LB ;r4 H,!fc*"M.F *B 300 ?i 4 GRIFT OF John B» Leighlfr fiJl+AjfZIl, iff KX*"f< Y ^L r^m f on the Mercator plan. But the north pole of the earth, which in reality is a point, becomes, in the Mer- cator projection, a circle equal in size to the circle of the equator. The land masses situated in high lati- tudes appear greatly dis- torted, therefore, in width. In order to obviate this, the distance between parallels constantly increases as the latitude increases, as will be seen in the accompanying diagram. These distances are not taken hap-hazard, to suit convenience, but are determined 1 Kaufmann is the German word for merchant, which in Latin is mercator. g Method by which Mercator Charts are projected M- y^Jtr itc f*t*~ <£^*»^ f^Tf^- ^ 52 HINTS TO TEACHERS for a purpose, and their positions calculated with mathematical precision. Technically speaking, the distance of each parallel from the equator is equal to the tangent of the angle of latitude. Let us imagine that UXYZ is a hollow cylinder of paper surrounding a terrestrial globe PQR. From O, the centre of the globe, lay off angles of io°, 20 , 30 , etc., and draw lines until they meet the side of the paper cylinder. Now the points where these lines meet the surface of the cylinder will be the distances of the respective parallels from the equator. When we unroll the paper cylinder, it will be about 3^- times the length of AB, the diameter of the globe. For all practical purposes the maps projected on the Mercator plan are limited to 8o° N. and 6o° S. latitude, as the land and all the navigable waters of the earth are situated between these parallels. The chief objection to this plan of projecting a map is, that where large areas are to be shown, the size of those portions situ- ated in high latitudes is greatly exaggerated. This objection, how- ever, fails when small areas are to be charted, and for state and county maps it is an excellent projection. It is the only conven- ient projection, too, in which the entire surface of the earth can be shown on a single, continuous map. Its greatest advantage lies in its use as a sailing-chart ; for it is in maps of this projection only that alt directions are measured in straight lines, and that parallel lines have the same direction in all parts of the map. Without the Mercator chart, deep-sea sailing would be out of the question, for any navigator who was not a good mathematician could not calculate the complex curves which on ordinary maps would represent straight lines on the surface of the earth. The ' commercial ' maps of the world, which now form a part of most common-school geographies, are excellent specimens of the Mercator projection, although not always correctly pro- jected. It need not be inferred from this that the chartographer does not know how to project them. The reason is, that a correctly MAP-DRAWING AND MAP-MAKING 53 projected map, to include all the surface between 8o° N. to 8o° S., if a two-page map is required, would be about three feet in length from top to bottom. So it is customary to reduce the distance between parallels by any convenient but arbitrary scale, the latter depending upon the size of the page. The Conic Projection. — The conic projection represents a part of the earth as drawn on the surface of a cone. Imagine a cone (or a part of the cone) covered with paper, on which the parallels are drawn parallel to the base of the cone, and the merid- ians from the apex to the base. If now the paper be removed and spread flat, we shall have a tolerably correct idea of the conic projection. This form of projection and the various modifications of it are much used in charting those grand divisions and areas which lie in the northern hemisphere. Obviously, the distortion will be the greatest towards polar and equatorial latitudes. If we bend the paper into a cone, and place the latter over a globe which shall just go inside of it, we can see what parts of the map are distorted or incorrect in outline. Along the circle where the sphere and cone touch, there will be no distortion. In polar lati- tudes there will be a north and south exaggeration, and in equa- torial latitudes, an east and west enlargement. Where the area to be charted extends well into equatorial latitudes, the meridians in- stead of being straight lines are commonly curved inwardly so as to prevent too much lateral distortion. Maps of Asia and Europe are usually thus conventionalized. In fact, two of the best chartog- raphers in the United States use ship-curves for projecting the meridians in the maps of these grand divisions. In using the ship-curve instead of the arc of a circle, their judgment is good. In a projection thus made, the northern regions, where there are but few details to be charted, are slightly contracted, while the southern parts, in which the details are numerous, are slightly enlarged. The parallels of a conic projection are always concen- tric arcs with the pole as a centre. The conic projection is one of the most convenient, and in many respects the best, for pupils' work. It is easily made, and requires no apparatus more costly # 5-4 HINTS TO TEACHERS than a pair of dividers with a long leg. The meridians may be straight lines, and the parallels, arcs drawn from the apex of the I A Conic Projection. cone as a centre. The outline on p. 48 conveys a practical idea of this form of projection. Bonne's Projection. — This projection, which, in a modified form, is known also as Flamsteed 1 s i is perhaps more extensively used in the maps of school geographies than any other. In many respects it is a difficult projection to construct, although the diffi- culty may be practically obviated by purchasing the meridian rules already made, or by using a flexible ruler. 1 In Bonne's pro- jection the parallels are equidistant arcs drawn from the pole (or apex of the cone) as a centre ; in Flamsteed's, they are straight lines. In the latter, each hemisphere (northern and south- 1 Both the meridians and the flexible ruler may be purchased of Williams & Brown, or of the Ball-Bennett Co., Philadelphia. MAP-DRAWING AND MAP-MAKING 55 ern) is assumed to have a shape much like that of a boy's top, conical at the apex, but rounding off to a nearly hemispherical shape at the base. In Bonne's modification, however, the cone is slightly concave at the apex, resembling in form the dome of a pagoda. A better example may be found in the illustrated ace of spades which accompanies each pack of playing-cards, the curves of this figure being constructed in one or the other of these projections. The chief merit about these projections is that true proportion of areas is preserved. The disadvantages are distor- tion at the margin, and the very oblique angle at which the paral- lels and meridians intersect in high latitudes. In nearly all the school geographies, the maps of the grand divisions, and often the state sections, are drawn on the Bonne or the Flamsteed pro- jection. Europe, Asia, North America and South America are generally constructed on the former ; Africa and Australia on the latter. Globular Projections. — The maps of the hemispheres which are found at the beginning of most geographies are drawn on what is commonly called a globular projection. One of these was planned by De la Hire about two hundred years ago, and a better one for the purpose was never made. Let us imagine a glass globe on which the parallels and meridians have been drawn, to be cut in two through the poles, and a sheet of half- transparent paper fastened over the cut edges. In the accompanying cut ABCDE is the hemisphere, and ADCE the sheet of paper. The observer stands directly in front of the flat side at a distance a little greater than the length of the axis of the sphere, the eye being at O, on the level of the equator. Now as one looks at the parallels 1 with the eye in the position shown at O, they seem to be curved lines ; and if we could have each one drawn as it seems to fall on the flat surface ADCE, we should have a set of parallels as seen in the next figure. The meridians are usually drawn at equal distances apart. The expert chartographer does not need 1 The meridians are omitted in order to avoid crowding the figure with a confusion of lines. 