratum of shale without any horizontal seams or partings, but broken by numerous irregular cracks which, at the point where the quarry tools lean against it, radiate from the bottom in gracefully curved lines like a sheaf of wheat tied at the butt. In the sunlight this shale shows innumerable glittering specks which, under a magnifier, prove to be minute cubic crystals of pyrite or fool's gold." These crystals are very hard and rapidly wear away the augers and drills used in quarrying. Last is about one foot of shale, soft enough to be cut with a knife. The floor of the quarry is limestone again. The exact arrangement of material described above could hardly be found anywhere else in the world; but certain features are of general occur rence. (1) The growth and decay of vegetation produces chemical changes in the top soil, which are indicated by its color; sometimes darker, and sometimes lighter, than the material immediately below. (2) The mantle rock is usually a very thin layer compared with the known crust of the earth; no thicker than the cuticle compared with the whole skin. (3) The mantle rock is growing thicker by additions at the bottom. This is due to the weathering or decomposition of bed-rock by percolating water and air. (4) Some mantle rock is carried away by water, ice or wind and deposited again at a distance; some remains undisturbed where it is formed. The glacial clay and sand was brought by the icesheet from the North, a portion of it from Canada. The clay formed by the weathering of the shale lies undisturbed and is called residual clay. (5) Shale is a bed-rock formed when clay is subjected to great pressure. It is compacted mud and is a very common rock always accurring in strata which, outside of mountainous regions, are nearly horizontal. The "soapstone" and "slate," socalled by the miners, are varieties of shale. There is no real soapstone or slate in Indiana except fragments found in the glacial drift. (6) The character of shale may vary considerably within a few feet of depth, owing to varying conditions when the original clay of which it is made was laid down. (7) Different kinds of bed-rock, as shale and limestone, occur in beds of varying thickness and order. (8) Bed-rock is not continuous for any great distance vertically or horizontally, but is broken by seams and cracks in both directions, by means of which surface water is able everywhere to penetrate the crust of the earth to an indefinite depth. A half day spent by a class in sketching the general features of such an exposure, drawing sections and examining the materials on the spot, followed by full and free discussion in the classroom and a more minute examination of specimens brought away, then finally by a second visit to settle disputed points, is a piece of truly scientific work, and may be expected to expand knowledge and to develop power as only scientific work can. I urge upon you that the school of to-day must to-morrow be the school of yesterday. There must be constant improve ment. It is the education of our youth in every department of our present military science that has strewn the shores with twenty-one of the finest European warships. We must have not only the best navy in the world, but the best university in the world, the best artists, the best musicians, the best men in every line of mental activity. To possess Hawaii, to possess the Philippines is but little. But it is the whole world which we must conquer with ideas that are American, and it is the American school that must accomplish this.A. E. WINSHIP, at the Washington meeting. MATHEMATICS. EDITED BY ROBERT J. ALEY, Ph. D., Bloomington, Ind. HISTORY OF ARITHMETIC. I. ORIGIN OF NUMBER. Leslie, in his Philosophy of Arithmetic says: "The idea of number, though not the most easily acquired, remounts to the earliest epochs of society, and must be nearly coeval with the formation of language. The very savage, who draws from the practice of fishing or hunting a precarious support for himself and family, is eager, on his return home, to count over the produce of his toilsome exertions. But the leader of a troop is obliged to carry further his skill in numeration. He prepares to attack a rival tribe, by marshalling his followers; and, after the bloody conflict is over, he reckons up the slain, and marks his unhappy and devoted captives." Leslie goes on to show that when the numbers were small the savage could easily represent them by portable objects, such as small pebbles or shells. In that stage, the correspondence of one to one, was all the number idea needed. A single pebble would correspond to each warrior of the party or to each victim of the chase. As the savage developed and extended his operations, this method became cumbersome and there arose a need for a better method of representation. Out of this need came grouping and naming. Dr. Brooks, in his Philosophy of Arithmetic, says: "Number was primarily a thought in the mind of Deity. He put forth his creative hand, and number became a fact of the Universe. It was projected everywhere in all things, and through all things. The flower numbered its petals, the crystal counted its faces, the insect its eyes, the evening its stars, and the moon-Time's golden horologe, marked the months and the seasons. Man was created to apprehend