font ague, C.8 THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES ROBERT W. WEBB GEOLOGY DEPT., U.C.U The RALPH DJfcEED LIBRARY DEPARTMENT OF GEOLOGY UNIVERSITY OF CALIFORNIA LOS ANGELES, CALIF. ROBERT W. WEBB GEOLOGY DEPT., U.C.LA. All Naval and Military Books, whereso- ever Published, are kept in Stock, and can be supplied without delay, by EDWARD STANFORD, Naval and Military Publisher and Bookseller, 26 & 27, Cockspur Street, Charing Cross, London, S.W. CATALOGUE POST FREE. MILITARY TOPOGRAPHY ILLUSTRATED BY PRACTICAL EXAMPLES OF A PRACTICAL SUBJECT BY MAJOR-GENERAL W. E. , MONTAGUE, C,B, p. s. c. LATE GARRISON INSTRUCTOR; INTELLIGENCE DEPARTMENT, ETC. WILLIAM BLACKWOOD AND SONS EDINBURGH AND LONDON MDCCCXCIII All Riijhts reserved CONTENTS. INTRODUCTION PAET I. ELEMENTARY. 1. To find the distance from a hill, its height and angle of elevation being known 13 2. Example of resection . . . . . . 13 3. Example of intersection ; also to find the height of a hill, its distance arid angle of elevation being known ; also to fix the position of a point by its H E, one bearing being given . . . . . . 14 4. To find the height of an object, distance and angle of depression being known ...... 15 5. Method to be used when the scale is not normal . . 15 6. To fill in the contours where several valleys unite . 16 7. Plotting from a " section line," also to fix the position of a point, its H E and one bearing being given . 16 562963 6 CONTENTS. 8. " Form lines" used to mark a change in slope on a hill- side 17 9. Example of the principal terms used in Topography in connection with the ground 18 10. Intersection ; also to find heights, the H E and angle of elevation being given . . . . . . 18 PART II. THE FIELD-BOOK. 11. To sketch hilly country by a traverse . . . . 21 12. To plot a traverse line across hilly country ... 22 13. To plot from a field-book, and to find the R F of the sketch 23 14. To plot a winding road, and the hills on either side . 24 1 5. To plot a hill from contours noted in a field-book . . 25 16. To fix and traverse the initial contour of an isolated hill . . . 26 17. To plot a road winding up a valley, the scale not normal ......... 27 18. To plot a road crossing a hill and a valley ... 28 19. To plot the traverse of a road winding up a hillside . 29 20. To traverse and plot the initial contour of a hilly feature 30 21. To plot in the head of a valley from notes in a field- book 31 22. The use of " Reference Points " when plotting hilly country 32 CONTENTS, 7 PART III. FORM LINES. 23. " Section lines " to give the height of a hill, and " Form lines " to show the change of slope .... 33 24. Example of " Section lines " and " Form lines . . 34 25. " Form lines " showing small features which occur be- tween contours ....... 35 2G. To find the height of a hill by a " Section line," a good exercise in plotting in contours .... 36 PART R 7 . ADVANCED SKETCHES. 27. Intersection and resection ...... 37 28. To assume a datum, and find the R F on which the sketch is to be executed ...... 38 29. Intersection, resection, and use of the formula to find VI 38 30. Example in contouring 40 31. Conventional signs, and the value of the points of the compass 40 32. To fill in contours where several watercourses join . 41 33. Fixing a point by alignment 42 34. To calculate the height of a hill from the fall of a stream 44 35. To calculate heights when the angle of elevation is fractional. ........ 44 36. To fill in a sketch from scanty data .... 45 8 CONTENTS. 37. To survey an inaccessible position .... 46 38. To find the scale on which a portion of a combined sur- vey is to be executed 47 PART V. SECTIONS. 39. To draw the section of a hill . . . . ' . 51 40. To draw a section of a hill from notes taken carelessly . 52 41. To draw the plan of a hill from its section ... 53 NOTES TO DIAGRAMS . 55 INTRODUCTION. THE following exercises are intended to assist begin- ners in Military Topography to overcome the diffi- culty they constantly meet with on finding that the study of a most practical and out-of-doors subject is conducted at a table in a class-room, and that the ground, its slopes, its features, its hills, its valleys, and its streams, which they are told to depict, dis- appear in a mass of rules and formulae. In each of these exercises the student is introduced to a small portion of the ground, is given just so many data as will assist him to understand its features, and suffi- cient points to enable him to sketch it correctly. Each example is intended as a practical guide to some rule or formula, and to point out its use to the sketcher when on the actual ground. In the theoretical or indoor study of Military Topography a frequent cause of perplexity with beginners is to mix up the scale of the plan with 10 INTRODUCTION. the slopes of the ground, and it is not always easy to convince them that there is no connection between the two. No matter what the scale of our plan is the hard-and-fast mathematical truth remains that if we set out to pace down a slope of 1, we shall have to take fifty-seven paces before we are one pace lower than our starting-point, and that if the slope changes to 2 or 3, we shall have to complete one- half or one-third of the same fifty-seven paces before we have got down our one pace. The difficulty, no doubt, is owing to the use of the " normal system," in which the distance to be measured vertically between contours varies with the scale. To a man who has once mastered the subject, of course, no such difficulty can occur ; it is only with beginners it is possible, and it is mentioned here because these examples are intended for their benefit. It is also a trouble to beginners to find themselves so often face to face with that perfectly intractable 19.1, which appears to have jostled the original .",7.:; out of place. We know the change is made to save figures, but it is at the expense of sacrificing unity. Tme, we shall walk down our 1 slope for 19.1 yards before we shall find ourselves one foot below our starting-point, and the figures and the reason for their adoption are clear enough to the ordinary surveyor; but I have found that the original rule has far more hold on the student's mind, and that INTRODUCTION. 