! I |i I ! : :ii II '"T i; : '■ !i';.''!-.;;i :! : ..■.:;'■■■:: i I! II! Ill iii:!!in;ii;;:lii:i:0:i:l..':.=i::: ■;!'.,■:::::"'![ ajorttell InitterHttg Sibrarg BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND THE GIFT OF HENRY W. SAGE 1891 Cornell University Library TA 590.S55 Military map reading / 3 1924 004 698 654 Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004698654 MILITARY MAP READING BY CAPTAIN C. O. SHERRILL CORPS OF ENGINEERS, U. S. ARMY INSTRUCTOR IN ENGINEERING U. S. SERVICE SCHOOLS FORT LEAVENWORTH, KANSAS Fourth Edition Twenty-fifth Thousand Adopted by the War Department for use by the Organised Militia Adopted for use at the Army Service Schools, Fort Leaven- worth, Kansas Adopted for use of the U. S. Marine Corps GEORGE BANTA PUBLISHING COMPANY ■ Menasha, Wisconsin Copyright I h C. 0. Sherrill 1909 1911 1912 Sales Agents U: S. CiMtHB&l^i^iATiOH Fort LlSjiVEsVoiiTJi; Kahsas Press of George Banta Publishing Co. MfiNABHA, WilS. ' TABLE OF CONTENTS FAR8. MILITARY MAP READING Chapteu I. — Classes of maps; Map Reading; Scales of Maps; Methods of Representing Scales; Con- struction of Scales; Scale Problems; Scaling Dis- tances from a Map; Problems in Scaling Distances 10-21 Chapter II. — Methods of Representing Elevations; Contours; Relation of Map Distances, Contour Intervals, Scales and Slopes ; Problems ; Hachures 22-32 Chapter III. — Directions on Maps; Methods of Orienting a Map; To Locate One's Position on a Map; The True Meridian; Conventional Signs 33-40 Chapter IV. — Visibility; Visibility of Areas; Visi- bility Problems ; On Using a Map in the "Field ; Maps Used for War Games and Tactical Problems 41-54 MILITARY MAP READING. CHAPTER I. CLASSES OF MAPS. 10. Maps are representations to scale (usually on a plane) of portions of the earth's surface. They are of various kinds, depending on the use for which they are intended, and may or may not rep- resent relative heights as well as horizontal distan- ces and directions. For instance, the ordinary Coimty Map shows only roads, boundaries, streams and dweUings. A Topographical Map shows the horizontal relation of points and objects on the ground represented and in addition gives the data from which the character of the surface becomes known with respect to relative heights and depres- sions. 11. Suppose an officer is sent out by his com- mander in imknown country to pick out a good posi- tion for camp and outpost, and to report upon his return the military features of the site selected. On visiting the ground selected his eye can only take in a very limited portion from any one position, and even with the most careful examination from vari- ous points he would get only a very general idea of the larger features. But if on returning he tries to 1 2 MmtTAKY TOVOGRAPHY FOE MOBILE FOECES describe in words to his commander the position se- lected, he would find his task almost impossible. The simplest sketch, however, made by him on the gromid, even if not correct as to scale or elevations, woidd enable hini to give his commander as good an idea as he had himself obtained; but a report based on an accurate map or sketch would be full and complete. It is almost impossible to organize and cany out marches, reconnaissances, concentrations, etc., without maps upon which to base the orders. 12. Almost all classes of maps have some mili- tary uses. For example, an ordinary map showing the location of important towns, large rivers, and roads, is useful for arranging the concentration of large bodies of troops or for following the opera- tions of a campaign, but it is far from being in sufficient detail for the piu-poses of those who plan or study the smaller operations of war. A complete military map, on the contrary, must give both the horizontal and vertical relations of the groxmd and also a representation of aU mihtary features of the area. A Military Map, therefore, is one which gives the relative distances, elevations, and directions of all objects of military importance in the area rep- resented. MAP READING. 13. By Map Reading is meant the ability to grasp by careful study not only the general f eatiu-es of the map, but to form a clear conception or mental picture of the appearance of the ground represent- ed. This involves the ability to convert map distan- Military Map Reading 8 ces quickly to the corresponding ground distances; to get a correct idea of the network of streams, roads, heights, slopes, and all forms of military cov- er and obstacles. The first essential therefore, for map reading is a thorough knowledge of the scales of maps. SCALES OF MAPS. 14. A map is drawn to scale — that is, each unit of distance on the map must bear a fixed proportion to the corresponding distance on the ground. If one inch on the map equals one mile (63360 inches) on the ground, then J inch equals J mile, or 63360^3=21120 inches on the ground, etc. The term "Distance" in this book is taken to mean hori- zontal distance; vertical distance to any point is called elevation or depression, depending on wheth- er this point is higher or lower than the one from which the measurements are made. For example, the distance from Frenchman in a straight line to McGuire (Leavenworth Map) is 2075 yards, but to walk this distance direct would require the ascent and descent of Sentinel HiU, so that the actual length of travel would be considerably greater than the horizontal distance between the two points. In speaking of distance between towns, cities, etc., horizontal distance is always meant. In re- ferring to such distances, that by the shortest main road is usually intended. For example, from Fort Leavenworth to Kickapoo (Leavenworth Map) is 5 miles, measured over the 5-17-47 road. The fixed ratio (called the scale of the map) between distan- 4 MlLITAKY TOPOQBAPHY FOR MOBILE FOKCES ces on the map and the corresponding distances on the ground should be constantly kept in mind. METHODS OF REPRESENTING SCALES. 15. There are three ways in which the scale of the map may be represented : 1st. By an expression in words and figures; as 3 inches=l mile; 1 inch=200 feet. 2d. By what is called the natural scale or the Representative Fraction (abbreviated R. F.) , which is the fraction whose nimierator represents units of distance on the map and whose denominator repre- sents units of horizontal distance on the ground, beinff written thus ; R. F. rp- ^^^^^ » 1 :63360, ^ 1 mile 63360 or 1 is to 63360, — all of which are equivalent ex- pressions, and are to be understood thus; — -^ Ground that is the numerator is distance on the map, the denominator is horizontal distance on the ground. This fraction is usually written with a numerator of unity, no definite length of vmit being specified in numerator or denominator. In this case, the ex- pression means that one unit of distance on the map equals as many of the same horizontal units of dis- tance on the ground as there are units in the de- nominator. The R. F, is synonymous with the term scale of the map. Therefore, if the scale be changed the R. F. wiU be changed in exactly the same manner and amount. To increase the R. F., (being a frac- tion), its denominator is decreased. For the same MiLiTAKY Map Reading 5 reason the greater the distance on the ground rep- resented by an inch on the map, the smaller is the scale of the map. The greater the dimensions of a map to represent a given area the larger is the scale (that is R. F.) and the smaller the denominator of the latter. 