56 HINTS TO TEACHERS Method by which Globular Maps are projected. to take this trouble to locate the position or to find the curvature of the parallels ; he can calculate either much more easily. In a projection of this kind, the distortion is chiefly at the mar- gin of the map. On a globe the parallels must of course be equi- distant, but in our globular projection they are much farther apart at the margins than along the central meridian. Not unfrequently the question arises, ' Why is there not a scale of miles on maps of the hemispheres ? ' Such a question is readily answered when we recognize the fact of this marginal exaggeration. A scale of miles which would be accurate on the central meridian would be very inaccurate at the margin. To represent a fairly correct scale each unit must be 1.57 as great for the marginal as for the central meridian. It is evident that directions north and south, or east and west, are measured respectively along the meridians and par- allels, no matter what may be the direction of these lines on the map. A straight line on the map must, therefore, in nearly every case be a curved line on the globe ; it becomes not only a great inconvenience, but practically an impossibility for any but an expert mathematician to use such maps for sailing-charts. But MAP-DRAWING AND MAP-MAKING 57 inasmuch as a map projected for use as a sailing-chart has such exaggerated outlines as to be almost worthless for everything ex- cept rhumb lines and accuracy of direction, we must gracefully submit to the fact that two kinds of maps are necessary, — one for landsmen, and the other for seamen. We must also yield to the fact that while both are consistent, neither one is accurate, and that a perfect map cannot be made until we have a flat earth. One of the difficulties in trying to fit a round earth to a flat map is frequently encountered in the United States Land Office. EQUATOR 90 SO The Completed Projection. According to law a township must be bounded east and west by meridians, and must be six miles square. Now this is simply an impossibility. If, for instance, we survey two township lines north- ward from the 40th to the 41st parallel, we shall find that they have approached each other and are about two -thirds of a mile nearer at their northern than at their southern limits. In the sys- tem of land surveys adopted by the United States, standard par- allels are surveyed every few miles apart, and these are taken as 58 HINTS TO TEACHERS bases for new township surveys. The parallel taken for a new base is called a ' correction line.' Various other globular projections are occasionally employed, most of which, like the one just described, are perspective draw- ings rather than true projections, inasmuch as they depend mainly upon the position of the observer's eye. A Polar Projection. The Orthographic Projection 1 is one in which the eye is supposed to be at an infinite distance from the hemisphere, and the plane 1 Any true perspective view of a globe, the eye being situated at a distance, will be an orthographic projection. MAP-DRAWING AND MAP-MAKING 59 of the projection perpendicular to the line of vision. The meri- dians, which are at normal distance apart at the centre of the map, are gradually crowded together at the edges. The parallels are straight lines, but unequally distant. Briefly stated, this is the form the lines of a globe would naturally take if the observer were to stand, say, five hundred feet from the globe, with the eye in the plane of the equator extended. The maps of the hemi- spheres in Warren's Geographies are drawn on this projection. An illustration in which the projection is made on the plane of a meridian is here given. (See also p. 76.) The Stereographic Projection differs from the foregoing mainly in the position of the eye of the observer, which, instead of being at an infinite distance, is on the surface of the sphere, at the pole of a great circle. The maps of the hemispheres in the author's Complete and Elementary Geographies are on this projection. It makes a handsome map, but, though a very easy one to lay off, it is rarely used. If, however, the eye of the observer be shifted to the centre of the sphere, the resulting projection becomes Gno- monic, and, if the plane of the projection is tangent to a pole of the sphere, it does not differ greatly from any other polar projec- tion. A good example of this projection may be seen in the cut facing p. 60. Here the earth is projected on a cube tangent to the sphere about which it is circumscribed. It will be hardly necessary to add that the meridians of a gnomonic projection will always be straight lines. This projection is nearly always used in star charts and celestial maps. A very ingeniously constructed globular projection is shown on p. 58. Here the eye of the observer is at a slight distance above the north pole, and the largest continuous circle is the equator. If folded back, the rays of the star would meet at the south pole. This is a convenient projection for showing the distribution of land and water, and is a device much used by Mr. Russell Hinman. Babinet's Equal-surface Projection. — This projection, as its name implies, is so called because the surface bounded by any given lines has an area equal to the surface bounded by the same 60 HINTS TO TEACHERS lines on the sphere. The meridians are equidistant ; the parallels are plotted so as to preserve the proportionality of areas as above described. The projection readily admits being extended so as to embrace the whole surface of the sphere, the bounding line then becoming an ellipse. It is an excellent substitute for the Mer- cator projection in showing the distribution of physical features, but it is a difficult one to make. Mr. Russell Hinman has shown a very excellent example on p. 13 of the Eclectic Geography. This projection is, perhaps, best known as a homalographic projection. (See p. 78.) A Pofyconic Projection. Polyconic Projection. — This projection was probably con- ceived by F. R. Hassler, the first Superintendent of the U. S. Coast Survey. It conceives the earth to have a shape like that of a cone whose slant height is a convex instead of a straight line, — in other words, like that of the old-time sugar-loaf or bee- hive. Technically it employs a tangent cone for the development MAP-DRA WING AND MAP-MAKING 61 of every parallel, and this is its chief distinction when compared with the simple conic projection, where only one cone is em- ployed. But in the conic projection the map is accurate only where the sphere touches the circumscribed cone, whereas in the polycone the map is accurate along each parallel, and distorted only between them. The parallels are arcs of circles drawn from different centres, each centre receding from the pole of the sphere until, at the equator, the radius is infinitely long, and the equator becomes a straight line. In the delineation of small areas this is decidedly the most accurate of all projections, but in very large areas there is considerable distortion at the east and west margins, especially in high latitudes. A very meritorious feature is that the meridians cut the parallels practically at right angles. The proportionality of areas is not exactly preserved, and in a map, say, of Eurasia, the area bounded by lines of equal angular distance is about i \ times as great at the margin as at the centre, along the same parallel. The polyconic projection is not a very difficult one to lay off; it is certainly not beyond the com- prehension of any one possessing a fair knowledge of geometry. The curves of the meridians are scarcely more difficult to draw than arcs of a circle, in which respect the projection differs mate- rially from most of the others. Excellent illustrations of this pro- jection may be found in Appleton's Geography, map of Asia. It is also used for the maps of Asia and North America in the author's Complete Geography. (See p. 79.) Occasionally the cry is raised that the maps of our geographies are objectionable because they contain too many details. Cer- tainly the map should not contain so much matter as to be con- fusing, and all unnecessary lines and schemes are a source of evil rather than good. It is true that not every indentation of coast can be accurately shown, but it is equally certain that the char- acter of the coast may be delineated ; and if the map shows no difference between the coast-charting of Maine and Florida, it is not a true map. Mountains can be shown only in a conventional way, yet the character of highlands and canons can be distinctively 62 HINTS TO TEACHERS portrayed. If the hachure lines representing a mountain range, a plateau, a line of cliffs, and a canon show no difference in texture, the map is untrue. It is a mechanical impossibility to enter the names of cities and towns on a map of a section of states, sys- tematically, and in ratio to the population. The chartographer can only submit to what he cannot help, and use his best judgment. Now and then some one blindly proposes to introduce the names of a few of the larger cities only on each section map. Such a scheme is not only unnecessary, but misleading. It is unnecessary because in all the standard text-books of geography the greater centres of population are designated by larger type or by special symbols. It is misleading because it is untruthful. There is no more instructive lesson to be derived from the ordinary map than that shown by the distribution of population over an area of coun- try, and the wise teacher will not fail to recognize this feature. Aside from this, the text-book map has a very important use as a reference map, and if all but the salient features are removed, the map has no value whatever beyond its class-room use. Where maps containing only essential features are required they would best be drawn by the pupils themselves. For this purpose it is a good plan to take advantage of outline maps — that is, maps which have already been projected. The details, whether physical, political, or historical, may then be filled in progressively, using a different sheet for each purpose. 