UNIVERSITY OF CALIFORNIA 
 AT LOS ANGELES
 
 TELESCOPE COMPASS.
 
 A MANUAL 
 
 PLANE SURVEYING; 
 
 CONFINED TO 
 
 WORK WITH THE COMPASS. 
 
 WITH AN APPENDIX. 
 
 AMPLY ILLUSTRATED. 
 REVISED AND ENLARGED. 
 
 BY 
 
 THOMAS BAGOT, 
 
 SUPERINTENDENT OP RIPLEY COUNTY, INDIANA. 
 
 INDIANAPOLIS, INDIANA: 
 
 THE NORMAL PUBLISHING HOUSE. 
 
 J. E. SHERRILL, PROPRIETOR. 
 
 1889.
 
 Entered according to Act of Congress in the year 1881, 
 
 BY J. E. SHEERILL, 
 In the office of the Librarian of Congress at Washington. 
 
 CARLON A HOLLENBECK, 
 
 PRINTERS AND BINDERS, 
 
 INDIANAPOLIS.
 
 TA 
 
 I DEDICATE THIS BOOK TO MY MOTHER 
 
 THE AUTHOK. 
 
 356
 
 PREFACE. 
 
 EVERY person who studies Surveying from the text-books in gen- 
 eral use, and afterward is called upon to discharge the duties of a 
 surveyor, must, in the course of time, become aware of two things : 
 (1) that he has spent time in learning much that he has never 
 had, and probably never will have, occasion to use, and (2) that a 
 great deal he needs to know, and must know, is not to be found in 
 the books. 
 
 This is the case particularly under the Rectangular System, and 
 the author's experience has led him to believe that a necessity ex- 
 ists for a book dealing directly with the problems continually 
 coming up before surveyors throughout the country, and that such 
 a book will be cordially received by every person who wishes to 
 understand the subject as it is comprehended in general practice. 
 
 And this, dear reader, accounts for the existence of this little 
 book. You will find it simply a brief treatise on Compass-Sur- 
 veying, shorn of everything superfluous, and yet embracing all 
 that is necessary to a good understanding of the subject. Very 
 few geometrical or trigonometrical terms are employed, and all 
 the problems may be mastered by any person having a moderately 
 good knowledge of arithmetic. 
 
 The author does not claim that the book is above criticism, but, 
 on the contrary, he is well aware of the fact that a person disposed 
 to criticise may find in it an ample field in which to exercise his 
 talents. He trusts, however, that a search for its faults will re- 
 sult in disclosing enough merit, even among so much demerit, to 
 excuse him for writing it, and so trusting, he submits it to the 
 public. 
 
 NEW MARION, INDIANA, 
 May, 1883. 
 
 (4)
 
 CONTENTS. 
 
 CHAPTER I. INTRODUCTION. 
 No. of Art. 
 
 ( 1). Surveying defined. 
 ( 2). Branches. 
 
 1. Topographical surveying. 
 
 2. Geodetic surveying. 
 
 3. Plane surveying. 
 3). Measurements, how 
 
 1. Actual area nearly always greater than computed area. 
 
 2. Smooth surface conceived underneath. 
 
 3. Impossible in many instances to compute the area of 
 
 real surface. 
 ( 4). Corners defined. 
 ( 5). Surveying instruments used. 
 ( 6). Transit and compass. 
 
 1. Remarks on the transit. 
 
 2. Remarks on the compass. 
 7). Chain and pins. 
 
 ( 8). Chaining over hills. 
 
 ( 9). Flag-staff, drawing instruments, etc. 
 
 (10). Assistants needed. 
 
 CHAPTER II. DESCRIPTION OP THE COMPASS. 
 
 (11). The compass circle, how divided. 
 
 (12). Magnetic needle and center pin. 
 
 (13). Degrees, how marked. and 90 points. 
 
 (14). Compass box, plate, sights, etc. 
 
 (5)
 
 (15). Description of needle. Delicacy, how determine^. 
 
 (16). Horizontal angles, how measured. 
 
 (17). Letters "E" and " W" reversed on compass face. 
 
 (18). Eeason for this. 
 
 (19). Kule for reading bearings. 
 
 (20). Reverse bearing. 
 
 (21). Northerly and southerly bearings. 
 
 (22). Running lines east or west. 
 
 (23). Rules for measuring angles. 
 
 1. When both readings are in the same quadrant. 
 
 2. When one reading is in each of either the two north 
 
 quadrants or the two south quadrants. 
 
 3. When one reading is in each of either the two east quad- 
 
 rants or the two west quadrants. 
 
 4. When one bearing is in each of two opposite quadrants. 
 (24). Reasons for these rules. 
 
 (25). Glass cover to compass box. Electricity, how excited in it, 
 
 and how removed. 
 (26). Needle affected in other ways. 
 (27). Sight compass and telescope compass. Either may be either 
 
 a plain compass or a vernier compass. 
 (28). Description of the vernier. 
 (29). How used. 
 (30). Other kinds of verniers. 
 (31). Repairing the compass. 
 
 1. To re-magnetize the needle. 
 
 2. To sharpen the center pin. 
 
 3. To replace a spirit level. 
 
 4. To adjust a new sight. 
 
 5. To straighten the center pin. 
 
 6. To straighten the needle. 
 
 7. To put in a new glass. 
 
 8. To regulate the movement of the ball. 
 (32). The compass, how carried. 
 
 (33). Needle should be lifted from center pin when the compass is 
 
 not in use. 
 (34) Compass should be kept level when not in use, and the needle 
 
 allowed to assume its natural position. 
 (35). The telescope compass gradually growing in favor.
 
 CONTENTS. 7 
 
 CHAPTER III. THE VARIATION OF THE MAGNETIC NEEDLE. 
 
 (36). Meridian defined. 
 
 (37). The true meridian. 
 
 (38). Methods of determining the true meridian. 
 
 1. By a shadow. 
 
 2. By Polaris. 
 
 (a). Polaris and Alioth. 
 
 (b). Pole between them. 
 
 (c ). The plumb-line. 
 
 (d). Greater accuracy. 
 
 (e ). When upper culmination occurs during the day. 
 (39). Table showing time of culmination of Polaris. 
 (40). Magnetic meridian. 
 (41). East variation and west variation. 
 (42). Agonic line. 
 
 (43). Isogonic lines. [variation of the needle. 
 
 (44). The north magnetic pole; the effect of its movement on the 
 (45). Secular change of variation. 
 (46). Diurnal change and annual change. 
 (47). Table showing diurnal change by hours. 
 (48). Diurnal and annual changes usually disregarded in practice. 
 (49). Electric disturbances. 
 (50). The "dip" or inclination of the needle. 
 (51). Many magnetic phenomena imperfectly understood. 
 
 CHAPTER IV. EFFECT OF CHANGE OF VARIATION ON OLD 
 LINES, AND METHODS OF CORRECTING BEARINGS. 
 
 (52). Bearings of lines subject to constant change. 
 
 (53). Illustration. 
 
 (54). Effect of re-surveying lines without considering the change. 
 
 (55). Area of tract not affected. 
 
 (56). To determine the present bearing of a line. 
 
 1. Bearing at time of a previous survey. 
 
 2. Date of previous survey. 
 
 3. Annual amount of secular change. This may be de- 
 
 termined in various ways. 
 (1). By comparison of bearings. 
 (2). By establishing a true meridian. 
 (3). By interpolation.
 
 O CONTENTS. 
 
 (57). Table showing the variation of the needle at important sta- 
 tions. 
 
 (58). Table showing annual amount of secular change in certain 
 localities. 
 
 (59). Tables to be used in approximation. 
 
 (60). Determining variation for past times. 
 
 (61). Advantage of basing bearings on the true meridian. 
 
 (62). Magnetic meridian bearings subject to constant change. 
 
 (63). To determine the true bearing of a line from its magnetic 
 bearing. 
 
 1. When the variation is west. 
 
 2. When the variation is east. 
 (64). Bearings to be changed. 
 
 (65). When supplement is to be taken. 
 
 (65). Changing from the true meridian to the magnetic meridian. 
 
 CHAPTER V. METHOD OF RUNNING LINES. 
 
 (67). Finding a corner, etc. 
 
 (68). Determining position of corner from witnesses. 
 
 (69). Where trees are not available for witnesses, other things are 
 used. 
 
 (70). Method of describing witness trees. 
 
 (71). Starting the survey of a line. 
 
 (72). Course and distance of line must at least be known approxi- 
 mately before the line can be surveyed. 
 
 (73). Setting the compass and measuring the line. 
 
 (74). Setting off variation on the vernier. 
 
 1. When the variation is east. 
 
 2. W T hen the variation is west. 
 (75). Surveying the line. 
 
 (76). How chained. 
 (77). Pins, stakes, etc. 
 
 (78). Relative places on line of men engaged in the survey. 
 (79). Continuation of the line to the opposite corner. 
 (80). In case the line does not strike the corner. 
 (81). Illustration. 
 
 (82). Rules for correcting the stakes. 
 
 (83). Terminations of lines and starting point regarded as vertices 
 of an isosceles triangle.
 
 (84). Examples in moving (correcting) the stakes. 
 
 (85). Abbreviations used. 
 
 (86). Errors caused by imperfection of instruments, etc. 
 
 (87). Correction of assumed bearing. 
 
 (88). Rules for correcting bearings. 
 
 1st method. Derivation of rule. - 
 (1). Trigonometrical lines. 
 (2). Sine and cosine defined. 
 
 (3). Study of relation of sine and cosine important. 
 (4). Application of these lines. 
 (5). -When the angle is large. 
 2d method. 
 
 (1). Modification of first method. 
 (2). Illustration. 
 3d method. 
 4th method. 
 
 (89). Examples of lines whose bearings are to be corrected. 
 (90). Is amount of correction to be added or subtracted? 
 
 1. Rule for north-east and south-west courses. 
 
 2. Rule for north-west and south-east courses. 
 (91). Examples under these rules. 
 
 (92). Thus far, all bearings have been based on the true meridian. 
 (93). Bearings of lines based on the magnetic meridian. 
 
 1. Rule for correction. 
 
 2. Demonstration of the rule. 
 
 (94). Rule good while the needle moves westward. 
 
 (95). Bearings to be corrected. 
 
 (96). Abbreviations, etc. 
 
 (97). Completion of the survey. 
 
 (98). Assistants generally sworn. 
 
 (99). Instruments should be tested frequently. 
 
 (100). Backsights. 
 
 CHAPTER VI. UNITED STATES RECTANGULAR SURVEYING. 
 
 (101). Public lands, how divided. 
 
 (102). Townships, how divided. 
 
 (103). These provisions sufficient. 
 
 (104). Fundamental lines and initial point. 
 
 (105). Some imperishable mark chosen for the initial point.
 
 10 CONTENTS. 
 
 (106). Survey of range lines or meridians, etc. 
 
 (107). Survey of parallels, etc. 
 
 (108)". Convergence of meridians. Correction lines. 
 
 (109). Auxiliary meridians, etc. 
 
 (110). Survey of townships north of the base-line and east of the 
 
 principal meridian. 
 (111). Survey of townships north of the base-line and west of the 
 
 principal meridian, etc. 
 (112). Excesses and deficiencies. 
 (113). Congressional township and civil township. 
 (114). Survey of sections. 
 
 1. Preliminaries. 
 
 2. How to obtain bearings. 
 
 3. Sections, how numbered. 
 
 4. Survey of section 36. 
 
 5. Survey of the rest of eastern tier of sections. 
 
 6. Completion of the township. 
 
 (115). Full sections and fractional sections. The "double frac- 
 tional." 
 
 (116). Meander corners and meander lines. 
 
 (117). Making up the field-notes. 
 
 (118). Monuments adapted to the country surveyed. 
 
 (119). Work of Government deputy extends only to the division of 
 the township into sections. 
 
 (120). Advantages of the Rectangular system, etc. 
 
 CHAPTER VII. THE DIVISION AND SUBDIVISION OF THE 
 SECTION. 
 
 (121). Subsequent surveys must be made in accordance with the 
 
 original. 
 
 (122). The ideal section and the real section. 
 (123). The divisions and principal sub-divisions of the section. 
 (124). Names of these divisions and sub-divisions. 
 (125). Descriptions of land generally qualified by the words "more 
 
 or less." 
 (126). Corners, how named. 
 
 1. Section corners. 
 
 2. Quarter-section corners. 
 
 3. Half-quarter corners. 
 
 4. Fourth-quarter corners.
 
 CONTENTS. 11 
 
 (127). Section lines and center lines. 
 (128). Position of corners, how determined. 
 
 1. Section corners and exterior quarter-section corners. 
 
 2. Center corners, methods of setting. 
 
 (1). By crossing the center lines. 
 
 (2). By bisecting east and west center line. 
 
 3. Half-quarter corners. 
 
 4. Fourth-quarter corners. 
 
 5. Other corners. 
 
 (129). Examples in setting corners. 
 
 (130). Survey of the divisions and sub-divisions of the section: 
 
 1. Quarter section. 
 
 2. Half-quarter section. 
 
 3. Fourth-quarter section. 
 (131). General rule. 
 
 (132). When some of the boundary lines are known. 
 
 (133). Tracts to be surveyed. 
 
 (134). Independent corners, lines, and tracts. 
 
 (135). Illustration of independent corners, etc. 
 
 (136). Dependent corners, lines, and tracts. 
 
 (137). Dependent lines, etc., how surveyed. 
 
 (138). Examples of dependent tracts. 
 
 (139). Description by "metes and bounds." 
 
 (140). Rules for setting corners, etc., in full sections, generally 
 
 apply to fractional sections. 
 (141). When a tract of land lies partly in one section and partly 
 
 in another. 
 
 CHAPTER VIII. FIELD-NOTES. 
 
 (142). Field-notes of sectional survey by the Government deputy. 
 (143). Contents of full section, supposition regarding it, etc. 
 (144). Plot of township. 
 (145). Explanation of the plot. 
 (146). List of witnesses to corners. 
 
 1. Exterior corners. 
 
 2. Interior corners. 
 (147). Other particulars. 
 
 1. Area of fractional quarters. 
 
 2. Creeks, etc. 
 
 3. Offsets.
 
 12 CONTENTS. 
 
 (148). Surveyor needs copy of original field-notes. 
 (149). What surveyors' records should contain. 
 (150). Pocket record. 
 (151). Description of pocket record. 
 
 1. Left-hand page. 
 
 2. Right-hand page. 
 
 (152). Instructions regarding bearings. 
 (153). Representation of surveys on the plot. 
 (154). Approximating the bearing of a line. 
 (155). Illustration. 
 
 (156). Principles underlying the method. 
 (157). The field-book. 
 
 (158). Method of keeping the field-book in independent surveys. 
 (159). When new witnesses should be taken. 
 (160). Method of keeping the field-book in dependent surveys. 
 (161). Names of stations, witnesses, etc. 
 
 (162). Records by authorized surveyors taken as prima facie evi- 
 dence in favor of surveys recorded. 
 (163). Other methods of keeping field-notes. 
 
 CHAPTER IX. RE-LOCATION OF CORNERS. 
 
 (164). Trouble caused by lost corners. 
 
 (165). Nature of this trouble. Means of re-locating corners. 
 
 1. Remains of missing corner or witnesses. 
 
 2. By course and distance from some other corner. 
 
 3. By retracing old line by marks on trees, etc. 
 
 4. By projecting lines. 
 
 (1). Illustration of this method. 
 
 (2). The reverse of the method by which the corners 
 
 were established. 
 (3). Another illustration. 
 (4). Examples for practice. 
 
 5. A last resort. 
 
 (1). Setting S. } corner. 
 
 (2). 'May not agree in position with corner lost. 
 
 (S). A case illustrated. 
 
 (4). Lost section corner. 
 
 (5). Case of disagreement illustrated. 
 
 (6). When a quarter corner can not be found.
 
 CONTENTS. 13 
 
 (166). Re-locating original corners to the variable quarters of 
 
 fractional sections. 
 
 (167). To set a quarter corner between two fractional sections. 
 (168). To set an exterior corner to a fractional section, or to any 
 
 exterior section. 
 
 1. When there is an offset. 
 
 2. When there is no offset. 
 (169). Examples. 
 
 (170). He-location of subsequent corners, etc. 
 
 CHAPTER X. DESCRIPTIONS OF LAND. 
 
 (171). Necessity of a good description. 
 
 (172). Length of lines and area of tracts should be given in sur- 
 veyor's measure. 
 
 (173). Tables of equivalents. 
 
 (174). Examples for reduction. 
 
 (175). Fractions of a chain expressed in links. 
 
 (176). General rule for reduction. 
 
 (177). Area of tracts, how expressed. 
 
 (178). Description of independent tract. 
 
 (179). Examples of errors in descriptions. 
 
 (180). Examples for correction. 
 
 (181). Erroneous descriptions. 
 
 (182). Use the words " more or less." 
 
 (183). In describing dependent tracts the course and distance of 
 each boundary should generally be given. 
 
 (184). The description should state whether the bearings are based 
 on the true meridian or on the magnetic meridian. 
 
 (185). Lines running north, etc. 
 
 (186). Surveys generally made in accordance with the description. 
 
 CHAPTER XL OBSTACLES TO ALIGNMENT AND MEASUREMENT. 
 
 (187). Obstacles met on line. 
 
 (188). Two classes of obstacles. 
 
 (189). Methods of spanning obstacles of first class. 
 
 1. By perpendiculars. 
 
 2. By an equilateral triangle. 
 
 3. By a right-angled triangle. [urement. 
 
 (1). When an obstacle both to alignment and meas- 
 (2). When an obstacle to measurement alone.
 
 14 COXTENTS. 
 
 4. By symmetrical triangles. 
 
 5. When a fence is built on or near the line. 
 
 (1). When offset line terminates on the opposite side. 
 
 (2). When the offset line terminates on the same side. 
 
 (a). When the distance missed is greater than 
 
 the offset. 
 
 (b). When the offset is greater than the distance 
 missed. 
 
 6. Surveying over hills. 
 
 (190). Methods of spanning obstacles of the second class. 
 
 1. By a right-angled triangle. 
 
 2. By symmetrical triangles. 
 
 3. By similar triangles. 
 (191). Other methods, etc. 
 
 CHAPTER XII. COMPUTATION OP AREA. 
 
 (192). Advantage of expressing dimensions of tracts in chains and 
 
 links. 
 
 (193). Special rules deduced. 
 (194). Examples in computation. 
 (195). Every tract of land a polygon in shape. 
 (196). Rectangles. 
 (197). Parallelograms. 
 (198). Trapezoids. 
 (199). Triangles. 
 
 1. With base and altitude given. 
 
 2. With no altitude given. 
 (200). Trapeziums. 
 
 (201). Any figure. 
 
 (202). Computation of area by latitudes and departures. 
 
 (203). Latitude and departure, as applied to courses, defined. 
 
 (204). North and south latitudes, and east and west longitudes. 
 
 (205). Signs of latitudes and departures. 
 
 (206). Relation of sine and cosine to departure and latitude. 
 
 (207). Table of natural sines and cosines explained. 
 
 (208). Examples in computing latitudes and departures. 
 
 (209). Columns marked differently at top and bottom. 
 
 (210). Traverse tables.
 
 CONTENTS. 16 
 
 (211). Sum of latitudes and sum of departures in every cor- 
 rect survey. 
 
 (212). A trial survey. 
 
 (213). Explanation. 
 
 (214). When a discrepancy exists. 
 
 (215). Initial line or meridian. 
 
 (216). Difference between longitudes and departures. 
 
 (217). How to determine the longitude of a course. 
 
 (218). Algebraic sum must be used. 
 
 (219). Simplification of the rule. 
 
 (220). Computation of area by longitudes. 
 
 (221). North products and south products. 
 
 (222). Double longitudes. 
 
 (223). Method of keeping the data. 
 
 (224). General rule for computing areas by double longitudes. 
 
 (225). To determine the most westerly corner. 
 
 (226). Examples in computation. 
 
 (227). Courses without departures, etc. 
 
 (228). Not absolutely necessary that the meridian be drawn 
 through the most westerly station. 
 
 CHAPTER XIII. LAYING OUT AND DIVIDING UP LAND. 
 
 (229). No general rule can be given. 
 
 (230). What are known in problems to be considered. 
 
 (231). To lay out a square. 
 
 (232). To lay out a rectangle. 
 
 (233). To lay out a parallelogram. 
 
 (234). To lay out a right-angled triangle. 
 
 (235). To lay out a trapezoid. 
 
 (236). To lay off any figure. 
 
 (237). Things to be considered in making partition. 
 
 (238). Nature of problems chosen. 
 
 (239). To divide a rectangle into equal parts. 
 
 (240). To divide a rectangle into unequal parts. 
 
 (241). Problems. 
 
 CHAPTER XIV. SURVEYING TOWN LOTS. 
 
 (242). Description of town lots, blocks, etc. 
 (243). Survey of town, how based.
 
 16 CONTENTS. 
 
 (244). Usual shape of lots, etc. 
 
 (245). What the plot of a town should show. 
 
 (246). Particulars respecting Figure 58. 
 
 (247). Illustration of a town in which the lots vary in size. 
 
 (248). Method of surveying lot number 11 in the figure. 
 
 (249). Examples for practice. 
 
 (250). Chain or tape used in surveying should be tested frequently. 
 
 CHAPTER XV. PLOTTING. 
 
 (251). Plotting defined. 
 (252). Instruments used. 
 
 1. Drawing board. 
 
 2. T-square. 
 
 3. Euler. 
 
 4. Drawing pen. 
 
 5. Dividers or compasses. 
 
 6. Protractor. 
 
 7. Diagonal scale of equal parts. 
 
 (253). Units of the scale may have various equivalents. 
 
 (254). Plotting bearings. 
 
 (2551. Examples for practice. 
 
 (256). Plotting rectangular tracts. 
 
 (257). Plotting tracts in general. 
 
 (258). A particular case. When a survey does not "close." 
 
 (259). The pantograph. 
 
 (260). Locating objects on the plot. 
 
 (261). Coloring plots and maps. 
 
 CHAPTER XVI. SURVEYING WITHOUT A COMPASS. 
 
 (262). The compass nearly always necessary. 
 
 (263). Setting corners. 
 
 (264). Establishing lines. 
 
 (265). Setting out perpendiculars. 
 
 (266). Survey of rectangular tracts. 
 
 (267). Measurements. 
 
 APPENDIX. 
 Land Decisions. 
 Table of natural sines and cosines.
 
 MANUAL 
 
 PLANE SURVEYING. 
 
 CHAPTER I. 
 
 INTRODUCTION. 
 
 ART. ( 1 ). SURVEYING is that branch of applied mathematics 
 which embraces operations for finding, (1) the relative positions 
 of points on the earth's surace, (2) the area of any portion of its 
 surface, and (3) the contour or shape of any part of its surface, so 
 that it may be represented in maps and plots. 
 
 ( 2 ). It is divided into three branches : 
 
 1. Topographical Surveying, or Topography, includes operations for 
 determining the contour of portions of the earth's surface and re- 
 presenting it on paper. 
 
 2. Geodetic Surveying, or Geodesy, takes into consideration the 
 curvature of the earth's surface and is employed in extensive sur- 
 veys. 
 
 3. Plane Surveying does not regard the curvature" of the earth's 
 surface and all lines are measured as on a plane. It is used in lo- 
 cal work. 
 
 (3). All measurements in surveying are made as nearly hori- 
 zontally as possible, and the area of a tract of land is not its ac- 
 tual surface measure, unless the tract be perfectly level, but the 
 amount of land enclosed by its boundaries measured horizontally, 
 instead of with the inclinations of the surface over which they run. 
 2 (17)
 
 18 MANUAL OF PLANE SURVEYING. 
 
 1. The actual area, therefore, is nearly always greater than the 
 computed area, and increases in proportion to the inequality of 
 the surface. 
 
 2. We may conceive a smooth surface at the level of the ocean 
 underlying the surface of the land; then the area of a tract of 
 land is equal to the contents of a figure formed by projecting the 
 boundaries of the tract on the horizontal surface below. 
 
 3. Were the real surface considered, it would be impossible in 
 many instances either to compute its area or represent its figure 
 on paper. 
 
 ( 4 ). The extremities of lines in surveying are called corners, 
 and each corner marks the vertex of an angle formed by the meet- 
 ing of two lines. The corner is a mathematical point, and may 
 or may not be marked with a monument. 
 
 ( 5 ). Lines are surveyed either with a solar or a magnetic in- 
 strument. With the former, where more precision than expedi- 
 tion is required ; and with the latter, where expedition is of more 
 importance than precision. 
 
 ( 6 ). The principal magnetic instruments in use are the transit 
 and compass. 
 
 1. The transit is provided with a telescope, and at the present 
 time is so constructed as to be adapted to the measurement of 
 both horizontal and vertical angles. It serves many important 
 purposes independent of the assistance of the magnetic needle, and 
 is not strictly a magnetic instrument. 
 
 2, The compass is either supplied with sights or a telescope, 
 and is strictly a magnetic instrument. It is not usually adapted 
 to measuring vertical angles. The lightness, simplicity, and con- 
 venience of the compass have brought it into almost general use 
 in common surveying, and the following chapter is devoted to a 
 description of it. The transit may be found described in almost 
 any comprehensive work on Surveying. 
 
 ( 7 ). Measurements of lines in surveying are made with an 
 iron or steel chain* usually 33 feet or 2 rods long and divided 
 into 50 links. It has a handle at each end by which it is carried 
 during the survey, and the successive chain-lengths are maked 
 
 *For convenience in counting the links, this chain is divided into five 
 parts of ten links each by four brass or copper tags. The real chain is 100 
 links or 66 feet in length, and called a Gunter's chain, from its inventor. 
 Ihe half-chain of 50 links is used for convenience. A link is 7.92 inches in 
 length. In Government surveys, a chain 66.06 feet in length is used. The 
 M foot being added to make up for " slack," etc.
 
 MANUAL OF PLANE SURVEYING. 19 
 
 with pins of iron or steel wire, generally 10 or 12 inches in length, 
 sharpened at one end and bent into the form of a ring at the'other. 
 
 In the ring is sometimes tied a bright ribbon or piece of cloth to 
 render the pin more conspicuous, in order that it may be easily 
 found by the person who carries the rear end of the chain, and 
 such colors should always be chosen as will contrast most with 
 the surface to be surveyed. 
 
 ( 8 ). In chaining up and down hill, the chain must be kept taut 
 and horizontal, as on a level surface. In order to do this, it is 
 sometimes necessary to drop the pin from the front end of the chain, 
 or elevate the rear end of the chain to a point exactly over the 
 pin that sticks in the ground. 
 
 (9). A straight staff, about 1 inches in diameter and 8 or 10 
 feet high, surmounted by a small flag of brilliant color, is used in 
 alignment; and a good set of drawing instruments, drawing board, 
 t-square, triangle, protractor, ruler, etc., are necessary in drawing 
 and plotting. 
 
 (10). In field-work the surveyor generally needs four assist- 
 ants ; two chain-men, one flag-man, and a marker. The first two 
 measure the line with the chain, the third carries the flag, and 
 the fourth assists the chain-men by marking the line with stakes 
 at the proper distances. To this force it is sometimes necessary 
 to add one or more ax-men, as bushes may have to be cut out of 
 the way and trees marked. 
 