1 1 all difficulty is at an end when he is taught that in order to drop one unit vertically he must measure fifty-seven units horizontally down a slope of 1. In working out these examples do not be in a hurry, do not try to make a pretty picture and get the thing done ; in each example is wrapped up the application of one or more standard rules or for- mulae which it is important to learn and to under- stand. Above everything accuracy must not be sacrificed to pictorial effect; when the sketch is inspected the dividers will be applied to the various distances shown, and marks of approval will be in proportion to the difference between those on the sketch and those on the original. Another hint. Look out for your triangles ! Ee- member that the solution of most of the problems in Military Topography depends upon that of a right- angled triangle. First find out your triangle not always easy and this found look out which of the sides are given, and if there are two such, the third, representing the x of the puzzle, is easily forth- coming. Again, when following " section lines," or traverses in which changes of height occur, mark each change in order by the formula, by which the exact vertical height is found and a secure starting-point is gained for further progress. Do not be content to step the slopes up or down with the scale of horizontal equivalents on your protractor, that is well enough 1 2 INTRODUCTION. for adepts, or for rough out-of-door work when no examiner with his dividers will have the last word in the matter. In the following examples, those in Part I. deal with elementary problems in intersection, resection, the use of the formulae to ascertain heights and dis- tances, and plotting easy ground. Those in Part II. show how to plot the notes jotted down in the field- book, more especially when taken across uneven ground : the ordinary field-book problems are not given here as those in the text-books are always available. In Part III. " form lines " and " section lines " are worked out and their use fully explained. Part IV. takes the learner on to more advanced ground, the sketches being framed to include in each example most of the foregoing rules. Lastly, in Part V. two examples of sections are given, which are quite simple, but require considerable care to render with accuracy. The plans have been executed as they would have been had they been finished in the field, sufficient accuracy only being aimed at to enable the officer requiring them to read the configurations of the ground represented for military purposes. \V. E. MONTAGUE. 13 PART I. I. A, B, C, are hill-tops overlooking a lake which lies in their centre, and bearing from that central point respectively 15, 135, 255. Their summits are respectively 70 ft., 130 ft., 90 ft. above datum level ; the lake being 30 ft. above the same point. Slopes taken to each hill-top from the lake are 1|, 4, 2 respectively. Plot the above. Scale TTTT^IT. normal contours. II. A is a hill- top 100 ft. above datum level. B and C are under-features on a spur stretching S. from the main hill. A distance of 500 yds. 14 MILITARY TOPOGRAPHY. between A and B, and B and C ; each imder-feature is 40 ft. lower than the hill to the X. of it. D is another under-feature of the same height as B ; from it bearings were taken to B 300, to C 240. The col between A and B is 65 ft. below A ; those between B and C, and B and D, 45 ft. below 15. Plot the above at 6 in. to the mile, normal con- tours. III. A stream winds through a valley in a direction bearing 215 for a distance of 1000 yds., its average fall *V A, B, C, are hill-tops on either side. From the head of the stream the bearing of A is 245, the angle of elevation 4, slope concave ; and from the mouth of the stream it bears 357, the bearing of C being 60. From A the bearing of C is 120. From C the bearing of B is 33. The angle of elevation of B from the head of tin- stream is 4. C and B are each 40 ft. higher than the head of the stream. The col between B and C is 55 ft. above sea-level. Plot the above at 6 in. to the mile, normal con- tours. ELEMENTARY. 15 IV. A stream rises in a valley at a point 60 ft. above the sea, into which it flows in a direction due S. A and B are hill-tops W. and E. of the source of the stream, each 250 yds. distant from it, A being 40 ft. lower than B. The angle of depression from A to the sea, 670 yds. distant, is 4. From B a spur stretches southwards to the coast ; on it two under-features, connected by cols C and D, each one 40 ft. lower than the one to the N. The angle of depression from B to them 3. Plot the above at 6 in. to 1 mile, contours normal. V. A is a hill-top which sends a spur due S. to the sea. B is an under-feature on it, distant from A 382 yds., and 60 ft. above the sea-level. The angle of elevation from B to A is 3. The col which connects B with the main hill is 36 ft. below, and 180 yds. K of B. Contour the above, scale 12 in. to 1 mile, vertical intervals 12 ft. 16 MILITARY TOPOGRAPHY. VI. A, B, C are hill-tops. Two streams rise midway between A and C, and A and B, uniting at a point D, 300 yds. S. of A, and continue in that direction at a fall of T V. Bearings from A to B, 155. A C, 222. B .. C, through D, 280. Angles of elevation D to A, 6. D B, 6. D C, 4. The heads of the streams are 30 ft. below B and C. Contour the above at 12 in. to the mile, contours normal. VII. From the extremity of a cape projecting into the sea you pace due N. up a slope of 2 for a distance of 300 yds. to a small plateau 50 yds. across. You continue to pace down the northern slope of this knoll, still going N., the angle of depression the same as before, for 143 yds., and continue in the same direction on level ground till the hills A and ELEMENTARY. 