1 The plan of ' editing ' a map will be found an invaluable discipline to the pupil. Indeed, it is doubtful if a better plan to judge graphically of the pupil's progress could be devised. Thus, an outline map of the world on the Mer- cator projection may be edited to illustrate the following : — Drainage of river-systems. Contours of elevation of the land and depth of the sea. Magnetic variation. 1 The progressive outline maps sold by the publishers of this book will be found excellent for this purpose. I use them much in my private work, saving from a few hours to several days' time for each map edited. — J. W. R. MAP-DRAWING AND MAP-MAKING 63 Ocean currents. Cotidal lines. Distribution of volcanoes. Distribution of rain-fall. Winds. Isothermal zones — summer and winter, each. Distribution of life — animal and vegetable. Commercial routes — railway and marine. The map of any grand division or other specified area may be treated in a similar manner. That a pupil should be taught to project and draw at least one or two maps will certainly be admit- ted as proper, but to compel him to draw every map he uses is quite another thing. It is a needless waste of time, that brings neither additional knowledge nor mental discipline. In the study of history, outline maps are a necessity, and no amount of memo- rizing or minute description answers as a substitute. In most instances the ability to construct the strictly technical projections demands a knowledge of higher mathematics which the average pupil does not possess. In their construction an inconveniently large drawing-board and an expensive beam-com- pass are needed. Moreover, the student who investigates will find that the projections used in text-books are rarely constructed according to exact formulae ; on the contrary, they are commonly modified arbitrarily to suit the size and proportions of the paper on which the maps are to be printed. The following projections will be found available for pupil's work. That of Asia is a conic, and that of North America a modified conic projection. The illustrations given do not differ from the strictly mathematical projections to any greater extent than the latter differ from one another. The only apparatus re- quired is a pair of dividers with a long arm, a ruler or graduated paper scale, and a well-pointed lead-pencil. North America. — Let us suppose a projection for a map of North America is to be made. First of all we must find its posi- 64 HINTS TO TEACHERS o S S/fIl\ y' / / / I I j ; i \ \ \ \ \ % % North America — a Projection of Convergent Meridians. There is a slight, but intentional longitudinal distortion. MAP-DRAWING AND MAP-MAKING 65 tion on the earth. An inspection of a globe (or map) shows that it is practically included between parallels 8o° and io° N., and meridians 20 and 180 W. (excepting the Aleutian Islands). Almost the whole of its area may be included in a rectangle having the proportions 6:5. A sheet of paper 14X12 will be suitable for the purpose, but the lines which form the border of the map need not be drawn until the projection is laid off. In projecting a grand division it is conventional in the majority of maps to lay the parallels ten and the meridians fifteen degrees apart. Secure the paper to the board, and draw the line OD through the centre of the paper. At right angles to this line, and bisected by it, draw a line about one inch from the lower margin of the paper ; this line should be about fifteen inches from O, the apex of the cone (practically the centre of a circle). On this line as a base, lay off the rectangle, 12 X 10, which shall enclose the map. Divide the lower twelve inches of the central meridian into eight equal parts and draw the parallels, eight in number, the top and bottom of the rectangle each forming a parallel. This division will make the parallels ten degrees apart. At any convenient distance from O, draw the arc AB. This arc is only for convenience in spacing off the distance between meridians, and should be erased when it has served the purpose for which it is drawn. In the sketch on the opposite page there are seven meridians on each side of the central meridian, and this will be found a con- venient number, though a greater number would not affect the consistency of the map. This will be obvious when we consider that the cone which conventionally represents the earth may have any angle of apex. The central meridian will have a longitude of about 97 . The meridians should be numbered so as to have an assumed though arbitrary angular distance of fifteen degrees apart. In many of the school atlases the meridians are ten degrees apart, every even tenth being drawn. This plan will be no more difficult of projection than the foregoing. In this case it will be 66 HINTS TO TEACHERS MAP-DRAWING AND MAP-MAKING 67 best after calculating the space required to draw the' 90th and 1 ooth meridians equidistant from OD. In general it is most convenient to lay off the parallels and meridians to correspond with those on the map to be copied. When the projection is laid off in pencil, the coast-outlines may then be charted, also in pencil. Where the coast is greatly broken, it will be advisable to draw parts of the intermediate parallels and meridians as in the projection given. Indeed, where great accuracy is required, the chartographer may inter- polate parallels and meridians for every even degree, or possibly for fractional degrees. Establish by latitude and longitude the prominent points of the grand division, such as Point Barrow, Alaska, Cape Mendocino, Yucatan, Cape Sable, etc., and then fill in the intermediate parts of the coast. Next chart the islands, lakes, rivers, mountains, and political features in the order mentioned. The pupil should not be discouraged if his outline does not exactly correspond in form to that in his atlas. As a matter of fact it should not. Accuracy in a map of a large area is theoreti- cally an impossibility, but consistency is attainable ; and if the pupil's map has been faithfully charted, it will not differ from the true mathematical projections any more than the latter differ from one another. Of course the judgment of teacher and pupil must determine as to how elaborate such a map may be : such a map as is planned in the foregoing paragraphs may be drawn in five minutes or in five weeks, — just as circumstances may require. If the pupil prefers, a projection similar to that of Europe, p. 66, may be employed for North America. South America. — For this grand division a projection similar to that of Africa will be found suitable. The intersection of the 20th parallel with the 60th meridian is about the geographical centre, and from these lines as bases the other parallels and meridians may be spaced off ten degrees apart. There will be a slight but noticeable distortion in the southern part. If the dis- tance between parallels be made about i-j- times that between 68 HINTS TO TEACHERS Africa — Drawn on an arbitrarily modified Mercator Projection. In this projection the parallels and meridians are equidistant. It is sometimes called the ' Projection of Equal Squares.' MAP-DRAWING AND MAP-MAKING 69 meridians, the lateral distortion will be less apparent; a better plan, however, is to make the meridians converge towards the south. Europe and Asia. — These divisions may be drawn singly or together. In either case an unmodified conic projection is per- haps preferable. If they are projected together, about all of this area is included between the meridians of io° W. and io° E., and between the parallels of o° and 8o° N. The intersection of the 40th parallel with the 90th meridian is practically the geograph- ical centre. Notice that the parallels are arcs of concentric circles. If the size of the map is to be, say, 9X12 inches, the