3rd. By what is called a Graphical Scale. A Graphical Scale is a line drawn on the map, divided into equal parts, each division being marked, not with its actual length, but with the distance which it represents on the ground, (see figure 1. and Leavenworth Map). Every map should have a graphical scale because this gives true readings no matter how the size of the map is changed in reproduction or due to weather conditions; whereas the R. F. and the nimiber of inches per mile placed on the original map are no longer true if the size is altered. The R. F. is im- portant, however, because it is inteUigible to per- sons unf amihar with the units of distance used in making the map. An expression of the scale in words and figures is also valuable because rapid mental estimates can be made of the distance be- tween points on the ground by estimating the num- ber of inches between these points on the map. 16. Graphical Scales are of two kinds depend- ing on the purpose for which they are constructed : (1) Working Scales and (2) Beading Scales. A Working Scale is used in making a sketch or map and shows graphically the value of tens, him- dreds, etc. of the units of distance used in making 6 MiLITAEY TOPOGHAPHY FOK MoBILE FoBCES the map or sketch. For example, if distances were measured by counting strides or taking the time of a horse trotting, in making a sketch, then it would be necessary to construct a scale of strides or min- utes of horse's trot on the desired scale of the sketch. This enables you to lay off on the sketch distances, measured thus, directly from the working scale without the necessity of calculating at each halt how many inches on the sketch are equal to the num- ber of strides or minutes, passed over. A Reading Scale shows the distance on the map corresponding to even tens, hundreds etc. of some convenient and well known unit of measure, such as the foot, yard, mile. For example, figure 2 shows a reading scale of yards, reading to hundreds on the Main Scale, and to 25 yards on the Exten- sion ( see fig. 1 ) . A scale may be both a working and a reading scale when the unit of measure used in making the map is a well known length such as the foot, or yard. A reading scale in the units of one country often will not be satisfactory for use by persons of a different nationality, because of their unfamiliarity with the length of imits of dis- tance used. An officer coming into possession of such a map would be unable to get a correct idea of the distances between points represented. He would find it necessary to convert the scale into fa- miliar units as yards or miles, see problem 4, par. 19. It will readily be seen that a map's scale must be known in order to have a correct idea of distan- Plate 1. (ft "a o C3 8 MiuTAKY Topography for Mobile Forces ces between objects represented on the map. This is essential in determining lengths of march, rang- es of small arms and artillery, relative length of marches by different roads, etc. Therefore, if un- der service conditions you should have a map mth- out a scale or one expressed in mifamUiar imits, you would first of all be compelled to construct a graph- ical scale to read yai'ds, miles etc.. or one showing how many miles one incli represents. Or, if you were required to make a sketcli by pacing, it would be necessary to construct your scale of paces on the proper R. F. CONSTRUCTION OF SCALES.* In the construction of scales the following are the steps taken: (1). Find from tlie given data tlie R. F. of the map; (2) tlie lengtli in inches of the imit of measure used, as pace, diain, rate of horse's trot, yard, mile etc.; (3) tlie number of the units of measure corresponding to one inch on the map ; and (4) the lengtli in inches on the map corresponding to an even number of tens etc. of these xmits of dis- tance. 'The foUoiring relations are ooustantly used and should be familiar to every one: 1 mile=63360 inohes=5880 feet=:1760 yards. 1 a 1 1 1 1. i. 1 .1 I" tke seale prob- _ _ =Soa]e 1 inch to 1 mile. , .. . ,, B. P. 63360 lems, units of dis- j^ tanoe on the ground B. p 21150 ~®'^* ' ^°''^®' *** ^ °^'®" "^'^ ^* Indicated by small CAPITALS, ■D in « . « . V . , „ where any confusion "• *• IC5M=So*le 8 inolie* to 1 mile. ^^^ ^^^ MiLiTAKY Map Reading 9 SCALE PROBLEMS. Having Given the R. F. 19. Problem 1. Assume R. F. — i — . (a) 21120 ^ ' To find the value of one inch on the map in miles on the ground. Solution : If one inch on the map represents 21120 inches on the groimd, then one inch (on the map) , will represent as many MILES (on the ground) as one mile (=63360 inches) is contained in 21120 inches. 21120^68860==^, or one inch=J MILE is the scale of the map, usually expressed thus: 8 inches=l MILE. (b) To construct a graphical scale of yards. Solution: If one inch=21120 INCHES, the^ one inch=21120^86=586.66 YARDS. Now suppose a scale about 6 inches long is desired. 6 inches=6X 586.66=8519.96 YARDS, so that in order to get as nearly a six inch scale as possible to represent even hundreds of YARDS, assume 8500 YARDS to be the total number to be represented by the scale. The question is then, how many inch- es are necessary to show 8500 YARDS. Since 1 inch=586.66 YARDS, as many inches are neces- sary to show 8500 as 586.66 is contained in 3500 YARDS, or 8500^586.66=5.96 inches. Now lay off with scale of equal parts A I, figure 1,^5.96 inches (5 inches+48 50ths) and divide it into 7 equal parts by construction shown in figure 1, as fol- lows: Draw a line A H making any convenient an- gle with A I and lay off on it 7 equal convenient lengths, so as to bring H approximately opposite 10 MnjTAKY Topography fob Mobile Forces I. Join H and I, and witli ruler and triangle draw the intermediate lines tlirough B, C, D, etc., paral- lel to H I. These lines divide A I into 7 parts each=500 yards. The left di^-ision, called the ex- tension, is similarly di^^ded into 5 parts each equal to 100 yards. Prohlem 2. R. F. ^^j^. length of stride 60 inches. Construct a working scale of strides. Solution: 1 STRIDE=60 IXCHES. 1 inch= 10000 INCHES=^v?r^ STRIDES. 60 Suppose a 3 inch scale is desired. 8 inches=8X 10000 g^ — 500 STRIDES. Construct the scale by dividing up three inches into 5 parts of 100 STRIDES eacli by the method of figure 1. Problem 8. A sketcher's horse trots one mile in 8 minutes. Construct a scale of minutes and quar- ters, R. F. .,.. QQ . Solution: 8 MINUTE S=63360 INCHES. ' ^^^^-(eie^) ^"NUTES. ^ ,., ^^.^^^^r, (21120 X 8 ) From which 21120 INCHES- ) 68860") MINUTES=f =2§ MINUTES. Since 1 inch=21120 INCHES, 1 inch==2§ MINUTES. 6 inches=(6X2§) MINUTES=16 MIN- UTES. Military Map Reading 11 Construct the scale by dividing the 6 inch line in- to 16 equal parts for MINUTES, and the left one of these spaces into 4 equal parts to read quarters of a minute. R. F. NOT GIVEN. Problem 4. An American officer in Germany seciires a map showing a scale of 1 centimeter=l KILOMETER. Required (a) the R. F. of this map, (100 centi- meters=l meter; 1000 meters=l kilometer.) r, 1 .■ 1 cm .01 m 1 T> -c' Solution: — =ri^=-f-= ^r5-= ^R- F. 1 KM 1000 M 100000 (b) How many inches to the MILE in this scale? (c) Construct a reading scale of MILES for this map. Problem 5. (Where a map has a graphical scale on which the divisions are not in even parts of inches and are marked in ground distances of some unfamiliar unit as kilometers, meters, chains, etc. It is required to construct a graphical scale in familiar units) . By measurement on the scale of a German map, 1.08 inches reads 1 KM. (a) What is the R. F. of the map? (b) Construct a graphical scale to read YARDS. Solution 1.08 inches=l K= 1000 METERS (1 m=39.87 in.). 1.08 inches= 89370 INCHES or 1 inch=864.53 INCHES, or R. F.= --. ■ „ ; whence construct graphical scale as in Problem 1 (b). 