17 B bear E. and W. of your position ; the angle of elevation to A being 4, to B 6 ; the latter is marked on the Ordnance map as 60 ft. above sea- level. From the centre of the knoll bearings were taken, to A 30, to B 327. Plot the above, scale 12 in. to the mile, normal contours. VIII. Being desirous to plot and contour an isolated hill you proceed to the summit, which is formed by a plateau stretching 300 yds. N. and S., and 150 yds. E. and W. The edge of this plateau you take as your initial contour, and from a central point on it lay out " section lines " A, B, C, bearing respectively 40, 160, 280. You then pace down each as follows : ( 238 yds. at 6 slope. Line A, { Atro II O II _ 5 it ** I ft Cl Ct AO II 4 (I normal contours : Forward angle A to B 60. Forward angle B to C 300. Forward angle C to D 180. Yds. Yds. Yds. Rise 6 . for 320 Level . for 50 Level . for 50 Level . ii 100 Fall 4 . 190 Fall 4 . n 95 Fall 5 . 228 Level . 20 Level . n 20 Level . n 20 Rise 2 . 191 Rise 4 . 285 Rise 5 . ,, 152 Level . .1 50 Level . ii 50 Level . n 50 22 MILITARY TOPOGRAPHY. xrr. 628 481 441 299 7.1 180" ffl) 330 310 238 198 158 50 90 (n) Fall 9; closing angle on (T) 270 evel. Rise 2. Fall 3'. Level. Level. Rise 8. Level. Level ; stream's source, fall -fa- Fall 7. Level. Level. Rise 7. Rise 5 s . Rise 3\ Rise. 2. Rise 2 ;. stream 150 yds. 90. Plot the above entries in a field-book; scale 12 inches to 1 mile, normal contours. THE FIELD-BOOK. 23 XIII. 140 to A 134" 800 360 150 125 260 100 49" (n) 560 150 136 (T) 50^ to A 180.- spur 203* slope 4'. A tract of hilly country three-quarters of a mile square is to be represented on a plan three inches square. The features are a plateau and a ridge stretching from it, both 250 feet above datum level; an under- feature, A, connected with the main hill by a col, a spur, and a valley in which is a stream. Angle of depression from the extremity of the ridge to A 2|, to the col 320 yds. distant, 6. The above traverse was made of the plateau and ridge commencing in the N.W. corner of the ground. Sketch the above to scale, normal contours. 24 XIV. MILITARY TOPOGRAPHY. 100 angle of elevation B 3 1800 1650 1300 700 360" angle of elevation D 2. 150'-: '4* Plot the above traverse of an unenclosed road winding through a valley between B, C, D, hill-tops, from sea-coast to sea-coast, the highest point upon it 45 feet above the sea. B is 20 feet higher than C, and D is 10 feet higher than B. Scale 6 inches to the mile, normal contours. THE FIELD BOOK. 25 XV. slope 3 608 417 341 150 33* 1310 1210 1019 637 382 7 -t 100) slope 7 Plot the above traverse of a footpath crossing an isolated hill. Scale TTTSW? normal contours. What are the angles of the slope between the contours ? What is the general gradient of the path in going up and coming down the hill ? 26 MILITARY TOPOGRAPHY. rl ^ = closes on f. ^ I 212, 3' ^100- 920 ^\ 750 ^ 600 stream 15 5 tnt. 29 300 -, H 220", 2 ^100- 150 294" Hill-top 360. 160*, angle 3" 350 .s^ 225 ^ F 128, 6 ^100 ^v. 218 v on' 4 ^ 800 ^ D 26, 3 <300 650 ^^ 450 stream 23 5* 350 300 150 i XKir -x 112 Plateau 180', 140*, angle 3*. ^ 400 B 330, 6 <^70 200 A tyre.* o ^ 57' Plateau 90*. 170+, an^le H. flU , i . Plot and contour the above notes in a field-book of an isolated hill 125 feet above datum level. The traverse shown is that of the initial contour, 100 feet above datum. Scale TSTVV, VI. 20 feet. THE FIELD-BOOK. 27 XVII. 32.3 215 337 C (Hi) 480 36" (it) 286 337 (l) Plot and contour the above entries in a field-book of a road winding up a valley to a pass between two hill-tops. Scale 12 inches to 1 mile, YI. 15 feet. 28 XVIII. MILITARY TOPOGRAPHY. [. 382 t * 59 1 286 % 270. 5 191 c^ 5 g River Avon 98.**-> 360" 2 286 M 301 a 127 li 308 jm fi ^- 250. Ridge 150 _; Ridge end 100. ^ ^r 270*. Ridge 30* | Ridge end 80. r @ 382 48 g 1 Plot and contour the above notes from a field-book of a road crossing a ridge, descending a valley, and rising the opposite hillside. Slopes of the ridge, on the South 3. ii it North 5 for 76 yards, then 4. East 5. Slope of the hillside North of the river 2. Scale nr8TTT> normal contours. XIX THE FIELD-BOOK. 29 1146 955 860 765 620 526 382 286 60 (T) Plot the above entries in a field-book of the tra- verse of a road winding from the coast up the side of a hill, general slope 1, and put in the contours at 10 ft. vertical interval on the right of the road ; normal scale. 30 MILITARY TOPOGRAPHY. XX. Coast 328*, slope T 133" 5 180. - 3T 270, slope 10" Plot the above entries in a field-book of the initial contour of a hill overlooking the sea, and fill in the contours to the sea-level on the south ; scale 4 inches to 1 mile, normal contours. THE FIELD-BOOK. 31 XXI. Crest Stream 380 + ; slope 5. 1020 Crest 200+ ^ 382 1 'c* Crest -i i7i 955 3 Crest 300+ o 382 Stream 157 ?- Crest 190*| 86' .2 3 S*v^ 1370 3 990 Crest 400* jj 890 Stream 100* *- h Crest 790 410 ^ . Crc-t 300 260 335" 30* s 3 10^ Plot the above entries in a field-book of a valley- head ; scale 6 inches to 1 mile, normal contours. 