 QUESTIONS ON CHAPTER I. 
 
 1. Define Surveying. 
 
 2. Into what three branches is it divided? 
 
 3. What does each branch embrace ? 
 
 4. How are measurements made in surveying? 
 
 5. Why is the actual area of a tract of land nearly always 
 
 greater than its computed area? 
 
 6. What is a corner? 
 
 7. Name the two kinds of instruments used in surveying. 
 
 8. Name the principal magnetic instruments. 
 
 9. Describe the transit. The compass. 
 
 10. How are lines measured in surveying? 
 
 11. How should the chain be held in chaining over hills? 
 
 12. How many assistants does the surveyor usually need?
 
 CHAPTER II. 
 
 DESCRIPTION OF THE COMPAS& 
 
 (11). The compass consists essentially of the compass circle, 
 the magnetic needle, and the sights. The circle has its circum- 
 ference raised and divided into 360 equal parts or degrees, and 
 these are usually subdivided to half or quarter degrees. 
 
 ( 12 ). At the center of the compass circle" is placed a perpen- 
 dicular pin, called the center pin. Upon this pin the magnetic 
 needle is balanced in such a way as to mark opposite points of tht 
 divided circumference of the circle. 
 
 ( 13 ). The degrees on the circumference are marked from twa 
 opposite points, called points, up to 90 to the right and left. 
 The 90 points are, therefore, opposite one another also. One of 
 the points is called the north point, and the other the south 
 point, and one of the 90 points is called the east point, and the 
 other the west point. 
 
 ( 14). The compass circle is enclosed in what is known as the 
 compass box, and this rests upon the compass plate. The box is 
 usually between 5 and 7 inches in diameter, and the plate about 
 14 or 16 inches long. At the ends of the plate perpendicular 
 sights are placed. These sights have slits in them, and are so 
 placed that the line of sight from one of them to the other will 
 strike opposite points of the graduated circumference of the com- 
 pass circle. Between the compass box and the sights are usually 
 placed two spirit levels, one at right angles to the other. These 
 are used in leveling the compass. The compass rests upon a tri- 
 pod or Jacob's staff', at the head of which is a ball and socket 
 joint, enabling a person to move the compass as he may wish. 
 
 (15). The needle is a magnetized steel bar, very delicately 
 
 (20)
 
 MANUAL OF PLANE SURVEYING. 21 
 
 balanced upon the point of the center pin, and it is a little shorter 
 than the diameter of the compass circle. The delicacy of the 
 needle is determined by the number of horizontal vibrations it 
 will make before coming to rest after being disturbed. Needles 
 5 or 5 2 inches in length are generally preferred by surveyors to 
 longer or shorter ones. 
 
 ( 16 ). Horizontal angles are measured with the compass by 
 turning the sights from one line of the angle to the other and 
 noting the number of degrees passed over by the end of the needle. 
 The sights are sometimes arranged for the measurement of verti- 
 cal angles also. 
 
 ( 17 ). The letters "E" and " W" are reversed on the compass 
 face, but it will be plainly seen that the arrangement enables the 
 surveyer to take the direction (bearing) of a line more readily 
 from the compass face, and reduces the liability to err in the 
 reading. 
 
 ( 18 ). This may be illustrated by Fig. 1. 
 
 FIG. 1. 
 
 Suppose the sights set in the direction of the points of the 
 circle, and that the compass be turned until the north end of the 
 needle marks the point midway between the north point (gener-
 
 22 MANUAL OF PLANE SURVEYING. 
 
 ally marked with afleur de Its, instead of the letter N) and E, or 
 to 45. The sights have moved in the direction of the second 
 hand of a watch, and the bearing of the line marked by them is 
 N 45 E, which is read directly from the north end of the needle. 
 
 ( 19 ). The following is the general rule for all readings: 
 
 Note the letters between which the end of the needle comes, and 
 to what number. Then name the letter N or S (as the case may 
 be) that is the nearer to the end of the needle from which you are 
 reading, next the number of degrees to which the needle points, 
 and lastly the letter E or W that is the nearer to the same end of 
 the needle. 
 
 ( 20 ). If the preceding reading had been taken from the south 
 end of the needle, the bearing would have been S 45 W, the re- 
 verse of X 45 E, but equivalent to it, and indicating the bearing 
 taken from the opposite end of the line. S 45 W is called a 
 southerly bearing, and N 45 E is called a northerly bearing. 
 
 (21). No matter how the lines run, the same end of the com- 
 pass (the north end is preferred) should be kept in front. 
 
 (22). In running lines east, the E point of the compass circle 
 will be turned toward the north, and in running west, the W 
 point will be turned north. All bearings should be read from the 
 north end of the needle. 
 
 (23 ). In measuring angles observe the following rules: 
 
 1. When both readings are in the same quadrant, as between 
 N and E, N and W, S and E, or S and W, the angle is equal to 
 the difference between the two readings. Thus, the angle between 
 N 56 E and N. 43 E is equal to 13. 
 
 2. When one reading is in each of either the two north quad- 
 rants or the two south quadrants, the included angle is equal to 
 the sum of the two readings. Thus, the included angle of N 35 
 E and N 23 W is equal to 35 + 23 = 58. 
 
 3. When one reading is in each of either the two east quadrants 
 or the two west quadrants, the included angle is equal to the sum 
 of the readings subtracted from 180. Thus, the angle included 
 between N 50 E and S 37 E is equal to 180 (50 + 37) = 93. 
 
 4. When one reading is in each of two opposite quadrants, the 
 angle is equal to the difference of the readings subtracted from
 
 MANUAL OF PLANE SURVEYING. 
 
 180. Thus, the included angle of N 16 E and S 12 W is equal 
 to 180 (16 12) = 176. 
 
 ( 24:). The reasons for these rules will be seen in Fig. 2. 
 
 FIG. 2. 
 
 The angle included between the courses A B and A C is equal 
 to 59 28 = 31, as both readings are in the same quadrant. 
 
 The angle included between the courses A B and A D is equal 
 to 28 + 36 = 64, because one reading is in each of the two 
 north quadrants. 
 
 The angle included between the courses A C and A F is equal 
 to 180 (59 + 33) = 88, because one is in each of the two 
 east quadrants. 
 
 The angle included between the courses A D and A F is equal 
 to 180 (36 33) = 177, because the courses are in opposite 
 quadrants. 
 
 ( 25 ). The compass box is protected by a glass covering over 
 which fits a brass lid. Care should be taken while the brass lid 
 is off that no electricity be excited in the glass by the friction of 
 the hand or a cloth upon its surface, as it interferes with the work-
 
 24 MANUAL OF PLANE SURVEYING. 
 
 ing of the needle and may cause a serious error. However, when 
 the fluid does exist, it may be removed by breathing on the glass 
 or touching it in various places with the moistened finger. 
 
 ( 26 ). The action of the needle is also affected by pieces of iron 
 or steel brought or kept near it. This materially interferes with 
 its use at sea, particularly on iron ships. While surveying, noth- 
 ing having a tendency to affect the action of the needle should be 
 carried upon the person or allowed near the compass. 
 
 ( 27 ). Two kinds of compasses are in use the sight compass 
 and the telescope compass. Each of these may be either a plain 
 compass or a vernier compass. The plain compass is not very ex- 
 tensively used, as all readings are made from its face alone, and 
 can not be depended on for precision. In the plain compass, the 
 line of sight lies in the direction of the points of the compass 
 circle. The vernier compass differs from the plain compass in 
 having its compass circle, to which a " vernier" is attached, mov- 
 able, generally through a short arc, about its center, thus enabling 
 the surveyor to set the zeros or points of the circle at an angle 
 with the line of sight. This angle is read from the vernier. The 
 movement of the circle is effected by means of a thumb-screw that 
 gives it a slow motion. When the required angle is set off, the 
 vernier is clamped to the plate of the compass and the readings 
 taken. The vernier enables a surveyor to take a certain class 
 of readings "closer "or with greater precision than is possible 
 without it, as it gives him the advantage of a double index ; 
 yet readings down to a very small angle, say V or 30", are 
 hardly ever trustworthy, owing to the difficulty a surveyor meets in 
 setting the needle to exactity. The fault, however, is not in 
 the vernier. 
 
 ( 28 ). The VERNIER* consists of an arc divided into a certain 
 number of equal parts, and moving within another arc whose di- 
 visions are somewhat larger or smaller than its own. The first 
 arc (vernier), as stated before, is attached to the compass circle 
 and moves with it around a common center ; the second arc is 
 called the " limb," and is generally on the brass plate of the com- 
 pass upon which the circle moves, so that the outer edge of the 
 vernier coincides with the inner edge of the limb. 
 
 *The vernier is so called from its inventor, and on this account the word 
 is sometimes written with an initial capital. It was first applied to the 
 compass by David Rittenhouse of Philadelphia.
 
 MANUAL OF PLANE SURVEYING. 2D 
 
 ( 29). Let us now suppose the divisions on the limb to equal 
 half-degrees, and that the vernier-arc, corresponding to twenty- 
 nine divisions of the limb, is divided into thirty equal parts. 
 
 It is plain, since 30 divisions of the vernier equal 29 divisions 
 of the limb, that one division of the limb equals ? divisions of 
 the vernier, and that one division of the vernier equals f di- 
 vision of the limb. 
 
 But each division of the limb equals 30' or one-half of one de- 
 
 OA/\xOQ 
 
 gree ; therefore, one division of the vernier will equal HQ = ^9' > 
 which is one minute less than a division of the limb. 
 
 Now, suppose the zero of the vernier to correspond with the 
 zero of the limb ; then the points of the compass circle lie in the 
 line of sight. If now we turn the vernier until its first division 
 from zero coincides with the first division from zero on the limb, 
 and on the same side of zero as the division of the vernier, the 
 points of the compass will make an angle of V with the line of 
 sight; if the second division of each coincide, the angle will be 2'; 
 if the third, it will be 3', and so on by the same increase, so that 
 if we make the twenty-ninth division of each correspond, the an- 
 gle will be 29' ; and if we turn still further until the first division 
 of the limb coincides with zero of the vernier, the angle will be 
 SO'. In the same manner, 30' acting as a base, the angle may be 
 increased to 1, and so on. 
 
 ( 30 ). Sometimes verniers read lower than V, but they are not 
 of much practical use on magnetic instruments. They may also 
 differ in construction from the kind described above, but they all 
 work on the same principle. The plate on page 26 represents a 
 vernier compass; the vernier may be observed on the compass 
 plate in front of the box. 
 
 ( 31 ). As a general thing, when a compass needs repairing, 
 either from wear or on account of some mishap, it is best to for- 
 ward it to some maker of mathematical instruments. This, how- 
 ever, may not always be convenient or practicable, and it may be 
 well enough to give some directions, which may be of service in 
 case of an emergency : 
 
 1. To Re-magnetize the Xeedk. When the needle works lazily, 
 on account of losing a portion of its magnetism, it may be re- 
 magnetized with a common bar or horse-shoe magnet by passing 
 the south pole of the magnet along the north end of the needle
 
 26 MANUAL OF PLANE SURVEYING. 
 
 from the center to the extremity and bringing the magnet back to 
 the starting point in a circle of five or six inches radius. The 
 south end of the needle should be treated in the same manner, 
 except that the north pole of the magnet should be used on this 
 end. From twenty to thirty passes will give it an ample charge. 
 2. To Sharpen the Center-pin. Sometimes the needle moves slug- 
 ishly when the cenler-pin upon which it turns becomes dull. 
 
 When this is the case, take out the plate in which the center-pin 
 is set and then unscrew the pin. It may then be sharpened on a 
 very fine stone and finished on a piece of smooth leather. Care 
 must be taken to grind equally from every side of it.
 
 MANUAL OF PLANE SURVEYING. 27 
 
 3. To Replace a Spirit-level. Eemove the brass tube from the 
 plate and take off the caps at the ends of it. Then with some 
 pointed instrument, as an awl or a penknife, scrape out the plas- , 
 ter or other substance that holds the vial in place, and next force 
 out the old vial by pressing on one end of it. Xow slide the new 
 vial into place, keeping the proper side up, and if it is too small 
 for the tube, wedge it up with pieces of wood or paper. Notice 
 carefully its position with regard to the opening in the tube, and 
 when it is set in its proper place press some beeswax, boiled plas- 
 ter, or putty of the proper consistency, around the ends of it, so as 
 to fasten it firmly to the sides of the tube; then put on the brass 
 caps and replace the tube on the compass plate. To re-adjust the 
 level, press on the compass plate until the bubble stands in the 
 center of the opening in the tube; then turn the compass one-half 
 round, and if it remains there, the level is properly placed, but if 
 it runs toward the end of the vial, and it probably will, the end 
 toward which it settles is too high, and should be lowered or the 
 other end raised, whichever is necessary in order to keep the tube 
 parallel with the compass plate. After this, give the compass 
 another half-turn and repeat the process given above until the 
 bubble will remain in the middle of the opening in the tube in 
 every horizontal position of the plate. 
 
 4. To Adjust a Ifeiv Sight. Fit it to its place on the plate, and 
 notice how the slit lines with that of the old one on the opposite 
 end. If it inclines to one side, remove it and file off its base on 
 the opposite side where it rests on the plate. Then try it again, and 
 keep up the operation until the two slits coincide throughout their 
 whole length. If both sights need adjusting, hang a plumb, using 
 a fine thread or hair, and regulate both sights by it. The com- 
 pass should be perfectly level whenever an observation of the 
 thread is taken, and the sights will be properly adjusted when- 
 ever they correspond with the plumb-line. 
 
 5. To Straighten the Center-pin. Remove it with its base from 
 the rest of the compass and bend it with a pair of pincers or 
 wrench made for the purpose, always grasping it about an eighth 
 of an inch below its point. 
 
 6. To Straighten the Needle. It sometimes happens that the nee- 
 dle of the compass does not " cut " opposite degrees on the circle, 
 as, for instance, when its north point is placed at its south point 
 inclines either to the right or left of the opposite 0; when this is
 
 28 MANUAL OF PLANE SURVEYING. 
 
 the case the error may be corrected by bending the needle with the 
 fingers. 
 
 7. To put in a new Glass. First take off the brass ring that con- 
 tains it (bezzle ring) and remove the putty. Then take out the 
 old glass and put in the new by reversing the process. If the new 
 glass is so large that it will not go in readily, hold the edge on a 
 grindstone and grind it down. The manner in which it should be 
 ground may generally be seen by noticing the glass just taken out. 
 
 8. The motion of the ball at the head of the Jacob's staff may 
 be regulated by a screw-cap that fits down upon it. It should be 
 kept reasonably tight in order that the compass may not be too 
 easily jarred out of level. If it works loosely, screw the cap down 
 tighter. After long usage the ball may not fit the cavity well, 
 and in this case it may be taken out and a small piece of sheet 
 brass placed under it, or even a piece of paper will answer for a 
 short time. 
 
 ( 32 ). In carrying the compass it need only be lifted from the 
 staff and put under the left arm so that one of the sights may pro- 
 ject up behind the shoulder, and the staff makes a good walking 
 stick; but in transportation over the country the sights should be 
 taken off and all packed snugly in a box or something else that 
 will answer the purpose. A suitable box is usually furnished 
 with the compass by the manufacturer. 
 
 ( 33 ). All compasses are provided with a lever or spring with 
 which to raise the needle from the center-pin when the compass 
 is not in use, and this should not be neglected. 
 
 ( 34 ). The compass when not in use should be placed in a hor- 
 izontal position and the needle allowed to assume its natural di- 
 rection. If this precaution is taken, the needle will better retain 
 its polarity. 
 
 ( 35 ). The telescope compass is gradually growing into favor 
 with surveyors and seems to be taking the place of the sight com- 
 pass in many localities. The telescope enables the surveyor to- 
 set a flag at longer ranges, at greater elevations and depressions, 
 and discern it more easily among trees and bushes. It is not quite 
 so convenient to handle as the sight compass, however, but this is 
 no great disadvantage. Either may be used on a tripod, instead 
 of a Jacob's staff. For plate of a telescope compass see frontis- 
 piece. This engraving represents the very fine instrument manu- 
 factured by T. F. Randolph, Cincinnati.
 
 MANUAL OF PLANE SURVEYING. 29 
 
 QUESTIONS ON CHAPTER II. " 
 
 1. Describe the compass. 
 
 2. How are the degrees numbered on the circumference of the 
 
 compass circle ? 
 
 3. How are the sights arranged ? 
 
 4. Describe the magnetic needle. How is the delicacy of a 
 
 needle determined? 
 
 5. Explain the method of measuring horizontal angles. 
 
 6. How are vertical angles sometimes approximately meas- 
 
 ured? 
 
 7. Why are the letters E and W reversed on the compass face? 
 
 8. State the rule for taking the readings from the compass 
 
 circle. 
 
 9. The north end of the needle points 20 to the right of N. 
 
 What is the bearing of the line of sight? What is its 
 reverse bearing? 
 
 10. What is a northerly bearing ? A southerly bearing? 
 
 11. In running lines east what letter on the compass face should 
 
 be turned north? In running west, what one? Why?' 
 
 12. Give the four rules for measuring angles. 
 
 13. What is the included angle in each of the following cases : 
 
 N 40 E and N 62 E? S 15 W and S 39 E? N 29 W 
 and S 43 W ? 
 
 14. How is electricity excited in the glass of the compass ? How 
 
 may it be removed ? 
 
 15. How do iron and steel affect the action of the needle ? 
 
 16. What two kinds of compasses are in use ? 
 
 17. How many kinds of sight compasses are there ? 
 
 18. What is the difference between a plain compass and a ver- 
 
 nier compass? 
 
 19. Describe the " vernier." Of what advantage is it ? 
 
 20. How is the needle re-magnetized ? 
 
 21. Explain the manner in which the center-pin is sharpened. 
 
 22. How is a spirit level replaced ? 
 
 23. In what way is a new sight adjusted ? 
 
 24. How do you determine, when the two extremities of the 
 
 needle do not " cut " opposite degrees, whether it is the 
 needle or the center-pin that is bent? Answer Turn the 
 compass and notice the amount of the error in several
 
 30 MANUAL OF PLANE SURVEYING. 
 
 positions. If it decreases in certain places and increases 
 in others, it is the center-pin. If it remains about the 
 same in every position, it is probable that the needle 
 alone is bent. 
 
 25. Why should the needle be raised against the glass when 
 
 the compass is not in use ? 
 
 26. What is the proper position for the compass during the in- 
 
 terval between surveys? 
 
 27. What are the advantages of the telescope compass over the 
 
 sight compass?
 
 CHAPTER III. 
 
 THE VARIATION OF THE MAGNETIC NEEDLE. 
 
 ( 36 ). The meridian of any point on the earth's surface is a due 
 north and south line connecting the point with the poles of the 
 earth. 
 
 ( 37 ). This is called the true meridian of the place, in order to 
 distinguish it from the magnetic meridian, which will be considered 
 further on. 
 
 ( 38 ). Various methods are employed in determining the true 
 meridian, but only two of the most simple and satisfactory will 
 be described : 
 
 1. By a Shadow Cast by a Perpendicular Otgect. Erect a perpen- 
 dicular staff on a level surface, so that its shadow will remain on 
 
 the surface from about 8 o'clock, A. M., till 4 o'clock, p. M., as in- 
 dicated in the horizontal projection, Fig. 3, in which S N repre- 
 sents the staff. 
 
 (31)
 
 32 MANUAL OF PLANE SURVEYING. 
 
 Three or four hours before noon, with a radius, P S, shorter 
 than the length of the shadow, and from the point S as a center, 
 describe an arc through the point P and produce it beyond, opposite 
 P. Then mark the point P, where the shadow last touches the arc, 
 and in the afternoon the other point P where it first touches it 
 again, and connect these two points with a line PP. Bisect this 
 line at O, and the line SO, produced in either or both directions, 
 will represent the true meridian of the place. It is not exactly 
 correct, except at certain times during the year (at the solstices), 
 but it is always sufficiently accurate for ordinary purposes. 
 
 2. By the Polar Star. The Polar star (Polaris) is situated about 
 1J degrees from the north pole of the heavens, and appears to re- 
 volve around the pole once in 23 hr. 56 min. If, now, we suppose 
 a vertical plane to pass through the north pole and the eye of the 
 observer, then twice during the time of revolution Polaris will be 
 in this plane, and consequently in the meridian of the observer 
 (once when above the pole and again when below it). These are 
 called its upper and lower culminations, respectively. 
 
 ( 1 ). On the opposite side of the pole from Polaris is a star 
 known as Alioth, or more commonly as Epxilcm, of the constellation 
 of the Great Bear or " Dipper" This is the first star in the handle 
 of the Dipper, and is situated next to the four that form the quad- 
 rilateral, the outside two of which, Dubhe and Merak, are called 
 " the pointers," because they indicate the position of Polaris. 
 
 ( 2 ). Since these stars, Polaris and Alioth, are almost exactly 
 on opposite sides of the pole, it is evident that they will both be 
 on the meridian of the observer when one of them is above the 
 other, and it is more convenient to make the observation during 
 the upper culmination of Polaris. 
 
 (3). Suspend a plumb-line from some elevated projection, as 
 the limb of a tree or a strip nailed to the side of a building or 
 high post, and at a point south, not so distant that Polaris will 
 rise above the point of suspension of the plumb, arrange a short 
 board horizontally east and west, a little below the level of the 
 eye. On this board place some kind of a contrivance containing 
 an opening across which a thread may be stretched so that it will 
 be parallel to the plumb-line when the instrument is in use, and 
 slide the instrument along the board until the thread ranges with
 
 MANUAL OF PLANE SURVEYING. 
 
 the plumb-line and Polaris. Continue to move the instrument 
 west as Polaris moves to its point of superior culmination, and 
 watch also the approach of Alioth to the meridian. As soon as 
 the plumb-line falls on both stars, fasten the instrument to the 
 
 POLARIS. 
 
 NORT.fr 
 
 (- ALOTH. 
 
 FIG. 4. 
 
 OUBHE. 
 WERAK 
 
 board, and you have two points in the true meridian. The line 
 through these may be produced at pleasure and permanently 
 marked. Fig. 4 represents the plumb-line covering both stars. 
 
 (4). Still greater accuracy may be reached by following Polaris 
 for twenty-two minutes after the plumb-line falls on it, and then 
 marking the line. 
 
 (5)- When the upper culmination occurs during the day, the 
 lower culmination must be used, but Alioth is then very high. 
 
 ( 39 ). The following table shows the time of the upper culmin- 
 ation of Polaris for each tenth day. The time for intermediate 
 days may be approximated by interpolation. The time is given 
 to the nearest minute: 
 3
 
 34 
 
 MANUAL OF PLANE SURVEYING. 
 
 MONTH. 
 
 1st Day. 
 
 llth Day. 
 
 21st Day. 
 
 January . . . 
 
 h. m. 
 6 : 30 P. M. 
 
 h. m. 
 
 5: 50P.M. 
 
 h. m. 
 4: 50P.M. 
 
 February . . 
 
 4 : 27 " 
 
 3 : 47 " 
 
 2 : 48 " 
 
 March .... 
 
 2 : 32 " 
 
 1:53 " 
 
 12:50 " 
 
 April 
 May 
 
 12 : 26 " 
 10 : 29 A.M. 
 
 11: 47A.M. 
 9 : 49 " 
 
 10: 49 A.M. 
 
 8: 50 " 
 
 June 
 
 8:27 " 
 
 7 : 48 " 
 
 6 : 49 " 
 
 July 
 
 6:29 " 
 
 5: 50 " 
 
 4 : 51 " 
 
 August . . . 
 
 4 :28 " 
 
 3:48 " 
 
 2:49 " 
 
 September . 
 
 2: 26 " 
 
 1 : 47 " 
 
 12:48 " 
 
 October . . . 
 
 12 : 29 " 
 
 11: 49 P.M. 
 
 10: 50P.M. 
 
 November. . 
 
 10 : 27 P. M. 
 
 9:47 " 
 
 8:48 " 
 
 December . . 
 
 8:28 " 
 
 7 : 49 " 
 
 6: 50 " 
 
 (40). If a magnetic compass be placed on the true meridian 
 thus established, the needle of the compass, pointing toward thenorth 
 magnetic pole, instead of toward the north poleofthe earth, marks a line 
 called the magnetic meridian, which coincides with the true merid- 
 ian in comparatively few places on the earth. The angle formed 
 by the difference in direction of these two lines is called the varia- 
 tion or declination of the needle. 
 
 (41). If the north point (south pole) of the needle points to the 
 east of the true meridian, the variation is said to be east, and if it 
 points to the west, the variation is said to be west. The amount ot 
 variation is determined by the size of the angle. 
 
 ( 42 ). In the United States there is a line extending southeast 
 through the eastern part of Michigan, western part of Lake Erie, 
 eastern Ohio, central West Virginia, Virginia, and North Carolina, 
 reaching the Atlantic ocean near Wilmington, that is called the 
 agmic line or line of no variation, because at all points thereon the 
 magnetic meridian and true meridian coincide. Places east of 
 this line have west variation, and those west of it have east varia- 
 tion.
 
 MANUAL OF PLANE SURVEYING. 35 
 
 ( 43 ). Isogonic lines or lines of equal variation run through places 
 having the same variation. For instance, the line of three degrees 
 west variation passes through Chesapeake Bay, Maryland, central 
 Pennsylvania, and western New York, and the line of three de- 
 grees east variation passes through western South Carolina, eastern 
 Georgia, Tennessee, Kentucky and Indiana, and western North 
 Carolina, Ohio, and Michigan.- The variation increases in both 
 directions from the agonic line, reaching about 18 degrees west 
 variation in eastern Maine and 22 degrees east variation in the 
 northern part of Washington Territory. 
 
 ( 44 ). The isogonic lines converge toward the north magnetic 
 pole, situated at present in longitude about 96 west from Green- 
 wich, and latitude about 70 north. This pole has been gradually 
 moving westward for several years, and will perhaps continue to 
 do so for several years to come. This causes the agonic line and 
 all the isogonic lines to move in the same direction, so that west 
 variation is constantly increasing and east variation constantly 
 decreasing throughout the eastern and central portions of the 
 United States. 
 
 ( 45 ). The change that takes place in the variation of the 
 needle at any place from this cause is called its secular change. 
 This varies in different localities, and is generally greater in the 
 northern part of the United States than in the southern part. It 
 is determined by comparing the variation at the time of any ob- 
 servation with that of a preceding or succeeding one. 
 
 ( 46 ). But this is not the only change to which the needle is 
 subject. Its action is modified by other influences. The north 
 end of the needle moves westward from about 6 o'clock A. M., 
 until about 2 o'clock p. M., and then gradually returns to the 
 starting point. This is called its diurnal change, and it sometimes 
 amounts to 10 or 12 minutes of a degree. 
 
 This change is about twice as great in summer as in winter, 
 hence an annual change must be taken into consideration. 
 
 ( 47 ). The following table, taken from the Keport of the United 
 States Coast Survey, illustrates these changes. The mean magnetic 
 meridian is the average position of the needle for the day :
 
 MANUAL OF PLANE SURVEYING. 
 
 
 
 ^ 
 
 d 
 
 
 
 HOUK. 
 