12 Melitaky Topography for Mobile Forces Problem 6. (Where a map has no scale at all. In this case measure the distance between two defin- ite points on the ground represented, by pacing or otherwise, and scale off the corresponding map dis- tance. From this find the R. F. and construct the graphical scale as above). For example, suppose the distance between two road crossings, identified on map and ground, is found to be 500 PACES (31 inches each), and on the map to be f inch. In thiscasefinch=( 500X31) INCHES. 1 inch=^^^j^=20666.66 INCHES; R. F.= 20666.66 From this R. F. a scale of yards is constructed as in Problem 1 (b) . CHANGING THE SCALE OR THE AREA OF MAPS. Note the difference between increasing or de- creasing tJie scale {linear dimensions) of a map, and its stse (area). To double the size of a map whose sides are six inches and 4 inches (6X4=24 square inches), the reproduction would be 48 sq. inches that is 6 ^/ 2 by 4 \/ 2 on the sides. To re- duce a 9 inch by 6 inch map to J its size (area) , the sides would be ;^ and ^^^. y 3 X yf = 64 y =18=^ of 54. The general rule is that to diange the area of a map any multiple, as 2 times, 3 times, ^ times, \ times, its original area, eadi of Military Map Reading 18 the linear dimensions is multiplied by the square root of the multiple as V 2, V 8, — — — r-, etc. Problem 7. A map, R. F. ^^ , is enlarged so that the distance on the map between two towns A and B is 3 times as great as on the original. What is the new R. F.? Answer. R. F. ^ , (R. F, 2000 ^ multiplied by 3). Problem 8. A map has R. F. (a) 8000 ^ ' What is the scale of this map in inches per MILE if its hnear dimensions are decreased one-fifth in reproduction? (b) The original area of the map was 8 by 16 inches. What is the new R. F., if its area is four times as large as that of the original? Solution to (b) : ^ X V^= ^ X 2= ^ ' 8000 ^ 8000 ^ =R. F. 4000 CORRECTION OF ERRONEOUS SCALES. It sometimes happens that in making a map an error exists in the length of the unit of measure that is not discovered until later. The question is then (1) how to find the true scale of the map as made, and (2) how to correct the working scale so it will be true for the future work. Problem 9. An officer is ordered to make a posi- tion sketch, scale 6 inches=l MILE. He uses a working scale of 62 inch strides. Afterwards he finds that his stride is actually 58 inches. 14 MlLITAKY TOPOGBAPHY FOR MOBILE FORCES Required: (a) What is the R. F. of the sketch actually made/ and (b) is the scale larger or small- er than ordered? Solution: (a) R. F. assumed ^..„^ - Smce his stride was shorter than assumed, in plotting any given distance on the sketch (as 1 inch), he had actually passed over a shorter distance on the ground than he thought. Consequently his true R. F. would have a smaller denoviinator in the pro- portion of the tme and assumed rates, 58 to 62. =y»Y».vu iiNi 1 10560 X —=9878.70 INCHES. 62 The true R. F. of sketch was 9878.70 (b) TheR. F. g-gA_ is larger than R. F. having a smaller denominator, and therefore 10560 the scale of the sketch as made is too large. Problem 10. A mounted sketch is made on the scale of 8 inches=l MILE, with a horse rated at 5.5 MINUTES=1 MILE. The true rate of the horse is 1 MILE in 6 MINUTES. Required: The true R. F. of the sketch. Solution: Since the horse took longer to pass over a mile, than was thought, he traveled slower than he was rated. There was accordingly too short a distance covered at the end of any given number of minutes. Hence the distance on the ground corresponding to any plotted map space, say one Military Map Reading 15 inch, was less than supposed, or the denominator of the R. F. is really less than 21120, in the propor- tion of the two rates: 21120 X —=19360. The 6 1 true R. F. is . 19360 Problem 11. A sketcher is ordered to make a sketch on the scale R. F. He supposes he 21120 ^^ takes a 29 inch pace and uses this for his working scale. Afterwards he finds that a distance of 4000 yards scaled from his sketch measures on the grotmd 4125 yards. Required (a) His true length of pace. (b) The true R. F. of the sketch as made. 4000 X 36 .„„_ u * 4. 1 • — =4965=number oi paces taken m 29 ^ traveling the distance, whether he assumed the cor- rect length of pace or not. But in-as-much as the corresponding distance on the ground measured 4125 yards, therefore dividing this distance by the nimiber of paces taken in passing over it, gives the true length of each pace: LI =29.9 inch- 4965 es=actual length of pace. (fc) If the distance of 4000 yards scaled from the sketch actually measured 4125 yards on the ground, the sketch is smaller than intended and the R. F. is too large and must be decreased 21120 in the proportion of these two distances, i. e. its 16 Military Topography for Mobile Forces denominator must be increased. (See par. 15). Therefore, ^ X ^^= ^ =true R. F. 21120 4125 21780 THE LARGEST SCALE POSSIBLE ON A GIVEN SHEET. Problem 12. A sheet of drawing paper 28 inch- es by 21 inches is to contain a map of an area of ground ten miles by seven miles and leave a border of at least Ij inches. Required: The largest scale that can be used. Solution: Taking out the border of 1^ inches on every side leaves 25X18 inches available. The largest possible scale will be determined by findicg the R. F. of a map that would require 25 inches to show 10 miles, and one that would require 18 inches to show 7 miles and using the smaller of the two. 25 inches=10MI.=63360 X 10=633600 INCHES. 1 inch = ^^^ ^ 25344 INCHES. R. F. 25 is the scale of a map that will exactly fit the 25844 length. 18 inches=7 MI.=63360X 7=443520 INCH- ES. 1 inch=24640 INCHES. R. F. ^ is the 24640 largest scale that can be used on the width. The map that just will go on the 25 inch length wiU cover less than the 18 inch width and therefore Military Map Reading 17 R. F. — — is the greatest scale that can be used. 25344 * The map on any larger scale, as for instance , would not go on the length of 25 inches. 24640 ^ ® GENERAL SCALE PROBLEMS. Problem 13. Construct a working scale of paces for a map on the scale of 12 inches;=l MILE, one hundred and twenty paces being equal 100 yards. 14. A reduction of the General Staff map of France is published on a scale of R. F. ^ 200000 (a) Construct a graphical scale to show 15 miles on this map. 4.752 inches = 15 Mi. (b) Construct a graphical scale to show 15 kilo- meters (1 meter^39.37 inches, 1 kilometer=1000 meters) . 2.95 inches = 7.5 c. m. = 15 K. M. 15. The R. F. of a map size 10 x 12 inches is 1 62500 ' (a) What is the scale of this map when reduced to one-fourth its present size? ^ 125000 (b) Suppose that the length of the map be- comes 9.5 inches in a photographic reproduction. Is the map enlarged or reduced ? What is its R. F. ? 16. What is the R. F. of the Leavenworth Map herewith? How many inches on it equal one mile? 17. A map was drawn on the scale R. F. ^ 10000 but in reproduction its dimensions were changed so 18 MiLITAEY TOPOGBAPHY FOE MOBILE FOECES that 800 yards on the ground scales 875 yards on the map. Required: (a) Construct a reading scale to give correct distances from this map. (b) What is the correct R. F.? 1 -=- 9143. 18. Draw a suitable scale of yards for a map 10 by 12 inches to show an area of 5 by 6 miles. 19. The R. F. of a map is H-IOOOO. Required: (a) the distance in miles shown by one inch on the map. (b) Construct a graphical scale of yards; also one to read miles (problem lb). 20. The map from which figure 16 was reduced has a graphical scale on which 1.56 inch=one kilo- meter. Required (a) the R. F. of the original map. (b) Number miles represented by one inch. (c) Graphical scale to read hundreds of yards; one to read miles. 