32 MILITARY TOPOGRAPHY. XXII. >., v 800 57 (v) ...<"*" % Reference Points, same level ^ (I) North bridge col between A and B^- ^^^^ ^ 1 *37* >**i * l^J/ 620 14 C * 570 360 570 327" f ^ mm mr ^__ ** 40* Angle of elevation to A 670 314" Plot the above entries in a field-book of a traverse line up a valley enclosed on the east by A and B, hill-tops, on the west by a long ridge. A river flows through the valley, its average fall 1, crossed by a bridge about 600 yds. from its mouth, and by another higher up. The traverse follows an unfenced road which crosses the river at the bridges. Scale normal contours. 33 PART III. FORM LINES. XXIIT. A, B, C are hill-tops on a ridge to the N. of and parallel with the sea-coast. Streams rise under A and in the cols on either side, and fall into the sea at the head of sandy bays. From a point S at the head of one of these bays, here 100 yds. across, the bearing of A is 360, distant 1020 yds. Bearings from A to B, 266 ; angle of depression, 1 ; distance, 760 yds. A to C, 78^ ; angle of depression, 1| ; distance, 760 yds. Cols between A and B, 420 yds. from A ; slope, 5. A C, 525 u it ii ; 4 e . c 34 MILITARY TOPOGRAPHY. General slopes to the sea south of B and of C, ." and 2 respectively. The central bay is about 600 yds. across at its entrance. The following " section lines " were taken : A to F, bearing, 202. A to D, 190 yds. ; slope, 5. D E, 1050 .. 1. E M F on the sea, 350 yds. ; slope, 3. A to G, bearing, 137 ; dist., 382 yds. ; slope, 3. f dist., 382 yds. ; slope, 1. 115 .. 2. H ii K oil the sea, bearing, 198; slope, 1. Scale, 6 in. to 1 mile, normal contours. G to H, bearing, 164 ; XXIV. A is a hill-top 90 ft. above sea-level, and from its summit " section lines " were taken to the coast, as follows : A B H, bearing, 180. A to B, 190 yds. ; slope, 3. B to H, slope, 2. A D E G, bearing, 135. A to D, 134 yds. ; slope, 6. D to E, 82 yds. ; slope, 7. E to G, slope, 8. A F K, bearing, 230. A to F, 115 yds. ; slope, 8. F to K, slope, 10. FORM LINES. 35 Plot and contour the above under the following O conditions : Scale of plan, 12 in. to 1 mile. Contours at 12 ft. vertical interval. Calculate the heights of E and F above high o o water. XXV. From the top of a spur the following section lines were taken : A 1. General slope, 5. A 2. A to B, 760 yds., slope, 4. B to C knoll, 380 yds., depression, 1 ; level, 50 yds., (300 yds., N. and S.) ; fall to C, 290 yds. ; C to D, 380 yds., slope, 4. A 3. A to B, 380 yds., slope, 2. B to C knoll, 255 yds., depression, f ; level, 200 yds. ; fall to C, 290 yds., depression 2 ; C to D, slope, 2|. A 4. A to B, 1275 yds., slope, 3. B to C, 380 yds., slope, 2. C to D knoll, 300 yds. ; level, 300 yds. ; fall to D, 5 for 135 yds. A 5. General slope, 5 for 1070 yds. The points D are on the datum level. Plot and contour the above, scale ^TI^TT* normal contours. Calculate the heights of the three knolls. 36 MILITARY TOPOGRAPHY. XXVI. A, B, C are hill-tops on an island. Bearing of B from A, 17 ; distance, 350 yds. Bearings of A and B respectively from C, 252, 305. Angle of depression from C to A, 3 ; to B, 2. From C a " section line " is taken due E. to the coast, as follows : C to D, 110 yds., 6 ; D to E, 180 yds, 4; E to F, 175 yds., 3. The coast-line is indented by bays stretching in- land to points midway between A and B, A and C, B and C. The head of the bay between A and 1'. is formed by a cliff 20 ft. high. The sea is 200 yds. north of B, and 100 yds. south of A. Slope north of C, 10 ; south of C, 8. Plot and contour the above at a scale of 12 in. to the mile, normal contours. 37 PART IV. ADVANCED SKETCHES. XXVII. A stream, after winding down a valley for about 2270 yds., joins the sea ; its average fall yy^ ; gen- eral direction, 153. A and C are hill-tops, B an under-feature of C. From the mouth of the stream, A bears 292, and from a point 40 ft. higher up 201. The bearings of C from A and from the stream's source are 24 and 85. From B the bearing of A is 240 ; of the stream's source, 309. The sea is 750 yds. south of A. From A the following angles were observed with the clinometer: to B, depression, 1; to a rock in 38 MILITARY TOPOGRAPHY. the sea marked on the chart as H mile distant, depression, 1 ; to C, elevation, 1. Plot and contour the above at a scale of 4 in. t<> the mile, normal contours. XXVIII. A tract of hilly country about 1800 yds. square. A lake,, about 150 yds. across, lies in the centre of three hills, ABC. A stream leaves it on the S.E., average fall, T V. From the centre of the lake A bears 314, B bears 70, C bears 225 ; and from the shore the distance to A is 900 yds., to B 800 yds., to C 1100 yds. The angle of elevation from the lake to A is 5, but the slope is only 3 for the first 380 yds. A is 100 ft. higher than B, which is 175 ft. lower than C. Between A and B, and A and C, are cols each 100 ft. higher than the lake. Plot the above to scale so that the distance be- tween the shore of the lake and the hill-top C shall occupy 2| in. on the plan. Contour the plan on the normal scale. XXIX. A lake, its shores irregular, thrusting themselves into the valleys between the six hills A, B, C, D, E, ADVANCED SKETCHES. 39 F, which enclose it ; cols, 25 ft. above the lake, con- necting the hills one with another. Distance from A to B, 600 yds. Bearing of Depression to lake. A to B, 50 5 from A (same level as D). A C, 106 C, 205 5 B, distant 190 yds. i D, 310 10 C (same level as B). B D, 255 5 D, distant 230 yds. E A, 186 8 E, 190 .. E F, 133 6 F, ,. 