equator should be drawn with a radius of about twelve inches. From the centre of the map space off ten (or twelve) meridians on each side of the central meridian, and four parallels on each side of the central parallel. Then sketch in the outlines in the order as directed in North America. When a hastily drawn map is required, the alternate parallels and meridians may be omitted. If a sketch of Europe only is required to be drawn on the black- board, the parallels may be drawn as straight lines. Africa. — The Mercator projection is an excellent one for Africa, for, on account of its position, there is but little distortion. The intersection of the 20th meridian with the equator is about the geographical centre. Draw meridians and parallels for every tenth degree. It is well to include the Mediterranean Sea and the southern shores of Europe, and also Asia Minor and the Arabian coast. Locate the prominent coast-features first, and then complete the outline. Oceania. — In projecting a map of this region, the draughts- man should first decide on how much is to be shown. A large map of Australia will of necessity exclude the greater part of the coral island groups ; and conversely, a map which shall show all the groups from the Sunda to the Feejee group will show the Australian continent on a reduced scale. Use the Mercator pro- jection, and after deciding upon the extent of the region to be shown, proceed as directed in the preceding cases. 70 HINTS TO TEACHERS PROGRESSIVE OUTLINE MAPS.-Drawn by J. C. Thompson, Providence. R. I. Copyright by J. C. Thompson. 1686. l^tLZsrri- page 51, it is assumed that the earth is a sphere. For a spheroid earth, it is necessary to use the following table. The length one degree at the equator, 60 minutes of arc, is taken as the unit of measurement. The distance of each parallel will be as follows : A 10 . . 599 60 . . • 45<#' 20°.. 1217' 6 5 °. • .5158' 30°. • 1877' 7o°. • • 5944' 4 0°. . 2608' 75°-. . 6948' 5 0°. . 345 7' 8o°. . • 8352' of J cWi The fact that either formula gives a projection that is contracted in the part where, in physical maps, the details are most numer- ous, is a very great objection. The teacher or pupil therefore who desires a more convenient map for such purposes may use the following plan : Draw the meridians one hour (15 degrees) apart. Take two-thirds of this value for the distance to the 10th parallel, <~ c- 78 HINTS TO TEACHERS 5\7S and use this distance as a unit. Lay off the 20th parallel a a distance of 1.25, the 30th 2.5, the 40th 3.75, the 50th 5.0, units from the equator, etc. Of course such a projection is worthless for sailing purposes, but it is far more practical for a map showing the distribution of physical features. Projection of Convergent Meridians. — A moment's inspec- tion will show that the column of ' Radii for Parallels,' Table I, may be used to find the common point at which the meridians will inter- sect. Thus the line OD, page -e^ will be 325 units in length, on the supposition that the map extends to the 10th parallel. An Orthographic Projection. The Orthographic Projection. — Draw a circle of the size required. Draw the equator, and at right angles thereto, the axis, which is also the central meridian. On the supposition that the parallels are ten degrees apart, divide each quadrant into nine equal parts, and draw the parallels through these points, as in the MAP-DRAWING AND MAP-MAKING 79 cut on page 76. (It will be proper to say here that one-half of each parallel, that is, the perpendicular distance from the end of the arc to the central meridian, is technically the cosine of the angle of latitude. This is usually expressed as cos <£, in which may be any given latitude.) On the equator, on each side of the central meridian, lay off distances equal to the distance from the equator to the successive parallels. Through each of the points thus determined, a meridian must be passed, terminating at the poles. Each meridian is a semi-ellipse whose major axis is the central meridian, and whose minor axis is the distance from the central meridian to the point through which the meridian is to be drawn. Technically the minor axis equals 2 sin . A Stereographic Projection. The divisions of AD and DB show the points through which the meridians are to be drawn. The Stereographic Projection. — The above figure will illus- trate the construction of this projection. AB is the equator of a hemisphere. Draw any circle OED tangent to AB at its middle point, and divide its upper semi-circumference into as many parts as there are to be meridians. From O, the point of vision, draw lines through these points until they cut A, B. These are points through which the meridians pass. To construct the meridians, with AB as a diameter, draw the circumference of the circle which bounds the hemisphere. Draw arcs which shall pass through both 80 HINTS TO TEACHERS poles of the hemisphere, and each through its proper point on the equator. The centre of each arc is most quickly found by trial. To construct the parallels, divide the arc of each quadrant into as many parts as there are parallels required, and in the same man- ner divide the central meridian. Draw arcs of circles with a radius of such length that each arc shall cut the central meridian at its proper point, and meet the circumference of the hemisphere at corresponding points. An arbitrary, but very serviceable modification of this projec- tion may be made by subdividing the equator equally, and passing the meridians through these points. This modification does not differ greatly from De la Hire's projection. The Babinet Homolographic Projection. — Lay off the circle, equator, and central meridian. Then, if the parallels are ten de- grees apart, beginning at the pole, divide each half of the central meridian in the proportion of if, if, if, if, if, i|, if, if, 2. 1 Space off, say 20, equal distances along the equator for the merid- ians. Then each meridian will be a semi-ellipse whose major axis is the central meridian, and whose minor axis is the distance from the central meridian to the one to be projected. The Conic Projection. — In laying off a conic projection the chartographer may construct one in which the cone is tangent to the sphere at the middle parallel of latitude, but it is better on the whole to conceive that the cone cuts or pares off a part of the surface of the sphere, thereby becoming an ' intersecting ' cone. This is done practically by drawing the parallels each with a radius slightly shorter than that given, but spacing off the longitudinal distances, according to the table. For instance in the map of Europe if we assume that the cone is tangent at the 50th parallel, then (Table I.) the radius for drawing the parallels is 48.08 units ; but if we take an intersecting cone which cuts the sphere at lat. 40 , 1 This is only an approximation. The following formula gives the exact dis- tance. Let

= - (2/1 + sin 2a). MAP-DRAWING AND MAP-MAKING 81 the radius is 68.3 units. For a map of a grand division it is well to follow the scheme laid down on page 00, but in projecting the map of a state or any other small area, careful, mechanical meas- urements will give a better result. Suppose the map to be that of Pennsylvania. Determine the size of the map and draw the central meridian. From Table II. lay off the points where the 40th, 41st, and 42d parallels cross it. With a radius of 68.28 units (Table I.) draw an arc for the 40th parallel, and from the same centre draw the 41st and 4 2d parallels each through its proper point on the central meridian. On this parallel of 40 lay off the degrees of longitude, each 53.06 miles in length; and on the 42d parallel space off the degrees 51.48 miles each. Draw the meridians each through its proper series of points. Bonnet Projection. — The parallels are drawn from the same centre, using a length of radius according to Table I. The merid- ian distances may be laid off from either table and the meridians drawn with a flexible rule, or they may be drawn by means of curves made for the purpose. A set of three or four ' ship-curves ' will answer all practical purposes. For FlamsteedVs modification, make the parallels equidistant straight lines, space off the meridian distances according to Table I., and through each set of points draw the meridian with a flexi- ble rule. From the foregoing it may be inferred that while the map is theoretically projected on a tangent cone, the meridians are spaced off as if the cone were spheroidal. It is for this reason, also, that on a projection for a large area, a meridian, instead of cutting the parallels at right angles, may cut them at very oblique angles, — acute in high, and obtuse in low latitudes. The