21. A map has marked on it R. F. l-f-62500. Required: (a) graphical scale to read miles, halves and quarters, (b) What is the value in yards of one inch on the map? 1 inch = 1736.1 Yds. 22. You are in hostile country and secure a map of the locality without a scale. 20 inches on the map is the distance apart of the 20th and 21st de- grees of latitude. Required: (a) a graphical scale of yards, (b) The R. F. of the map. (1° lati- tiide=68.8 miles) . 28. What is the R. F. of map, figure 20 A? SCALING DISTANCES FROM A MAP. 20. Having considered the scale relation and the construction of scales, it is well to mention the use of scales in taking distances from a map. Military Map Reading 19 1st. Apply a piece of straight edged paper to the distance between two points to be measured and mark the distance on the paper. Now apply the paper to the graphical scale as shown in figure 2, and read the number of yards on the main scale adding the number on the extension, with a total of 600+75=675 yards. 2d. Take the distance A B, figure 2, ofi' with a pair of dividers and applying the dividers, thus set, on the graphical scale read ofi" 675 yards. 3d. Use an instrument called a map measurer,* figure 3. Setting the hand on its face to read zero, roll the small wheel from A to B. Now roll the wheel back to zero in an opposite direction along the graphical scale, noting the number of yards passed over on the scale. Or, having rolled from A to B, note the number of inches on the dial and multiply this by the number of miles per inch given on the map. A map measurer is especially valua- ble for use in map problems and war games. 4th. Apply scale of inches to the line and mul- tiply the number of inches between the points by the nimiber of miles per inch given on the map._ 5th. Copy off the graphical scale on the edge of a piece of paper, and then apply this directly to the map. If the line to be measured changes direction, the same methods are used. By the 1st Method, Each portion in succession is taken off on the straight-edge paper. •For sale by Keuffel ft Esaer Co., New York. Price ♦2.00. 20 Military Topography for Mobile Forces By the 2d Method: The dividers are first ap- plied to B a (figure 4), then the leg at B is placed at B' in the extension of h a; now the leg at a is placed at h, making h B'=& a + a B. Now rotate the leg from B' to B" in prolongation of h c. Move leg at h to c. The total distance is now included in the spread of the legs and the dividers are applied to the scale. By the Sd Method: The map meas- urer is rolled from B to a^ a to h,h\,o c (figure 4) , causing the small wheel always to rotate in the same direction. By the 4ith Method: The scale of inch- es is placed on B a, then rotated about a and placed along h a, thus adding B a to a &^ etc., to the end, then obtain the number of miles as explained above. PROBLEMS IN SCALING DISTANCES. 21. Problem 1. What is the distance from 70 (U. S. Pen.) to A via Prison Lane and Pope Ave- nue (Ft. Leavenworth Map) ? Check by 3d method. Problem 2. What is the distance from 70 to G over the Atchison Pike? Use the 4th method and check with the divider method. Problem 3. A patrol at XVII (On Grant Ave- nue) is ordered to move by the shortest road to 17. Which road will it take? Problem 4. Company A is at Grant and Met- ropolitan Avenues, Company B is at the Polo Grovmds. They are ordered to arrive at French- man's at the same time. Assuming both move at 8 miles an hour, which will start first and how much? Give route of each. Fig. 5 A CHAPTER II. METHODS OF REPRESENTING DIF- FERENCES OF ELEVATION. 22. Since maps are representations, on a plane surface, of ground which has not only extent hori- zontally but vertically, it is necessary to have some means of rapidly determining elevations. This is accomplished in one of two ways. 1st. By means of contours, which are the lines cut from the surface of the earth by imaginary hori- zontal planes at equal vertical intervals from each other, figure 5 A.* The representations of these lines to scale on a map are called contours, figure 5 B, and this is the meaning usually intended by the term "contour." These relations of contours will be evident from figures 5 A and 5 B. Suppose that formerly this island was entirely submerged and that by a sudden disturbance the lake subsided until the highest peak of the island extended slightly above the water. Later a succession of falls of the water level of 20 feet each occurred, imtil now the island stands more than 100 feet out of the lake, and at each of the 20 foot elevations a distinct water line is left. These water lines are perfect contours re- ferred to the lake as a reference (or datum) plane. It will be observed that on the gentle slope along 'Based on photograph of Crater Lake made by Geological Survey. 21 22 Military Topoqeaphy foe Mobile Forces F-H the 20 foot contour is far from the lake, and from the 40 foot contour. But on the steep slope at R the contours are very close together horizon- tally and almost directly over the water. Hence, it is seen that contours far apart horizontally indi- cate gentle slopes, and contours close together hori- zontally, steep slopes. It is also seen that the shape of the contours gives an accurate idea of the form of the island. Figure 5 B shows the horizontal projec- tion of the contours in 5 A, that is, each point dropped vertically down on a plane. The contours in 5 B give an exact representation not only of the gen- eral form of the island, the two peaks, the stream M- Nl, the saddle M, the water shed from F to H, and the cliff at K, but the slopes of the ground at all points. From this we see that the nearer the contours on a map are to each other the steeper the slope represented. The contours of a cone (figure 6) are concentric circles, equally spaced because the slope of a cone is constant at all points. The contours of a concave cone are close together at the center (top), growing farther apart toward the outer circle (bot- tom), figure 8, showing that the slope is steeper at the top than at the bottom. The contours of a hem- isphere are far apart at the center (top), growing closer together near the circimiference (bottom), figure 7. 23. The following additional points should be remembered about contours: (a) A water shed or spur, along which the wa- ter divides, flowing away from it on both sides, is a) 24 MiLiTAEY Topography foe Mobile Forces indicated by the higher contours bulging out to- ward the lower ones. ( F-H figures 5 A and 5 B ) . (b) A water course, or valley j along which rain falling on both sides of it joins in one stream, is indicated by the lower contours bending out sharp- ly toward the higher ones. (M-N figures 5 A and 5B). (c) Contours of different elevations which unite and become a single contour, represent a ver- tical cliff. The contours of the vertical faces of the quadrant cut out of the cone, figure 6, would be shown by two single lines, perpendicular to each other at the center of the concentric circles. (d) Two contours of different elevations which cross each other represent an overhanging cliff. (e) A closed contour represents either a hill top (crest) , as P-B figure 5 B, or a depression. A hiU top is shown when the smallest closed contour is higher than the adjacent contour, and a depression when the smallest closed contour is lower than the contour next to it. (f ) A saddle {or col) is shown by two contours of greater elevation on two sides of it, and two of lower elevation on the other two sides, as at M fig- ure 5 B. M is a saddle between the two peaks 90 and 100. 