127 E B, 98 F A, 255 Plot and contour the above at the same scale as that of a combined survey of which it is to form a part. On arriving on the ground you find that you have lost your note-book in which the scale was entered. You can only call to mind that it was to be contoured on the normal scale. You are able to ascertain the position of five consecutive contours by marks left on the ground, the slope at that point being 5, and the distance between the whole of the marks on measurement you find to be 152 yds. 40 MILITARY TOPOGRAPHY. XXX. A stream rises under a hill A, which is 1250 yds. N. of an inlet of the sea into which the stream flows. A section line from A bearing 180 gives 288 yds., 6 slope; 480 yds., 4 slope. The remaining distance to the sea, 2 slope. B, an tinder-feature of A, bears from it 213 ; distance, 700 yds. ; angle of depression, 2. The col connecting it with A is 18 ft. below B. C is an under- feature of B, and bears from it 180 ; distance, 800 yds.; angle of depression, 1|. The col connecting it with B is 30 ft. above the sea. From C to the coast, due S., the slope is 7. From A a narrow ridge runs in a direction 140 for 600 yds., when it opens out into a plateau, covered with heath, its general direction 180 for 600 yds. ; it is 300 yds. across at its widest part. Slope from its southern crest to the sea, 10. Plot the above, scale 6 in. to 1 mile, and fill in the contours at 20 ft. vertical interval. xxx r. A stream flowing in a direction from N.N.W. joins the sea, having an average fall of ^ . At 1), where it ADVANCED SKETCHES. 41 enters the sea, it is 100 yds. wide, gradually narrow- ing to 50 yds. 300 yds. from its mouth. Here it is crossed by an iron bridge over which a road leads to the church at a gradient not exceeding 3 ; another road follows the right bank of the stream up the valley, a line of telegraph on one side of it. On the W. of the stream where it enters the sea is a small village. The coast W. is marshy, but rises E. of the stream into cliffs 40 ft. high. The church, on a hill A, bears from D 70 ; angle of depression to D, 4. A is an under-feature of B, a hill which bears from D 22 ; angle of elevation, 4. The col between A and B is 75 ft. below A. From a point 1340 yds. up the stream the bearing of B is 94 and of A 134. 500 yds. W. of this point is the head of another valley through which a stream flows to join the first stream at the village, average fall to D J^, the valley- sides covered with oak-trees. Plot the above at 6 in. to 1 mile, and fill in the contours at the normal intervals. XXXII. A hill A is due W. of another hill B, each 120 ft. above a small lake which lies between them. 42 MILITARY TOrOGUAPHY. A stream leaves the lake on the S., and continues its course due S. ; its average fall 5 V A point H on the stream marks where two smaller streams join it from the hills to the eastward, and bears from A 155, from B 204. From B a spur stretches in a direction 150 ; two under-features C and I) on it, connected by cols with 15 and with each other; a distance of 350 yds. between B and C, and C and D; angle of depression from B to both, 3. Streams rise below these cols and join the main stream at H. From the lake-shore the angles of elevation to A and B are 5 and 7. The slopes of A are gentle at first, becoming steeper as they ascend. Plot the above, scale 6 in. to 1 mile, and contour it according to the normal system. XXXIII. A lake, about 400 yds. E. and W. and 200 N. ami S., lies in the hollow of some hills, at a height of 90 ft. above datum level. A, B, E are hill-tops ; C and D extreme points of a ridge ; K a knoll, its summit circular, about 80 yds. across ; F and G streams which rise under the cols on either side of B and flow into the lake. Another stream leaves the lake on its southern side at a point ADVANCED SKETCHES. 43 M with a uniform full of yV, and a fourth stream quits the basin at H, flowing S.W. M is in the direct line between I) and K, 700 yds. distant from D. Searings f ram D, C, 360, distant 900 yds. E, 256. K, 282. A, 302. B, 321. F, 314. G, 346. Searings from A. H, 173. Bearings from C. E, 227. K, 239. A, 273. B, 275. G, 300. Bearings from K. E, 2. H, 240. Angles of elevation. K to B, 2. K A, 3. M E, 4. Angles of depression. K to M, 2. D .. M,4. B M Y, 2f. B M G, 2. E 11 H, 8 . Plot the above, at 6 in. to 1 mile, and put in the contours at 20 ft. vertical interval. 44 MILITARY TOPOGRAPHY. XXXIV. A stream rises at A midway between two hill-tops B and C, east and west of it, and each 100 ft. higher ; slopes from A to B and to C, 4. Two narrow spurs start from B and C, falling 1 .1 for a distance of 1000 yds. to F and E, and bearing respectively from B and C 140 and 160. The sea is 300 yds. S. of E, the coast rising in a cliff 40 ft. high. The sea is 600 yds. E. of I'.. The stream has an average fall of T V from A in a direction 157 for 500 yds., till it meets the northern slopes of the knoll D, where it divides, one half flowing S.E. into the sea a distance of about 1400 yds., falling in that length 50 ft.; the other half circling W. and S. round D till it loses itself in the marshy ground on the coast 200 yds. S. of D. From the summit of D the bearing of C is 317, of B 25 ; the angle of depression to the point where the stream divides, 5. Hot the above at a scale of T u!*ff> an d contour it on the normal system. XXXV. A stream rises on the S. of and 20 ft. below the crest of a small plateau 250 ft. above the sea-level, and flows down a valley in a direction bearing 210 ADVANCED SKETCHES. 