Polyconic Projection. — Determine the extent and scale of the map, and lay off the central meridian. Along the central meridian lay off divisions through which the parallels are to be drawn, five, ten, or any number of degrees apart, as may be desired. The parallels may then be laid off from Table I. On the suppo- sition that the distance between meridians at the equator is ten 82 HINTS TO TEACHERS units (each, say, \ of an inch, or any value the draughtsman adopts), the radius for drawing the parallel of ten degrees is 324.9 units in length; for the parallel of twenty degrees, 157.4 units, etc. The distance between adjacent meridians may then be spaced off. Referring to the same table, the distance at the equator is 10 units ; on the tenth parallel, 9.84 units ; on the twentieth parallel, 9.39 units, etc., throughout the extent of the map. With the flexible rule, draw curved lines which shall pass, each through a set of points thus established. The second column of Table I. has been constructed on the hypothesis of a spherical earth. A slightly more accurate result may be obtained by dividing each member of the second column of Table II. by 69.172 ; the quo- tients will be ordinates for each degree of a geoid. As a matter of fact, this table is used in spacing off the meridian distances on the maps published by the U. S. Coast Survey. It is practically a table of cosines ; and the radii by which the parallels are drawn from a table of natural cotangents, each member being multiplied by a constant factor N. In Table I. this factor is 57.296. It is deduced as follows : If the cosine of an arc of i° of a great circle of a sphere is 1.000, then the radius of that sphere is 57.296-f. The formula for the radius of the developed parallel is, therefore, R = N cot$. .1 nL J MAP^DRAWING AND MAP-MAKING 83 T LBLE I. — For 1 he Construction of Polyconic Projections. 1 Dec. Radius Dec. Radius Dec. Radius Lat. I OF for Lat. of for Lat. of FOR ILONG. Parallei . Long. Parallel. Long. Parallel. 0° 1.000 CO 31° .857 95.356 62° .469 30.465 1° .999 3282.473 32° .848 91.962 63° .454 27.945 2° .999 1640.736 33° .838 88.228 64° .438 26.717 3° .998 1093.268 34° .829 84.944 65° .423 26.717 4° .997 819.368 35° .819 81.827 66° .407 25.510 5° .996 654.894 36° ' .809 78.861 67° .391 24.321 6° .994 545.133 37° '.799 76.034 68° .374 23.149 7° .992 466.637 38° .788 73.335 69° .358 21.194 8° .990 407.681 39° .777 70.254 70° .342 20.854 9° .9S7 361.751 40° .766 68 282 71° .325 19.729 10° .984 324.940 41° .755 65.911 72° .309 18.617 11° .981 294.761 42° .743 63.633 73° .292 17.517 12° .978 269.556 43° .731 61.442 74° .275 16.429 13° .974 248.175 44° .719 59.332 75° .259 15.352 14° .970 229.801 45° .707 57.296 76° .242 14.285 15° .965 213.831 46° .694 55.330 77° .225 13.228 16° .961 199.814 47° .682 53.429 78° .208 12.179 17° .956 187.406 48° .669 51.589 79° .191 11.137 18° .951 176.338 49° .656 49.806 80° .174 10.103 19° .945 166.399 50° .643 48.077 81° .156 9.075 20° .939 157.419 51° .629 46.397 82° .139 8.052 21° .933 149.261 52° .615 44.764 83° .122 7.035 22° .927 141.812 53° .602 43.175 84° .104 6.022 23° .920 134.980 54° .588 41.628 85° .087 5.013 24° .913 128.688 55° .573 40.119 86° .070 4.007 25° .906 122.871 56° .559 38.646 87° .052 3.001 26° .899 117.474 57° .544 37.208 88° .035 2.001 27° .891 112.449 58° .529 35.802 89° .017 1.000 28° .883 107.758 59° .515 34.427 90° .000 0.000 29° .874 103.364 60° .500 33.080 30° .866 99.239 61° .485 31.760 84 HINTS TO TEACHERS Table II. —The Lengths of One Degree of Longitude in Different Latitudes. Lat. Stat. Mi. Lat. Stat. Mi. Lat. Stat. Mi. Lat. Stat. Mi. 0° 69.164 23° 63.695 46° 48.124 69° 24.860 1° 69.145 24° 63.216 47° 47.253 70° 23.725 2° 69.122 25° 62.718 48° 46.363 71° 22.584 3° 69.072 26° 62.202 49° 45.462 72 c 21.437 4° 68.998 27° 61.666 50° 44.545 73° 20.284 5° 68.901 28° 61.113 51° 43.614 74° 19.124 6° 68.785 29° 60.537 52° 42.670 75° 17.957 7° 68.652 30° 59.947 53° 41.713 76° 16.784 8° 68.496 31° 59.333 54° 40.743 77° 15.608 9° 68.315 32° 58.711 55° 39.760 78° 14.427 10° 68.117 33° 58.065 56° 38.765 79° 13.240 11° 67.900 34° 57.397 57° 37.758 80° 12.049 12° 67.661 35° 56.714 58° 36.740 81° 10.854 13° 67.402 36° 56.018 59° 35.710 82° 9.656 14° 67.121 37° 55.308 60° 34.669 83° 8.456 15° 66.821 38° 54.570 61° 33.617 84° 7.253 16° 66.499 39° 53.819 62° 32.555 85° 6.048 17° 66.163 40° 53.053 63° 31.4S3 86° 4.840 18° 65.798 41° 52.269 64° 30.402 87° 3.631 19° 65.419 42° 51.476 65° 29.310 88° 2.421 20° 65.014 43° 50.660 66° 28.210 89° 1.211 21° 64.5S9 44° 49.830 67° 27.101 90° 0.000 22° 64.156 45° 48.982 68° 25.985 Geography. Progressive Outline Maps. North America; South America; Europe; Central and Western Europe*; Asia; Africa; Australia; United States; New England; Middle Atlantic States ; Southern States, Eastern Division ; Southern States, Western Division ; Central States, Eastern Division ; Central States, Western Division ; Pacific States ; the Great Lakes ; New York ; Ohio ; Washington ; Pennsylvania ; British Isles * ; England*; the World on Mercator's Projection*; Greece*; Italy*; Pales- tine * ; and Ancient History *(the world as known to the Ancients). Printed on substantial drawing paper, adapted to lead-pencil or to ink. 10 x 12 inches. U. S. and Mercator's Projection, 12 x 20 inches. Price by mail 2 cents each; #1.50 per hundred. Map of Ancient History, 3 cents each ; $2.50 per hundred. An edition of the Maps, at same price, is issued in black ink, on heavy white writing paper, about three-fourths the size. These are especially adapted for use in grades using the Primary Geography. When ordered by mail at the hundred rate, the postage, which on full hundreds is 25 cents for the small maps and 50 cents for the large, must be paid by the purchaser. * These maps may also be had for historical work with outline printed in black ink. THESE outlines are for the use of the pupil, and are based on the assumption that map-drawing should be taught as a means, and not as an end ; that its purpose is to assist the mind in acquiring and fixing geographical facts, and that to memorize the construction lines of other methods and the hundreds of nameless projections and indentations of a tortuous coast-line is a waste of iime and of nervous energy which would be better employed in studying important and in- teresting particulars concerning the physical features, climate, pro- ducts, etc., of the interior. In tracing the outline, the pupil acquires a correct knowledge of the form of the country, and, as each day's lesson proceeds, he can fill in his map to correspond with the detailed knowledge gained. Among the advantages of the Progressive Outline Maps, we may mention the following : — I . Economy of time. By using the Progressive Outline Maps all the practical benefits of map-drawing are secured. By tracing the dim outline, and then developing a continent along such special lines as the teacher may direct, every important feature is clearly fixed in the mind of the pupil, in as little time as is ordinarily consumed in mem- orizing the construction lines and diagrams of other systems ; and the still longer time required to memorize the irregularities of a contour can be devoted to the study of the more important topics. 167 i68 GEOGRAPHY. 2. Accuracy. They keep a correct form of the country under con- sideration constantly before the pupil. 3. General usefulness, (a) These maps may be used to indicate, besides the usual facts of indentations, projections, mountains, rivers, countries, states, towns, etc., the location of areas of mineral deposits, of forest growth, of prairies, deserts, plateaus, of the various kinds of soil, of staple productions, of dense population, of manufacturing districts, etc. (b) For developing the features of continents, made specially prom- inent in Physical Geography, these maps are very valuable. (c) In connection with the study of Ancient History, these maps may be used to represent the location of ancient tribes and barbarous hordes of men, the provinces of ancient empires, the distribution of territory after conquests, etc., etc. (d) In Modern History, the Maps of North America and the United States may be used for indicating the early discoveries, the settlements and the general development of the continent, the colonies and the nation, in connection with the text-book study of these fea- tures. No time can be spared in History for practice in map-drawing. (e) For rapid and thorough tests of pupil's knowledge of Political, Descriptive, and Physical Geography, and of many facts in History, no series of questions and answers can equal in three hours what may be ascertained, practically, of their knowledge of these subjects by the Outlines in thirty minutes. Such a map can be easily and rapidly inspected by the examiner. 