 A 
 
 1 
 
 a 
 
 a 
 
 S 
 
 
 
 i 
 
 
 
 3 
 
 'S 
 
 .S 
 
 
 
 OJ 
 
 
 "*! 
 
 ^ 
 
 
 
 / 
 
 1 
 
 i 
 
 f 
 
 
 6 A. M. 
 
 3 
 
 4 
 
 2 
 
 i 
 
 
 
 7 " " 
 
 4 ' 
 
 5 
 
 3 
 
 i 
 
 3 <B 
 
 8 " " 
 
 4 
 
 5 
 
 3 
 
 2 
 
 I! 
 
 9 " " 
 
 3 
 
 4 
 
 2 
 
 2 
 
 ! 
 
 10 " " 
 
 1 
 
 1 
 
 
 
 1 
 
 
 11 " " 
 
 1 
 
 2 
 
 2 
 
 
 
 * 
 
 12 M. 
 
 4 
 
 4 
 
 3 
 
 2 
 
 II 
 
 IP. M. 
 
 5 
 
 6 
 
 4 
 
 3 
 
 i? 
 
 2 " " 
 
 5 
 
 5 
 
 3 
 
 3 
 
 ^ 5" 
 
 of 
 
 3 " " 
 
 4 
 
 4 
 
 2 
 
 2 
 
 ^ 
 
 4 ' " 
 
 3 
 
 3 
 
 1 
 
 1 
 
 2, 
 
 5 *' ** 
 
 2 
 
 2 
 
 1 
 
 1 
 
 g 
 
 6 " " 
 
 1 
 
 1 
 
 
 
 
 
 3 
 
 ( 48 ). Probably as good a time as any to get the variation of 
 the needle is between 5 and 7 o'clock in the evening, as it then 
 pretty nearly indicates the mean magnetic meridian. The diur- 
 nal and annual changes are usually disregarded in practical work 
 with the compass. 
 
 (49). The needle is also subject to disturbances that do not 
 appear conformable to any known law. These generally take 
 place during a thunder storm, aurora, or other electrical phe- 
 nomenon, and sometimes cause a surveyor no small amount of 
 vexation. 
 
 (50). The north end of the needle is also inclined to point 
 downward. This is called its " dip " or inclination, and increases 
 as we go northward. It is overcome by making the north end of 
 the needle the lighter, and in order to render the needle adjusta- 
 ble, a small counterpoise is arranged in a groove on its south end. 
 
 (51 ). A great many magnetic phenomena are at present very 
 imperfectly understood, and many of the conclusions based upon
 
 MANUAL OF PLANE SURVEYING. 37 
 
 partially accepted theories are liable to be overthrown at almost 
 any time. A discussion of these belongs to Philosophy. 
 
 QUESTIONS ON CHAPTER III. 
 
 1. What is meant by the meridian of a place? 
 
 2. What is the difference between the true meridian and the 
 
 magnetic meridian? 
 
 3. Explain each of the methods given for establishing a true 
 
 meridian. 
 
 4. What is meant by the culmination of Polaris? 
 
 5. To what does the north end of the needle point? 
 
 6. What do you understand by " the variation of the needle? " 
 
 7. What is east variation? West variation ? 
 
 8. What determines the amount of variation ? 
 
 9. Through what part of the United States does the agonic 
 
 line run? 
 
 10. What are isogonic lines? 
 
 11. What is the situation of the north magnetic pole? 
 
 12. In what direction is the agonic line and all the isogonic 
 
 lines moving at present? 
 
 13. What effect does this movement have on east variation? 
 
 West variation? 
 
 14. What other influences act upon the needle? 
 
 15. What is the difference between the diurnal change and the 
 
 annual change? 
 
 16. What is meant by "dip?" 
 
 17. How is it overcome ?
 
 CHAPTER IV. 
 
 EFFECT OF CHANGE OF VARIATION* ON OLD LINES AND METH- 
 ODS OF CORRECTING BEARINGS. 
 
 FlG. 5. 
 
 <! The terms variation and declination have become synonymous in mean- 
 ing, although it would be better, etymologically speaking, to use the word 
 variation to denote the change of declination. We would then 
 of declination, instead of change of variation as at present. 
 
 (38)
 
 MANUAL OF PLANE SURVEYING. 
 
 30 
 
 ( 52 ). As the variation of the needle is constantly changing, so 
 the bearing of a line surveyed at any time is also subject to con- 
 stant change. This renders it necessary in the re-survey of any 
 line to take into consideration the amount of change that has taken 
 place since the previous survey; otherwise the location of the line 
 will be changed. 
 
 To illustrate : Let the line A B, Fig. 5, represent the line of 
 direction of the magnetic needle (magnetic meridian) at a certain 
 time, and the line C D which makes an angle of 22 with the mag- 
 netic meridian, and whose course is N 22 E, represent a line sur- 
 veyed while the needle marks this meridian. 
 
 Since the north end of the needle is continually moving toward 
 the west, it is evident that the angle between A and C, formed by 
 the crossing of the two lines, will be constantly growing larger, 
 and that the bearing of the line C D will consequently increase 
 
 f C 
 
 Fro. 6.
 
 40 
 
 MANUAL OF PLANE SURVEYING. 
 
 with each succeeding year, as long as the westward movement of 
 the needle continues. 
 
 ( 53 ). Let us now suppose that several years after this survey 
 is made, the needle assumes the position of the dotted line E B, 
 Fig. 6, making an angle with A B equal to 5. The line C D will 
 now make an angle with the magnetic meridian equal to (22 -j- 
 5) = 27. It will be seen that the bearing of the line has in- 
 creased 5, the change of variation of the magnetic needle. 
 
 ( 54 ). If now the surveyor, through ignorance or carelessness, 
 should neglect to take this change into consideration, and run the 
 line at the old bearing (22) marked in the description of the line, 
 he would change its position to that of the dotted line D F, and 
 it is easy to see what an error this would cause in the survey of 
 a tract of land. 
 
 ( 55 ). A survey of this kind, however, does not affect the form 
 or area of a piece of land, but simply changes its boundaries and 
 seems partly to revolve the tract about the corner from which 
 the surveyor starts, as a center. For instance, suppose a mistake 
 
 ==r- -.B 
 
 FIG. 7. 
 
 of this kind to be made in the survey of the tract A B C D, Fig. 
 7 ; its position would be changed to that of the dotted quadri- 
 lateral. In this survey the corner D was made the starting point. 
 ( 56 ). In order to determine the present bearing of a line, it is 
 an advantage to know three things : 1. The bearing of the line
 
 MANUAL OF PLANE SURVEYING. 41 
 
 at the time of a previous survey. 2. The riumber of years that 
 have elapsed since that survey was made. 3. The annual amount 
 of secula'r change of variation. 
 
 1 and 2. Where field-notes of the former survey have been pre- 
 served, they generally and should always, give the necessary in- 
 formation in regard to the bearing of the line and date of the sur- 
 vey ; but where no record of the survey can be found, the bearing 
 may sometimes be approximately determined from old deeds or 
 descriptions of the land, and these frequently assist the surveyor 
 in arriving at a conclusion with regard to the time the survey 
 was made. Persons living in the neighborhood may also know 
 something of the previous survey. 
 
 3. In order to determine the annual change of variation, vari- 
 ous methods may be employed. 
 
 (1). The bearing of a line at the present time may be compared 
 with that recorded by a competent surveyor some time previous. 
 
 (2). A true meridian may be established by the second method 
 explained in the preceding chapter, and the variation of the needle 
 found from this by observing the angle the magnetic meridian 
 makes with the true meridian. This result may then be com- 
 pared with the variation recorded after a previous observation. 
 
 In both of these cases the amount of change in minutes will 
 equal the quotient obtained by dividing the difference of varia- 
 tion in minutes between the two observations by the number of 
 years that have elapsed between them. For instance, if the varia- 
 tion of the needle at a certain time is found to be 5, and in twenty 
 years after an observation shows that it has decreased to 4, the 
 annual change will equal (5 4) = 1= 60', which divided by 
 20 = 3'. From this the variation for any subsequent time may 
 be found by multiplying the annual change, 3', by the number of 
 years, and adding or subtracting the product, as will be explained 
 further on. 
 
 (3). When the annual change at several important points is 
 known, the change at intermediate points throughout the country 
 may be determined by interpolation, but this method is not trust- 
 worthy in all cases. 
 
 (57). The following table is taken, somewhat modified, from 
 the report of the U. S. Coast Survey of a few years ago, and con-
 
 42 MANUAL OF PLANE SURVEYING. 
 
 tains the variation of the needle at various important stations 
 throughout the United States for the year 1881 : 
 
 Bangor, Me 16 Sff W. 
 
 Wolfsboro, N. H 12 15' W. 
 
 Middlebury, Vt 11 35* W. 
 
 Marblehead, Mass 1? 54' W. 
 
 Schenectady, N. Y., 9- 58' W. 
 
 Chambersburg, Pa 4 33' W. 
 
 New Haven, Conn 9 Off W. 
 
 Providence, R. I., 11 27' W. 
 
 Wilmington, N. C., 1 04' W. 
 
 Jackson, Miss., . 6 33' E. 
 
 Washington, D. C 3 17' W. 
 
 Camden, N. J 6 W W. 
 
 Columbus, O., W E. 
 
 Savannah, Ga 1 50* E. 
 
 New Orleans, La 6 33' E. 
 
 Quincy.Wis 6 33' E. 
 
 Decatur, Ind., 1 5ff E. 
 
 Grand Rapids, Mich 1 5(X E. 
 
 Havana, Cuba 4 46' E. 
 
 Carlinville, 111 6 33' E. 
 
 Aiken, 8. C 1 50 E. 
 
 Monterey, Cal 16 06' E. 
 
 Sitka, Alaska ... 28 27' E. 
 
 This list is not full enough to be of much practical use, but I 
 think best not to extend it any further, as the surveyor can easily 
 find the variation at any point himself. 
 
 ( 58 ). The next table, also taken from the Eeport of the Super- 
 intendent of the Coast Survey, gives the annual amount of secular 
 change in certain localities in the United States. 
 Maine, Long Island, Delaware, Maryland, 
 Virginia, South Florida, South Alabama 
 
 and Mississippi, and New Jersey 3' 
 
 East Maine, West Tennessee, Missouri, and 
 West Louisiana 2'
 
 MANUAL OF PLANE SURVEYING. 4 
 
 Ohio, East Tennessee, East Louisiana, and 
 
 East Massachusetts 2' 15" to 2' 45" 
 
 Kew Hampshire, West Massachusetts, Khode 
 
 Island, Connecticut, AVest Virginia, North 
 
 Carolina, South Carolina, Georgia, and 
 
 North Florida 3' 15" to 3' 45" 
 
 North and West New York 4' 30" 
 
 Vermont 5' 30" 
 
 In all these places the change marked to the right indicates an 
 increase of westerly or decrease of easterly variation. 
 
 ( 59 ). These tables will enable us to approximate to the vari- 
 ation of the needle at points included in both tables, for perhaps 
 several years. For example, the variation of the needle at Cam- 
 den. N. J., this year is 6 50' W; in 1885 it will be about 6 50 / + 
 (4 X 3') = 7 02'. If the variation is easterly, as in the western 
 part of the United States, the amount of change is subtractive, 
 instead of additive. Take this for example: What will be the 
 variation of the needle at New Orleans in 1884? 
 
 18841881=3 years. 
 
 Variation in 1881 = 6 33'. 
 
 Annual change about 2' 30". 
 
 Amount of change = (3 X 2' 30")=7' 30". 
 
 Variation in 1 884=6 33' 7 / 30"=6 25' 30". 
 
 (60). In order to find what the variation of the needle was a 
 few years ago, we have only to reverse the rule given ; that is, add 
 where the variation is easterly, and subtract where it is westerly. 
 
 The following examples may be used for practice: 
 
 ( 1 ). The variation of the needle at a certain place in 1880 was 
 N 5 32' E, and the annual change 2' 20" ; what will be the vari- 
 ation 1889? 
 
 (2). In 1878 the variation at a certain place was 4 15" W, 
 annual change 3' 30"; what will be the variation in 1886? 
 
 (3). In 1880 the variation at A was 2 36' W; what was the 
 variation in 1874, supposing the annual change to be 4'? 
 
 ( 4 ). The annual change at B is 3' 45" and the variation of the 
 needle in 1879, 3 47' E; what was the variation at this place in 
 1870?
 
 44 
 
 MANUAL OF PLANE SURVEYING. 
 
 ( 61 ). It would frequently be better if the bearings of lines 
 were taken from the true meridian as a basis, as no change would 
 then take place in the bearings. 
 
 This may be easily explained. Suppose the line A B to repre- 
 
 A C 
 
 FIG. 8. 
 
 sent a section of a true meridian of the earth, and the line C D to 
 represent one of the boundaries of a piece of land. Both of these 
 lines are fixed, and consequently the angle between them can 
 never change. 
 
 ( 62 ). If, however, the line A B represents a section of the mag- 
 netic meridian, it is constantly changing, and this of course affects 
 the angle. 
 
 ( 63 ). In order to determine the true bearing of a line from its 
 magnetic bearing, two cases must be considered : 
 
 1. When the variation is west. RULE. Add the variation to the 
 bearing for northwest and southeast courses, and take their differ- 
 ence for northeast and southwest courses. 
 
 In Fig. 9 let A B represent a due north and south line and C B 
 represent the direction of the needle. D B and E B are two lines 
 whose bearings are to be changed from the magnetic bearing to 
 the true bearing. Suppose the variation of the needle to be 10 
 W ; then the true bearing of the line E B will be N (25 + 10)
 
 MANUAL OF PLANK SURVEYING. 
 
 45 
 
 W = N 35 W, and the true bearing of the line B D will be N 
 (35 10) E = N 25 E. 
 
 FIG. 9. 
 
 2. When the variation is east. RULE. Reverse the preceding op- 
 eration ; that is, take the difference between the bearing and vari- 
 ation for northwest and southeast courses, and their sum for north- 
 east and southwest courses. 
 
 The line A B, Fig. 10, represents a section of the true meridian, 
 and the line B C a section of the magnetic meridian. As before, 
 the bearings of the lines D B and E B are to be changed to the 
 true bearings from the magnetic bearings. If the variation of the 
 needle be 10 E, the true bearing of the line B D will be N (25 
 -f 10) E = N 35 E, and the true bearing of the line B E will be 
 N (35 10) W = N 25 W.
 
 MANUAL, OF PLANE SURVEYING. 
 
 (64). The variation in the following examples is 5E; what is 
 the true bearing of each course ? 
 
 1. N 45 W. 
 
 2. N 32 W. 
 
 3. S 16 W. 
 
 4. N 17 E. 
 
 5. S 25 E. 
 
 6. N 25 E. 
 
 (65). If in any case the sum of the variation and bearing 
 amounts to more than 90, the supplement* of the sum must be; 
 taken, and the first letter changed to its opposite. 
 
 Take, for instance, the bearing N 88 W when the variation is 
 6 W. This gives us the following result : 88 + 6 = 94, and 
 taking 94 from 180 to get the supplement, we have (180 94) 
 
 *The supplement of an arc is what remains after subtracting the arc from
 
 MANUAL OF PLANE SURVEYING. 47 
 
 = 86. After changing the first letter of the magnetic bearing, 
 we see that the true bearing of the line is S 86 W. 
 
 ( 66 ). In changing from the true to the magnetic bearing, it is 
 necessary only to reverse the foregoing rules. 
 
 QUESTIONS ON CHAPTER IV. 
 
 1. What effect does the change of variation of the magnetic 
 
 needle have upon the bearings of lines? 
 
 2. Why must this change be taken into consideration in a re- 
 
 survey ? 
 
 3. Why would it not affect the figure or contents of a tract of 
 
 land if this change were not regarded ? 
 
 4. What three things are necessary in order to determine the 
 
 present bearing of a line from its magnetic bearing at a 
 former time, without a re-survey of the line? 
 
 5. How is its bearing at the time of a former survey found ? 
 
 The annual change ? 
 
 6. Two observations thirty years apart show a change of 1 15' 
 
 in the variation of the needle. What is the annual change? 
 
 7. What is meant by east variation? West variation. 
 
 8. How do you find the true bearing of a line from the mag- 
 
 netic bearing ? The magnetic from the true ?
 
 CHAPTER V. 
 
 METHOD OF RUNNING LINES, ETC. 
 
 ( 67 ). The first thing a surveyor does in making a survey is to 
 find a corner from which to start, and this is frequently a matter 
 of no little trouble, but its discussion belongs further on in our 
 work. Let us suppose for the present that the monument which 
 marks the corner (generally a stone or a stake) is still standing, or 
 that the witnesses to it are yet to be found. These witnesses are 
 generally trees, although any other immovable object will answer 
 the purpose equally well. When the corner is put down the course 
 and distance from it to one or more of these objects are carefully 
 noted in the record (field notes) of the survey, so that, no matter 
 if the monument that marks the corner has disappeared, its posi- 
 tion can easily be determined as long as any of the witnesses 
 remain. The witnesses, if trees, are called witness- trees, and 
 are marked about eighteen inches from the ground on the side 
 facing the corner. The mark consists of a blaze about six or eight 
 inches long, which generally has a cross notch cut in it. 
 
 ( 68 ). If the monument at the corner remains, its center should 
 be taken as the point from which to run the line; but if it can not 
 be found, its position must be determined from the witnesses. It 
 is probable that the approximate location of the corner is known, 
 so that the surveyor or some of his attendants know where to look 
 for it. Suppose the surveyor examines his record and finds that 
 when the corner was set, a beech tree 18 inches in diameter was 
 taken as a witness to it. This tree stood in a direction N 43 E 
 from the corner, and was distant 78 links. He looks in that direc- 
 tion and sees a tree which he believes to be the one, and after an 
 examination he finds the surveyor's mark and is convinced of its 
 identity. All he has to do now is to set the compass in front of the 
 (48)
 
 ?. r ;6 
 
 MANUAL OF PLANE SURVEYING. 49 
 
 mark on the tree and turn it until the needle indicates the reverse 
 bearing, S 43 W; a staff is then set in the line of sight somewhat 
 further from the tree than the distance given for the corner, and a 
 measurement of 78 links made from the notch on the tree in the 
 direction of the staff; the termination of this measurement is the 
 corner. 
 
 ( 69 ). On prairies, where no trees are available for witnesses, 
 mounds of earth thrown up around a stake are usually made to 
 answer the purpose, and in clearings it is sometimes necessary to 
 make the same kind of witnesses, or supply their places with stones 
 set at suitable distances from the corner. A good monument 
 should always be put down at the corner, and one not easily 
 moved or destroyed does not particularly need any witnesses to it. 
 
 (70). The method of describing a witness-tree employed by 
 surveyors in making up their field-notes, is much abbreviated from 
 the method used above. The above description would read as fol- 
 lows : Be 18 N 43 E 78. The first number signifies the diameter, 
 the second the bearing, and the third the distance in links. The 
 bearing and distance of the tree from the corner are called its 
 "course and distance." Likewise the course and distance of any 
 line are its bearing and length. 
 
 ( 71 ). After the corner has been found, the next thing is to run 
 a line from this corner to the next. In surveying, a line always 
 connects two corners, and in plane surveying it represents the 
 shortest distance between them. 
 
 ( 72 ). In order to run this line, its course and distance must be 
 at least approximately known, and should be exactly known. 
 
 ( 73 ). Let us suppose that the true bearing of the line is N 3 E, 
 and its length 6 chains and 50 links. Since the true bearing ia 
 given it has remained unchanged (Art. 61), and the surveyor has 
 only to turn the vernier of the compass until he sets off the varia- 
 tion of the needle, and then set the north end of the needle at N 
 3 E. The sights of the compass are then set Oil the line, and a 
 measurement of 6 chains and 50 links on the line of sight will 
 bring him to the next corner. 
 
 ( 74). In setting off the variation of the needle on the vernier, 
 two cases arise: (1) when the variation is east, and (2) when the 
 variation is west. 
 
 1. To Set Of East Variation. KULE. Turn the sights so as to 
 throw the line of sight to the left until the angle between the line 
 4
 
 50 MANUAL OF PLANE SURVEYING. 
 
 of sight and the points of the compass circle equals the vai-i- 
 ation of the needle. 
 
 2. To Set Off West Variation. RULE. Turn the sights of the com- 
 pass so as to throw the line of sight to the right until the angle be- 
 tween the line of sight and the points of the circle equals the 
 variation. 
 
 These rules obtain whether the movement of the needle is toward 
 the west or east, and the vernier should generally not be changed 
 during the survey. 
 
 We are now prepared to run lines whose true bearings are 
 known. 
 
 The course and distance of a line are N 43 E 16 chains and 50 links. 
 
 ( 76 ). After finding the first comer on this line, the surveyor 
 sets off the variation of the needle on the vernier, and then sets 
 the compass at the corner, levels it, and turns the sights until the 
 needle indicates the bearing of the line. He then starts the flag- 
 man in the direction of the line of sight to a suitable distance 
 from the compass, and then moves him either to the right or left 
 until the sights strike the flag-staff. The staff is left in this posi- 
 tion until the surveyor comes up and sets the compass where it 
 stood, and then the flagman seeks another position further along 
 the line. 
 
 ( 76 ). The chain-men commence at the center of the monument 
 that marks the corner as soon as the surveyor has set the flag on 
 the line. The one that takes the lead is called the " leader," and 
 the one at the rear end of the chain is called the " follower." At 
 setting out, the leader takes a certain number of iron or steel pins 
 (usually ten) and puts one down at the end of the chain. The 
 chain is then carried forward another length and its rear end held 
 against the pin just put down while the leader sticks another into 
 the ground. Great care should be taken to keep the chain free of 
 " kinks," taut, and as nearly horizontal as possible, no matter how 
 uneven the ground may be, and the follower should line each pin 
 with the flag-staff or compass, whichever may be set at the point 
 to which they are running. 
 
 (77) When ten pins are nsed the "marker" drives a stake* 
 where the last pin stood ; the leader takes the ten pins from the 
 follower, and the measurement proceeds just the same as from the 
 corner. If eleven are used the follower retains one in starting out 
 from the corner, and as soon as the leader puts down the last of 
 
 *The points on the line marked by the stakes are called "outs," because 
 the leader runs out of marking pins at these places.
 
 MANUAL OF PLANE SURVEYING. 51 
 
 his ten he receives ten from the follower, and the new measure- 
 ment begins at the last pin put down, instead of at the stake, as 
 hefore. As we said before, the chain usually employed in survey- 
 ing is only two rods, fifty links, or thirty-three feet in length, and 
 since a stake is put down at every ten lengths, it leaves the stakes 
 twenty rods, or five chains apart. The first stake from the corner 
 has one notch cut in it, the second two, the third three, and so on. 
 The surveyor should sight back while the marker is setting the 
 stake and see that it is put exactly on the line. 
 
 ( 78 ). The relative places on the line of the persons engaged in 
 the survey are as follows : (1) flagman, (2) surveyor, (3) chain 
 carriers and marker. 
 
 ( 79 ). The measurement is continued in the direction N 43 E 
 until the length of the line, 16 chains and 50 links, has been meas- 
 ured, and if the line thus run strikes the corner, it coincides with 
 the true line, but if it does not, the stakes must be moved, either 
 to one side or the other, until it is made to coincide. 
 
 ( 80). Let us suppose that in the case before us the line has 
 been found to terminate at a point 8^ links to the left of the cor- 
 ner. This line is called a " random line," and it is evident that 
 it has been diverging from the true line gradually since leaving 
 the starting point, and that this divergence is always in propor- 
 tion to the distance from this point. 
 
 Dividing now the distance between the terminations of the two 
 lines by their length in chains, we have 8} -5- 16| = link for 
 the increase of divergence for each chain from the point from 
 which the lines start, and since the first stake is 5 chains from 
 this point, it is 5 X 2 link = 2 links off the true line. In like 
 manner the second stake is 10 X link = 5 links off the true 
 line, and the third one 15 X J link = 7\ links off the true line. 
 The stakes are put on the true line by moving them the given dis- 
 tances in the proper direction which is always the opposite of the 
 direction of the termination of the random line from the corner. 
 
 ( 81 ). This may be illustrated by the figure. 
 
 FIG. 11.
 
 52 MANUAL OF PLANE SURVEYING. 
 
 Let A C represent the true line, and A B the random line. 
 Since the termination of the random line lies to the left of the true 
 corner, the stakes must be moved to the right. The numbers on 
 the random line indicate the order in which the stakes are num- 
 bered, and those on the true line represent the distance that each 
 stake must be moved to the right. 
 
 ( 82 ). This enables us to deduce the following rule for correcting 
 the stakes: Divide the distance between the terminations of the 
 two lines in links by their common length in chains, and multi- 
 ply the quotient by the number of chains the stake is distant from 
 the starting point. The product will equal the number of links 
 the stake is to be moved. Then move the stake in a direction op- 
 posite to that of the termination of the random line from the 
 corner. 
 
 Where the length of the line is a multiple of five chains (the 
 distance between stakes), the following rule will be found more 
 simple : Divide the distance between the terminations of the two 
 lines in links by the number of stakes on the line, and multiply 
 the quotient by the number of the stake from the starting point. 
 The product indicates the number of links the stake is to be moved 
 as before. 
 
 ( 83 ). In both of these rules the terminations of the two lines 
 and the starting point are considered as the vertices of an isosceles 
 triangle, and the distance between the terminations of the two 
 lines should be measured on a line that will make the same angle 
 with one as with the other. 
 
 ( 84 ). In the following examples, give the distance and direc- 
 tion each stake should be moved : 
 
 (1). Length of line, 20 chains. Ran to the left of true corner 
 40 links. 
 
 (2). Line 40 chains long. Ran to the left 20 links. 
 
 (3). Line 20 chains. Ran to the right 30 links. 
 
 (4). Line 18 chains. Ran to the left 12 links. 
 
 (5). Line 16 chains. Ran to the right 32 links. 
 
 (6). Line 26 chains. Ran to the right 45i links. 
 
 ( 85 ). In making up his field-notes, the surveyor usually writes 
 links as hundredths of a chain. For instance, ten chains and 
 forty links would be written 10.40. He also sometimes uses the 
 word " missed " to denote that the termination of the random line 
 lies either to the right or left of the true corner, and accompanies
 
 MANUAL, OF PLANE SURVEYING. 53 
 
 it with the word " right " or " left," as the case may be. These 
 terms are frequently abbreviated in writing by using their initial 
 letters instead of the words themselves. Thus, " missed left " may 
 be cut down to M. L. 
 
 ( 86 ). Owing to the imperfection of magnetic instruments it is 
 common, particularly on long lines, for a surveyor to run either 
 to one side or the other of the corner to which he is running, even 
 when he knows the bearing of the line. In this case, however, he 
 seldom misses the corner any considerable distance perhaps only 
 two or three links and the bearing he has taken may be assumed 
 to be correct, the error being due to the manipulation of the in- 
 strument. 
 
 ( 87 ). But where the bearing is only approximately known, the 
 random line may vary greatly from the true line, and when this 
 happens the assumed bearing must be corrected in order that the 
 true bearing may be subsequently determined without a resurvey 
 of the line. 
 