the numerical idea. Finding it embodied in the material world, he exclaimed, with the enthusiasm of Pythagoras, -Number is the essence of the universe, the architype of creation.' If we accept the ideas of Leslie and Dr. Brooks, then, we must find the origin of number in the contemplation of the material world. The inquiry, how many, that arises in the presence of the multitudinous combinations of the material world gives rise to the idea of number. In this way the number idea of the Deity becomes, through objects, the number idea of the human being. This idea, at first indefinite, becomes definite through counting. The regular succession of count ing implies time; in fact, is only possible in time. Hence, the idea of number, in its origin, is due to the fact of time. Time is related to number very much as space is to extension. Space conditions geometry, time conditions arithmetic, the science of number. Thus we see that time and space are responsible for the two great divisions of mathematics. Whewell, in his Inductive Sciences, develops this thought very fully. The majority of writers upon the origin of number substantially agree with the statements made above. McLellan & Dewey, however, in The Psychology of Number, take a different view. They claim that number is psychical in its nature. In the summary on page thirty-two they say: "The idea of number is not impressed upon the mind by objects even when these are presented under the most favorable circumstances. Number is a product of the way in which the mind deals with objects in the operation of making a vague whole definite." On page forty-two they say: "Number arises in the process of the exact measurement of a given quantity with a view to instituting a balance, the need of this balance, or accurate adjustment of means to end, being some limitation." This view is admirably worked out in The Psychology of Number to which the reader is referred. When thoroughly understood, it is seen to not differ very greatly from the first view. What is the actual origin of number will probably always be an unsettled question. Such is the opinion of Dr. Conant, who has given the subject years of careful study. No barbarous race has been found without number ideas. Of course the lower in the scale the race is, the more limited are its number ideas. In some the ideas do not extend beyond one and two. Dr. Conant says: "We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought." Sir: THE NO-RATIO FAD. There is a leading article in the March number of THE EDUCATOR entitled the "Ratio-Fad" which appears to be intended as a criticism of McLellan & Dewey's Psychology of Number and of the Public School Arithmetic based upon that work. I have not time (nor at present health) to spend upon psychological crudities and fertile misconceptions of the plain teachings of the book; but in this case as there is a show of logical apparatus and an ostentatious pretense of fairness, I shall, with your permission, notice a single and essential point to show your readers the worthlessness of such criticism for either instruction or reproof. From a few garbled extracts, the critic asserts that the Psychology of Number "teaches that number is nothing but ratio." The rules of polite writing forbid the application of the only epithet that rightly describes this statement. I will say only that it is marked by a unique economy of truth. For it is absolutely false to both the spirit and the formal teaching of the book. If there is one thing more than another emphasized in the Psychology of Number it is that ratio is not the whole of number; that counting is the fundamental numerical operation; that number is the tool of measurement, a means to an end. The end, namely, of making definite some vaguely known total; that therefore the number process involves three factors: (1) Some whole to be defined; (2) discriminated parts-units; (3) the how many of these parts making up or equalling the defined whole. Now, there need be no controversy about the meaning of the book. Upon this the very essence of its doctrine, all who are interested in arithmetic and its teachingeven the youngest teachers in the country, may decide this question for themselves, independent of all critics and of all criticism, whether due to imbecility or ignorance, to perversity or prejudice. They have only to glance at The Psychology of Number itself, and at The Public School Arithmetic, based on The Psychology of Number, and published by the Macmillans last year; or at The Primary Public School Arithmetic, based on The Psychology of Number-introductory to the Public School Arithmetic, and published by the same firm a few days ago. This entire series of books, both in their doctrine and their practice, are a standing proof of "the lack of understanding," or presence of "wilful misrepresentation" on the part of the critic. As I have said elsewhere: There are two extreme views regarding the nature of number leading to two quite different pedagogical methods; one of these, No Ratio in Number; the other, No Number in Ratio. The one begins with the ratio idea and ignores or subordinates the how many (counting) idea, leaving it to struggle into being incidentally in the development of ratio. The other begins with the vague how many and subordinates ratio, |