24. Fig. 14 shows the stream system of the area represented in figm-e 15. Note the steep cliffs at A, figure 15, also observe that the roads generally fol- DlFFEB£NC£S OF ELEVATION 2fi low the flat coimtry. The road from Mt. Airy Lodge to Chilton makes a detour to avoid the steep slopes between these two places, but the road from Chilton to Stratford lies straight across the valley because its slopes are gentle, as shown by the greater distance apart of contoiu*s. A study of the network of streams in figure 14, in comparison with the con- tours in figiu'e 15, wiU show the value of carefully noting the position and direction of flow of streams in map reading, RELATION OF MAP DISTANCES, CONTOUR INTER- VALS, SCALES AND SLOPES. 25. The horizontal distance on the ground be- tween two contours is called the Horizontal Equiv- alent (H. E.) The horizontal distance between two contours on the map is always referred to by using the abbreviation M. D. (map distance) . Since the M. D. depends on the slope of the ground rep- resented, it can be calculated for various degrees of slope of the ground and a scale of M. D.'s con- structed with which slopes can be at once read ofi' from the distance apart of any particular contours. This is based on the fact that 57.3 feet (688 inches) horizontally on a 1 degree slope gives a rise of 1 foot. These relations are not absolutely correct, but up to 20° are so nearly exact that the error is not appreciable on the scales used on military maps. 26 MiLiTAEY Topography foe Mobile Forces Slope degrees Rise feet Inches Horizontal 1° »° 4° 688 688 2 688 8 688 =844 =829 4 688 =172 188 26. To construct a scaj e of M. D.'s for a map on which it is not shown, take the distance in inches cor- responding to one degree of slope, multiply this by the contour interval (V- I. in feet) and by the R. F. The result is the M. D. in inches for a 1° slope. Divide this value by 2, 3, 4 etc., then lay off these distances on a line to show 1°, 2°, 8°, etc., fig- ure 10, p. 38. This relation between M. D., slope, V. I., and scale, is shown mathematically by the follow- ing formula: M. D. (inches) =B. F.XV. I. (ft.) X688 (inches)-^ (degrees). A discussion of the relations between the four terms of this formula gives rise to the principles governing slopes, map distances, scales, and vertical intervals of maps. These principles may be deduced by assuming that two of the quantities are fixed in value, and show- ing how the other two vary imder those circum- stances. DiTFEKENCES OF EUEVATION 27 27. The equation may be written tilius: ^I. D. X S = R. F. X V. I. X ihSS. If now M. D. and S on two maps are assumed to be definite fixed val- ues (as for exami^le .i>5 inch ]M. D. and a corre- sponding slope of 1^ on each map), their product is a constant. Hence the product of R. F. times V. I. must be constant to maintain the equality of both members of the equation and the K. F. must vary inTcrsely TN-ith the V. I. for this conditiraa to ex- ist ' That is. }/ the B. F. (scale) is INCREASED the r. I. miusi he proportionally DECREASED and vice versa. This principle is of great value in map readuig and sketdiing because on all maps made on such a sj'stem a given ^I. D. represoaits the same slope. The above principle may ;ilso be shown graphi- cally as follows: Let figure (a) be assimied to be a vertical section of the ground in which the line A B is the horizontal distance and BC the V.I. be- tween two eontoius A and C on the ground. If a certain M. D. on a map (Xo. 1) represents tiie dis- tance AB on the ground, and the same M. D. on another map (Xo. 9) represents a gretder ground distance, as AD, then the R, F. (scale) of map Xo. 2 is smaller than that of map Xo. 1 (see p. 4, last paragraph). But Map Xo. 2 has the larger V- 1., as shown by the line ED in the figure; and hence the smaller the R, F. tiie larger the Y. I. will be, if a given M. D. represents the same slope on all the maps. 28 MiLiTAEY Topography for Mobile Forces I "SI Z -^.--^ " " (a) A^'-' -""S B D' Ground Boss 28. Based upon the above principle, the Nor- mal System of Scales prescribed for U. S. Army field sketches is as follows: For road sketches, 8 inches = 1 milej vertical interval between contours 20 feet. For position sketches 6 inches = 1 mile, V. I. = 10 feet. Fortification sketches, 12 inches = 1 mile, v. I. = 5 feet. On maps made according to this system, any given length of M. D. always corresponds to the same slope. Figure 10 gives this normal scale of M. D.'s for slopes up to 8°. A scale of M. D.'s is usually printed on the margin of maps, near the graphical scale. Having given the scale of the map to find what its V. I. would be on the normal system: Divide the number of inches to 1 mile into 60, and the quotient will be the required V. I in feet. The normal system is valuable both in sketching and map reading, be- cause the map distances which represent slopes up to 8° or 10° are soon learned and no time is lost in determining the slopes represented on the map, or the M. D.'s corresponding to observed slopes on the ground. Differences of Elevation 29 REPRESENTATION OF SLOPES. 29. Slopes are usually given in one of three ways: 1st in degrees, 2d in percentages; 8d, in gra- dients. 1st. A one degree slope means that the angle between the horizontal and the given line is 1 de- gree (1°). 2d. A slope is said to be 1, 2, 3, etc., percent, when 100 units horizontally correspond to a rise of 1, 2, 3, etc., of the same imits vertically. 3d. A slope is said to be one on one (1h-1), two on three (2-=-3), etc., when one horizontal unit corresponds to one vertical, three horizontal cor- respond to two vertical. The numerator usually refers to the vertical units. Degrees of slope are usually used in military matters; percentages are often used for roads, almost always for railroads; gradients are used for steep slopes, and usually for dimensions of trenches. Since 1° gives a rise of 1 foot at 60 feet (approximately), then 1° slope is equal to a gradient of 1 on 60 ( — ) . 2° to 2 on 60= — . S° to 3 on 60= — etc. These values 30 20 are useful for quickly giving an idea of the various degrees of slopes corresponding to gradients, and for converting one form of expression into another. 30 TABLE OF MOVEMENTS Gait. Distance. Reduction for Slopes. In yards horizontally per ten feet vertically* Maxfm Slope Practi- Yards per Minute. Miles per hour cable. Deg. Vert .2- Hor. Infan- try March 88 8 Up: 10 Down: 10 for slope above 10° 45 1-v-l Double 147 5 Down: 10 Up: 20 for slope above 10° 10 20 * Advancing by rushes 16 Advancing and firing 40 Cav- alry Walk 117 4 Up: 40 for slope above 5° Down : 60 for slope above 5° 25 20 y2 4 Trot 234 8 Up: Same as walk Down: Same as walk 15 10 Gallop 852 12 Up: Same as walk Down: Same as walk For slope above 8° 10 5 Charge 440 15 Up: Same as walk For slope above 8° Down: Same as walk For slope above 2° 5 5 Artil- lery Walk 117 4 Up: 10 Down: 60 For slope above 5° 10 10 * Trot S34 8 Up: 20 Down : 60 For slope above 8° 5 5 Gallop 852 12 Up: 80 Down : 60 For slope above 2° 5 A A "Example. Artillery travels 60 min. on hilly road, going up hill a total of 100 ft. (vertically) and down hill a total of 50 ft. Required actual distance 117 X 60 = 7020 yds., distance if road had been level, j^ X 10+ '" traveled X 60 = 400 yds. 7020 — 400 = 6620 yds. actually traveled. 50 Differences of Elevation 81 PROBLEMS. 31. 1. Construct a scale of M. D.'s for slopes from 1 to 3 degrees for a map whose V- I. is 20 feet, R. F. l-f-21120. Assume formula par. 26. Solution: M. D.= (1-t-21120) X20 ftX688 inches-T-l°=.65 inch. Divide .65 inch by I, 2, 8, giving M. D.'s for 1°, 2°, 3°. Lay these off as in figure 10. 