 ( 88 ). Suppose a line 40 chains long is to be surveyed, and 
 from the best evidence the surveyor has, he assumes its bearing to 
 be N 2 E. The line is accordingly surveyed, and upon reaching 
 the other end the surveyor finds that he has missed the corner 70 
 links. It is plain that he assumed a bearing considerably in 
 error, and he wishes to correct it. To do this, he may employ 
 any of the following rules: 
 
 1. Multiply the length of the line by .01745 and divide the pro- 
 duct into the product of the distance between the extremities of 
 the two lines by GO. The quotient will be the correction in min- 
 utes of a degree. In this case we have 
 
 (.70X60)-r-(.0174nX40)=60 / +=l+. 
 
 All distances should be in chains and hundredths of a chain. 
 
 This rule is derived as follows : In Fig. 12 the lines A B and A 
 C represent the true line and random line, respectively, of the 
 survey. C B represents the distance between their extremities. 
 ' (1). The line CD is called the sine of the angle B AC, and where 
 the angle is small, it does not vary much in length from the chord 
 of C B which connects the extremities of the two lines. The line 
 A D is called the cosine of the angle B A C, and where the angle 
 is small it does not differ materially in length from the line A B. 
 
 (2). The sine of an angle, therefore, is a perpendicular raised
 
 54 MANUAL OF PLANE SURVEYING. 
 
 GL i " 
 
 FIG. 12. 
 
 from one of its sides to the other, and the cosine of an angle is the 
 portion of one of its sides intercepted between the foot of the sine 
 and the vertex of the angle itself. In these definitions no distinct- 
 ion is made between the sine or cosine of the angle and the 
 sine or cosine of the arc. 
 
 (3). Particular attention should be paid to the relation of the 
 sine and cosine to one another, and they should also be studied in 
 their application to the lines of the survey, as explained above. 
 The surveyor needs to employ sines and cosines frequently. 
 
 (4). If now we call the length of the radius 1, the length of the 
 sine of an angle of one degree will be .01745 which is the number 
 we employed in the rule. The sine will increase in the same ratio 
 that the radius increases. Therefore, if the radius is 40, the sine 
 will be (40 X -01745) = .69800; and as this is to the distance be- 
 tween the extremities of two lines, so is 60, the number of minutes 
 in a degree, to the number of minutes of correction ; hence the 
 rule. 
 
 (5). Where the angle is large, .the sine may differ considerably 
 in length from the chord, but this is a case that will seldom come 
 up in practice, except where the surveyor chances to make a mis- 
 take, and in this case he would better resurvey the line. 
 
 2. In rectangular surveying, nearly all the lines to be surveyed 
 in usual practice in dividing and sub-dividing the section, are i 
 mile, $ mile, or one mile in length. Now, the sine of an angle of one 
 degree for a radius of 20 chains, or J mile, is very nearly 35 links ; 
 therefore, for 40 chains, or \ mile, it is (2 X 35) = 70 links; and 
 for 80 chains, or 1 mile it is (4 X 35) = 140 links. 
 
 (1). This enables us to modify the rule already given, as follows :
 
 MANUAL OF PLANE SURVEYING. 55 
 
 Multiply the distance between the extremities of the two lines by 
 60, and divide the product by the sine of one degree for a radius 
 equal to the length of the line surveyed. The quotient will be 
 the number of minutes of correction to be made. 
 
 (2). If, for example, in a line \ mile long, the surveyor miss 
 the corner 70 links, the correction is made as follows: 
 
 70 : 70 : : 60 : x 70 X 60 = 6CK = 1. 
 
 3. Measure the distance between the extremity of this random 
 line and the true line. Multiply this distance by 57.3 and divide 
 the product by the length of the line surveyed. The quotient 
 will be the change of variation expressed in degrees. 
 
 Suppose the length of the line to be 18.25 and the distance be- 
 tween the extremities 35 links. Then, 57.3X-35=20.055, and 
 20.055-^18 25=1.09 1 ' 24".* 
 
 4. Multiply the distance between the extremities of the two 
 lines by .3438 and divide the product by the length of the line to 
 get the result in minutes. 
 
 ( 89 ). In determining the correction to be made in the follow- 
 ing examples, use whichever one of the preceding rules appears 
 most expeditious : 
 
 (1). Length of line, 16 chains. Distance between terminations 
 18 links. 
 
 (2). Length of line, 36 chains. Distance between extremities, 
 32 links. 
 
 (3). Length of line, 20 chains. Bearing 7 32'. Distance be- 
 tween extremities, 30 links. 
 
 (4). Length of line, 40 chains. Distance between extremities, 
 48 links. Bearing 16. 
 
 ( 90 ). Let us now see whether this correction to be made is to 
 be added to the assumed bearing of the line, or subtracted from it. 
 
 This involves two cases : 
 
 ^Suppose the random line and true line to represent two radii of a circle, 
 and the line connecting their extremities to be a portion of the circumfer- 
 ence of the same circle. We shall then have this proportion: 
 
 Whole circumference : arc : : 360 : angle of lines. 
 
 Whence, in case under consideration, we have 
 (36.50 X 3.1416) : 35 : : 360 : 1.09. 
 
 To generalize, let A represent the starting point of the lines and B and C 
 their extremities. The angle formed by them will be expressed by B A C. 
 
 Then 2 A B X 3.1416 : B C : : 360 : B A C. 
 
 Whence, B A C = ?-| X 57.3, very nearly
 
 56 
 
 MANUAL OF PLANE SURVEYING. 
 
 1. In Northeast and Southwest Courses. RULE. Add the minutes 
 of correction to the assumed bearing of the line (bearing of ran- 
 dom line) when the random line lies to the left of the true line, 
 and subtract when it lies to the right. The sum or difference will 
 be the true bearing of the line. 
 
 To illustrate, let the line A B, Fig. 13, represent a section of the 
 true meridian, A C the line to be surveyed, A D a random line 
 lying to the left, and A E a random line lying to the right of the 
 true line. 
 
 Fio. 13. 
 
 The fact is apparent that the bearing of the line A C is equal to 
 the bearing of the line A D plus the angle D A C; and it is 
 equally apparent that the bearing of the same line, A C, equals 
 the bearing of the line A E minus the angle C A E. 
 
 2. In Northwest and Southeast Courses. RULE. Reverse the pre- 
 ceding rale; i. e., subtract the minutes of correction from the as- 
 sumed bearing (bearing of random line) when the random line lies 
 to the left of the true line, and add when it lies to the right.
 
 MANUAL OF PLANE SURVEYING. 57 
 
 (91). In the following examples the bearings of the random 
 lines are given, and the words " right " and " left " signify their 
 position with regard to the true line. What is the bearing of the 
 true line in each case ? 
 
 (1). N 40 E 40.25, left .40. 
 (2). S 32 W 16.50, " .25. 
 (3). N 71 W 14.00, right .12. 
 (4). N 15 30' E 8.40, " .06. 
 (5). S 5 15' W 20.00, " .13. 
 (6). S 6 17' E 20.03, "left .13. 
 (7). N 4 06' W 15.50, " .23. 
 (8). N 3 21' E 40.00, right .10. 
 
 The distances are all given in chains and hundredths of a chain. 
 
 ( 92 ). So far, we have based all our bearings on the true merid- 
 ian, but in many cases lines are surveyed and their magnetic bear- 
 ings, instead of their true bearings, given. 
 
 ( 93 ). When this is the case, and a resurvey is to be made of 
 these lines, it is necessary to know what change has taken place 
 in the variation of the needle since their bearings were determined, 
 because the bearings change with the variation. Having found 
 this, their present bearings may be determined by the following 
 rule: 
 
 1. To Correct Magnetic Bearings. In northeast and southwest 
 courses, add the change to the given bearing, and the sum will be 
 the present bearing. In northwest and southeast courses, sub- 
 tract the change from the bearing, and the difference will be the 
 present bearing. 
 
 2. In Fig. 14 let A B and A C represent two courses, one bear- 
 ing northeast and southwest, and the other northwest and south- 
 east. Also, let A D represent the direction of the needle when the 
 lines were surveyed, and A E its direction at the present time. 
 The change of variation equals the angle BAD, and it will be 
 seen that the present bearing of the line A C is equal to the sum 
 of D A C and D A E. Likewise, that the present bearing of the 
 line A B is equal to the difierence between DAB and DAE 
 
 ( 94 ). This rule holds good while the needle moves toward the 
 west If its movement change, the rule will have to be reversed.
 
 MANUAL OF PLANE SURVEYING. 
 
 FIG. 14. 
 
 ( 95 ). Correct the bearing of each of the following courses for 
 the present year : 
 
 (1). N 14 E, annual change 2' 30". Survey made in 1856. 
 
 (2). N 7 34' W, annual change 3'. Survey made in 1862. 
 
 (3). S 1 13' E, annual change V. Survey made in 1874. 
 
 (4). S 3 02' W, annual change 2' 15". Survey made in 1858. 
 
 ( 96 ). Sometimes the letters T. M. are placed after a bearing to 
 denote that it is based on a true meridian, and M. M. sometimes 
 follows a magnetic bearing to show that it is based on the mag- 
 netic meridian. These precautions are necessary, and their omis- 
 sion is frequently a cause of much perplexity to surveyors. 
 
 After the bearing of the line has been determined, the survey of it is 
 entirely similar to the survey of lines whose true bearings are given, 
 
 ( 97 ). When the surveyor finishes a random line, he generally 
 walks back along it and moves all the stakes to the true line, and 
 perhaps marks trees that stand on or near the true line, so that it 
 may be the more easily found in he future.
 
 MANUAL OF PLANE SURVEYING. 59 
 
 He then enters its course and distance in his field-notes, or sur- 
 veyor's record, and this completes the survey, although he may 
 sometimes draw a plot of the survey, particularly if it is of a tract 
 of land. 
 
 ( 98 ). Flag-men, chain-men, and markers are usually sworn 
 before the survey begins. 
 
 ( 99 ). The surveyor should be careful about keeping his chain 
 of the proper length by testing it frequently with a standard 
 measure, and should watch his assistants closely until they un- 
 derstand what is required of them. 
 
 It would also be well for every county to have a true meridian 
 established, so that the variation of the needle might be found at 
 any time, and with but little trouble. 
 
 ( 100 ). Back sights should always be taken at intermediate 
 stations along the line in order to avoid possibility of deflection. 
 
 Having set off the change of variation on the vernier, the lines 
 of the tract may all be surveyed without moving the vernier again. 
 QUESTIONS ON CHAPTER V. 
 
 1. What is a "witness?" 
 
 2. How are witnesses marked ? 
 
 3. How are corners found from witnesses ? 
 
 4. What is meant by the "course and distance " of a line? 
 
 5. What must we know before we can run a line? 
 
 6. How do you set off east variation on the compass vernier.' 
 
 West? 
 
 7. Of what length is the chain usually employed in surveying? 
 
 8. If the random line lies to the right of the true line, in what 
 
 direction do you move the stakes? 
 
 9. Give the rule for correcting the stakes. 
 
 10. How should the distance between the extremities of the true 
 
 line and the random line be measured? 
 
 11. How is 5 chains and 12 links usually written by a surveyor? 
 
 16 chains and 4 links? 
 
 12. Give the first rule for finding the amount of error in as- 
 
 sumed bearing. The second. 
 
 13. What is meant by sine f Cosine ? 
 
 14. Give the two rules for correcting assumed bearings. 
 
 15. Give the rule for correcting old magnetic bearings. 
 
 16. What is the meaning of N 42 E, T M ? S 14 30' W, M M? 
 
 NOTK. Observe that when the true meridian is taken as the basis of the 
 survey, the variation of the needle is set off on the vernier, and when the mag- 
 netic "meridian serves as the basis, the change of variation is set off on the 
 vernier.
 
 CHAPTER VI. 
 
 UNITED STATES RECTANGULAR SURVEYING. 
 
 ( 101 ). The statutes of the United States provide that, " The 
 public lands shall be divided by north and south lines run accord- 
 ing to the true meridian, and by others crossing them at right 
 angles, so as to form townships of six miles square, unless where 
 the line of an Indian reservation, or of tracts of land heretofore 
 surveyed or patented, or the course of navigable rivers may render 
 this impracticable ; and in that case this rule must be departed 
 from no further than such particular circumstances require." 
 
 ( 102 ). Again, that, "The township shall be divided into sec- 
 tions, containing, as nearly as may be, six hundred and forty acres 
 each, by running through the same, each way, parallel lines at the 
 end of every two miles, and by marking a corner on each of such 
 lines at the end of every mile." 
 
 ( 103 ). There are many other important provisions relating to 
 the subject of Public Land Surveying, but these will suffice. We 
 shall now see how they are carried out. 
 
 ( 104 ). The fundamental lines upon which a survey is based 
 are called the principal, meridian and base line. The first of these is 
 a meridian of the earth, and the second is a parallel of latitude. 
 Their point of intersection is called the initial point. Upon these 
 lines every piece of land included in the survey has a direct bear- 
 ing, and the whole survey itself is located by the number or name 
 of its meridian. For instance, the position of a small tract of land 
 in Indiana is determined by its distance north or south of the base 
 line and east or west of the principal meridian, but the survey of 
 nearly the whole State, as well as of other contiguous territory, is 
 governed by the second principal meridian which runs north and 
 south a short distance west of the center of the State. In like man- 
 (60)
 
 MANUAL OF PLANE SURVEYING. 61 
 
 ner, the survey of Ohio is based upon the first principal meridian 
 which serves as the western boundary of the State, the survey of 
 Michigan is regulated by the Michigan meridian, and the surveys 
 of Minnesota are referred to the fourth and fifth principal meri- 
 dians. 
 
 ( 105 ). The selection of an initial point is the first step in the 
 survey of any new territory, and this is always chosen at some 
 natural and imperishable land-mark found in or near the lands to 
 be surveyed. From this point the principal meridian is surveyed 
 north or south, or north and south, and the base line east or west, 
 or east and west. Upon these lines, which are surveyed with a 
 fine instrument and with the greatest possible precision, six-miles 
 distances are marked for township corners, one-mile distances for 
 section corners, and half-mile distances for quarter section corners. 
 Each of these corners is marked with a suitable monument, and 
 appropriate witnesses are also chosen. 
 
 (106). From each six-mile point on the base-line, east and 
 west of the initial point, another meridian is surveyed, and the 
 territory is thus divided into strips, each six miles wide, lying 
 north and south. These strips, when divided into townships, are 
 called ranges. The first one east of the principal meridian is called 
 range 1 east, the second is called range 2 east, the third range 3 
 east, and so on. In the same way the first one west of the meridian 
 is called range 1 west, the second range 2 west, etc. 
 
 ( 107 ). Similarly, lines running east and west from the six- 
 miles points on the principal meridian, divide the territory into 
 strips, each six miles wide, lying east and west. The meridians 
 running north and south and the parallels running east and west 
 thus divide the territory into townships, each of which is about six 
 miles square, and consequently contains thirty -six square miles 
 or sections. The first township north of the base-line in each 
 range is called township 1 north, the second township 2 north, and 
 so on ; and those south are named 1 south, 2 south, etc., to the 
 limit of the survey. The first township north of the base-line and 
 east of the principal meridian is described as township 1 north, 
 range 1 east, and, in a similar manner, every township is named 
 with regard to its distance from the base-line and from the princi- 
 pal meridian. This is conveniently shown in Fig. 15. 
 
 ( 108 ). Since meridians converge as they approach the pole, it 
 a evident that townships can not be quite square, and that every
 
 MANUAL OF PLANE SURVEYING. 
 
 township must be somewhat smaller than the township south of it 
 and larger than the one north of it, except in certain cases on the 
 base-line. In the northern part of the United States this conver- 
 gence is greater than in the southern part, and the north line of a. 
 
 
 
 1 
 
 
 
 
 
 
 
 s 
 
 
 T, 3 N 
 R.2E. 
 
 
 
 
 
 
 
 
 
 
 Base 
 
 T.I N, 
 R.2W. 
 
 
 T.I N. 
 R, 1 E. 
 
 
 
 Line. 
 
 
 
 
 
 
 
 
 
 
 T,2 S. 
 R.1W, 
 
 
 T.2 S, 
 R.2E. 
 
 
 
 
 
 e 
 
 J 
 
 
 
 FIG. 15. 
 
 township in some places is more than one hundred feet shorter 
 than the south line. To keep the error arising from this conver- 
 gence within reasonable bounds, lines called "correction lines" 
 have been surveyed every twenty-four miles or four townships on 
 the north side of the base-line, and every thirty miles or five town- 
 ships south of the base line, and always parallel to it. Upon 
 these correction parallels, the distances are measured off anew, 
 same as on the base-line, and they become secondary bases in the
 
 MANUAL OF PLANE SURVEYING. 63 
 
 survey, although townships are all referred to the base-line, just 
 as if they did not exist. 
 
 ( 109 ). For convenience, auxiliary meridians are also estab- 
 lished every eight ranges or forty-eight miles east and west of the 
 principal meridian, and the territory is, in consequence, divided 
 into rectangles each 48 miles long by 24 miles wide north of the 
 base-line, and 48 miles long by 30 miles wide south of the base-line. 
 
 ( 110). The manner in which the townships are surveyed may 
 easily be explained by Fig. 16. Those north of the base-line and 
 east of the principal meridian are surveyed by commencing at 
 the southeast corner of township 1 north, range 1 east, and run- 
 ning north, establishing section and quarter-section corners at 
 proper distances, four hundred and eighty chains, or six miles, to 
 the northeast corner of the township. From this point the sur- 
 veyor runs west six miles, or four hundred and eighty chains, to 
 the principal meridian and finishes the survey of the first town- 
 ship. He then surveys the next township north in exactly the 
 same way, and continues, as indicated by the numbers, until he 
 closes the first tier of townships on the correction parallel. In the 
 same way he begins at the base-line and surveys the next tier east. 
 The townships south of the base-line are surveyed in the same 
 way, except that the surveyor works toward the base-line instead of 
 from it, as when north, as shown by the numbers. 
 
 ( 111 ). West of the principal meridian and north of the base- 
 line the survey begins at the southwest corner of township 1 north, 
 range 1 west, and proceeds in the order of the numbers. South of 
 the base-line the process is entirely similar. It will be observed 
 that townships east of the principal meridian are surveyed by run- 
 ning first north and then west, and those west by running first north 
 and then eaxt. 
 
 ( 112 ). Excesses and deficiencies in the length of township lines 
 are thrown on the north and west sides of the townships so as to 
 fall ultimately into the north and west tiers of sections. These 
 are called fractional sections, and will be considered in due time. 
 
 ( 113). The township (congressional township) which we have 
 had under consideration must not be confounded with the civil 
 township. The former is always, when not fractional, six miles 
 square, but the latter may be any reasonable size or shape whatever. 
 
 ( 114 ). Let us now observe how the townships are divided into 
 sections. 
 
 NOTE ON ARTICLE 109. In later surveys the rectangles are made 24 miles 
 square north and south of the base-line.
 
 64 
 
 MANUAL OF PLANE SUKVEYING. 
 
 CORRECTION i $ 
 
 I \PARALLEL 
 
 
 22 
 11 
 
 " 
 
 /O 
 
 II 
 
 10 
 
 21 
 
 
 
 
 19 10 
 18 
 
 8 5 
 
 7 
 
 9 & 
 
 7 
 
 10 /9 
 
 rt 
 
 
 
 16 17 
 15 
 
 5 6 
 4 
 
 6 5 
 4 
 
 /7 /6" 
 /5 
 
 
 BASE 
 
 13 /4 
 12 
 
 Z J 
 
 3 2 
 
 74- /3 
 12 
 
 LINE: 
 
 
 18 
 27 
 
 14- 
 13 
 
 14- 
 /3 
 
 28 
 27 
 
 42 
 41 
 
 
 
 25 25 
 24 
 
 II 12 
 10 
 
 /2 /J 
 
 /O 
 
 26 ,25 
 
 40 39 
 38 
 
 
 
 21 ^3 
 
 21 
 
 8 9 
 
 7 
 
 9 8 
 
 7 
 
 23 22 
 21 
 
 37 36 
 35 
 
 
 
 13 20 
 18 
 
 5 6 
 4 
 
 5 5 
 4 
 
 20 /9 
 18 
 
 34 03 
 
 
 
 if n 
 
 15 
 
 2 3 
 
 , 1 
 
 3 1 
 
 17 l 
 IS 
 
 Zl 00 
 29 
 
 
 COH.| | ^ 
 
 1 | I/'AA, 
 
 FIG. 16.
 
 MANUAL OF PLANE SURVEYING. 65 
 
 1. Before the surveyor attempts to make this division, he ascer- 
 tains the bearings of the boundary lines of the township, so as to 
 be able to run the interior lines as nearly parallel to them as pos- 
 sible. 
 
 2. These bearings may generally be easily obtained from the 
 notes of the previous survey, according to the, directions we have 
 already given, but he may also obtain them by retracing a section 
 of one or more of the exterior lines of the township and determin- 
 ing the bearing from the line itself. He should also measure sec- 
 tions of the township line to see how his chain agrees in length 
 with the chain used in the previous survey. Having attended to 
 these preliminaries, he is ready to begin work. 
 
 3. The townships, as we have before stated, contain thirty-six 
 sections each, and these sections are numbered, as shown in Fig. 17. 
 
 
 90 
 
 68 
 
 5'l | 34 
 
 "7 
 
 6 
 
 5 
 
 4 
 
 3 
 
 2 
 
 1 
 
 
 39 
 
 67 
 
 50 
 
 31 
 
 16 
 
 
 86 87 
 
 65 66 
 
 4* 49 
 
 3" i* 
 
 .4 -.5 
 
 7 
 
 8 
 
 9 
 
 to 
 
 11 
 
 12 
 
 34 
 
 85 
 
 <H 
 
 47 
 
 30 
 
 13 
 
 
 82 3 3 
 
 62 63 
 
 45 46 
 
 28 39 
 
 1 12 
 
 18 
 
 17 
 
 16 
 
 15 
 
 14 
 
 13 
 
 BO 
 
 81 
 
 61 
 
 44 
 
 27 
 
 10 
 
 
 78 -79 
 
 69 60 
 
 42 43 
 
 25 2J6 
 
 8 9 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 76 
 
 77 
 
 58 
 
 41 
 
 24 
 
 7 
 
 
 74 75 
 
 56 5 7 
 
 39 40 
 
 22 2 3 
 
 5 C 
 
 30 
 
 29 
 
 28 
 
 27 
 
 26 
 
 25 
 
 72 
 
 73 
 
 55 
 
 38 
 
 2t> 
 
 4 
 
 
 70 71 
 
 5 3 5 4 
 
 36 s 
 
 15 20 
 
 2 3 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 
 6 3 
 
 5? 
 
 35 
 
 iS 
 
 
 
 FIG. 17.
 
 66 MANUAL OF PLANE SURVEYING. 
 
 The manner in which the sections are surveyed will now be ex- 
 plained. 
 
 4. The surveyor goes to the south-west corner of section thirty- 
 six to begin the survey. At this point he sets his compass at the 
 bearing of the east line of the township, which should be, but sel- 
 dom is, the true meridian, and runs north forty chains. Here he 
 establishes a quarter-section corner between sections thirty-five 
 and thirty -six, and then proceeds forty chains or one- half mile 
 further to the corner of the section, or rather to the corner of sec- 
 tions twenty-five, twenty-six, thirty-five and thirty-six, since these 
 four sections have a common corner here. Distances from the 
 starting point at which brooks, creeks and other objects of im- 
 portance are met on the line, are carefully noted. From this cor- 
 ner he runs a random line to the east line of the township. If 
 this line intersects the township line at the first mile corner, it is 
 marked back as the true north line of section thirty-six, but if it 
 does not, the distance which it misses the corner, either right or 
 left, is noted, and the line changed accordingly. 
 
 5. Having returned to the north-west corner of section thirty- 
 six, he next proceeds to survey section twenty-five in the same 
 manner, and he follows the route indicated by the figures until he 
 completes the survey of the eastern tier of sections. It will be ob- 
 served that when he completes the survey of section twelve, he 
 then finishes up the survey of section one by running north on a 
 random line and correcting back to the south-west quarter. 
 
 6. He next surveys the second tier of sections by beginning at 
 the south-west corner of section thirty-five, and proceeding north 
 in the same manner as in the survey of the first tier, and thus he 
 continues until he reaches the fifth tier. Here, after surveying 
 section thirty-two, he runs west from its north-west corner to the 
 range line or meridian and completes the survey of section thirty- 
 one, and continues to work north, surveying the fifth and sixth 
 tiers together, until he reaches the north line of the township. 
 
 (115). The township is now divided into sections, each of 
 which, except those in the north and west tiers, called fractional 
 sections, is sold as containing six hundred and forty acres of land, 
 more or less, and each quarter-section as containing one hundred 
 and sixty acres, more or less. The fractional sections generally 
 contain a greater or less quantity of land than the other sections, 
 because all excesses and deficiencies fall to them. In surveying
 
 MANUAL OF PLANE SURVEYING. 67 
 
 them, -however, the quarter-section corners between them are so 
 placed that the excesses and deficiencies fall to the exterior quar- 
 ters, and the interior quarters, or those touching the other sections 
 of the township, are sold as containing the proper amount of land 
 one hundred and sixty acres each. The exterior quarters are sold 
 as containing whatever the measurements of the survey indicate 
 that they contain. Section six is sometimes called the "double 
 fractional," and usually contains only one exact quarter. 
 
 (116). Whenever, in the course of a survey, an impassable bar- 
 rier, such as a lake or navigable river, is met, the surveyor estab- 
 lishes what is called a meander corner on its margin, and then 
 runs a meander line from this corner along the edge of the obsta- 
 cle. The rivers and lakes thus meandered are reserved in the sale 
 of the public lands. 
 
 (117). The surveyor, from the time the survey of the principal 
 meridian is begun until the township is divided into sections, 
 marks every half-mile of true line that he surveys with a corner, 
 and keeps an account in his field-notes of every important object 
 he meets in the survey, as well as a topographical description of 
 the country. He also makes two sets of corners on the correction 
 parallels, one for townships north, and the other for townships 
 south of the line. Aside from this it is not unusual to find two 
 sets of corners on interior parallels and meridians, owing to dis- 
 crepancies between contiguous surveys. 
 
 (118). The monuments used in marking corners are always 
 adapted to the country in which the survey is made, and their 
 position is generally witnessed by one or more bearing trees, or 
 mounds of earth thrown up around a stake or a stone, whose 
 courses and distances from the corner are carefully noted in the 
 field-books of the survey. These witnesses, if trees, are always 
 marked facing the corner, which enables them to be more easily 
 found at any subsequent time. 
 
 (119). This completes the work of the Government Surveyor, 
 or deputy, as he is usually called. He returns his notes to the 
 Surveyor General of his district, and these notes become the basis 
 of all subsequent surveys. The work of dividing and sub-dividing 
 the sections, which belongs to the county and private surveyors, 
 we shall consider in the next chapter. 
 
 (120). This beautiful system of land surveying, not unlike the 
 old Roman system, was devised about the year 1785, for the pur- 
 
 NOTE ON ARTICLE 117. In a few instances three sets of corners have been 
 established on range lines, but at the present time only one set is established 
 except on the base-line and correction parallels.
 