4. Economy in price. These maps cost the pupil two cents each. Several times that amount is usually expended for paper required for the practice in producing a satisfactory map by other methods. For opinions, other than the following, from teachers and school officers who have used, or carefully examined the maps, see special circular which is sent free on application. Albert G. Boyden, Prin. State Normal School, Bridge-water, Mass.: They are admirable, and greatly facilitate the study of geography and history. We use them with much satisfaction for his- tory as well as geography. Geo. H. Martin, Agent Mass. State Board of Education : Both the idea and execution commend themselves fully to my judgement If they can be made to displace the old "systems" of map-draw- ing, they wiU be a boon. GEOGRAPHY. 169 Progressive Outline Maps of the World. No. 1. World Outline, on the Plane of London. \\\ X t8 inches. No. 2. World Drainage Outline, on the Plane of the North Pole. 14J X 18. No. 3. Southern Hemisphere, Drainage Outline, on the Plane of the South Pole. *32 X 18. Introduction price, 3 cents each. #2.50 per hundred. THIS series of Progressive Outline Maps of the World is based on the latest and best means of presenting by maps geographical and historical facts, especially those of world-wide significance. The series has been proven, by actual work with pupils from the fifth year upward, to be unexcelled for the ease, accuracy, and truthfulness with which World Relations, both in Geography and History, can be represented. Pupils are enabled to perceive and express in Geography, (1) the ideas of the relations of relief, drainage, climate, productions, of all the continents, (2) the distribution, occupations, settlements, etc., of people, O") the intercontinental lines of travel, (4) the extent of the interdependence of geographical objects; in History, (1) the territorial limits, (2) the movements of nations in the past and present, in war and peace, (3) the influence of physical features on the development of a people or nation. A list indicating the uses of the series in the teaching of the World as a Whole, or Globe Lessons, is given in a special circular on these maps. Historical Outline Map of England. For the Use of Students. By Thomas C. Roney, Chicago. 19 x 24 inches. Retail price, 5 cents each. Introduction price, #4.00 per hundred. THIS map is especially valuable for showing the vital relation be- tween Geography and History, and for illustrating the historic sequence of events. The skillful teacher will make it serve many other subordinate uses. It is an admirable help to the study of English Literature. The outlines of the counties of modern England and Wales, and of the earldoms and vassal kingdoms of England in the tenth and eleventh centuries are indicated, and suggestions and illustrations as to the use of the map are given on it. 170 GEOGRAPHY. Outline Maps of the United States. Prepared by Edward Channing and Albert B. Hart, Assistant Professors in History in Harvard College. The Large Map is on strong white paper, in four sections, each 26x42 inches. Price, 15 cents per section; 50 cents com- plete. Mounted, $3.00. The Small Map is on tough white paper, in blue ink, and 1 1£ x 18 inches. Price, 2 cents each ; #1.50 per hundred. THE sections of the large maps are divided by the 95th meridian and the 37th parallel. They may be used separately or pasted together. The location of the principal cities is indicated by dots and there is no lettering on the map except the numbering of the parallels and meridians. These maps are suitable for large classes or for public lectures as they can be clearly seen for a distance of more than forty feet. By the simple use of shading and colors they may be made to serve in place of elaborate maps of various kinds ; physical, geological, political, etc., with the further advantage of allowing teachers to exercise their individual knowledge. The small map has a broad margin on the right hand side which furnishes space for written comments. The names of the principal rivers and the numbers of the parallels and meridians are printed on these maps. They are useful to the teacher or lecturer, where a map may be passed from hand to hand, and convenient for recording geo- graphic facts in graphic form, and for copying rare or expensive maps. They may serve well for a great variety of exercises in Political History, Economics, Meteorology, Geology, and Physical Geography. In use at Harvard, Johns Hopkins, University of Pennsylvania, etc., etc. Special circular, more fully describing the method of using these maps, sent free on application. The Educational Courant, Louis- ville, Ky.: Map drawing is one of the best methods possible in teaching geo- graphy, but has not been used by teachers generally on account of the time necessary to teach children how to make outlines. This series of maps, which embraces all that any class will need to use, does away with that stumbling block. If you see them you will use them. School Education, Minneapolis, Minn.: Many teachers whose time is limited are deterred from map sketching by the labor of drawing details. Here we have maps faultlessly proportioned and ready for names. The advantage of such work is incalculable. The larger sectional maps of the United States are also in blank ready for a large historical wall map which will grow in completeness as events are unfolded during the progress of the term's work in history. Each student may work up his own map, or one may be made by the class in common. GEOGRAPHY. Historical Outline Map of Europe. Printed on bond paper, 12x18 inches, in black outline. Price by mail, 3 cents each ; #2.25 per hundred. THIS map, though belonging to the Progressive Outline Map Se- ries, is especially intended for the use of classes in History or Science, as fully described under the Historical Outline Map of the United States (seepage 170). In addition to the outline of the continent, the principal mountain ranges are also given. Topics in Geography. By W. F. Nichols, Principal of Hamilton School, Holyoke, Mass. Cloth. 176 pages. Retail Price, 65 cents. THIS book contains a comprehensive outline of all geographical facts usually taught in our best primary and grammar schools, together with many excellent suggestions for increasing the interest of pupils by object lessons and language work in geography. In preparing the Topics the author has aimed : to increase the value of geographical study, to shorten the time usually spent on the study, to give a brief outline for the scientific study of any continent as based upon structure or slope, to deal sparingly or not at all with statistics, but rather to have all areas taught by comparison, to make more prominent the natural curiosities and wonders, and to combine language and geography. It is a practical guide, containing much in- formation concisely stated. A list of books for reference, including many interesting and reliable tales of travel is added. G. R. Showhan, Co. Supt. Schools, Urbana, III. : I believe it will be a very useful auxiliary to teachers of our com- mon schools. They do not so much need to be told what to teach as how to teach ; as how to select from the great mass of geographical facts those which will prove to be most useful. Your little work will certainly prove to be a valuable guide. Isaac H. Stout, lately of Dept. of In- struction, Geneva, N. Y. : I have exam- ined it carefully and am much pleased with it, believing that it is directly in the line of what so many of our teachers need for their work in the school- room. E. S. Kirtland, recently Supt., Holyoke, Mass. : The Topics in Geog- raphy were made in and for our schools, and have been used long enough to prove their value ; indeed, I regard the little book as the most useful school-room work that has ever been given to this department. Miss A. G. Baldwin, Teacher in Hampden Nor. and Agri. Inst., Va. : It seems to me admirably fitted for the pur- pose for which it was intended- 172 GEOGRAPHY, Lessons in the New Geography. By Spencer Trotter, Professor of Biology and Geology in Swarthmore Col' lege, Pa. Cloth. 