2. Suppose you have a given slope between two contours, where the M. D. is 1 inch. How is the R. F. changed if, with the same V- I. and slope, the M. D. is 2 inches. Solution: V. I. and slope are constant, hence the M. D. varies directly with the R. F. The M. D. is doubled, hence the scale is doubled. 8. If on a given map a slope of 5° gives an M. D. of J inch, with a 10 foot V. I. what V. I. would give an M. D. of 1 inch to show the same slope. Solution: R. F. and S are constant, hence the V. I. varies directly as the M. D. which is doubled, hence the V. I. is 20 feet. 4. An M. D. of 2 inches, on a certain map represents a slope of 5°. How much must the scale of the map be altered for an M. D. of 5 inches to show 3° with the same V. I. as before? 2nd R. F. = 8/2 1st R. F. These problems may^be solved, by those familiar with the solution of equations, directly from the formula by substituting the quantities given direct- ly in formula par. 26. 5. What is the steepest slope of the ground be- tween 'V of the word Engineer and the bridge 82 Military Topography for Mobile Forces VIII east of Engineer HiU*? Ans.— 6°, between the 830 and 850 contours. Solution: Take off on edge of a piece of paper the distances between the contours on line "r" — VIII. Applying these to the scale of M. D's, on the map it is found that 6° is the greatest angle of slope. 6. What is the percentage of grade along Grant Avenue from 800 contour (north of XVII) north to the 8.50 contour*? Ans. 5j%. Solution: Take off the distance between the 800 and 850 con- tours on a piece of paper, and, applying this to the graphical scale on the map, it is found to be 300 yards (900 feet). There are five contour intervals between the two points, or a rise of 50 feet. In 900 feet horizontally there is a rise of 50 feet; in 100 feet, a rise of 50-T-9 feet^5.5H-feet, or the grade is 5j%. (See definition of slope in percentage, par. 29.) 7. How would you express the above slope as a gradient? 8. Construct a scale of M. D.'s for the map in figure 15. 9. What is the steepest slope in degrees on the line A-B south of the Chilton-Mt. Airy Lodge road (figure 15) ? What is the slope from B to the top of the first hill toward A (figure 15) ? 10. Is the slope from the top of Sentinel Hill down to the main road at Gauss a convex, a con- cave, or a uniform slope? (see figures 6, 7 and 8) 11. Lay off a road from XXVI to the top of Long Ridge with a uniform 2° slope. Solution: 'Leavenworth Map. DiFFEBENCES OF ELEVATION 88 Take the 2° M. D. on edge of piece of paper from scale of M. D.'s. Place one end of the 2° distance at XXVI (880) and note where the other end touches the 840 contour. From this point proceed as hefore to 850 contour, etc. Join up the points marked on the successive contours by a liae, which is the road with grade of 2°. Could more than one road with a 2° slope be laid off from XXVI to the hilltop? 12. Given the following information, draw 20 foot contours to show the features named, on the scale horizontally of 8 inches = 1 mile: A hill is a mile long and rises 200 feet high from a plane; one side is a concave slope ; another, convex ; at one point there is a vertical cliff 50 feet high. 18. With the same scale and V. I., show a hill with two peaks connected by a saddle from which a stream runs down the hill. 14. Model on a sand-pile the hill shown on Plate 2 and mark on the model the contours as shown in the plate. HACHURES. 82. A second method of representing, on a map, elevations on the ground, is by means of vertical hues called Hachures, figure 17. This method is not used in the United States, and most of the coun- tries of Europe have abandoned it. Germany, how- ever, still uses hachures for its small scale maps. Figui'e 17 shows a full size copy of the 1-f-lOOOOO map of Metz and vicinity accompanying Griepen- kerl's Letters on Applied Tactics, and it should be understood by every military student. By compar- 84 Military Topography for Mobile Forces ing the Metz l-r-lOOOOO map, figure 17, with the same area reduced from the I-t-25000 map, figure 16, on which contours are used, it will be seen that Fig. 16 the contours give not only the exact elevations, but a much clearer idea of the slope of the ground than the hachures. "^'VTiere no hachures are found on a hachured map, the ground is either a hill top or flat low land, and the slopes are roughly indicated by Differences of Elevation 85 the varying blackness and nearness of the hachures. The darker the section the steeper is the slope. It often happens that a flat area is only known to be a Fig. 17 hiU top or valley by reference to surrounding feat- ures. Usually, however, figures indicate the heights of important points. For reading maps of small scale a reading glass is of great assistance. CHAPTER III. DIRECTIONS ON MAPS. 33. Having given the means used for determin- ing horizontal distances and relative elevations rep- resented on a map, the next step is the determina- tion of horizontal directions. When these three facts are known of any point, its position is fully determined. The direction line from which other directions are measured is usually the true north and south line (known as the t7'ue meridian) ; or it is the line of the magnetic needle, called the Mag- netic Meridian. These two lines do not usually coin- cide, because at all points of the earth's surface the true meridian is the straight Une joining the obser- ver's station and the north pole of the earth whereas the direction of the magnetic meridian varies at dif- ferent points of the earth, at some places point- ing east, and at others west, of the true pole. At the present time the angle which the mag- netic needle makes with the true meridian (called Magnetic Declination) at Fort Leavenworth is 8° 23' east of north. It is important to know this relation, because maps usually show the true meridian, and an obsen'^er is generally supplied with a magnetic compass. Figure 11 shows the usual type of Box Compass furnished to officers. It has marked on its face the four cardinal points, N, E, S and W., and a circle which should be grad- 36 DiBECTIONS ON MaPS 87 uated in degrees to read from zero clockwise around to 360, i. e. an observation to the east being read 90°. METHODS OF ORIENTING A MAP. 34. In order that directions on the map and on the ground shall coincide, it is necessary for the map to be oriented, that is, the true meridian of the map must lie in the same direction as the true meridian through the observer's position on the ground. Ev- ery road, stream or other feature on the map will then be parallel to its true position on the ground, and all the objects shown on the map can be identi- fied and picked out on the ground. 1st Method. When the map has a magnetic meridian marked on it, as on the Leavenworth map. Place the sighting line of the compass, a h, figure 12 (i. e. the north and south line of the compass face) , on the magnetic meridian of the map and ro- tate the map horizontally, until the north end of the needle points towards the north of its circle, where- upon the map is oriented. 35. Where only the true meridian is on the map: Construct a magnetic meridian, figure 12, if the declination is known, as follows : Place the true meridian of the map directly under the magnetic needle of the compass, while it is pointing to zero, then, keeping the map fixed, rotate the north of the compass circle in the direction of the declination of the needle until the needle has passed over an angle equal to the declination. Draw a line on the map in the extension of the N-S line of the compass circle (a' 6'), and this will be a magnetic meridian- Plate f Fig. 11 //a/J true J/oi-th Fig. 12 'o^VK true, South Fig. 10 I ■• I '• i^-i«-,»-mBi M.D. DiBECTIONS ON MaFS 89 Having constructed the magnetic meridian on the map, orient it as under the 1st method. If the magnetic dechnation at the locaUty is not more than 4 or 5 degrees, the orientation will be given closely enough for map reading purposes by taking the true and magnetic meridians to be iden- tical. 