 MANUAL OF PLANE SURVEYING. 
 
 pose of preparing the North West Territory for settlement, and 
 has answered the purpose in an admirable manner. It is the re- 
 sult of mature deliberation, and exhibits no mean knowledge of 
 engineering skill, and, like many other great inventions, its beauty 
 and utility consist in its extreme simplicity. It has long since 
 outgrown the limits for which it was intended, and soon nearly 
 the whole territory between the western boundary of Pennsylvania 
 and the Pacific ocean will be united in one complete net-work of 
 sections. 
 
 The readiness with which it enables a surveyor to re-trace old 
 lines and determine the location of lost corners prevents an end- 
 less amount of litigation common to States not surveyed accord- 
 ing to this system. 
 
 QUESTIONS ON CHAPTER VI. 
 
 1. What are the fundamental lines of a survey? 
 
 2. What is their point of intersection called? 
 
 3. Upon what principal meridian is the survey of Indiana 
 
 based? 
 
 4. What is a range? A township? 
 
 5. Draw a diagram representing town 4 south, range 3 east. 
 
 6. How is the error caused by the convergence of the merid- 
 
 ians arrested? 
 
 7. How are townships north of the base-line and east of the 
 
 principal meridian surveyed ? South of the base-line and 
 west of the principal meridian? 
 
 8. What is the difference between a congressional township 
 
 and a civil township? 
 
 9. How may a surveyor ascertain the bearing of the lines that 
 
 bound a township? 
 
 10. How many sections in a township? How are they num- 
 
 bered? 
 
 11. Where does a surveyor begin work when he divides a town- 
 
 ship into sections ? 
 
 12. Describe the method of surveying the eastern tier of sec- 
 
 tions. The western. 
 
 13. Name the fractional sections. The double-fractional section. 
 
 14. What causes fractional sections? 
 
 15. How many acres in a section?
 
 MANUAL OF PLANE SURVEYING. 69 
 
 16. What quarters of fractional sections are generally full? 
 
 17. What is a meander line? 
 
 18. Why are two sets of corners needed on correction lines? 
 
 19. How far apart are the corners on lines surveyed by the gov- 
 
 ernment surveyor? 
 
 20. For what purpose was the rectangular system devised? 
 
 When? 
 
 NOTE ON CHAPTER VI. The system of surveying described in this Chapter 
 was not set forth in its present completeness at the beginning. The first 
 act of Congress on the subject was that of May 20, 1786, and under this act 
 the first public surveys were made. The territory covered by these surveys 
 forms a part of the State of Ohio, and is generally called the " Seven 
 Ranges " In it the sections are numbered north and south from the south- 
 east corner of the township. The Geographer of the United States directed 
 the surveys. Although the principles of the system have virtually re- 
 mained unchanged, the system itself has been made definite and concise 
 since iis inception.
 
 CHAPTER VII. 
 
 THE DIVISION AND SUB-DIVISION OF THE SECTION. 
 
 ( 121). The county or other surveyor makes all his surveys in 
 accordance with the field-notes of the original survey, a copy of 
 which forms a part of the public records of each county. 
 
 Subsequent surveys may prove that great irregularities exist in 
 the original survey, but none of the lines or corners can be changed. 
 
 (122). The ideal section of the young surveyor frequently 
 
 3 If 
 
 FIG. 18. 
 
 differs greatly from the real section he meets in practice. The 
 ideal section is very nearly a perfect square varying a little on 
 account of the convergence of the meridians ; it is bounded by 
 four straight lines, and contains almost exactly 640 acres of land. 
 
 (70)
 
 MANUAL OF PLANE SURVEYING. 71 
 
 The real section may sometimes be far from square; its boundary 
 lines may deflect every half-mile on its perimeter, and its area 
 may exceed by several acres the area of another section adjoining. 
 The surveyor, however, must adhere as closely as possible to the 
 original survey, and let the section and divisions and sub-divisions 
 of the section contain whatever the government deputy saw proper 
 to put into them. 
 
 (123). Let us now see what the principal divisions and sub- 
 divisions of the section are, and then consider the method of sur- 
 veying them, locating the corners, etc. 
 
 (124). Fig. 18 represents a section, with some of the main di- 
 visions and sub divisions laid off on its face. They are described 
 .as follows : 
 
 1. S. W. qr. 
 
 2. N. W. qr. 
 
 3. S. } N. E. qr. 
 
 4. E. \ S. E. qr. 
 
 5. W. } S. E. qr. 
 
 6. N. E.JN. Kqr. 
 
 7. S. J N. W. J N. E. qr. 
 
 8. N. E. i N. W. i N. E. qi. 
 
 9. N. W. \ N. W. \ N. E. qr. 
 
 Of these tracts, Nos. 1 and 2 each contain 160 acres; 3, 4 and 5 
 each 80 acres ; 6, 40 acres ; 7, 20 acres ; and 8 and 9 each 10 acre? 
 
 ( 125 ). Whenever an instrument of writing, such as a deed or 
 mortgage, implying responsibility to the amount of the descrip- 
 tion, bears on a tract of laud, the area is usually qualified by the 
 compound term " more or less." For instance, No. 1, above, would 
 be described as containing 160 acres, more or less ; No. 3, as con- 
 taining 80 acres, more or less, and so on. 
 
 ( 126 ). The corners of the section, or of the different parts of it, 
 are named from their position. The principal ones are the sec- 
 lion corners, J corners, \ corners, and J- J corners.
 
 72 
 
 MANUAL OF PLANE SURVEYING. 
 
 The numbers on the diagram correspond with the 
 names after similar numbers below. 
 
 to 
 
 !l 
 
 
 
 a / 
 
 S Z 
 
 3 
 
 
 / 3 
 
 1 
 
 3 
 
 z 
 
 S 2 
 
 B 
 
 
 
 
 
 
 IS 7 If 
 
 FIG. 19. 
 
 1. Section Corners : 
 
 (1). N. E. Corner. 
 (2). S. E. " 
 (3). S. W. " 
 (4). N.W. " 
 
 2. Quarter-Section Corners: 
 
 (5). N. \ Corner. 
 (6). E. \ 
 (7). S. \ " 
 
 (9). Center
 
 MANUAL OF PLANE SVRVEYING. 73 
 
 3. Half-Quarter Corners: 
 
 (10). N. H W. Corner. 
 
 (11). N. HE. 
 
 (12). E. i i K " 
 
 (13). E. \ S. " 
 
 (14). S. J i E. 
 
 (15). S. J i W. 
 
 (16). W.H& ' 
 
 (17). W.H>'. " 
 
 (18). N. H 
 
 (19). E. H 
 
 (20). S. H 
 
 (21). W.H 
 
 4. Fourth-Quarter Corners: 
 
 (22). N. W. Center Corner. 
 (23). N. E. " " 
 (24). S. E. 
 (25). S. W. " 
 
 ( 127 ). The exterior lines of the section are called section lines, 
 and the two lines that cross at the center of the section are called 
 center lines. 
 
 ( 128 ). We are now ready to examine the method by which the 
 position of each of the various classes of corners is determined. 
 
 1. The section corners, and the exterior quarter-section corners, 
 except in an occasional case on a town or range line, are set by the 
 Government deputy, and the surveyor who follows him sets the re- 
 maining quarter-section corner (center) and all the minor corners. 
 
 2. The section is divided and corners set according to instruc- 
 tions from the proper authority, and the following is the author- 
 ized method of setting the center corner : 
 
 (1). A line is run connecting the N. J corner with the S } cor-
 
 74 MANUAL OF PLANE SURVEYING. 
 
 ner, and another connecting the E. | corner with the W. corner. 
 The point of intersection of these two lines is taken for the center 
 of the section. 
 
 The preceding is the method in general use, and is perhaps the 
 most equitable one that could be devised, but the following has 
 been used in some places : 
 
 (2). A line is surveyed connecting the E. corner with the \V. } 
 corner, and the middle point of this line is taken for the center 
 of the section. 
 
 If the section lines were straight from one corner of the section 
 to the other, and the quarter-section corner midway between the 
 section corners, the corner determined by this method would coin- 
 cide in position with the one determined by the other; but as this 
 is not always the case, they may differ considerably in position. 
 
 3. To Set a Half-Quarter Corner. Kun a line along the quarter- 
 section, on the side upon which the corner is to be set, and from 
 one corner to the other. Bisect this line for the corner. 
 
 For example : To set the E. J $ corner, we connect the center 
 corner and E. J corner with a line, and the middle point of this 
 line is the required corner. 
 
 4. To Set a Fourth- Quarter Corner. -First set a i } corner on each 
 of two opposite sides of the quarter-section. Then connect these 
 two corners with a line, and bisect this line for the } corner. 
 
 To illustrate : In order to set the N. E. center corner, it is nec- 
 essary first to set the N. i E. corner and the E. i J- corner, or the 
 E. J J N. corner and the N. } corner. The middle point of a 
 line connecting one corner with the other, in either set, for it is 
 immaterial which is taken, will be the required corner. 
 
 5. The same methods are employed for setting corners to the 
 divisions of the fourth of quarter-sections. For instance, to set 
 the north-east corner of the S. $ N. W. J N. E. qr., it is necessary 
 only to bisect the line between the N. E. center corner and N. 
 E. corner. 
 
 EXAMPI/2S. 
 
 ( 129 ). (1). How would you set the S. H corner? 
 (3). How is the S. J J W. corner set? 
 (4). Describe the method of setting the S. W. center 
 corner. 
 
 ( 130). We are now prepared to understand how the divisions 
 and sub-divisions of the section are surveyed. 
 
 1. A quarter-section is surveyed by running the two exterior
 
 MANUAL OF PLANE SURVEYING. 75 
 
 Lalf-mile lines, and the two center lines of the section, in order to 
 locate its interior corner and fix its interior boundaries. 
 
 2. A half-quarter is surveyed by first surveying as many of the 
 lines of the quarter as enter wholly or in part into its boundaries, 
 then whatever other lines are necessary to determine its remain- 
 ing corners, and finally the lines connecting these corners with 
 one another, or with others. 
 
 For instance, to survey the S. S. E. qr., it would be necessary 
 to run the south line of the quarter, the east line, the two center 
 lines of the section, and the E. and W. center line of the south- 
 east quarter. 
 
 3. A fourth-quarter is surveyed on the same principle as the 
 half-quarter. 
 
 For example, in surveying the S. E. J S. E. qr., it is necessary 
 to survey the south and east lines of the quarter, the E. and W. 
 and N. and S. center lines of the section, either the E. and W. or 
 the N. and S. center line of the S. E. qr., and finally the north line 
 of the fourth-quarter, if the N. and S. center line has been sur- 
 veyed, or the west line, if the E. and W. center line has been sur- 
 veyed. 
 
 ( 131 ). As a general rule for the survey of a tract of land bear- 
 ing a relation to the section, the following is submitted : Run 
 lines to connect the known corners of the tract when no unknown 
 corner intervenes between them, then such lines as are necessary 
 to determine the location of unknown corners, and finally lines to 
 connect these newly located corners with one another, or with 
 others. 
 
 ( 132 ). In many cases some, if not quite all, the boundary lines 
 of a tract of land are known. There is seldom any need of re- 
 surveying these, except where it must be done in order to establish 
 other lines or corners. 
 
 EXAMPLES. 
 
 (133). What lines would a surveyor have to run in order to 
 establish all the boundaries of each of the following described 
 tracts? 
 
 (1). S. W. qr. 
 
 (2). N..JN. E. qr. 
 
 (3). S. } N. W. qr. 
 
 (4). N. E. J S. W. qr. 
 
 (5). N.W.JN.W.qr.
 
 /6 MANUAL OF PLANE SURVEYING. 
 
 ( 134 ). So far we have dealt exclusively with corne-s, lines, 
 and tracts which may be called independent : 
 
 The corners, because their position is determined by the division 
 of certain lines, and is not definitely fixed, so far as distance is 
 concerned, by any other point in the section. 
 
 The lines, because they connect the corners, and may, therefore, 
 vary in a limited degree either in course or distance, or both. 
 
 The tracts, because they are limited by the lines and are not 
 definitely fixed as to area or figure. 
 
 ( 135 ). To illustrate the preceding still further, suppose the 
 north line of a quarter-section to be 36 chains long, instead of 40 
 chains long, and the contents of the quarter-section to be 148 
 acres, instead of 160 acres. The J J corner on the north line will 
 then be 18 chains from the section corner, and the same distance 
 from the \ corner, and each of the lines will be but 18 chains in 
 length, and a fourth-quarter out of the quarter-section may fall 
 short three or four acres. If, now, the north line of the quarter- 
 section had been longer, the N. 5 \ corner would have been 
 further from each of its north corners, and the area of the 
 fourth-quarter would have been greater. 
 
 (136). There is a class of corners, lines, and tracts, however, 
 that may be called dependent : 
 
 The corners, because their distance is fixed from some given 
 point, and is not obtained by bisecting a line. 
 
 The lines, because they connect the corners, and are conse- 
 quently of a definite course and distance. 
 
 The tracts, because they are bounded by the lines, and their 
 area, therefore, is not affected by the excess or deficiency of land 
 in the section. 
 
 Dependent corners, then, are those whose position is definitely 
 fixed ; dependent lines connect dependent corners, and dependent 
 tracts are bounded by dependent lines. 
 
 (137). Dependent lines and tracts are surveyed without any 
 reference whatever to the division or sub-division of the section, 
 although they may depend on some corner in the section as a base. 
 
 A tract may be partly dependent and partly independent. 
 
 ( 138). The following are examples of descriptions of depend- 
 ent tracts: 
 
 (1). N. 45 E. 16.00; thence N. 45 W. 10.00; thence S. 45 W. 
 16.00; thence S._45 E. 10.00, to the place of beginning.
 
 MANUAL OF PLANE SURVEYING. 77 
 
 (2). Commencing at the S. E. corner of section 22, town 3 N., 
 range 4 E. and running thence N. 15 E. 12.00; thence S. 45 E. 
 12.00; thence S. 75 W. 12.00, to the place of beginning. 
 
 ( 139). In a dependent tract the course and distance of each of 
 its boundary lines are usually given in the description of it, and 
 it is then said to be described by " metes and bounds." 
 
 ( 140). The rules given for setting corners, running lines, and 
 surveying tracts, in full sections, also apply to fractional sections, 
 except where their fractional sides do not contain half, or much 
 more than half, the usual amount of land found in these parts 
 of sections, or where the amount they contain considerably ex- 
 ceeds the usual amount. In the first case, the outside tier of 
 fourths of-quarter is omitted, and in the second the excess is 
 usually thrown to them, and the inside tier of fourths-of -quarter 
 in the outside quarters of the sections, are left of their usual size. 
 If the deficiency is very great, perhaps the entire outside tier of 
 quarters is wanting. By act of Congress approved April 24, 1820, 
 fractional sections containing less than 160 acres are not to be di- 
 vided in the original survey. In the division of fractional sec- 
 tions, generally, such rules must be adopted as the exigencies of 
 the case seem to require. 
 
 ( 141 ). When a tract of land lies partly in one quarter of a 
 section and partly in another, each part should generally be de- 
 scribed and surveyed separately ; and the same may be said of 
 tracts extending into two or more sections, and sometimes also of 
 those extending into different fourths of the same quarter. The 
 following are examples : 
 
 (1). N. } N. E. qr., and N. E. J N. W. qr. 
 
 (2). S. W. i N. E. qr., and N. J N. W. J S. E. qr 
 
 (3). N. E. qr. Sec. 4, and N. W. qr. Sec. 3. 
 
 (4). S. E. i S. E. qr. Sec. 35, and W. \ S. W. qr. Sec. 36. 
 
 (5). S. E. J N. W. qr., and E. } N. E. \ N. W. qr. 
 
 In some of the cases an occasional line may be a boundary to 
 each part of the tract, as the east line of No. 5, described above. 
 
 QUESTIONS ON CHAPTER VII. 
 
 1. Does the section always contain exactly 640 acres? 
 
 2. Draw a diagram of a section and represent the following 
 
 tracts on it : N. E. qr.; N. W. } N. W. qr.; S \ S. W. qr.; 
 N. } N. E. } N. W. qr. 
 
 3. Why is the phrase " more or less " used in descriptions of 
 
 land in deeds, etc.?
 
 78 MANUAL OF PLANE SURVEYING. 
 
 4. Name the quarter-section corners. The J \ corners. The 
 
 J } corners. 
 
 5. What are the " center lines "? 
 
 6. What eight corners does the Government deputy establish 
 
 to nearly every section ? 
 
 7. Does he ever set an interior corner of a section? 
 
 8. Give the first method of finding the center of a section? 
 
 9. Prove that the first and second methods would agree, if the 
 
 section lines were straight from one section corner to 
 another. 
 
 10. How do you set a \ \ corner? A \ \ corner? 
 
 11. How would you survey a quarter section? A half-quarter? 
 
 A fourth-quarter? 
 
 12. Give a general rule for the survey of a tract of land bearing 
 
 a relation to the section. 
 
 13. What is the difference between independent and dependent 
 
 corners? Lines? Tracts? 
 
 14. Describe an independent tract. A dependent tract. 
 
 15. When do the general methods for dividing and sub-dividing- 
 
 sections not hold good in fractional sections? 
 
 16. When should different parts of a tract be surveyed sepa- 
 
 rately?
 
 CHAPTER VIII. 
 
 FIELD-NOTES. 
 
 ( 142 ). The field-notes of sectional surveys by the Government 
 deputy show : 
 
 1 . The witnesses taken at section and quarter-section corners. 
 
 2. The length of the fractional lines in fractional sections. 
 
 3. The number of acres in each of the fractional quarters of 
 fractional sections. 
 
 4. The offsets between section corners in one township and the 
 corresponding ones in the adjoining township. These offsets are 
 sometimes found on town and range lines as well as on correction 
 parallels. 
 
 5. The distances from the starting point of a line at which 
 brooks and creeks are crossed, and trees and other objects met with 
 on the line. 
 
 6. A description of the timber, surface, soil, etc. 
 
 7. The courses and distances of meander lines surveyed along 
 rivers, lakes, etc. 
 
 (143). Each full section is supposed to contain 640 acres of 
 land, and it is always taken for granted that the distance between 
 a section corner and a quarter-section corner is 40 chains. The 
 lines are also supposed to run due north and south and east and 
 west. These suppositions, however, are strictly correct only in 
 comparatively few cases. 
 
 Quarter-section corners, like section corners, on town and range 
 lines answer for sections on each side of the line, but where an 
 offset occurs aud the closing section corner is set either at one side 
 or the other of the corner already on the line, the quarter-section 
 corner for the closing section is omitted. In this case the closing 
 section has only seven corners instead of eight. 
 
 NOTE ON ARTICLE (142). The field-notes of several .-tates have been turned 
 over to the State authorities, and may be procured from them when needed. 
 
 (79)
 
 80 
 
 MANUAL OF PLANE SURVEYING. 
 
 ( 144 ). For convenience of reference a plot of the township is 
 drawn after the survey is completed, and whatever is essential to 
 subsequent surveys is represented on it. 
 
 ( 145 ). Fig. 20 will give an idea of the manner in which a plot 
 of this kind is drawn, although space will not permit its being 
 made as complete as it should be. 
 
 
 
 A 
 J 
 
 I 
 
 ^ 
 
 / 
 K 
 
 L 
 
 l 
 
 6 < 
 
 3 5 < 
 
 > 4 * 
 
 > 3 c 
 
 > 2 < 
 
 
 7 > 
 
 > 8 > 
 
 n 9 i 
 
 r 10 i 
 
 i 11 i 
 
 > 12 
 
 18 ' 
 
 17 
 
 * (6 - 
 
 * 15 
 
 i- 14- 
 
 * 13 
 
 19 , 
 
 j 20 < 
 
 o 21 < 
 
 i 22 t 
 
 , 23 * 
 
 > 24 
 
 30 c 
 
 a 29 , 
 
 j 28 r 
 
 j 27 , 
 
 2G < 
 
 j 25 
 
 3! - 
 
 - 32 - 
 
 - 33 - 
 
 - 34 - 
 
 - 35 - 
 
 - 36 
 
 w; 
 
 u 
 
 T 
 
 FIG. 20. 
 
 The capital letters on the margin designate the section corners 
 on the town and range lines, and the small letters the quarter- 
 section corners. 
 
 The interior section corners are designated by the numbers of 
 sections. Thus, the southwest corner of section one is numbered
 
 MANUAL OF PLANE SURVEYING. 81 
 
 1, 2, 11, 12, because it serves as a corner to each of these sections. 
 
 The interior quarter-section corners are designated as corners 1 
 to 6, respectively, on the line B E, I W, or whatever line it may be. 
 
 ( 146 ). Attached to the plot of the township is a list of the wit- 
 nesses at each of the corners, generally on the principle of the fol- 
 lowing : 
 
 1. Exterior corners. 
 
 Sections. 
 
 At A. Be 6 N 14 W 32, Ash 16 S 12 W 17. 
 At B. Oak 10 S 19 E 11, Hickory 18 N 5 W 6. 
 At C. Maple 14 N 12 E 41, Poplar 28 S 72 W 19. 
 Qu arter-sections. 
 
 At a. Oak 14 N 61 W 14, Sugar 15 S 16 W 13. 
 At b. Elm 26 S 12 E 25, Ash 9 S 63 W 14. 
 
 2. Interior corners. 
 
 Sections. 
 
 (1). Cor.ofl,2,ll,12,Maplel5N10E19,Elml6S71E12. 
 
 (2). Cor. of 2, 3, 10, 11, Oak 36 S 15 W 12, Ash 20 N 82 W41. 
 On the line B R (Quarter-section corners). 
 
 (1). At 1. Be. 12 N 16 E 42, Gum 14 S 15 W 22. 
 
 (2). At 2. Pop. 28 S. 46 E 27, Ash 20 N 29 W 31. 
 
 In a similar manner the quarter-section corners on the lines H 
 X, I W, J V, etc., are also numbered and the witnesses given to 
 each. 
 
 Each of these lists is extended so as to include all the corners of 
 that particular class. 
 
 ( 147 ). The following particulars are usually shown on the face 
 of the plot : 
 
 Length of fractional lines : 
 
 B to 6, 39.07. 
 
 C to 6, 38.49. 
 
 D to 6, 38.03, and so on with all the other fractional lines.
 
 82 MANUAL OF PLANE SURVEYING. 
 
 1. Area of fractional quarters. 
 
 N. E. qr. sec. 1, 159.17 acres. 
 N. W. qr. sec. 1, 157.51 acres. 
 N. E. qr. sec. 2, 155.70 acres. 
 
 2. Creeks, etc. 
 
 N from R 31.42, creek running S. W., 43 links wide. 
 
 E from 25, 26, 35, 36; 22.16, creek running S.W., 41 links wide. 
 
 3. Offsets. 
 
 B 41 links E. of corner in town north. 
 L 59 links S. of corner in range west. 
 
 Only a few instances are cited in each case to show the general 
 plan. 
 
 SUBSEQUENT NOTES. 
 
 ( 148 ). Every surveyor should be provided with a copy of the 
 original field-notes of his county, together with notes of all the 
 surveys made by his predecessors. These notes, with the addi- 
 tions he himself makes from time to time (provided he and his 
 predecessors are authorized surveyors), constitute the surveyor's 
 records of the county. 
 
 ( 149 ). These records should contain a plot of each piece of 
 land surveyed, showing its area and the course and distance of 
 each of its boundary lines. The manner of drawing these plots is 
 explained in the chapter on " PLOTTING." 
 
 ( 150 ). From the regular county record is usually drawn a 
 pocket record for field use (1) of the original survey, and (2) of the 
 subsequent surveys. The notes of the original survey generally 
 fill but a small book, and may be arranged according to the 
 method given above ; but, unless the county is unusually small, it 
 is more convenient to have a separate book for each range in 
 which to enter the notes of the subsequent surveys. 
 
 ( 151 ). Each of these books should contain at least twice as 
 many pages as there are sections in the range. The left-hand 
 page in each one sh6uld contain a plot of a section about 4 inches 
 square divided into quarters, and the right-hand or opposite page 
 should be left blank, so that notes of the successive surveys in the
 
 MANUAL OF PLANE SURVEYING. 
 
 section may be entered upon it. These refer to the plot by num- 
 bers or letters in the manner shown in the figure. 
 
 1. (Left-hand page). 
 
 SECTION , 
 
 TOWN , RANGE 
 
 t C I 
 
 k 
 
 
 tO. 20 
 
 
 
 ^ * 
 
 
 A 
 
 ^ $ 
 
 75 
 
 . 
 
 Oa tO . 18 *> 
 
 ti ^ 
 
 h 
 
 
 3 " 
 
 A 
 
 
 to . /f 
 
 
 
 > 
 
 
 
 40. S/ 
 
 g 
 
 FIG. 21. 
 
 (This plot is only one-fourth the size suggested above, but will 
 serve to illustrate.) 
 
 2. (Eight hand page). 
 a. Be. 16 N 12 E 19, Ash 14 S 6 E 12. 
 B. Pop. 28 S 60 W 19, Walnut 30 N 16 E 41. 
 
 c. Be. 13 S 16 E 17, Elm 18 N 22 E 31. 
 
 d. Pop. 16 N 19 E 27, Ash 18 N 23 W 21. 
 A. Be. 23 S 17 W 40, Elm 16 N 21 W 14. ' 
 
 Bearings of principal lines : 
 a f. N 89 35 7 E. 
 c e. N 1 16 X W. 
 
 ( 152 ). In these cases the bearings are all given on the basis of 
 the true meridian. When the magnetic bearings are given, they 
 should be accompanied with the date at which they were taken.
 
 84 MANUAL OF PLANE SURVEYING. 
 
 ( 153 ). All interior surveys in the quarter-sections should be 
 represented by proper lines on the plot. The dotted line through 
 the north-east quarter in the figure indicates that this quarter has 
 been divided into north and south halves. The courses of roads 
 and creeks may also be shown on the plot. 
 
 (154). When the bearing of any independent line is not 
 known, it may generally be approximated by comparing it with 
 other lines in the section or adjoining sections. For instance, 
 there is but little difference between the bearing of the line a b 
 in the figure and that of the line c d, since the distance between 
 their northern extremities differs but 4 links from the distance be- 
 tween their southern extremities, and both lines are about of the 
 same length. 
 
 (155). The bearing of the line ab may be determined by the 
 following method, which has been explained in a preceding chap- 
 ter : 
 
 70 : 4 : : 60 / ^z=3'-f- = amount of correction. 
 1 16' 3 / =l 13'= bearing of line a b. 
 
 (156). This method of determining the bearing of one line 
 from that of another depends on the following principles: (1) 
 Two parallel lines have the same bearing, and (2) the difference 
 in bearing of two lines not parallel is in proportion to their incli- 
 nation to one another. The error caused by convergence in north 
 and south lines may be disregarded when the lines are short. 
 
 By reversing this rule we may determine the distance between 
 two lines at successive points when their distance apart at one 
 point and their difference of bearing are known. 
 
 ( 157 ). The surveyor's field-book is the memorandum he keeps 
 of his field-work. It contains only the rough entries, which are 
 changed in form and transmitted to the records. 
 