45 for 730 yds. at an average fall of ^. Here a second stream joins it from the N. and W., the ground at this point marshy, and the two united flow round the slopes of the hill A till they join the sea about 400 yds. S.E. of that hill. From the point where the streams unite the bearings of two hills A and B are 126 and 278, A being 50 ft. and B 30 ft. higher than the ob- server's position. The bearing from the same point to the col between A and B is 215, distant 200 yds. ; angle of elevation, i. From this col the angles of elevation to A and B are 2 and 1 respectively. The sea is 325 yds. S. of A, and 360 yds. S. of B. At a point on the main stream 180 ft. above the sea an under-feature C bears 312, distant 400 yds. ; angle of elevation, |. The col between B and C is 20 ft. below B, and the col connecting the under-feature C with the plateau is 20 ft. below C. Plot the above at a scale of 6 in. to 1 mile, normal contours. XXXVI. B is an elevation at the head of a valley in which is a stream flowing easterly, and is 1000 yds. S. of a hill-top A. 46 MILITARY TOPOGRAPHY. C is an under-feature of A, the bearings from it to A and to B 73 and 139. The direction of the sea-coast is E. and W., and at a point S. of B is 220 yds. from that height. A stream rises in the valley between A and B, its source 80 ft. above the sea, bearing from A 141, from B 33, and flows S.W. till it enters the sea S. of C. From A and from B the angles of depression to the source of this stream are 2 and 1. From A the angle of depression to C is 1. 40 ft. below A is a spur forming a plateau about 400 yds. across ; in it is a lake, a stream leaving it on the E. and flowing down a valley in that direc- tion ; another stream rises under the col between A and C, and enters the sea at the same point as the main stream. Plot the above at a scale of 4 in. to 1 mile, and fill in the contours at the normal intervals. XXXVII. From the mainland you wish to make a survey of an island to which you cannot gain access because of a channel, called the " half-mile water," on account of its width. On an old chart, not drawn to scale, you find the ADVANCED SKETCHES. 47 heights given. Thus the hill from which you intend to conduct the survey is marked 300 ft. ; of the two peaks on the island, that on the N. is marked 90 ft., that on the S. 70 ft., the col connecting them 30 ft. In appearance the island consists of these peaks, the slopes to the sea on the W. steep, those on the E. very gentle, stretching out into two low points, which enclose between them a bay. The slope of the hill on which you stand is 10, the base a cliff about 100 ft. high. From the summit the following observations are taken : Bearings to Northern shore of island, 64. Southern n. n 118. N. peak n 75. S. peak 109. Col 91. Angles of depression to Eastern extremity of N. peak, 2|. n ii S. peak, 2f. Plot the above at a scale of 4 in. to 1 mile, and fill in the contours according to the normal scale. XXXVIII. An irregular ridge, indented on the S. by the heads of two valleys, lies to the N. of and parallel to 48 MILITARY TOPOGRAPHY. the sea-coast, which here stretches E. and "W ; the extremities of the ridge marked by cairns C and D. A and B, knolls below the ridge towards the coast, both the same height, angle of depression from B to the sea, 3. Two streams rise under the ridge at points 180 yds. and 380 yds. from C, and flow southwards, uniting towards the E. of A, and then falling S. again till they join the sea. General slope of the watersheds, 2. A line of telegraph, the poles 200 yds. apart, fol- lows the coast; two of these are marked X and Y, the former "W. of Y. Bearings. C to D, 95. A C, 333. B 0,350. B D, 50. Y to A, 360. Y B, 327. X A, 45. X B, 5. Angle of elevation from B to C, . The plan to be executed on the same scale as that of an old map of the same ground to which no scale was attached. On it, however, you find that the ADVANCED SKETCHES. 49 distance between A and B is 1.6". On arriving on the ground you find it impossible to measure this distance as you intended, owing to ,the broken nature of the hills. Hot the above on the required scale, and contour it on the normal system. 51 PART V. SECTIONS. xxxix. Draw a section of a hill from the following data Scale for horizontal distances, TITBIT- it vertical M T |- T . Vertical interval, 12 ft. A to B, rise of 4 in 200 yds. B C, rise of 6 ft. in 100 yds. C D, level for 80 yds. D E, rise of 38 ft. in 200 yds. E ,. F, fall of 15 ft. down a slope of 3. F G, rise of 18 ft. for 225 yds. G r, H, rise of 33 ft. for 150 yds. H I, fall down slope of 6 for 300 yds. I n K, level for 150 yds. K n L, rise of 25 ft., slope ^ T - 52 MILITARY TOPOGRAPHY. L to M, fall of 30 ft. for 75 yds. M it N, fall down slope of 2 for 220 yds. XL. You make the following notes of a detached hill of which you wish to take a careful section. Commencing on the W., the angle of elevation from datum level is 2. You pace up this slope till you come to where it changes to 4, but have for- gotten to count your paces, but a " reference point " on an adjacent hill gives your height at 78 ft. above datum. Before leaving the point where the slope changes you take the angle of elevation to the top of the hill and find it is 5. You now pace up the slope of 4 for 352 yds., when the slope again changes and continues at this fresh angle to the top of the hill, which you find by another " reference point " to be 200 ft. above datum. The summit is a small plateau about 50 yds. across, and the slope on the E. to the datum is uni- form at 6. Draw a section of the hill under the following conditions : Scale of horizontal distance, n vertical n Normal scale of contours. SECTIONS. 