192 pages. Retail price, pi. 00. THE New Geography is new in the sense that its point of view is essentially human . The old methods of geography teaching dealt almost exclusively in the hard facts and dry detail of surface features, political divisions, — an endless, meaningless collection of names, with Jittle if any reference to the true value of geographical conditions as factors in the development of man. As the earth is the theatre of human action, the true study of geography is a study of human life under the varied conditions of existence imposed by the different regions of the earth. It is thus synonymous with History. One object of these " Lessons" is to bring this view of the study of Geography, — with a fresh and living interest to the mind of every teacher and student. Not the least important feature of geographical study, as of all study, is the extent to which the imagination is brought into play in forming ideas of things. A mental picture must be created in the child's brain ; and the teacher is successful in so far as he or she is able to form this picture in his or her own mind, and vividly reflect it to the pupil. So with a book : its words and sentences must convey living ideals. To the extent that it does this will it be interesting, instructive, and valuable as an educational factor. These " Lessons 11 aim to fulfil these two phases of the study, — the human and the imaginative. The purpose of the book is to present an outline sketch, suggestive and stimulating, and it is intended as a Reader to supplement the regular work of the teacher and the class. The various subjects presented in the chapters and lessons are not to be viewed as special and separate treatises. They are brought for- ward simply to indicate their relationships to the whole subject. This is especially true of the lessons dealing with the elementary questions of climate and geology. The book does not aim to train the student, but to stimulate interest in the wider relations of Geography. From our special circular on this book we quote the following : in an excellent manner. It is interestingly written, and it deals with matter which ought to be learned by all pupils. K. S. Tarr, Prof, of Geology \ Cornell Univ. y Ithaca N.Y.: The book is well conceived, well prepared, and published GEOGRAPHY. *73 Manual of Geography, Modern Facts and Ancient Fancies in Geography. A book for teachers. By Jacques W. Redway. Cloth. 175 pages. Retail price, 65 cents. BEING a world-wide traveller and professional geographer, as well as a practical teacher, Mr. Redway is excellently fitted to make fresh and original suggestions on the study of this subject. His book renders the latest discoveries in Geography available for the use of teachers. Chapters on Out-of-door Lessons, Clay and Sand- modelling and Map-drawing are full of interesting information else- where unpublished. The most striking part of the work is devoted to the discussion of the time-worn traditions that still cumber many even of the most re- cent text-books. The facts given concerning volcanoes, storms, deserts, sea-depths, ocean-currents, glaciers, etc., etc., have never be- fore found their way into modern school-books, and will be a surprise to most teachers. It is full of useful hints to teachers, and of bright, interesting information for the general reader. Alex. E. Frye, Author of " Frye's Geographies : " I consider it a very valua ble contribution to geographical literature. It should be in the hands of all progress- ive teachers. Its Hints to Teachers are invaluable ; while its chapters on Modern Facts and Ancient Fancies will be a revelation to many. The work is stimulating, logical and practical ; and reflects much credit upon the scholarly attainments of its author. J. M. Greenwood, Supt. of Pub. Instruction , Kansas City, Mo. : One of the most suggestive hand-books for teachers I have ever read. I will recom- mend it to our teachers. J. P. Welch, recently Inst, in State Normal School, West Chester, Pa. : I read it with much pleasure and profit, and was not surprised at its excellence, be- cause I know the author to be the best in- formed man, on that subject, that I ever knew, Miss B. M. Reed, Prin. Springfield Training School, Mass. : I think it will be cordially received by teachers. It is very suggestive and covers ground that must have required a lifetime, nearly, to become acquainted with. Wisconsin Journal of Educa- tion : It helps where help is most needed, in effecting a change from mechanical to rational teaching of geography. It is not a dull manual of directions, but an inter- esting and suggestive treatment of modern pedagogical views in geography. We venture to affirm that teachers of geog- raphy will find in it much that is new to them, and plans of work, with practical discussions of ways and means for realiz- ing them, which if followed will make ele- mentary geography a new branch to them and their pupils. The book is thus a man- ual of methods and matter, the sort of a book which a good geography teacher will want always at hand until familiar with every paragraph in it. 174 GEOGRAPHY. The Reproduction of Geographical Forms. I. Sand and Clay-Modelling with Reference to Geographical Forms. II. Map- Drawing and Map Projection. By JACQUES W. Redway, author of " A Man- ual of Geography." Illustrated. Paper, 84 pages. Retail price, 30 cents. THE object of this pamphlet is to group the various forms and outlines of relief into types. The pupil is taught to classify the various types of relief and earth-sculpture, and to reproduce them in sand or in clay, either from pictures or photographs, or from a study of the form as it occurs in nature. By this method the modelling of geo- graphical forms becomes a science instead of an aimless expenditure of energy. In the chapter on Map-projection the pupil is taught not only how to draw a map, but also how to project it as well. A number of easy projections, requiring no more elaborate apparatus than a pair of dividers and a straight-edge, are plotted for the practical use of the pupil. The very important question of how to read and interpret a map is also discussed. Schoolmaster, London, Eng. : This book is full of practical suggestions. We have nowhere seen collected so many hints as to the best methods of modelling in sand and clay, and of utilizing out- door lessons in acquiring the essential facts and principles of geographical study. We commend this work to our readers. Educational Journal of Va. : This is emphatically a working book, and we have seen nothing which so fully ac- cords with our ideas on the subjects treated. Wisconsin Journal of Educa- tion : The single chapter on out-of door lessons is full of suggestions which would enable any intelligent teacher to substi- tute something better for the text-book memorizing now so common. There are few teachers who would not learn much from this little manual. Iowa Nor. Monthly ; Teachers in primary as well as in grammar grades will find this little book very helpful. The cuts are such as will enable the teacher to fully understand the work in hand. Intermediate Outline Map /£ United States. For Historical and Geographical Study. Prepared by William A. Mowry, Editor of " Education " and *' Common School." 28 x 40 inches. Price, each 30 cents ; per set of four, #1.00. WITH this map colored pencils should be used to fill in the history as it occurred and as fast as the lessons develop the facts. For a full course of U. S. history four maps should be used : (1) Discoveries and explorations to 1763 ; (2) through the Revolution to 1783 ; (3) de- velopment and growth to 1861 ; (4) the War of Secession. GEOGRAPHY. 175 The Earth in Space ; Or, a Fortnight in Astronomical Geography. By Edward P. Jackson, In- structor in Science at the Boston Latin School. Illustrated. Cloth. So pages. Retail price, 40 cents. Special price for class use. TO many persons otherwise well informed, this subject is an ever- perplexing mystery. Familiar with the topography, geology* and political history of the world they inhabit, they know little of it as a unit, in its relation to other worlds. This book presents, in a few simple lessons, the main features of this important branch of Geography. It is adapted to grammar and intermediate schools. The following is the Table of Contents : How we know that the earth is spherical ; How we know that the earth is flattened at the poles; Latitude and Longitude ; Zones; Dimensions and Distances: How we know these ; Gradual changes in light and heat during the day and the year ; How we know that the earth rotates ; Apparent daily motion of the heavens ; How we know that the earth revolves : The inclination of the axis ; The sun's declinations ; The change of seasons ; The variation in the length of day and night ; Appendix. Boston School Board, June 11, I89 : Ordered, that Jackson's Manual of Astronomical Geography be authorized C. F. King, Master of Dearborn School, Boston : I consider it a most valu- able treatise on the subject. I have been looking for years for such a book. J. M. Sawin, Master of Grammar School, Providence : Delighted with it. I have never read anything on the subject so short, simple, and interesting. for use as supplementary reading for the Grammar Schools, one set of sixty copies to be supplied to each of the Schools. The Epoch : There is about as much solid meat packed into this little volume as could be put into such small space. Outline Maps to accompany Sheldon s Amer- ican History. Printed in black outline on bond paper. Price, 2 cents each; $1.50 per hundred. THESE six outline maps include the following: The World on Mercator's projection, North America, the United States west to Santa Fe, west to the Mississippi, west from the Mississippi, and the Southern and Middle States for use in studying the Civil War. This series of maps is of great service when used in connection with any text-book on American History. 