 ( 158 ). In surveys of independent tracts, perhaps the following 
 method of keeping it is as good as any : 
 
 Let us suppose a survey of the south-east quarter of section 9, 
 town 8, range 10, commencing at the south-east corner of the sec- 
 tion, and made March 29, 1881. If all the corners to the quarter- 
 section have been established previously, and the surveyor runs 
 the east line first, the entries may be somewhat as follows : 
 
 Mar. 9, 1881. 
 9 8 10. 
 
 Commenced S E cor. and ran N 2 15' W, 40.20 to E } cor., Be
 
 MANUAL OF PLANE SURVEYING. 
 
 85 
 
 20 N 15 E 36, Ash 10 N 41 W 12, M E 16 links. At 16.30 from 
 S E cor. crossed brook 8 links wide flowing S E. 
 
 Com. E J ran S 88 40' W, 40.12 to center of section. 19.00 
 crossed brook 6 links flowing S E. 
 
 Com. cen. ran S 2 30' E, 40.20 to S J. 
 
 Com. S J ran N 88 40' E, 40.15, M L 5 links. 
 
 The first line terminated 16 links east of the corner, showing 
 that the assumed bearing was about } degree too small. The 
 second and third lines struck the corners, but the fourth ran 5 
 links to the north, perhaps on account of some slight error in set- 
 ting the compass, as the assumed bearing was correct, if we com- 
 pare with the second line run. 
 
 (159 ). Wherever the witnesses are found in bad condition new 
 ones are taken, as was done at the E corner in this survey. 
 
 (160). In dependent surveys it is generally best to have the 
 page of the field-book ruled in five vertical columns: The first 
 giving the relative name or number of the station or corner at 
 which the line begins; the second, its course; the third, its dis- 
 tance; the fourth, the number of links missed to the right; the 
 fifth, the number of links missed to the left, as follows : 
 
 Sec. 5, Town 6, Kange 4. 
 Mar. 18, 1881. 
 
 Sta. 
 
 Course. 
 
 Dis. 
 
 R. 
 
 L. 
 
 A 
 
 N10W 
 
 16.00 
 
 4 
 
 
 B 
 
 N 4W 
 
 4.00 
 
 
 
 C 
 
 N 16 3<y E 
 
 18.00 
 
 
 6 
 
 D 
 
 ssiiyvf 
 
 9.00 
 
 
 
 E 
 
 N 14 W 
 
 11.24 
 
 
 
 F 
 
 S29W 
 
 7.26 
 
 5 
 
 
 FIG. 22. 
 
 ( 161 ). The station at which the surveyor begins is called "A," 
 and the succeeding ones are named in the order of the letters that 
 follow. 
 
 Witnesses taken at any of the corners may be described on the
 
 86 MANUAL OF PLANE SURVEYING. 
 
 opposite page and referred to the corner by the proper letter, n 
 follows : 
 
 At B. Be 24 N 23 W 16, S E corner house N 81 W 46. 
 " E. Elm 22 S 16 E 32, Oak 23 M 12 W 29. 
 " F. Large stone at corner. 
 
 The names of all the assistants in the survey are generally re- 
 corded, so that they may be known, if evidence should be needed* 
 in case of future disputes over the survey. 
 
 ( 162). The record made by county and other authorized sur- 
 "veyers is taken as prima facie evidence in favor of the surveys 
 made by them, and particular care should be taken in making 
 this record, as well as in field-work, to see that no mistakes are 
 committed. 
 
 ( 163 ). Other methods of keeping field-notes are also employed 
 by surveyors, but the ones described above are perhaps the most 
 simple, and they will answer every purpose. 
 
 QUESTIONS ON CHAPTER VIII. 
 
 1. What particulars are enumerated in the original field- 
 
 notes? 
 
 2. By referring to the original notes, how would you find the 
 
 witness to the south-west corner of section 21 ? The W 
 corner of section 9? The S J of section 22? 
 
 3. What sections touch section 15? 29? 26? 
 
 4. What do you understand by "Subsequent Notes?" 
 
 5. What constitute the surveyor's records of a county? 
 
 6. How is the bearing of an independent line sometimes ap- 
 
 proximated? 
 
 7. The north line of a quarter-section is 40.32 long, and the 
 
 south line 39.97 long. If the bearing of the east line is 
 N 2 19 W, what is the bearing of the west line? 
 
 8. Describe the field-book for independent tracts. For de- 
 
 pendent tracts. 
 
 9. When are new witnesses taken to a corner? 
 
 10. What is meant by prima facie evidence? Answer Evidence 
 that is held to be good until set aside by stronger evi- 
 dence.
 
 CHAPTER IX. 
 
 RE-LOCATION OF CORNERS. 
 
 ( 164). Perhaps, as a general thing, the most perplexing part 
 of a surveyor's work consists in re-locating the corners of the 
 original survey. As long as these or the witnesses to them re- 
 main, he seldom has any serious trouble in the survey of any 
 independent line of the section; but if one of them chance to 
 he lost, it must be re-located before any line bearing on it can be 
 surveyed, and its re-location, except in certain cases, is frequently 
 a matter of difficulty, if not, in some instances, of impossibility. 
 
 In the latter case there is no alternative, except to establish a 
 new corner. 
 
 (165). This difficulty arises from the fact before stated, that 
 section lines are usually broken at every original corner, and 
 these parts, into which the lines are divided, differ from one an- 
 other in length, so that the course and distance of one line may 
 not be the same as that of any other line in the vicinity, and it 
 would not do, therefore, to re-locate a corner by a line having the 
 same course and distance of a similar line, either in the same sec- 
 tion or any other section. The surveyor, consequently, must 
 resort to other means. 
 
 1. In the first place a diligent search should be made for re- 
 mains of the monument or witnesses at the missing corner. If 
 the witness trees have disappeared, it may be possible to find the 
 roots, especially if the ground has not been plowed, as traces of 
 them remain for many years. It is probable that some person in 
 the vicinity can give him some information relative to the corner 
 that will enable him to judge approximately as to where he 
 should look for the witnesses. 
 
 2. If, however, all search prove futile, and the course and dis- 
 
 (87)
 
 MANUAL OP PLANE SURVEYING. 
 
 tance of a line connecting this corner with some other corner that 
 can be found, be known, the missing corner may sometimes be 
 found by running this line from the known corner. 
 
 3. Or if the line run through the woods, it may be possible to 
 retrace it by the blazes on the trees, and thus determine the miss- 
 ing corner, providing the length of the line be known. 
 
 4. And, again, where subsequent surveys have been made in 
 one of the sections touching the corner, some of the subsequent 
 corners, taken in connection with the original corners, may enable 
 the surveyor to re-locate the missing corner by "projection," a* 
 follows : 
 
 (1). Suppose the S J corner of the section to be missing, and 
 that the S E corner and S } E corner can both be found. Now, 
 the S J E corner was evidently set while traces of the S corner 
 remained, and is midway between it and the S E corner. If now 
 we begin at the S E corner and survey a line westward, measuring 
 to the S J J- E corner and producing the line an equal distance 
 beyond it, the extremity of this line must mark the missing cor- 
 ner. If the line run either to one side or the other of the S J \ E 
 corner, the distance to the right or left must be noted. The S \ 
 corner will be twice this distance on the same side from the ex- 
 tremity of the line, as may be seen by noticing Fig. 23. 
 
 The numbers on the horizontal (true) line indicate the length 
 of each section of it, and those on the dotted vertical lines show 
 the distance between the random line and the true line at each of 
 the corners. 
 
 (2). This is simply the reverse of the method used in setting 
 the S \ \ E corner. 
 
 (3). If, instead of the S E corner and S \ \ E corner, we have, 
 for instance, the S E, E \ }, and S E center corners, it will be 
 necessary first to project the S \ \ E from the E \\ and S E cen- 
 ter, and then we may project the S , same as before. 
 
 EXAMPLES : 
 
 (4). 1. If we have the center and S \ \ corners, how may we 
 find the S i? 
 
 2. The W J, S \ }, and S W center corners are known, how may 
 the S W corner be determined? 
 
 3. The E }, E \ }, and S \ }, corners can be found, how may the 
 S \ be re-located?
 
 MANUAL OF PLANE SURVEYING. 
 
 (5). It must be borne in mind that two corners must be found 
 on the same side of a quarter-section before the third can be re- 
 located by this method. 
 
 16 
 
 FIG. 23. 
 
 5. When the surveyor finds it impossible to re-locate a missing 
 corner by any of the foregoing methods, or any other method, he 
 proceeds to establish a new corner, and in doing this he presumes 
 that the quarter-section lines do not bend at the corner to be established, 
 and, if it be a quarter-section corner, that it is midway between the 
 corners of the section. 
 
 NOTE ON SECTION 5, ARTiCLE(165). The surveyor must bear in mind that the 
 method here proposed is to be used only as a last resort. The original field 
 notes nearly always give the length, and sometimes the bearing, of every 
 half-mile of line surveyed, and by foilo\ying these as nearly as possible and 
 noticing the recorded objects on the line, the missing corner may gener- 
 ally be re-located without resorting to this method. In Fig. 24 the cor- 
 ner might be set by taking the distances on the two half mile lines, as 
 shown by the original notes, and in Fig. 25 by taking the distances on the 
 four half-mile lines as shown by the same. If the measurements do not 
 correspond with those of the Government Deputy, proportionate distances 
 must be taken and the corner set by them. This is the authorized method, 
 and the principles involved are general in their application.
 
 90 MANUAL OF PLANE SURVEYING. 
 
 ( 1 ). Suppose the missing corner to be the S J, the new corner 
 would be set by bisecting the line connecting the S E and S W cor- 
 ners of the section in the same way that a i } corner is set by bi- 
 secting the line between the two corners of the quarter-section. 
 
 ( 2 ). The corner thus established may be identical with the lost 
 corner, or may be some distance from it, but it is the best that can 
 be done. 
 
 (o). In the figure a case is illustrated in which the new corner 
 
 f 
 
 40,21 >/4 40.21 
 
 FIG. 24. 
 
 is a considerable distance from A. the supposed approximate loca- 
 tion of the old corner. The dotted lines represent the old lines, 
 and the numbers below the new line show the length of each sec- 
 tion of it. 
 
 (4). If the corner of a section be lost, a new one is set by sur- 
 veying the exterior lines of the adjacent quarter-sections as if they 
 did not bend at the section corner. The new corner will be at the 
 point of intersection of the two lines thus surveyed. 
 
 For instance, to set a new S E corner to section 2, connect the 
 S J corner of section 1 with the S ^ corner of section 2, and the E 
 J corner of section 2 with the E } corner of section 11. The point 
 at which the lines cross will be the new corner. 
 
 (5). As in the former case, this corner may not be identical 
 with the old corner. Fig. 25 represents a possible case in which 
 they are some distance apart. In actual work, however, such ex- 
 treme cases as we have noticed will seldom, if ever, come up. 
 
 ( 6 ). In any case, in setting a new section corner, if any J cor- 
 ner can not be found, the line must be produced to the next corner 
 that can be found. This may cause one of the lines to be li or 
 even 2 miles long, but the corner is set at the point of intersection, 
 same as before. 
 
 (166 ). In re-locating the original corners to the variable quar-
 
 MANUAL OF PLANE SURVEYING. 
 
 ters of fractional sections any of the first four methods given above 
 may be employed, but when a new corner must be established the 
 oth or last does not always hold good, except for the \ corner on 
 the town or range line, which is set midway between the section 
 corners, as in full sections. 
 
 ( 167 ). To set the i corner between two fractional sections, run 
 
 Set. Z. / 
 
 '# cor, 
 
 Sec, l t 
 
 Sec, II. 
 
 ^ COT. 
 
 FIG. 25. 
 
 a line from the interior section corner westward or northward, as 
 the case maybe, to the exterior section corner on the town or range 
 line, and locate the corner 40 chains from the starting point. 
 
 ( 168 ). To set an exterior corner to a fractional section, or to 
 any exterior section. 
 
 1. If there be an offset between the corner of one section and 
 that of the corresponding section in the other town or range, the
 
 92 MANUAL OF PLANE SURVEYING. 
 
 corner may be re-located by measuring this offset along the town 
 or range line, or correction parallel, in the proper direction. 
 
 2. When there is no offset, the corner must be set by crossing 
 the lines, according to the method used in interior sections. 
 
 EXAMPLES. 
 
 ( 169 ). 1. How may a new E } corner be set to section 11, pro- 
 viding the section corners on that side can both be found? 
 
 2. What must be done, if one or both of the section corners are 
 lost, before the quarter-section corner between them can be set? 
 
 3. How do you establish a new interior section corner? 
 
 4. If one or more of the exterior corners to the adjacent quar- 
 ter-sections be lost, what must be done in order to establish the 
 section corner? 
 
 5. How do you establish the ^ corner section between two frac- 
 tional sections ? 
 
 6. How do you re-locate an exterior section corner when there 
 is an offset on the town or range line? 
 
 (170). When possible, all corners, whether independent or de- 
 pendent, are re-located according to the rules by which they Vrere 
 located at first. 
 
 QUESTIONS ON CHAPTER IX. 
 
 1. When it is found impossible to re-locate a corner, what must 
 
 be done? [corner? 
 
 2. Why is not the new corner always identical with the original 
 
 3. Explain each of the different methods of re-locating original 
 
 corners. 
 
 4. In re-locating an original J corner by "projection," the ran- 
 
 dom line was found to be 16 links to the left of the $ ^ 
 corner. In what direction and how far will the re-located 
 corner be from the extremity of the random line? 
 
 5. How many corners must be found on the side of a quarter- 
 
 section before the remaining one can be re-located ? Why ? 
 
 6. What section in the township north corresponds with section 
 
 2? With section 5? What one in the township west cor- 
 responds with 7? With 30? 
 
 7. What townships touch T 2 N, R 3 E? T4S, B5W? Tft 
 
 N, E 1 W? 
 
 8. How are subsequent corners re-located?
 
 CHAPTER X. 
 
 DESCRIPTIONS OF LAND. 
 
 (171 ). No piece of land can be sold or surveyed, unless its de- 
 scription is known, and this description should be just as concise 
 and simple as possible. 
 
 (172). It would be better, if the length of lines and area of 
 tracts were always given in surveyor's measure, instead of in or- 
 dinary linear and square measure; yet when this is not done, they 
 may be reduced to their equivalents in surveyor's measure by the 
 following tables : 
 
 (173). LINEAR MEASURE. 
 
 100 links = 1 chain = 4 rods. 
 1,000 " =10 " =1 furlong. 
 8,000 " =80 " =1 mile. 
 
 SQUARE MEASURE. 
 1 sq. chain = 16 sq. rods. 
 10 " " =1 acre. 
 6,400 " " = Isq. mile. 
 
 It is plain that rods maybe reduced to chains by dividing by 4; 
 furlongs to chains by multiplying by 10 ; and miles to chains by 
 multiplying by 80. 
 
 EXAMPLES. 
 
 (174). 1. Reduce 15 rods to chains. 
 
 2. Reduce 1 fur. 3 rods to chains. 
 
 3. Reduce 1 mi. 3 fur. 24 rods to chains. 
 
 (175). Fractional parts of a chain should be expressed in 
 links: Thus, lOf chains should be written 10 chains and seventy- 
 five links, or simply 10. 75. 
 
 (93)
 
 94 MANUAL OF PLANE SURVEYING. 
 
 (176). As a general :mle for reducing from ordinary long or 
 linear measure to surveyor's measure, perhaps it would be well to 
 use the following: 
 
 Eeduce the denominations expressing the length of the line to 
 rods, and multiply by .25. The product will be the length of the 
 line expressed in chains and links. 
 
 To illustrate, suppose the length of a line to be 7 fur. 16 rods = 
 296J rods. = 296.5 rods. This multiplied by .25 equals 74.125, or 
 74 chains 12J links. 
 
 (177). The area of tracts in surveyor's measure is always 
 given in acres and hundredths, instead of in acres, roods, rods, 
 etc., as ordinarily. This will be explained in the chapter on 
 Computation of Area. 
 
 (178). Whenever an independent tract is to be described, 
 nothing whatever should be said of the course and distance of any 
 of its boundary lines, and it should be described simply as such a 
 division or sub-division of the section ; as, for instance, the south- 
 west quarter, or the north half of the north-east quarter, or the 
 north-west fourth of the south-east quarter, or the north half of 
 the south-east fourth of the north-west quarter, etc., etc. 
 
 ( 179). Errors like the following are frequently made in de- 
 scriptions: Forty acres in the form of a square in the south-east 
 corner of the section ; eighty acres off the south side of the north- 
 east quarter; one hundred and sixty acres in the north-east corner 
 of the section ; a strip twenty chains wide off the north side of the 
 south-west quarter; and so on. 
 
 Each of these descriptions is faulty, because the independent 
 division intended to be described may overrun or fall short in the 
 amount of land named in the description. If the tracts were not 
 independent, the descriptions would be good. 
 
 Correct the following descriptions : 
 
 ( 180 ). 1. 160 acres off west side of section. 
 
 2. Forty acres in the south-west corner of the north-east quarter. 
 
 3. Commencing at the X E cor. of the section ; thence running 
 south 20 chains; thence west 40 chains; thence north 20 chains to 
 the N } cor.; thence east to the place of beginning. Containing 
 80 acres. 
 
 4. 60 acres off the south side of the south-east quarter.
 
 MANUAL OF PLANK SURVEYING. 95- 
 
 (181 ). Sometimes descriptions contain errors that render them 
 worthless. The following are a few examples; tell where the 
 error lies in each one : 
 
 1. NEJNWqr. 
 
 2. S W } N E qr., containing 80 acres. 
 
 3. SJNJXEqr. 
 
 4. 60 acres in N E qr. 
 
 5. N W qr sec. 28, containing 80 acres. 
 
 6. Running north ; thence east 50 chains. 
 
 7. Eunning S 43 E, 11.21 ; thence N 32 W, 5.26 ; thence 
 
 S 8 3V E, 16.32, to the place of beginning. 
 
 Mistakes like the preceding are frequently made by persons who 
 are careless, or do not understand how lands should be described> 
 and sometimes give rise to vexatious litigation. 
 
 ( 182 ). It is best in nearly all cases to qualify the area of the 
 tract described by the phrase " more or less," as, perhaps, no two 
 surveys of the same tract, particularly if it be large, will ex- 
 actly coincide throughout, and of course the area will vary with 
 the length of the lines. 
 
 ( 183 ). In describing dependent tracts the course and distance 
 of each of their boundaries should be given, except, perhaps, in 
 occasional cases where they have a natural or artificial boundary, 
 as for instance, a creek or road, whose course and distance may be 
 determined at any time; but it is always best to be definite in re- 
 gard to boundaries when possible. 
 
 ( 184 ). The description should also state whether the bearings 
 are based on the true meridian or on the magnetic meridian. If 
 based on the magnetic meridian, the date at which they were 
 taken should be given. 
 
 ( 185 ). Where a line is described as running north, a due north 
 and south line is meant, and the same is true of south. Similarly, 
 an east line means one running due east, and a west line one 
 running due west. 
 
 ( 186). The survey of a tract of land is always made in ac- 
 cordance with the description, except where an obvious mistake 
 occurs, in which case the surveyor will have to exercise his judg- 
 ment in regard to the course to be pursued, as no rule can be given 
 that will apply to all cases. However, the decisions in the "Ap- 
 pendix " may assist him somewhat in arriving at a conclusion.
 
 96 MANUAL OF PLANE SURVEYING. 
 
 Sometimes the mistake is made in writing the original descrip- 
 tion of the tract, and at others in copying from preceding titles 
 and deeds. In the latter case, a comparison of the deeds will show 
 in what it consists. As soon as a mistake is discovered in a deed 
 or mortgage, or in any other instrument in which a great deal 
 may depend upon the description, steps should be taken by those 
 interested to have it corrected. 
 
 None but competent persons should be chosen to write descrip- 
 tions of land. 
 
 QUESTIONS ON CHAPTER X. 
 
 1. Why can not a tract of land be sold or surveyed without a 
 description ? 
 
 2. How many links in a rod? Chains in a mile? 
 
 3. Write 17 chains and 46^ links decimally. 
 
 4. Give the general rule for reducing from ordinary long or 
 
 linear measure to surveyor's measure. 
 
 5. How is the area of a tract of land expressed in surveyor's 
 
 measure? 
 
 6. Why should not the metes and bounds of an independent 
 
 tract be given in a description ? 
 
 7. Why should the phrase " more or less " be inserted in a de- 
 
 scription ? 
 
 8. Why is it necessary to state whether the bearings are based 
 
 on the true meridian or on the magnetic meridian? 
 
 9. If on the magnetic meridian, why should the date at which 
 
 they were taken be given ?
 
 CHAPTER XI. 
 
 OBSTACLES TO ALIGNMENT AND MEASUREMENT. 
 
 ( 187 ). It frequently happens in the course of a survey that the 
 line strikes an obstacle of some kind as, for instance, a building, 
 or a large pond, or creek that obstructs the measurement, if not 
 both line of sight and measurement. 
 
 (188). These obstacles may be divided into two classes: (1) Ob- 
 stacles that may be spanned by measurements along their sides 
 or margins, as a building, a pond, etc. ; (2) obstacles that can not 
 be spanned in this way, as rivers and lakes. 
 
 ( 189). Various methods are employed for spanning obstacles, 
 but only a few will be given, in order to prevent confusion. 
 
 FIRST CLASS OF OBSTACLES. 
 1. By Perpendiculars. Fig. 26 represents an obstacle on the line 
 
 FIG. 26. 
 
 A B which runs nearly to the side of it. At the extremity B, a 
 perpendicular, B C, is measured long enough to permit the line C 
 D to pass the obstacle. In this case the perpendicular is fifty link* 
 long. The line C D is then run at the bearing of the line A B, and 
 is, consequently, parallel to it. From the extremity, D, of this 
 line another perpendicular, D E, of the same length as the first, 
 7 (97)
 
 98 MANUAL OF PLANE SURVEYING. 
 
 is measured, which, of course, terminates on the original line pro- 
 duced through the obstacle. The survey of the line may then be 
 continued from E in the direction E F at pleasure, and the length 
 of C D added to the regular sections, A B and E F. 
 
 2. By an Equilateral Triangle. The line A B terminates some- 
 what further from the side of the obstacle than before, and the 
 
 FIG. 27. 
 
 line B C is then laid off at an angle of 60 with the line A B pro- 
 duced and measured to a suitable distance. In the case before us 
 it is 1 chain and 25 links in length. From the extremity, C, of 
 this line, the line C D, of equal length with it, is surveyed at an 
 angle of 60 with C B. We then have an equilateral triangle, and 
 the side B D is also 1 chain and 25 links in length. The line may 
 then be continued, and the distance through the obstacle, 1 chain 
 and 25 links, added to the other sections, as before. 
 
 3. (a) By a Right-angled Triangle. This method is similar to 
 the preceding one, and differs from it only in having a right-angle 
 
 FIG. 28. 
 
 at C, and angles of 45 at B and D in the triangle used. The side 
 B C is first surveyed, and then C D at right-angles to it and of
 
 MANUAL OF PLANE SURVEYING. 
 
 equal length. The distance from B to D is found by extracting 
 the square root of the sum of the squares of B C and C D, as the 
 side B D is the hypothenuse of the triangle. In this case the dis- 
 tance from B to D is equal to y(100)+ (100)* = 1.414. 
 
 (6) When the obstacle is a pond, or something that does not 
 obstruct the line of sight, the following method will be found most 
 convenient : 
 
 C 
 
 FIG. 29. 
 
 The line is measured to B, near the margin of the pond, and the 
 flag set at D on its continuation on the opposite side. C B is then 
 measured perpendicular to A B, and lastly the line C D is meas- 
 ured. We have now a right-angled triangle whose base is required 
 and may be found by extracting the square root of the difference 
 between the squares of C D and B C. In this example the base 
 B D equals /(125) 2 (75) 2 = 1.00. 
 
 In every case the line is to be continued from D at the bearing 
 of the first section, A B, and the distance through the obstacle 
 must be added. 
 
 4. By Symmetrical Triangles. When, as in the last case, the line 
 of sight is not obstructed, the following method may sometimes 
 be used : 
 
 F 
 
 A 
 
 FIG. 30.
 
 100 MANUAL OP PLANE SURVEYING. 
 
 From the extremity, B, of the line A B measure a line to C and 
 produce it to F, an equal distance beyond, and then from D meas- 
 ure the line D E so that C will be in the center. The line E F 
 will then be equal to the line B D. 
 
 5. When a fence is built on a line to be surveyed, it is best to 
 take an offset either to one side or the other, and allow for it when 
 the stakes are set on the true line, or the stakes may be moved back 
 a distance equal to the offset as they are set. They will thus be on 
 the random line, and may be corrected the same as if no offset 
 had been taken. 
 
 It is customary, after an offset has been taken, to measure back 
 to the random line as soon as the obstruction is cleared, but if the 
 corner be reached before this is done, the offset must not be forgot- 
 ten in measuring the distance the line runs to the right or left of it. 
 
 In doing this observe the following rules : 
 
 (1). When the offset is taken either to the right or left and the 
 offset line terminates on the opposite side of the corner, the dis- 
 tance missed by the random line will be equal to the distance 
 missed by the offset line, plus the offset, and it will terminate on 
 the same side of the corner as the offset line. 
 
 A. 
 IQ\ 
 
 FIG. 31. 
 
 In the figure an offset, A B, of 10 links was taken to the right, 
 and the offset line, B C, ran 10 links to the left of the corner A. 
 The random line, A B, will therefore terminate 20 links to the left 
 of the corner. 
 
 (2). When the offset line terminates on the same side as that on 
 which the offset is taken. 
 
 This involves two cases: (a) When the distance missed is 
 greater than the offset, and (6) when the offset is greater than the 
 distance missed. 
 
 (a). Subtract the offset from the distance that the offset line 
 misses the corner; the remainder will be the distance missed by 
 the random line. The termination of the random line will lie on 
 the same side of the corner as the termination of the offset line. 
 
 (6). Subtract the distance missed by the offset line from the
 
 MANUAL OF PLANE SURVEYING. 101 
 
 offset ; the difference will equal the distance missed by the random 
 line. The termination of the random line will be on the opposite 
 side of the corner from the termination of the offset line. 
 
 The offset line is always parallel to the random line. 
 
 In correcting the stakes on the offset line, it is best to correct as 
 if they were on the random line, and then move them a distance 
 equal to the size of the offset, and in a direction opposite to that 
 in which the offset is taken. This will put them on the true line. 
 
 6. Sometimes, when surveys are made over hills, it is impossi- 
 ble for the chain-men to see the compass or flag to which they are 
 running. In this case a stake should be put up at some promi- 
 nent point on the line by the surveyor, to which they may meas- 
 
 FIG. 32. 
 
 ure until they come in sight of the compass or flag. For instance, 
 if the chain-men are down in the valley A, of the figure, a stake 
 or flag should be set on the ridge, as it is impossible for them to 
 see the compass at B. 
 
 In chaining up and down hill it is frequently necessary to 
 double the chain or divide it into two sections, so that it may be 
 held in a horizontal position. A light steel chain is always pref- 
 erable to a clumsy iron one, as it will not sag so much. 
 
 SECOND CLASS OF OBSTACLES. 
 