53 XLT. Draw a plan of the hill shown in section in the last example. On the N. the slope is uniform at 10 ; on the S. is a watercourse running in a direc- tion due S. from a point 20 ft. below the summit ; slope, 7 ; the slopes which enclose the valley in which it lies bearing about S.E. and S.W. at uniform slopes of 4. Scale the same as that of the section. 55 NOTES TO DIAGRAMS, i. SIMPLE exercise in finding the HE by the formula. The size of the lake is immaterial, as the slopes would be taken from its shore at points where the three bearings intersect it. II. Easy example of resection to fix the position of D. III. The height of the head of the stream being found by the fall given, that of A can be found, the distance and slope being also given. The position of B is found by calculating the HE between it and the head of the stream, and marking where this distance cuts the bearing taken to B from C. IV. An easy example of finding the heights, the slope and HE of one (A) being given. The cols should be taken at heights intermediate to contours. The fall of the stream and slope from D to the coast can be assumed. 56 MILITARY TOPOGliAI'IIV. V. The scale not being normal, it must be drawn on the sketch. VI. An exercise in finding the height of hills by the for- mula, and of plotting in contours where several valleys unite. VII. The point which the " section line " followed arrives at N of the knoll is 15 ft. above the sea. Find the II K of B from this level (slope and VI given), adjust your compasses to this distance, and when they cut the bearing of B from the knoll, being placed at right angles to the "section line," the position of B is fixed. The line thus fixing it being produced to the right iixes the position of A, when its height can be found by the formula. VIII. An example of "form lines" marking the change of slope on a " section line " that on A occurring at 2^ contours, on B at 2J contours, and on C at 3| contours from the highest contour. IX. An example of filling-in a small space with several conventional signs e.g., a plateau, a valley, a col, an under-feature, and a spur. To produce a satisfactory sketch the head of the valley must make a considerable indentation in the plateau at the named point. NOTES TO DIAGRAMS. 57 X. Easy exercise in plotting, and calculating the VI by the formula. None of the summits are on contours, so they may be indicated by " form lines." XL An easy example of traversing in a hilly country; the traverse should close on D. XII. The entries mark the contours on a "section line" up to the top of the hill at II, a " form line " marking one station. If the work is done carefully the final station will close on I. XIII. The scale is found by comparing the size of the plan with the area of the ground to be sketched, f of a mile is to be represented by 3 in. e.g., 4 in. to the mile. The plateau not falling on a contour must be indi- cated by a "form line." The lowest part of the ground shown will be 90 ft. above datum level. XIV. The positions of B and D are found by finding the HE from the points on the traverse line from which the angles of elevation are taken, setting the compasses to this distance and marking where they cut the bearings 58 MILITARY TOPOGRAPHY. from I. None of the points marked on the trim-in- line are on contours, so care must be taken to find the exact height of the spot whence the heights of U and J) are taken. The col between C and 3) is taken in tin- sketch at 45 ft. XV. An example of contouring a road, the sketcher noting a station at each contour. The slopes are 1, 1|, 1, 2, and 2, 2, 5, 2. The general gradient is found by calculating the height over the distance. XVI. The initial contour is taken 25 ft. below the highest point so as to show more exactly the general shape of the hill. It is traversed with great care and "section lines" taken down the principal features. XVII. The scale not being normal, a scale of slopes must be added to the plan. XVIII. An example of a road carried up a slope at a gradient less steep than the slope. The height of I station must be assumed at above 0, otherwise the river when crossed by the road will be a minus quantity. The shape and size of the ridge are only roughly shown by the bearings, and the contours W. of it lend themselves to several modes of rendering. NOTES TO DIAGRAMS. 59 XIX. The zigzag lines represent the windings of the road, the arrow-heads are " section lines " taken down the hill at right angles to the traverse line. First mark off the contours on the traverse line, the last will be 60 ft. The road in one instance only cuts one of these, so in calculating the slopes care must be taken to allow for the fraction of a contour from whence the " section line " starts. XX. The irregular line represents the initial contour, its height above the sea found by the distance and slope given from IV viz., 120 ft. The height of the knoll is found in the same manner. XXI. The crest line being drawn and its height determined by the rise from I, which can be assumed at any height above datum level, the lowest point of the stream is found from IV. XXII. An example of the use of " reference points." At III three points are found to be on the same level as the observer. The height of III is not known, but that of the N. bridge can be found by the fall of the stream to be 120 ft., and as that is one of the points on the observer's level, it follows that III is at 120 ft.; also the col between A and B, and station I. 60 MILITARY TOPOGRAPHY. XXIII. An example of " form lines " used to denote a change of slope. The height of A is found by working up fmm the sea at F ; the intermediate heights at E and D, also that of A, being found by the formula. The heights of G and H should be found in the same way. XXIV. Easy example of " form lines " marking a change of slope. The intermediate points B, I), E, and F should have their respective heights calculated by the formula ; the distance to the sea from B, E, and F can be found in the same manner. As the scale is not normal it must be added to the sketch. XXV. An example of " form lines " showing features inter- mediate between contours which otherwise would not appear. The height of A is obtained from section line A 5. XXVI. An exercise in " form lines " to indicate a change of slope. The height of C is found by the slopes and dis- tances given by the " section line," then the heights of A and B can be found. Care should be taken to show the indentations in the coast-line. NOTES TO DIAGRAMS. 