176 GEOGRAPHY. Picturesque Geography. A set of 12 pictures, printed in oil colors, size, 15 x 20 inches. Price, per Set, in Sheets, with 24 pages of letterpress description, #3.00. Mounted on Boards, per Set, #5.00. INTENDED primarily to picture to the beginner the natural divi- sions of land and water, which are usually named in abstract defini- tions, and at the same time to meet the modern demand for artistic and instructive pictures for decoration of school walls. These pictures are produced in the finest style of chromo-litho graphy. They consist of twelve beautiful landscapes from Nature, selected for their prominent geographical features. The series consists of : 1. River and Valley. 7- 2. Roads and Railways. 8. 3. Hills, Plain and Con- 9- fluence of Rivers. 10. 4. Mountain-Pass and Torrent. 11. 5. Glacier. 12. 6. Lake. Cliffs and Cape. Strait. Islands. Isthmus, Peninsula, and Haven. Coral Islands and Reef. Volcano and Gulf. W. T. Harris, U. S. ComW of Ed- ucation, Washington, D. C. : It gives me great pleasure to commend the new Pictur- esque Geography. It is calculated to be of real service in teaching the child the concrete meaning of technical terms used in Geography. Olive Adele Evers, Prin. of Teachers' Training Class, Minneapolis, Minn. : I am delighted with the pictures, and can make good use of them. Journal of Education, Boston : By far the finest presentation of natu- ral formations and scenic characteris- tics of the various countries that has yet appeared. National Schoolmaster, London : The artistic beauty of these pictures ex- ceeds anything we have previously seen for school use. Mrs. Louisa Parsons Hopkins, late Supervisor, Boston, Mass.: I think it altogether the best set of illustrative plates of the kind I could find, and have urged very strongly that a set should be furnished to every Primary School. I hope the time will come when sufficient progress in method will be reached to in- sure the introduction of the series of Pic- turesque Geography as a part of the fur- nishing of every first class in the Primarv Schools. Educational Times, London : They will supply the mind with images more definite and lasting than those gained from books alone. Tablet, London: The subjects chosen, as well as the artistic excellence in execu- tion, are well calculated to fix Geography on the mind. READING. Badlands Suggestive Lessons in Language and Reading. A manual for prt- mary teachers. Plain and practical; being a transcript of work actually done in the school-room. $1.50. Badlam's Stepping-Stones to Reading.— A Primer. Supplements the a8 3 -page book above. Boards. 30 cts. Badlam's First Reader. New and valuable word-building exercises, designed to follow the above. Boards. 35 cts. Bass's Nature Stories for Young Readers: Plant Life, intended to supple- ment the first and second reading-books. Boards. 30 cts. Bass's Nature Stories for Young Readers: Animal Life. Gives lessons on animals and their habits. To follow second reader. Boards. 40 cts. Firth'S Stories Of Old Greece. Contains 17 Greek myths adapted for reading in intermediate grades. Illustrated. Boards. 35 cts. Fuller's Illustrated Primer. Presents the word-method in a very attractive form to the youngest readers. Boards. 30 cts. Hall's HOW tO Teach Reading. Treats the important question: what children should and should not read. Paper. 25 cts. Miller's My Saturday Bird Class. Designed for use as a supplementary reader in lower grades or as a text-book of elementary ornithology. Boards. 30 cts. Norton's Heart Of Oak BOOkS. This series is of material from the standard imagin- ative literature of the English language. It draws freely upon the treasury of favorite stories, poems, and songs with wnich every child should become familiar, and which have done most to stimulate the fancy and direct the sentiment of the best men and women of the English-speaking race. Book I, 100 pages, 25 cts. ; Book II, 142 pages, 35 cts. ; Book III, 265 pages, 45 cts. ; Book IV, 303 pages, 55 cts. \ Book V, 359 pages, 65 cts. ; Book VI, 367 pages, 75 cts. Penniman'S School Poetry BOOk. Gives 73 of the best short poems in the English language. Boards. 35 cts. Smith's Reading and Speaking. Familiar Talks to those who would speak well in public 80 cts. Spear's Leaves and Flowers. Designed for supplementary reading in lower grades or as a text-book of elementary botany. Boards. 30 cts. Ventura's MantegaZZa'S Testa. A book to help boys toward a complete self-develop- ment. $1.00. Wright's Nature Reader, NO. I. Describes crabs, wasps, spiders, bees, and some univalve mollusks. Boards. 30 cts. Wright's Nature Reader, NO. II. Describes ants, flies, earth-worms, beetles, bar- nacles and star-fish. Boards. 40 cts. Wright's Nature Reader, NO. III. Has lessons in plant-life, grasshoppers, butter flies, and birds. Boards. 60 cts. Wright's Nature Reader, NO. IV. Has lessons in geology, astronomy, world-life, etc. Boards. 70 cts. For advanced supplementary reading see our list 0/ books in English Literature. D. C. HEATH & CO., PUBLISHERS, BOSTON NEW YORK, CHICAGO. English language. Hyde's LeSSOns in English, Book I. For the lower grades. Contains exercises for reproduction, picture lessons, letter writing, uses of parts of speech, etc. 40 cts. Hyde's LeSSOns in English, Book II. For grammar schools. Has enough techni- cal grammar for correct use of language. 60 cts. Hyde's Lessons in English, Book II with Supplement. Has, in addition to the above, 118 pages of technical grammar. 70 cts. Supplement bound alone, 35 cts. Hyde's Practical English Grammar. For advanced classes in grammar schools and for high schools. 60 cts. Hyde's Lessons in English, Book II with Practical Grammar. The Practical Grammar and Book II bound together. 80 cts. Hyde's Derivation of Words. 15 cts. Penniman's Common Words Difficult to Spell. Graded lists of common words often misspelled. Boards. 25 cts. Penniman's Prose Dictation Exercises. Short extracts from the best authors. boards. 30 cts. Spalding's Problem of Elementary Composition. Suggestions for its solution. Cloth. 45 cts. Mathews's Outline of English Grammar, with Selections for Practice. The application of principles is made through composition of original sentences. 80 cts. Buckbee's Primary Word Book. Embraces thorough drills in articulation and in the primary difficulties of spelling and sound. 30 cts. Sever'S Progressive Speller. For use in advanced primary, intermediate, and gram, mar grades. Gives spelling, pronunciation, definition, and use of words. 30 cts. Badlam's Suggestive Lessons in Language. Being Part I and Appendix of Suggestive Lessons in Language and Reading. 50 cts. Smith's Studies in Nature, and Language Lessons. A combination of object lessons with language work. 50 cts. Part I bound separately, 25 cts. MeiklejOhn'S English Language. Treats salient features with a master's skill and with the utmost clearness and simplicity. $1.30. Meikle John's English Grammar. Also composition, versification, paraphrasing, eta. For high schools and colleges, qo cts. Meiklejohn's History of the English Language. 78 pages. Part ill of Eng- lish Language above, 35 cts. Williams's Composition and Rhetoric by Practice. For high school and col- lege. Combines the smallest amount of theory with an abundance of practice. Revised edition. $1.00. Strang's Exercises in English. Examples in Syntax, Accidence, and Style for criticism and correction. 50 cts. Huffcutt's English in the Preparatory School. Presents advanced methods of teaching English grammar and compositon in the secondary schools. 25 cts. Woodward's Study Of English. From primary school to college. 25 cts. Genung'S Study Of Rhetoric. Shows the most practical discipline. 25 cts. See also our list of books for the study of English 'Literature* D. C. HEATH & CO., PUBLISHERS, BOSTON. NEW YORK. CHICAGO. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. 5Nov'52BH WJI221952 10 c_u\ INTER L1BRAF CEIPT 'F£i - wei 6hn'62l1! HE „D JAN 5 1962 LD 21-95m-ll,'50 (2877s 16)476 YB 44290 M522503