 (190). 1. Suppose the obstacle to be a large creek. The line 
 is surveyed up somewhere near the edge and the flag set on the 
 line on the opposite shore. In Fig. 33, let A represent the point 
 to which the line is measured, and B the flag set on the opposite 
 shore. From the point A, a line of indefinite length is sighted at 
 right angles to A B. The compass is then set at any point not too 
 near A, as C, on this line, and turned so the sights will strike B. 
 The size of the angle A C B is then noted, and the point D on the
 
 102 
 
 MANUAL OF PLANE SURVEYING. 
 
 line A E sighted at an equal angle on the other side of A C. The 
 distance from A to B will then equal the distance from A to D. 
 
 FIG. 33. 
 
 2. From the point A, a perpendicular, A C, may be sighted and 
 another, C D, set off from its extremity. The point E, on the line 
 
 FIG. 34. 
 A C, is then found, and each of the sections, E C and E A, meas-
 
 MANUAL OF PLANE SURVEYING. 
 
 103 
 
 red. The distance from A to B may then be found by the fol- 
 lowing proportion : 
 
 CE : EA :: CD : (x = A B) ; 
 E AXCD 
 
 whence A B = 
 
 CE 
 
 3. A perpendicular is set off from the line B F at F, and another 
 at A, extended to the line B D. The distances, A F, A C, and 
 
 D 
 
 FIG. 35. 
 
 whence A B = 
 
 D F, are measured and the distance A B, found as follows : 
 (D F A C) : AC : : A F : (x = A B) ; 
 ACXAF 
 ' AC 
 
 ( 191 ). A great many other methods might easily be given, but 
 these will suffice. 
 
 These methods will, of course, answer equally well where the 
 point B is inaccessible and at the termination of a line. 
 
 In field-work the method that seems best adapted to the peculi- 
 arities of the case should be adopted. 
 
 QUESTIONS ON CHAPTER XI. 
 
 1. What is meant by an obstacle to measurement? To align- 
 
 ment? 
 
 2. How many classes of obstacles are there? Name one of 
 
 each class.
 
 104 MANUAL OF PLANE SURVEYING. 
 
 3. Describe the method of spanning an obstacle by perpen- 
 
 diculars. By an equilateral triangle. 
 
 4. In the survey of a certain line an obstacle is met. A line 
 
 is then surveyed 1 chain and 40 links, bearing from the 
 termination of the main line so as to pass the obstacle. 
 From the end of this line a perpendicular 90 links long 
 is measured back to the original line produced through 
 the obstacle. What is the distance through the obstacle? 
 
 5. Describe the method by symmetrical triangles. 
 
 6. What is an offset? 
 
 7. What is the difference between the offset line and the ran- 
 
 dom line? 
 
 8. An offset of 12 links is taken to the right, and the offset 
 
 line misses 13 links to the left. How far will the random 
 line miss the corner? 
 
 9. What two cases arise when the offset and termination of the 
 
 offset line both lie on the same side of the corner? 
 
 10. Give the rule for correcting the stakes on an offset line. 
 
 11. How do you set an intermediate stake for the flag-men to 
 
 run to when an elevation of land prevents them from see- 
 ing the compass or flagstaff? 
 
 12. When is it necessary to double the chain or divide it into 
 
 two sections ? 
 
 13. Explain each of the methods used in the second class of 
 
 obstacles. 
 
 14. In Fig. 34, A E = 1.40, C E = 90, and C D = 1.10. What 
 
 is the length of A B ? 
 
 15. In Fig. 35, AC = 1.22, A F = 98, and DF= 1.54. What 
 
 is the length of A B?
 
 CHAPTER XII. 
 
 COMPUTATION OF AREA. 
 
 ( 192 ). In computing areas the length of all lines should be 
 expressed in chains, chains and links, or links, as the case may 
 be, and the areas may then be reduced to acres and decimals of 
 an acre by the rules for multiplication and division of decimals. 
 Thus: 
 
 (1). 11.25 X 2.50 = 28.1250 sqch.; 
 28.1250 -=-10 = 2.81250 acres. 
 
 (2). 21.32 X 8= 170.56 sq.ch.; 
 170.56 -i- 10 = 17.056 acres. 
 
 (3). 22X15 = 330 sq.ch.; 
 330 -=-10 = 33.0 acres. 
 
 ( 193). The following special rules are deduced from the pre- 
 ceding processes : 
 
 (1). When each dimension contains hundredths of a chain 
 (links), the product may be reduced to acres by pointing off five 
 decimal places. 
 
 (2). When one contains hundredths and the other is expressed 
 in full chains, the product is reduced to acres by pointing off 
 three decimal places. 
 
 (3). When each dimension is in full chains, reduce to acres by 
 pointing off one decimal place. 
 
 If either dimension contain a fraction of a link, point off as 
 many additional places in the prodnct as are necessary to express the frac- 
 tion. Thus : 
 
 (1 ). 5.125 X 3.20 = 1 .640000 acres. 
 
 (2). 2.3725X5 = 1.18625 acres. 
 (105)
 
 106 MANUAL OF PLANE SURVEYING. 
 
 EXAMPLES. 
 
 (194). (1). 21.52 X 12.40 = how many acres? 
 (2). 40.24 X 20.31 = " 
 (3). 16.42 X18 = " 
 (4). 12 X13 = " " " 
 (5). 12.165 X 15-30 = " " " 
 (6). 15.2425X12.125= " 
 
 ( 195). Every tract of land is in figure a polygon, and its area 
 is computed according to the rule for finding the area of the par- 
 ticular polygon representing its contour. 
 
 ( 196 ). EECT ANGLES. 
 
 1. Multiply the length by the breadth and the product will be 
 the area. 
 
 2. If the rectangle be a square, the area may be found by squar- 
 ing one side. 
 
 ( 197 ). PARALLELOGRAMS. 
 
 Multiply the length of one side by the perpendicular distance 
 between this side and the opposite. The product will equal the 
 area. 
 
 In Fig. 36 the line A B represents the perpendicular, and the 
 
 AC 
 
 /5.60 
 
 FIG. 36. 
 
 area of the parallelogram is therefore equal to the product of 15.60 
 by 7.55= 11.778 acres. 
 
 If either of the sides B C or D E be given instead of B E or C D, 
 the perpendicular must be measured in the direction of the length 
 of the figure.
 
 MANUAL OF PLANE SURVEYING. 107 
 
 ( 198 ). TRAPEZOIDS. 
 
 Multiply the sum of the parallel sides by the perpendicular 
 distance between them, and half the product will be the area. 
 
 7*. 30 
 
 FIG. 37. 
 
 In Fig. 37 the line A B represents the distance between the par- 
 allel sides, and the area Is equal to ( (16.24 -\- 14.90) X 6.40) H- 2 = 
 9.4648 acres. 
 
 When the trapezoid contains two right-angles, the line between 
 them represents the perpendicular distance between the parallel 
 sides. 
 
 ( 199 ). TRIANGLES. 
 
 In computing the area of triangles, two general classes will be 
 considered : 
 
 1. Triangles whose base and altitude are given. 
 
 The area of triangles of this class is found by multiplying the 
 base by the altitude and taking half the product. 
 
 FIG. 38. 
 
 Fig. 38 represents a triangle whose base is 18.05 and altitude 
 5.90. Its area, therefore, is (18.05 X 5.90) -=- 2 = 5.32475 acres. 
 Eight-angle triangles belong to this class.
 
 108 MANUAL OF PLANE SURVEYING. 
 
 When the three sides are given, isosceles triangles may be 
 brought under this class by the following rule: 
 
 Square one of the equal sides and subtract the square of half 
 of the odd side. The square root of the difference will equal the 
 altitude. 
 
 The altitude of an equilateral triangle is found by extracting 
 the square root of the square of one side minus the square of 
 half of one side. 
 
 EXAMPLES. 
 
 (1 ). The base is 14.75 and the altitude 2.90. What is the area of 
 the triangle? 
 
 (2). The base and perpendicular of a right-angle triangle are 5.60 
 and 7.42, respectively. What is its area? 
 
 (3). In an isosceles triangle the even sides are each 9.16 in 
 length and the odd side 7.45. What is the area? 
 
 (4). What is the area of an equilateral triangle each of whose 
 sides is 7.25 in length? 
 
 2. Triangles whose altitude is not given. 
 
 The general rule for triangles of this class is the following : 
 
 (a). Take half the sum of the three sides. 
 
 (6). Subtract from the half sum each side severally. 
 
 (c). Multiply the half sum and three remainders together. 
 
 (d). Extract the square root of the product for the area. 
 
 FIG. 39. 
 
 Let Fig. 39 represents a triangle whose area is to be computed. 
 Then, 10.54 -f 14.60 + 8.72 = 
 33.86 -4- 2 = 16.93 
 16.93 10.54 = 6.93 
 16.93 14.60 = 2.33 
 16.93 8.72 = 8.21 
 
 ^716.93 X 6.39 X 2.33 X 8.21 = area.
 
 MANUAL OF PLANE SURVEYING. 
 
 109 
 
 EXAMPLES. 
 
 1. What is the area of a triangle, the sides of which are 4.20, 
 2.65, 3.71, respectively ? 
 
 2. The sides of a triangle are 2.91, 6.90, and 5.42, respectively. 
 What is its area? 
 
 It is sometimes more convenient to measure the altitude, and 
 'lius place the triangle under the first class. 
 
 ( 200 ). TRAPEZIUMS. 
 
 Divide the trapezium into two triangles. The sum of their 
 areas will be the area of the trapezium. 
 To do this, measure a diagonal of the trapezium. 
 
 to. 7? 
 
 FIG. 40. 
 Fig. 40 represents a trapezium, one of whose diagonals has been 
 
 A
 
 110 MANUAL OF PLANE SURVEYING. 
 
 measured. It will be seen that its area will equal the sum of the* 
 areas of the triangles A B D and B C D. 
 
 A serious mistake is sometimes made by incompetent persons by 
 multiplying together the half-sums of the opposite sides for the 
 area. 
 
 When one angle of the trapezium is re-entrant, as in Fig. 41, the 
 area may be found by subtracting the area of the triangle BCD 
 from that of the triangle A B D ; or it may be computed the same 
 as when the angles are all salient by omitting the triangle BCD 
 and measuring a diagonal from A to C. 
 
 ( 201 ). ANY FIGURE. 
 
 Divide the figure into triangles and compute their areas sepa- 
 rately. The sum of the areas of the triangles will be the area of 
 the figure. 
 
 The area of the tract of land represented in Fig. 42 is equal to- 
 
 FIG. 42. 
 
 the sum of the areas of the triangles A B F, B E F, B C E, and 
 CDE. 
 
 Sometimes, when a tract of land is narrow and has one irregn- 
 lar boundary, its area may be approximated by dividing it into 
 trapezoids. Fig. 43 represents a tract of this kind bounded on 
 one side by a creek. In cases of this kind the area of the tract m 
 equal to the sum of the areas of the trapezoids that compose it
 
 MANUAL OF PLANE SURVEYING. 
 
 Ill 
 
 FIG. 43. 
 
 (202). 
 
 COMPUTATION OF AREA BY LATITUDES AND DEPARTURES. 
 
 The method of latitudes and departures now to be developed is 
 simple, precise, expeditious, and universal in application, if the 
 course and distance of each of the boundary lines of the tract 
 whose area is to be computed are given. 
 
 (203). In plane surveying, meridians, like parallels of lati- 
 tude, are supposed to be parallel to one another, and the latitude 
 of a course is the distance between two parallels running through 
 its extremities, while the departure of a course is the distance be- 
 tween two meridians drawn through its extremities. In Fig. 44 
 the latitude of the course A B is represented by B C, and its de- 
 
 rl_ m 
 
 FIG. 44.
 
 112 
 
 MANUAL OF PLANE SURVEYING. 
 
 parture by A C. It is evident that the latitude of a course is equal 
 to the difference of latitude of its extremities, and that its depar- 
 ture is equal to the difference .of longitude of its extremities. 
 
 ( 204). The latitudes of courses bearing north are called north 
 latitudes or northings, and of those bearing south, south latitudes or 
 southings. Likewise the departures of courses bearing east are 
 called east departures or eastings, aud of those bearing west, west de- 
 f Tortures or westings. 
 
 In Fig. 45 the latitudes of A B and A F are northings, and of 
 
 FIG. 45. 
 
 A C and A D southings ; while the departures of A B and A C are 
 eastings, and of A D and A F westings. 
 
 (205). North latitudes are additive and are marked with the 
 sign -)-, plus, while south latitudes are subtractive and marked with 
 the sign , minus. In the same manner, east departures are 
 additive and marked +, and west departures are subtractive and 
 marked . 
 
 ( 206 ). If we now refer to Fig. 12, we shall see that the radius 
 A F, may represent the course A C, Fig. 46, whose latitude and 
 departure we wish to find. Then will C E, the departure, equal
 
 MANUAL OF PLANE SURVEYING. 
 
 113 
 
 the sine of the angle BAG, and E A, the latitude, equal the cosine 
 of the angle B A C. 
 
 ( 207 ). A Table of Natural* Sines and Cosines is given in the 
 
 FIG. 46. 
 
 APPENDIX, by which the latitude and departure of any course may 
 be easily found. In this table the length of the sine and cosine is 
 given for a radius equal to unity, for each degree and minute of 
 arc between and 90; and, hence, to find the latitude of any 
 course, it is necessary only to multiply the cosine of its bearing by the 
 length of the course, and to find the departure of any course, to mul- 
 tiply the sine of its bearing by the length of the course.!' 
 
 For instance, suppose it is required to find the latitude and de- 
 parture of a course bearing N 42 33' E, and 20.22 in length. 
 
 By referring to the Table, we find the cosine of the bearing to 
 to be .73669, and the sine of the bearing to be .67623. 
 
 Therefore, the latitude of the course will equal 
 
 .73669 X 20.22 = 14.8958, 
 and the departure of the course will equal 
 
 .67623 X 20.22 = 13.6733. 
 
 In using the Table, when the bearing is 45 or less, take the de- 
 grees from the top of the page and the minutes from the left-hand 
 
 * Called natural sines and cosines to distinguish them from logarithmic sines 
 and cosines. 
 
 fin this rule observe that the angles are measured to the right and left of 
 the vertical radii. If, as in Fig. 12, they were measured from horizontal 
 radii, the word "sine" would be used for "cosine," and "cosine" for 
 "sine" in the rule. 
 
 8
 
 114 MANUAL OF PLANE SURVEYING. 
 
 column, and when the bearing is greater than 45, use the degrees 
 at the bottom of the page and the minutes in the right-hand 
 column. 
 
 ( 208 ). EXAMPLES. 
 
 The course and distance are given in each of the following cases. 
 Find the latitudes and departures : 
 
 (1). N 52 16' W, 10.12. 
 
 This bearing is greater than 45; so the degrees must be taken 
 from the bottom of the page. Having found the double column 
 marked 52, ascend it to the line marked 16' on the right. We 
 now find the cosine to be .61199, and the sine to be .79087; there- 
 fore the Latitude =.61199 X 10.12, and the 
 Departure = .79087 X 10.12. 
 
 (2). S 15 40 / E, 11.41. 
 
 (3). N 21 32' W, 19.71. 
 
 (4). S 88 56' E, 73.98. 
 
 (5). N 66 25' E, 46.12. 
 
 ( 209 ). It will be seen that the columns in the table marked 
 "sine" at the top are marked "cosine" at the bottom, and that 
 those marked "cosine" at the head are marked "sine" below. 
 Care must be taken to use the heading for bearings read from the 
 top, i. e., for bearings not greater than 45; and the bottom mark- 
 ings for bearings read from below, i. e., for bearings greater than 
 45. 
 
 ( 210 ). TRAVERSE TABLES are sometimes used instead of the 
 Table of Natural Sines and Cosines in determining the latitudes 
 and departures of courses, and somewhat facilitate calculations in 
 many cases; but they are usually computed only to quarter- 
 degrees, and it has been thought best to use in the present work 
 only the more accurate method of natural sines and cosines. 
 
 (211). In the survey of every tract of land, the sum of the 
 north latitudes should equal the sum of the south latitudes, and 
 the sum of the east departures should equal the sum of the west 
 departures; and, hence, in plotting a survey, or making prepara- 
 tions to compute the area of the tract, we have an almost infalli- 
 ble means of testing the accuracy of the survey by which the 
 course and distance of each of its boundaries were determined. 
 
 (212). Let us now make an application to the survey of the
 
 MANUAL OF PLANE SUBVEYISG. 
 
 115 
 
 following described tract of land : Running N 10 E, 5.60 ; thence 
 S 35 3V E, 4.00; thence S 55 30' W, 4.00, to the place of begin- 
 ning- 
 Taking each course separately, we find the respective latitudes 
 and departures. 
 
 (1). Latitude of first course equals .98481 X 5.60 = 5.51. 
 
 Departure equals .17366 X 5.60 = .97. 
 (2). Latitude of second course equals .81412 X 4.00 = 3.25. 
 
 Departure equals .58070 X 4.00 = 2.32. 
 (3). Latitude of third course equals .56641 X 4.00 = 2.26. 
 
 Departure equals .82413 X 4.00 = 3.29. 
 
 The latitude of the first course is a north latitude, and must be 
 marked +, and the latitudes of the second and third courses are 
 south latitudes, and take the sign . Likewise, the departures 
 of the first and second courses are east departures and should be 
 marked +, while the departure of the third course is a west de- 
 parture and should be marked . 
 
 The separate courses, with the latitude and departure for each 
 one, may be entered in a diagram similar to the one used in keep- 
 ing field-notes (Art. 160), and a space left at the bottom for the 
 footings, as follows : 
 
 Sta. 
 
 
 Dis 
 
 Lat. 
 
 Dep. 
 
 
 
 
 + 
 
 
 
 + 
 
 . 
 
 A 
 
 N 10 OP E. 
 
 5.60 
 
 5.51 
 
 
 .97 
 
 
 B 
 
 835 3^ E. 
 
 4.00 
 
 
 3.25 
 
 2.32 
 
 
 c 
 
 C 55 3ff W 
 
 4.00 
 
 
 2.26 
 
 
 329 
 
 
 
 
 5.51 
 
 5.51 
 
 3.29 
 
 3.29 
 
 FIG. 47. 
 
 ( 213 ). The reason why the east departures should balance the 
 west departures, and the north balance the south latitudes will be 
 seen by noticing Fig. 48, which represents the above tract of land. 
 The north and south lines represent the latitudes, and the east 
 and west lines the departures. 
 
 ( 214). When the + latitudes balance the latitudes, and the 
 -f- departures balance the departures, as in the case just con-
 
 116 
 
 MANUAL OF PLAXE SURVEYING. 
 
 sidered, the survey is said to " close." Usually, however, owing 
 to slight inaccuracies in sighting the flag, reading the bearing of 
 the line, measuring the line, or, perhaps, all combined, neither the 
 latitudes nor departures balance. If the disagreement is consider- 
 able, a re-survey should be made, as there is probably an error 
 
 FIG. 48. 
 
 somewhere in the work; but if it is only slight, as, for instance, 1 
 or 2 links in 7 or 8 chains, it is probably due to some unavoidable 
 inaccuracy in the survey, and may be corrected by the following 
 rule: 
 
 Find the amount of the error for each chain, and distribute it among 
 the latitudes or departures, as the case may be, in proportion to their re- 
 spective lengths. Adding to those that are too small, and subtracting from 
 those that are too large.
 
 MANUAL OF PLANE SURVEYING. 117 
 
 This will cause them to balance and answer all ordinary pur- 
 
 ( 215 ). The longitude or meridian distance of a line is its mean 
 distance from an initial line or meridian. Preparatory to finding 
 the area of a tract of land, this meridian is conceived to be drawn 
 through its extreme western or eastern corner usually the west- 
 ern and the longitude of each of the courses of the tract is com- 
 puted from this meridian as a base. 
 
 In Fig. 49 this meridian is drawn through the western corner 
 
 FIG. 49. 
 
 of the tract, and the lines, A B, C D, E F, G H, and M O, repre- 
 sent the longitudes of the various courses. 
 
 (216). It will be observed that there is a difference between 
 longitudes and departures: The former show the mean distance 
 of the line from the meridian, while the latter indicate the differ- 
 ence in longitude of the two ends of the line. 
 
 ( 217 )- By referring to the figure, it will be seen that the lon- 
 gitude. A .6, of the first course is equal to half of its departure,
 
 118 MANUAL OF PLANE SURVEYING. 
 
 a b; and also that the longitude, C D, of the second course is equal 
 to c d, which equals the longitude of the first course, plus half the 
 departure of the first course, plus half the departure of the second 
 course, and it may easily be shown that the longitude of any course 
 is equal to the longitude of the preceding course, plus half the departure of 
 the preceding course, plus half the departure of the course itself. 
 
 ( 218 ). It must be borne in mind that the algebraic sum is 
 meant, and that west departures, having the minus sign, are really 
 subtractive. 
 
 (219). In order to simplify the rule, and at the same time 
 avoid fractions, it will be preferable to double each of the pre- 
 ceding expressions and use double longitudes. The following will 
 then be the general rule for finding the double longitudes of courses. 
 
 The double longitude of the first course is equal to its departure. 
 
 The double longitude of the second course is equal to the double longi- 
 tude of the first course -\- the departure of the first course + the departure 
 of the second course. 
 
 The double longitude of any course is equal to the double longitude of 
 the preceding course + the departure of the preceding course + the de- 
 parture of the course itself. 
 
 COMPUTATION OF AREA. 
 
 (220). We are now prepared to compute areas by means of 
 longitudes. Take for example the tract of land described in 
 Art. 212. 
 
 The area of the triangle ABC, Fig. 50, is equal to the area of 
 the trapezoid E A B D,plus the area of the triangle BCD, minus 
 the area of the triangle ACE. 
 
 Finding the area of each of these figures, respectively, we have : 
 
 Area of trapezoid EABD = DEXab = the product of the 
 latitude of the course A B by its longitude = (3.25 X 2.13) = .692 
 acre. (See Fig. 48.) 
 
 Area of triangle BCD = CDXef = the product of the lati- 
 tude of the course B C by its longitude = (2.26 X 1-645) = .371 
 acre. 
 
 Area of triangle ACE = CEXcd = the product of the lati- 
 tude of A C by its longitude = (5.51 X -485) = .267 acre.
 
 MANUAL OF PLANE SURVEYING. 
 
 119 
 
 Therefore, the area of the triangle A B C = .692+ .371 .267 = 
 .796 acre. 
 
 FIG. 50. 
 
 ( 221 ). In computations of this kind the product of a longitude 
 by a north latitude is called a north product, and by a south latitude, is 
 called a south product, and the difference between the north products and 
 south products is the area of the tract. 
 
 ( 222 ). Hereafter double longitudes will be used, and the differ- 
 ence between the north products and the south products will then 
 be double the area of the tract. 
 
 ( 223 ). The differeht steps in the process of computation may 
 be shown very nicely, and the work kept in compact form, by rul- 
 ing a sheet of paper in fourteen columns, adding seven to the right 
 of the seven shown in Fig. 47. In the first four of the added 
 seven write the corrected latitudes and departures, in the fifth 
 the double longitudes, and in the sixth and seventh the north 
 and south products or areas marked -j- and , same as latitudes.
 
 120 
 
 MANUAL OF PLANE SURVEYING. 
 
 The following will serve as an illustration, and at the same time 
 indicate the process used in computation. 
 
 i 
 
 + 
 
 I' 
 
 S 8 
 
 s s 
 
 S IS 
 
 e g |S 
 o * t>: 
 
 FIG. 51. 
 
 In this example the error in latitudes and departures amounts 
 to very little in each case, and might have been disregarded in 
 the calculation.
 
 MANUAL OF PLANE SURVEYING. 121 
 
 ( 224 ). The following is the general rule for computing areas 
 by double longitudes : 
 
 Multiply the double longitude of each course by its latitude. 
 If the latitude is north or plus, write the product in the column of plus 
 areas. If south or minus, u'rite the product in the column of minus areas. 
 Half the difference between the sums of the areas of these two columns 
 will be the area of the tract. 
 
 This rule holds good for any tract of land bounded by straight 
 lines. 
 
 ( 225 ). When the most westerly corner of the tract can not be 
 determined readily it is best to draw a plot of the tract according 
 to the directions given in the chapter on PLOTTING. 
 ( 226 ). Compute the areas of the following tracts : 
 (1). N3415'E, 2.73. 
 N 85 00' E, 1.28. 
 S 5645 / E, 2.20. 
 S 34 15' W, 3.53. 
 N 56 3(K W, 3.20. 
 (2). S 7315'E, 19.08. 
 S 19 30' W, 13.68. 
 N 69 15' W, 10.34. 
 S 20 15' W, 11.36. 
 N6800 / W, 9.06. 
 N 20 15' E, 23.56. 
 
 (3). South, 3.75; S 35 OO' E, 1.04; S 86 30' E, 5.02; N 82 
 00' E, 1.72 ; S 34 30' E 2.46 ; S 77 30' E, 4. 25 ; N 45 
 30' E, 9.78; N 2 40 X W, 233; West, 2.18; N 4 00' E, 
 1.30 ; N 83 45' W, 5.35 ; S 76 (KK W, 1.94 ; S 60 15' 
 W, 2.27 ; S 76 00' W, 3.47 ; N 73 30' W, 2.90 ; N 57 
 30' W, 1.65 ; S 21 00' W. 2.67. 
 
 ( 227 ). It is, of course, plain that a due north or south course 
 has no departure, and that its latitude is equal to its length. 
 Likewise, that a due east or west course has no latitude, and its 
 departure is equal to its length. 
 
 ( 228 ). It is not absolutely necessary that the meridian should 
 be drawn through the most westerly station in calculating the con- 
 tents, but it is generally more convenient to compute from a me- 
 ridian so drawn. Sometimes the surveyor imagines the meridian 
 to pass through the most easterly station.
 
 122 MANUAL OF PLANE SURVEYING. 
 
 If necessary, the areas may be expressed in the ordinary de- 
 nominations of land measure (acres, roods, and rods), instead of 
 in acres and decimals of an acre, by reducing the decimals to in- 
 tegers. Thus, .82 of an acre = (.82 X 4) = 3.28 R. .28 X 40 = 
 11.20 sq. rods. Hence, .82 acre = 3 K. 11.2 rods. 
 
 QUESTIONS ON CHAPTER XII. 
 
 1. Why should the length of lines be written in chains and 
 
 links? 
 
 2. When links are multiplied by links, how many decimals 
 
 are pointed off in reducing the product to acres? Links 
 by chains ? Chains by chains ? 
 
 3. Give the rule for finding the area of a rectangle. A paral- 
 
 lelogram. A trapezoid. 
 
 4. How is the area of a triangle found when the base and al- 
 
 titude are given? When the three sides are given? 
 
 5. How may the altitude of an isosceles triangle be found ? Of 
 
 an equilateral triangle? 
 
 6. State the rule for finding the area of a trapezium. 
 
 7. When may the area of a figure be computed by dividing it 
 
 into trapezoids? 
 
 8. What is meant by the latitude of a course? Departure? 
 
 9. W T hat are north latitudes? South latitudes? East de- 
 
 partures ? West departures ? 
 