2nd Method. When neither the magnetic nor the true meridian is on the map: (a) If you can locate on the map your position on the ground, and can identify another place on the map which you can see on the ground, join th«se two points on the map by a hne and hold the map so that this hne points toward the distant point seen on the ground, whereupon the map is oriented, (b) If you can place yourself on the line of any two points visible on the ground and plotted on the map, rotate the map until the line joining the two points on the map points toward the two points on the ground, whereupon the map is oriented. TO LOCATE ONE'S POSITION ON A MAP. 36. (1) When the map is oriented by com- pass (a)- Sight along a ruler at an object on the ground while keeping the ruler on the plotted posi- tion of this object on the map, and draw a hne to- ward your body. Do the same with respect to a second point visible on the ground and plotted on the map. The intersection of these two points is your map position. 40 MnjTAiiY Topography for Mobile Forces ( 2 ) When the map is oriented by the 2nd meth- od (b). Sight at some object not in the Une used for orientation, keeping the ruler on the plotted position of this object and draw a line until it cuts the direction line used for orienting the map. This is your position on the map. Any straight line on the map such as fence, road, etc., is useful for ori- enting and thus finding yoin* position. Usually your position may be found by characteristic land- marks, as cross roads, a crossing of raUroad and highway, a jimcture of streams, etc. 37. Having learned to orient a map and to find your position on it, you should secure a map of your vicinity and practice moving along roads at the same time keeping the map constantly oriented and noting exact features on the map as they are passed on the grormd. This practice is of the great- est value in learning to read a map accurately; to estimate distances, directions and slopes correctly. The scale must be constantly kept in mind during this work, to assist in identifying your position at all times. Check oflp on the map the prominent points passed, such as bridges, cross roads, hill tops, villages, etc., and be svu-e that you identify correctly all objects of the terrain in your vicinity. You will find it difficult at first to constantly judge your position correctly, and from time to time will "lose yourself." "\^Tien this occtu's try to pick up your position again by careful observation of landmarks, assisted by an estimate of the map distance you should have traveled, at your present rate, from some point passed at a known hour- DiBJECTIONS ON MaPS 41 TRUE MERIDIAN. 88. The approximate position of the true merid- ian may be found as follows: Point the hour hand of a watch toward the sun; the line drawn from the pivot to the point midway between the outer end of the hour hand and XII on the dial will point toward the south, figure 13. To point the hour hand exactly at the sun, stick a pin, or hold up a finger, as shown, figure 13, and bring the hour hand into the shadow. At night a line .drawn toward the north star from the observer's position is approxi- mately a true meridian. The "pointers" of the big dipper are very nearly in line with the north star. CONVENTIONAL SIGNS. 89. Having learned the means used to repre- sent horizontal distances, elevations, and directions on a map, it is next in order to study the method of representing the military features of cover, obsta- cles, communications and supply. They include various kinds of growths, water areas, and the works of man. These features are represented by Con- ventional Signs, in which an effort is usually made to imitate the general appearance of the objects as seen from a high point directly overhead. On account of this similarity of the object to its repre- sentation, the student will usually have no trouble in deciding at once the meaning of a new symbol. There is a constant tendency toward simplicity in the character of conventional signs, and very often simply the outline of an object, such as forests, cul- tivated ground, etc., is indicated with the name of Fiq.18 Trees ooooooo ooo o o o ao o o o o o O O O Orchanf q q OOP OOOOOOO Bamboo * »■ Cultivated ■t- f » < J { »' ■0 a.oV?'. . O o O Q' O O O O O <^ O CJ >:> Railroads Sin^fe TracM Double T*'ach I I I I I I I t I I I I I I I :gt=» Roads Improved Unimproved Trail t + + (■ t CemetBry Church Postofftce WatertvorMs WW. Fences Hedge Stone Worm Wire barbed Wire smoolh aii>»Mi>iBattis "IC V 'M' Wz-e Entanglem't^^^^^&^ Palisades Demolitions ^jpimim" ^'(fc. Depression C Ceo^ J '•''^^uMUJliiliiiiiipU^ DiBECTIONS ON MaFS 48 the growth printed within the outline. Such means are especially frequent in rapid sketches, on account of the saving of time thereby secured. By referring to the map of Fort Leavenworth furnished herewith the meaning of most of its symbols are at once evident from the names printed thereon; for example, that of a city, woods, roads, streams, etc. Where no conventional sign is used on any area, it is to be understood that growths thereon are not high enough to furnish any cover. As an exercise, pick out from the map the follow- ing details: Unimproved road, cemetery, railroad track, hedge, wire fence, orchard, streams, lake. The numbers at the various road crossings have no equivalent on the ground, but are placed on the map to facilitate descriptions of routes or positions (as in the issue of orders) . Often the numbers at road crossings on maps denote the elevations of those points. 40. Figure 18 shows the conventional signs pre- scribed by the War Department for surveys. The conventional signs in figure 19 are those used in German maps and are generally very sim- ilar to those used in the United States. Every of- ficer should be familiar with them to properly use the German War Game and Tactical Problem maps. In the following table are the English equiva- lents for words and abbreviations found on German maps. 44 Military Topography for Mobile Forces WEGE— ROADS. Bridlepath (in Gebesserter W e g — Improved road. Gebauter W e g — Constructed road. Chaustee — Highroad (macad- am). Daemme — Dams. Saumpfad — mountains). Fuiitveg — Path, Footpath. Feld-und Waldweg — Field and forest road. Gen. FerbindungSTveg — Gener- al connecting road. EISENBAHNEN— RAILROADS. Eisenbahn — Railroad. Strassenbahn — Street railroad. GEWAESSER— STREAMS, Water. ScA«7/— Reeds. Bake — Beacon, buoy. Tonne oder Boje — cask or bar- rel used for buoy. Strauchbesen — ^broom corn. Duene — sand dune. Nasse Graeben — ^wet (damp) ditch. Strom — Stream. BooUhafen — Boat-landing Eisenbahnbruecke — Railroad Bridge. Kanal — Canal. Schleusie — Canal lock. Trochene Graeben — Dry ditch. Muehle—MiW. Wehr — Weir, Dam. Steinerne BruecJce — Stone bridge. Hoelserne BruecJee — Wooden bridge. Furt — Ford. Flutt — Stream, creek, river. Bach — creek. Steg — Narrow foot bridge. Bruecke mit Steinpfeilern — Bridge with stone piers. Bruecke mit Holspfeilern — Bridge with wooden piers. Shiffbruecke — Pontoon bridge Wagenfaehre — ^Wagon ford, (or ferry for vehicles). Kahnfaehre — Ferry (for foot passengers). Fliegende Faehre — Flying fer- Leuchtturm — Lighthouse. Buhne — Pier (landing stage). GELAENDEBEDECKUNGEN— FEATURES OF THE TERRAIN. Laubhols — ^trees with leaves. Nadelholz — trees with needles. Gemischte* Hols — ^trees of both kinds (mixed woods). Trockene Wiete — Dry Mead- ow. Nasse Wiese — Wet Meadow. E in s el n e Baeume — Single trees. Bruch, Sumpf — Swamp. Waldboden — Woods. Heide — Prairie. DiBECTIONS ON MaPS 45 Stadt — City. Flecken — Town. Dor/'— Village. Gut — Manor, farm. Vormerh — detached farm. Gehoeft — Farm. S chlo s s und ParJcanlage — Chatean and park. Weinberg — ^Vineyard. Baumschule — Niirsery. Hopfengarten — Hop Orchard. Kirche, Kapelle, Kp. — Church, Chapel, Ch. Forsihaus — Forester's lodge. Wxndmuehle — Windmill. Wassermuehle — ^WatermiU. Mauer — ^Wall (stone). Knick — part wall, part fence. Zaun — Fence. Kirchhof — Churchyard, Ceme- tery. Friedkof fuer Juden — Jewish Cemetery. Ausgeseichn. B au m — Lone Tree. Warte, Thurm — Town. Bergtoerkshetr — Mine. Ruine — Ruin. Denkmal — Memorial (statue or anything else). Steinbruch, Stbr. — Quarry. Grube — Pit, hole. Felten — Rock. Alte Schanse — Old (abandon- ed) trench (rifle pit). Trignometrischer Hoehenpunkt — Triangulation Station. Reichs- und Landet Grense — Kingdom and state frontier. Regie r.-B e zirle Grense — Frontier of governmental districts. Kreis-Grenze — District fron- tier. ffohlroeg Wege Fl QI-9 Cela3id£l>edeclam|eii. — . FuSSTDtg Gob. VofimduTysmeg Tngwitj^a, Musemesc. Geb'essei'ter Ue^ Oumssee Danvnje. Eisenbalinen rst. ■•'5vis.*;.-Tr..-..T.--. SinabieBawnz Gebiisch "TcT^iicli STADT Hecken BarT . StrtuseniaJut' GewELsser ^lamuoSjB'SoJt Gtlidft, •_W\BcaimsAuU *^^^lIopfrijarlai EismhahjibTilcke ^mU.Sruckc t ♦ JSrc^ , KapeUe Kp. * "Wimbnuhh. ■rmtSuirpfeam^ ..-CL2dlandeserenj!e <^ ^JWie ' SchiffiriUke Waffoi^ahv "^\KaJinfahr& ^Izt^endeFdhrt CHAPTER IV. VISIBILITY. 41. The problem of visibility is based on the relations of contours and map distances previously discussed, and includes such matters as the deter- mination of whether one point can or cannot be seen from another; whether a certain line of march is concealed from the enemy; whether a particular area can be seen from a given point; whether slopes are convex, concave or uniform. On account of the inherent inaccuracy of all maps it is impossible to determine exactly how much ground is visible from any given point over a given obstructing area; that is, if a correct interpretation of the map shows a given point to be just barely visible, then it would be unsafe to say positively that on the ground this point could be seen or could not be seen. It is, however, of great importance for the student to be able to determine whether such and such a point is visible or not, within about one contour interval; or whether a given road is gen- erally visible to a certain scout, etc. In the solu- tion of visibility problems, it is essential to thor- oughly understand the meaning of profiles and their construction, consequently these matters will be ex- plained here. 42. A Profle is the line cut from the surface of the earth hy an imaginary vertical plane. The 47 48 MiLiTAEY Topography fob Mobile Fokces projection of this line to scale on a vertical plane is also called a profile. Figure 20 B shows a pro- file on the line H a f, figiu-e 20 A, in which the horizontal scale is the same as that of the map, and the vertical scale is 1 inch = 40 feet. It is customary to draw a profile with a greater vertical than horizontal scale, in order that the slope of hills on the profile may appear more clearly to the eye for purposes of comparison. Always note especial- ly the vertical scale in examining any profile; the horizontal scale is usually that of the map from which the profile is taken. A profile is constructed as follows, Plate 8: Draw a line D' y' equal in length to D ^ on the map.* Lay off on this line from D' distances equal to the horizontal distances of the successive contours from D toward y on the map. At each of these contour points drop a perpendicular down to the elevation of this particular contour, as shown by the vertical scale on the left. For example, a is on the contour 870 and the perpendicular is dropped down to a" (870). Join successively the ends of these verticals by a smooth curve, which is the re- quired profile of the ground on the line D y. Pro- file or cross section paper (lines ruled at right angles) simplifies the work of construction, but or- dinary paper may be used. 48. Examining the profile, and drawing from •The line D'y' may be aasumed to have an elevation as great the highest point, or as low as the lowest point in the profile, •o that the profile will be entirely telow or entirely a6o»e this line of reference. as VisiBiLiry 49 your eye at D lines tangent to the various hill tops, it is evident that looking along the line D y, you can see the ground as far as a; from a to 6 is hidden from view by the ridge at a; & to c is visible; c to d is hidden by the ridge at c. 1st Method By thus drawing a profile and Unes of sight tangent to the various hill tops the visibility of any one point from another given point may be deter- mined. The work may be much shortened by draw- ing the profile of only the observer's position (D) ; of the point of which the visibihty is in question (Bridge XX) ; and of the probable obstructing points, (a and c). It is evidently tmnecessary to construct the profile from D to x, because the con- cavity of the slope shows that there is no obstruction along this portion. The above method of deter- mining visibility by means of a profile is valuable practice for learning slopes of ground, and the forms corresponding to different contour spacings. 44. Examining the profile we obtain the fol- lowing important principles of visibility: (1) Con- tours closely spaced on the top of a hill^ gradually getting farther apart toward the hottom^ as D x^ show a concave slope, and all points of the inter- vening surface are visible from top and bottom. (2) Contours spaced far apart at top, growing gradually closer together toward the bottom, as a n, show a convex slope, and neither end of the slope is visible from the other. (8) Contours spaced equally distant apart, as 50 MiLITAKY TOPOGEAPHY FOR MoBILE FOBCES c f, indicate a plane surface, and all intervening points are visible from top to bottom of the slope. The profile is the basis of all methods of deter- mining visibility, but their construction is too slow for general use, except in acquiring skill in map reading. A simple and rapidly applied method is as follows : 45. 2nd Method. Examine the line D 2/ on the map, and by inspection determine the point or points which will be liable to obstruct the view to the desired point, the bridge XX. It can be seen at once from the three principles of contour spac- ing that the hills at a or c wiU be the only points to be considered. First determine whether a or c is the obstructing point. In order that a may be the obstructing point, c must lie below the line of sight from D tangent to a; that is, below z. It will be observed that for each distance D a (1.8 inches) the line of sight D' a" falls 90 feet (from contour 960 to contour 870). Applying a scale of inches (or folded piece of paper) from a toward f, figiu-e 20 A, it is seen that one-half of 1.8^.9 inches hori- zontally gives a drop of J X 90 feet=45 feet in the line of sight, X)' a", which is here at an elevation of 825, and at c (on the map) it is stiU further below c" (at 2) . Hence c is the obstructing point with re- spect to the bridge XX. In the same way, for the bridge XX to be visible over c, it must lie ahove the line of sight tangent to c. Applying the scale, D'