61 XXVII. An example of intersection and resection. The height of A being found from the rock in the sea which is assumed to be ft., the other heights follow. XXVIII. The scale is found by making a length of 2| in. on the plan, equal to 1100 yds. on the ground. The lake must be assumed at a sufficient height above datum level to allow for the fall of the stream on the S.E. The size of the plan will be nearly 4 in. square. XXIX. An example of intersection and resection, the heights of the hills found by the formula. The lake is taken as datum. XXX. An example of " form lines " marking a change of slope, and of slightly more difficult contouring. The height of A is found by the " section line " to the sea. The cols should be placed so as to make the contours of the main valley fit in neatly. XXXI. An example of the use of conventional signs, and of calculating the value of the points of the compass in degrees. N.N.W. is the second point from N, each 62 MILITARY TOPOGIIAI'IIV. point being WOlth llj r ; the bearing <>f tin- sin-am lit- :$:57 from ]). The fall of the streams must lx: cal- culated from I ). XXXII. A more advanced example of filling in contours where several valleys meet. The larger the lake the nx in- distant will be the point H. The positions of A and 11 are found by calculating the HE from the lake-shore and marking this distance along the bearings from it. XXXIII. The bearing 282 taken through M gives the direction of D ; its distance is 700 yds. E. of M. The knoll K should be left till the surrounding contours fix its shape. XXXIV. The distance of B and C from A is found by the 1 1 !'.. slope and VI being given ; the height of A by calculat- ing the fall of the stream to the sea in the S.E. corner. The knoll D is found by resection, and requires care in filling in the contours. XXXV. The point where the streams unite must be carefully found and its height noted. The main stream rises two half contours below the plateau. An example of working with fractions of a degree. A good deal of the position of the contours is left to the draughtsman. KUbLKl W. VVbbD OGY DEPT NOTES TO DIAGRAMS. 63 XXXVI. The 90-foot contour forms the edge of the plateau, the position of the lake on it has always seemed to be the difficulty of the example. XXXVII. Aii example of surveying an inaccessible object. The western slopes of the island can be assumed, in the sketch 12 is taken. The eastern extremities of the island are found by calculating the HE from the top of the hill on the mainland. XXXVIII. To find the scale, make an independent triangulation of A and B from the base XY at any convenient scale ; this gives the distance between them in yards, when the RF can be found and the sketch made on that scale, begin- ning as before from the base XY. The heights of A and B are found by the slope from B to the sea. XXXIX. There is no difficulty in this problem, only care must be taken to mark the exact spot between contours where the vertical distances cut the uprights. The vertical scale is the GO on the Marquoise Scale. If properly worked out the slope ending at N" should be on the same level as A. The highest point is 122 ft. above datum level. 64 MILITARY TOPOGRAPHY. XL. The horizontal distance for the initial slope is found by the height, 78 ft., and the slope 2. From this point the distance to the top of the hill is found in the same way. The intermediate point, to which the slope is 4, is found by calculating its height, the horizontal distance and slope being given, and adding the result to tin- height of top of the first slope, 78 ft. The scale for vertical heights will be found to be 12| on the 50 Marquoise Scale. XLT. A datum line must be drawn of the same length as that of the section, the points on it which the contours cut being dotted off on a slip of paper and transferred to this datum line for the plan, care being taken to number them according to height. The slopes N. and S. of the summit can then be dotted in, and the contours traced round the central hill-top. It is merely to take a section of a plan reversed. I'Kl.NTKD BV WILLIAM IH.ArKWOOD ANFI SONS -.. Seal?. Toseo: VI. 20 feet. Scale, -nrhnr. W. 20feet. TEE. too rentes. VI. 20 feet iv: Scale wb: W. ZO feet. V. Scale.. 72*80- W. 12 feet. of Horizontal, 3' VI. Scale,. -TT&O VL 10 feet, Scale, s-iao: VI. W feet. Scale /3-zfor VI 3Ofi>?t IX. Scale, Tsfar. VI. 20 feet H VT 20 feet. xir. 7^ "to J Contours XIII Scale,, is a 40. VI. 30 fee>. .8 -5 Scale. JvAr VI. 20 feet. Scale,, ins-go Vf. Z0 feel.. Scale VI /(/>,.( 60 xrx: Scale. /7S4'f. VI. 3Ofiet XXI fe: VJ. 20 feet. 4 JKXLV. Scale. VI. IZfeet. JT .* 6* 7* ' IO Scale, of ff.E? Scale 3 inches to /mile,. VI W feet XKV: Scale s^ao VI. W feet. 230 60 VI. 30 feet Scale TSlhfo. VI. 3O feet,. XXIX. Scale -jihnr. VI. JO feet v 24-0 Scale Tojsa W. 20 feet. 160 Scale TTO n 20 feet. A. 22 Scale Ttrfea VI. 20 feet. 236 Scale. 7of6