 10. Describe the Table of Natural Sines and Cosines. 
 
 11. How do you find the latitude of a course from the Table? 
 
 The departure? 
 
 12. Give the rule for correcting latitudes and departures. 
 
 13. What is meant by the longitude of a line? What is the 
 
 difference between the longitude of a line and its depar- 
 ture? 
 
 14. State the rule for finding the double longitudes of courses. 
 
 15. W T hat are north products or areas? South products or 
 
 areas ? 
 
 16. Give the general rule for computing areas by double longi- 
 
 tudes.
 
 CHAPTER XIII. 
 
 LAYING OUT AND DIVIDING UP LAND. 
 
 ( 229 ). No general rule can be given either for laying out or 
 dividing up land, and in the present chapter only the most com- 
 mon cases that arise in practice will be considered. This is nec- 
 essary in order to keep our work within its intended limits as well 
 as to avoid the confusion that a multiplication of details would 
 cause. 
 
 As a general thing, a little ingenuity on the part of the surveyor 
 will enable him to devise a method to meet the exigencies of the 
 case he may have on hand when it can not be reached by any of 
 the rules given in this chapter. 
 
 ( 230 ). In the problems now to be taken up, the area and one 
 or more of the boundaries are in nearly all cases supposed to be 
 known, and it is required to find from these the length of certain 
 other boundary lines necessary to a survey of the tract. The pro- 
 cesses used in work of this kind are generally the reverse of those 
 employed in the last chapter, so that a careful study of operations 
 in computing areas will materially assist in the work now before us. 
 
 LAYING OUT LAND. 
 
 ( 231 ). To Lay Out a Square. The square root of the area ex- 
 pressed in square chains and decimals will represent the length 
 of one of its sides. 
 
 Thus, each side of a square tract of land containing 5 acres 
 equals v/50 = 7.07. 
 
 EXAMPLES. 
 
 1. What is the length of each side of a square tract containing 
 1 acre? 
 
 2. A piece of land in the form of a square contains 11 A. 3 R. 
 26 P. What is the length of its sides? 
 
 (123)
 
 124 MANUAL OF PLANE SURVEYING. 
 
 ( 232 ). To Lay Out a Rectangle. Divide the area by the length 
 of the given side. The quotient will be the length of the required 
 side. 
 
 Thus, if a rectangle contain 4 acres, and the given length be 5 
 chains, the length of the required side will equal (40 -*- 5) = 8 
 chains. 
 
 EXAMPLES. 
 
 1. The area of a rectangle is 14 acres, and the length 15.00, 
 what is the breadth ? 
 
 2. The area of a rectangular tract of land equals 10 A. 2 R 20 
 P., and it is 63 rods long. What is the breadth ? 
 
 Process 10 A. 2 E. 20 P. = 10.625 acres. 
 
 63 rods = 15.75. 
 (10.625 X 10) -s- 15.75 = 6.746. 
 
 ( 233 \. To Lay Owl a Parallelogram. (a). Divide the area by 
 the given length. The quotient will be the perpendicular distance 
 between the given sides. (Art. 197). 
 
 (6). Find one of the angles of the parallelogram according to 
 the methods explained in Articles (22) and (23). 
 
 ( c ). Divide the length of the perpendicular by the sine of the 
 angle thus found, and the quotient will equal the required side. 
 
 If the angle of the parallelogram be greater than 90, its sup- 
 plement* must be used in its stead. 
 
 Let Fig. 52 represent the parallelogram to be laid out ; its area 
 
 BACKS 
 
 A C 12 . o o 
 
 FIG. 52. 
 
 being 6 acres, and the length of the side A B, 12.00. Dividing 
 (6 X 10) = 60 sq. chains by 12, we find the perpendicular C D, to 
 be 5.00 long. 
 
 * The sine of an angle is always equal to the sine of the supplement of the 
 angle.
 
 MANUAL OF PLANE SURVEYING. 
 
 125 
 
 Suppose the angle A D E to equal 108; then its supplement 
 will be (180 108) = 72, the sine of which is .95106. 
 
 Dividing 5.00 by .95106, we find the length of the required side, 
 A D, to be 5.257. 
 
 Had the angle BAD been used, instead of A D E, the supple- 
 ment need not have been taken, as it is less than 90. 
 
 EXAMPLES. 
 
 1. In a parallelogram, the area is 12 acres, the length of one 
 side 14.00, and the measured angle equal to 61. What is the 
 length of the required side? 
 
 2. A field in the form of a parallelogram is 22.00 long and con- 
 tains 25 acres. The size of one of the angles is 96 45' ; what is 
 the length of the required side? 
 
 ( 234 ). To Lay Out a Eight-Angled Triangle. Let it be required 
 
 
 
 S 
 
 FIG. 53. 
 
 to lay out a right-angled triangle containing .3 acre by a line per- 
 pendicular to A B, Fig. 53. 
 
 (a). Measure the angle BAG and find its sine. 
 
 (6). Multiply the sine by any length of base, as A D, less than 
 the required base. The product will represent the altitude D E 
 of the triangle A D E. 
 
 (c). Compute the area of this triangle, and the length of the 
 side A B may be found by the following proportion : 
 
 Area A D E : Area A B C : : ( A D) 2 : (A B) J . 
 
 If A D = 1.20, and D E .80, the area of the triangle A D E will 
 be .048 acre. Then, 
 
 .048 : .3 : : (1.20) 2 : (A B) 2 ; whence (AB) 2 = 9, and A B = 3 chains.
 
 126 
 
 MANUAL OF PLANE SURVEYING. 
 
 The length of the side A C may be found by a similar propor- 
 tion: 
 
 Area A V E : Area A B C : : (A E) 2 : (A C) 2 . 
 
 ( 235 ). To Lay Out a Trnpezoid. Approximate the distance be- 
 tween the parallel sides by treating it as a parallelogram. The 
 distance thus found will be too short if the sides not parallel con- 
 verge, and too long if they diverge. Let Fig. 54 represent a tract 
 to be laid out or parted off. 
 
 B 
 
 FIG. 54. 
 
 By dividing the area by the length of the line A B, the perpen- 
 dicular is found to equal C D. The guess line E D is then meas- 
 ured, and the area of the trapezoid A B D E computed. The de- 
 ficiency of area is then added outside of D E, and the trapezoid 
 A B F G will then contain the required amount of land. If it still 
 vary a little from the exact amount, the line F G may be moved 
 further out or in, as the case may be. 
 
 In case of divergence of the sides, the overplus of area must be- 
 subtracted from the computed area, and the guess line moved 
 back instead of further out. 
 
 FIG. 55.
 
 MANUAL OF PLANE SURVEYING. 127 
 
 When the difference in length of the parallel sides can be deter- 
 mined without a measurement, no guess line need be surveyed, 
 providing the distance between the parallel sides be known. Let 
 A B C D, Fig. 55, represent a tract of land to be laid out or parted 
 off the main tract by a line perpendicular to its parallel sides. 
 
 Divide its area by the perpendicular distance between its par- 
 allel sides. The quotient will be the mean length of the trapezoid. 
 From this subtract half the distance D E for the shorter side, and 
 add for the longer side. 
 
 (236). To Lay Out any Figure. 'When the underlying princi- 
 ples of the particular problem differ from those obtaining in any 
 of the cases considered, it will probably be best to depend on cor- 
 rections made from guess lines, as in Art. 235, and thus reach the 
 result by approximations. Yet, in many instances, easy and beau- 
 tiful solutions may be reached by close observation and study. 
 
 DIVIDING UP LAND. 
 
 (237 ). Problems in dividing up land are such as grow out of 
 division of estates, generally among heirs. This division is made 
 with reference to the value of the respective shares (considering 
 location, improvements, quality of soil, etc.), and not with regard 
 to the quantity of land each share contains. If, however, taking 
 all these things into consideration, the value of the land is uni- 
 form throughout the tract to be divided, and the shares of the per- 
 sons among whom it is to be partitioned are equal to each other, 
 each should receive the same quantity. 
 
 In making a partition of land no share should be taken out in 
 such a way that it will injure any other share, when it possibly 
 can be avoided. 
 
 (238). The problems in dividing land introduced into this 
 chapter are of the nature of those that usually come up in prac- 
 tice where the land has been surveyed according to the Rectangu- 
 lar System. Only simple ones have been chosen. 
 
 ( 239 ). To Divide a Rectangle into Equal Parts by Lines Parallel to 
 a Side. Divide each of the lines upon which all of these parts are 
 to rest into as many equal sections as there are shares. Connect 
 the extremities of these sections by perpendiculars, and these per- 
 pendiculars will be the division lines of the shares.
 
 128 MANUAL OF PLANK SURVEYING. 
 
 Let Fig. 56 represent the south half of a quarter-section con- 
 ace 
 
 10.00 
 
 10.00 
 
 10.00 
 
 10.00 
 
 
 
 
 
 20 
 
 20 
 A. 
 
 i 
 
 I 
 
 20 
 A. 
 
 20 
 A. 
 
 10.00 
 
 ! 
 10.00 | 
 
 10.00 
 
 10.00 
 
 
 i d 
 
 / 
 
 
 
 FIG. 
 
 56. 
 
 
 taining exactly 80 acres. The perpendiculars, a b, e d, and e f, 
 divide it into four parts, each containing 20 acres. 
 
 ( 240 ). To divide a rectangle into any number of unequal parts bear- 
 ing a given relation to one another, by lines running parallel to a side. 
 Suppose that, on account of the varying value of the land in the 
 tract to be divided, the shares are to be to one another as the num- 
 bers 1, 2, and 5. In this case, divide the base lines into parts 
 bearing the same relation to one another as the shares, and con- 
 
 5.00 
 
 10.00 25.00 
 
 
 
 10 
 
 20 
 A. 
 
 ' 
 50 
 A, 
 
 5.00 
 
 10.00 
 
 25.00 
 
 FIG. 57. 
 
 nect the points of division by perpendiculars, as shown in the 
 division of the 80 acre tract in the figure. 
 
 Sometimes it is possible to divide land of varying quality so 
 that each share shall contain its portion both of the best and 
 worst. If we consider the unequal division in Fig. 57 to have 
 been caused by the difference in quality of the land in various 
 parts of the tract, it might have been possible to make the shares 
 all equal by dividing the tract in the direction of its length.
 
 MANUAL OF PLANE SURVEYING. 129 
 
 The figure of the shares may be almost as variable as the quan- 
 tity of land they contain. The rectangular form is preferred, but 
 of course can not always be preserved, even in the territory sur- 
 veyed according to the Rectangular System. 
 
 ( 241 ). Problems. 1. Divide a quarter-section of land into five 
 shares in the series 1, 2, 3, 4, 5, by lines running parallel to a side. 
 
 2. The commissioners, in a certain partition of a quarter-sec- 
 tion, set off the widow's dower of 30 acres in the form of a square 
 in the south-east corner, and divided the remainder, by lines 
 running north and south, equally among five children. What 
 was the width of each share ? 
 
 3. In a sale of a quarter-section for taxes, the lowest bid was 
 for fifteen acres, and this amount was set off in the form of a square 
 in the north-west corner. A few years afterward the remainder 
 of the quarter was offered again, and the lowest bid was for 
 twelve acres, which area was set off next to that first sold. What 
 were the dimensions of each piece ? 
 
 4. Divide the following described tract into four equal shares 
 by north and south lines: South half north-east quarter, and 
 east half north-east fourth north-east quarter, and south half 
 north-west fourth north-east quarter. 
 
 5. Divide a quarter-section into 7 equal shares by lines running 
 north and south, and write a description of each share, giving 
 metes and bounds. 
 
 6. Divide the following tract into 5 equal shares by north and 
 south lines, and write a description of each share : North half 
 south- west quarter, and south-west fourth north-west quarter, and 
 west half north-west fourth south-east quarter, giving metes and 
 bounds. 
 
 7., Divide the north-west quarter, and north half north-east 
 quarter, and north half north-east fourth south-west quarter, by 
 east and west lines, into 3 shares that will be to each other as 1, 
 2, and 3, and write a description of each share, giving metes and 
 bounds. 
 
 In the above examples each tract is supposed to contain exactly 
 the prescribed amount of land, and the boundaries to run due 
 east and west, or north and south, as the case may be.
 
 130 MANUAL OF PLANE SURVEYING. 
 
 QUESTIONS ON CHAPTER XIII. 
 
 1. Why will a study of methods used in computation of area 
 
 assist in laying ou.t and dividing up land? 
 
 2. How do you determine a side of a square from the area? Of 
 
 a rectangle ? 
 
 3. Give the rule for finding the required side of a parallelogram. 
 
 4. Explain the method given for laying out a right-angle tri- 
 
 angle. 
 
 5. How do you lay out a trapezoid from the area and 'length of 
 
 one of the parallel sides? 
 
 6. In partitioning land, which is considered, quantity of land 
 
 or value? 
 
 7. Explain the method of dividing a rectangle into equal parts 
 
 by lines running parallel to a side. 
 1 8. In dividing lands, what figure for the shares is preferred ? 
 
 NOTE ON CHAPTER XIII. The cases in dividing upland given in this 
 chapter do not apply except where the land has been surveyed according to 
 the Rectangular System. In States east of the Mississippi river, excepting 
 Michigan, Wisconsin, Illinois, Indiana, Ohio, Mississippi, Alabama and Flor- 
 ida, and even in many instances in these States, as well as in the ones west 
 of the river, the surveyor must modify the method as the case may require.
 
 CHAPTER XIV. 
 
 SURVEYING TOWN LOTS. 
 
 (242 ). The dimensions of town lots are usually given in feet, 
 instead of in chains and links, and, as a general thing, the lots are 
 all of the same size and numbered in regular order from 1 up, as 
 shown in Fig. 58. The larger figures indicate the numbers of the 
 
 FIG. 58. 
 
 blocks, and sometimes the lots in each block are numbered sepa- 
 rately ; as lot 5, block 2 ; lot 2, block 9, and so on. As the town 
 grows from the original plot, the lots in each addition are fre- 
 (131)
 
 132 
 
 MANUAL OF PLANE SURVEYING. 
 
 quently numbered and referred to the particular addition to which 
 they belong ; as lot 8, Brown's addition ; lot 7, Johnson's addi- 
 tion, etc. 
 
 ( 243). The survey of the town is generally based on some in- 
 dependent corner of the section in which it is situated, and im- 
 portant corners in various parts of the town should be marked 
 with durable monuments. Fig. 59 shows a few lots in a town lo- 
 cated on a section line, and the distance is given from the section 
 corner to the south-east corner of lot number 1. It will be seen 
 
 s 
 e 
 
 
 * 
 
 3 
 
 
 
 
 
 
 i 
 
 
 2 
 
 
 8 
 
 
 J 
 
 3 .ZS 
 
 c o 
 
 FIG. 59. 
 
 that stones are placed at the north-east corner of lot number 4 and 
 the south-west corner of lot number 8. These will enable the sur- 
 veyor at any subsequent time to make a survey in the town with- 
 out going to the section corner to find a starting point, thus saving 
 him time and trouble. 
 
 ( 244 ). Lots are usually rectangular in shape and about twice 
 as long as they are wide, but this is not always the case. They 
 may be any reasonable shape or size that adapts them to the plan 
 of the town. Likewise, streets and alleys generally cross one 
 another at right angles, though by no means always. 
 
 ( 245 ). The plot of a town should always be accompanied by 
 full explanations showing, 
 
 ( 1 ). The size of each of the lots. 
 
 ( 2 ). The width of each of the streets and alleys. 
 
 ( 3 ). The name of each of the additions. 
 
 ( 4 ). Any other explanations necessary to determine the bear- 
 ings of any of the lines which would have to be run in a survey 
 of the town.
 
 MANUAL OF PLANE SURVEYING. 
 
 133 
 
 ( 246 ). Suppose that in Fig. 58 the lots are each 100 feet long 
 and 50 feet wide, the streets 50 feet wide, and the alleys 16 feet 
 wide. Since the lots are rectangular, the north and south lines 
 are at right angles to the east and west lines. It is evident that 
 after finding a starting point, the surveyor need experience no dif- 
 ficulty in the survey of any of the lots. 
 
 If, for instance, he wishes to survey lot number 13, and can find 
 no corner except the one marked with a stone at the south-east cor- 
 ner of the town, he may start at the center of this stone, run west 
 266 feet to the west side of Main street, and thence north 166 feet 
 to the south-east corner of the lot to be surveyed. He can then 
 survey the lot without any trouble. Instead of running first west 
 and then north, he may run first north to the south-east corner of 
 lot number 29, and thence west to the corner of the lot to be sur- 
 veyed; or he may take other routes. 
 
 ( 247 ) Fig. 60 represents a portion of a town in which the lots 
 
 are of different sizes and shapes. All the lots west of Main street 
 are 50 ft. wide, except number 12, which is 60 ft wide, and num- 
 ber 14, which is 75 feet wide. 
 
 Main street bears N 40 W.
 
 134 MANTTAL OF PLANE SURVEYING. 
 
 Lots number 15, 16, 17, 18 and 19 do not belong to the regular 
 plot of the town, and are called out-lots. 
 
 The two alleys running north into Main street, and the one be- 
 tween lots 4 and 5 are each 20 ft. wide, and Main street and the 
 short street between lots 2 and 3 are each 50 ft. wide. 
 
 A stone monument marks the south-east corner of lot number 13. 
 
 The width of each tier of lots is marked in feet at the foot of 
 the tier. 
 
 ( 248 ). It is now a very easy matter to survey any of the lots 
 in the regular plot of the town. Take, for example, number 11. 
 To survey this lot, measure first west 280 ft., and thence north 200 
 ft. to its south-west corner. From this point set off a perpendicu- 
 lar and extend it to the street ; then measure north 50 ft. further 
 and set off another perpendicular as before. 
 
 ( 249 ). EXAMPLES. 
 
 1. How would lot number 1 be surveyed? 
 
 2. Explain a method of surveying lot number 14. 
 
 3. If the out-lots east of Main street were separated by lines 
 perpendicular to the street, what would be the bearing of the 
 lines? 
 
 ( 250 ). Town lots are measured either with a chain or tape. 
 
 The chain used for this purpose is usually 50 or 100 feet long 
 and divided into links, each 1 foot in length. It is made light, and 
 as greater accuracy is generally required in surveying town lots 
 than in ordinary surveying, its length should be frequently tested 
 by comparison with a standard measure. The length of the chain 
 is affected by wear, temperature, and accidents. 
 
 All measures used in surveying should be subjected to frequent 
 tests. Even in surveys where tolerable accuracy is sufficient, 
 there is no excuse for neglecting anything that would be conducive 
 to greater accuracy. 
 
 Tapes used in measuring town lots usually consist of a jointed 
 steel ribbon, but sometimes a linen tape through which a fine 
 brass wire is interwoven with the thread, is used. Common linen 
 tapes contract when wet and are not trustworthy. The steel tape 
 is the best.
 
 MANUAL OF PLANE SURVEYING. 135 
 
 QUESTIONS ON CHAPTER XIV. 
 
 1. How are town lots numbered ? 
 
 2. Upon what is the survey of a town usually based ? 
 
 3. What advantage is there in having important corners marked 
 
 by monuments? 
 
 4. What is the usual shape of town lots ? 
 
 5. State the explanations that should accompany the plot of a 
 
 town. 
 
 6. A street bears N 29 32' E. What is the bearing (obverse 
 
 and reverse) of a line perpendicular to it? 
 
 7. What kind of measures are employed in the survey of town 
 
 lots? 
 
 8. How is the length of the chain affected ?
 
 CHAPTER XV. 
 
 PLOTTING. 
 
 ( 251 ). Plotting is the operation of drawing to a scale upon 
 paper the lines of a survey, so that the plot will be a correct rep- 
 resentation of the actual lines surveyed. 
 
 ( 252 ). The instruments used in plotting are a drawing board, 
 t-square, ruler, drawing pen, dividers, protractor, and a diagonal 
 scale. 
 
 1. The drawing board should be made of pine, and its surface 
 should be perfectly smooth and level. The paper is fastened to 
 the drawing board while the plot is drawing. Perhaps the most 
 suitable size for a drawing board is about 30 inches square, 
 but 24 by 28 inches makes a very nice board. The paper should 
 be stretched evenly, and the edges pulled down over the edges of 
 the board and glued or tacked. 
 
 2. The t-square, so called on account of its resemblance to the 
 letter T, consists of a thin blade with parallel edges, to which is 
 attached a cross-head somewhat thicker than the blade, so as to 
 form a shoulder. The blade is usually about 24 inches in length, 
 and the cross-head about 10 inches. By laying the blade on the 
 paper and pressing the shoulder against the edge of the drawing 
 board, as shown in Fig. 61, perpendiculars may be drawn to any 
 edge of the paper. 
 
 3. A good box-wood ruler, about 12 inches long, divided to 16ths 
 of an inch, will answer every purpose in plotting. This ruler 
 should have one beveled edge, upon which the divisions are 
 marked, and one projecting edge, along which the pen should be 
 pressed in drawing lines. 
 
 4. The drawing pen consists of two steel blades, whose distance 
 apart is regulated by a thumb-screw. A little practice will en- 
 
 (136)
 
 MANUAL OF PLANE SURVEYING. 
 
 137 
 
 able any person to draw nice smooth lines of any desirable width 
 with the drawing pen. India ink should be used, as it flows more 
 smoothly from the pen than common ink. 
 
 I 
 
 FIG. 61. 
 
 5. The dividers or compasses is an instrument used in drawing 
 arcs, sub-tending angles, etc., and consists of two arms which open 
 and shut by a hinge joint at the end. Each of these arms termi- 
 nates in a sharp point, and one, if not both, is usually jointed so 
 as to permit the point to be taken out and a drawing pen put in 
 its stead. In drawing large arcs a lengthening bar is inserted in 
 
 FIG. 62. 
 
 the jointed arm. Fig. 62 represents a pair of plain dividers. It 
 will be seen that the arms are not jointed in this pair. 
 
 6. The protractor is an instrument used in laying out angles. 
 It is usually nothing more than a semicircle divided to degrees, 
 half-degrees, or quarter-degrees. The degrees are numbered from 
 to 180 in one or both directions from opposite extremities of 
 the arc. The best protractors are made of silver or German silver, 
 but the more common ones are made of brass or horn, and some- 
 times of paper. Fig. 63 represents a small protractor.
 
 138 
 
 MANUAL OF PLANE SURVEYING. 
 
 Where great accuracy is required, protractors are supplied with 
 an arm to which a vernier, like the compass vernier, is attached. 
 
 Sometimes rectangular protractors are used instead of semi- 
 circular. 
 
 7. The diagonal scale of equal parts is a flat scale a given num- 
 
 FIG. 63. 
 
 ber of units, say inches, in length, and has the space devoted to 
 one unit at the end divided by diagonals as shown in Fig. 64. 
 These diagonals with the assistance of the lines running parallel 
 to the edges of the scale, enable a person to take the length of a 
 
 3,8 J. 8.5.^. 3.2.7 
 
 FIG. 64. 
 
 line to T ^y of the unit of the scale. If the unit of the scale be 
 1 inch, then the length of a line may be taken to T J^ of an inch. 
 ( 253 ). In drawing plots and maps a unit of the scale repre- 
 sents a certain number of units of the line to be represented on the 
 plot. Suppose the real line is 20 chains long, and it is to be plot- 
 ted to a scale of 5 chains to the inch. The line on the plot will 
 therefore be (20 -4- 5) = 4 inches long. Fig. 65 represents a line 
 1 chain in length plotted to different scales.
 
 MANUAL OF PLANE SURVEYING. 139 
 
 1 in. = 5.00. 
 
 1 in. = 2.00. 
 
 1 in. = 1.00. 
 FIG. 65. 
 
 ( 254 ). Let us now employ the drawing instruments in plot- 
 ting lines. 
 
 Suppose an east and west line 2.27 in length is to be drawn to 
 a scale of 1 chain to an inch. 
 
 Arrange the drawing paper with its edges parallel to the edges 
 of the board, and then place the t-square, as shown in Fig. 61, 
 with its shoulder fitting squarely to the left-hand edge, and the 
 edge of the blade just moved up to the point from which the line 
 is to be drawn. Then spread the dividers so that when one arm 
 is placed two units from the inner edge of the divided unit and 
 on the line marked .07, the other will just reach the point where 
 this line crosses the line marked .2 at the top of the scale. The 
 arms then embrace the proper length of line. 
 
 Next place one arm of the dividers against the t-square with its 
 point on the point from which the line is to be drawn and swinging 
 the free arm round in the proper direction until it too touches the 
 same edge of the blade. Connect these two points by a line with 
 the drawing pen, and it will be the required line. 
 
 In like manner, a line 1.25 long to the same scale may be em- 
 braced by the dividers by placing one point at a on the diagonal 
 scale, and the other at e; and a line 1.40 long by placing one 
 point at E and the other at the point marked .4 at the top of the scale. 
 
 If the diagonal scale is not long enough to permit the required 
 line to be taken off, it may be extended by means of a ruler. 
 
 (255). EXAMPLES. 
 
 Draw lines representing the following distances : 
 
 (1). 2.50; scale 1 in. = 1.00. 
 
 (2). 3.79 ; scale 1 in. = 1.00. 
 
 (3). 4.75; scale 1 in. = 2.00. 
 
 (4). 6.42; scale 1 in. == 5.00. 
 
 (5). 10.00; scale 1 in. = 5.00. 
 
 (6). 12.31 ; scale 1 in. = 10.00.
 
 140 MANUAL OF PLANE SURVEYING. 
 
 ( 256). Rectangular tracts of land may be plotted with the in- 
 struments used in drawing lines already described. 
 
 Take, for instance, a rectangular tract 7.15 long, 4.35 wide. 
 
 First draw a line representing the length of the tract, then 
 another perpendicular to this at one end representing the breadth, 
 then from the end of this another parallel to the first and of equal 
 length, and close by connecting the extremities of the first and 
 third with one another. 
 
 If no diagonal scale is at hand, a common ruler will answer for 
 rough work. 
 
 ( 257 ). The protractor is used in nearly all cases where the 
 courses and distances of the boundaries of the tract to be plotted 
 are given, and its use will now be explained. 
 
 The bearing of a line represents the angle the line makes 
 either with the magnetic meridian or the true meridian drawn 
 through the point from which the bearing is taken ; and to deter- 
 mine this angle and represent the line on the plot, meridians 
 should be drawn through each station of tne survey as soon as the 
 station is located. 
 
 Begin at any important station to draw the plot by laying out a 
 meridian on the proper part of the paper and locating the station 
 on this meridian; then draw the first course at the proper angle 
 with this 1 meridian, producing it the required distance, as explained 
 in Art. 254; then draw another meridian through the other ex- 
 tremity of the course, and lay out the second course in the same 
 way ; proceed in this way until the lines are all drawn, and the last 
 line should terminate at the station taken as the starting point in 
 the plot. 
 
 ( 258 ). Let us now draw a plot of the following tract of land: 
 N 62 45' E, 9.25 ; thence S 36 E, 7.60 ; thence S 45 30' W, 10.40 ; 
 thence N 31 30' W, 10.00. 
 
 In this case we may commence at the first station in the de- 
 scription. Draw a meridian as N S, Fig. 66 and locate the sta- 
 tion at some point, as A, on the meridian. Then place the pro- 
 tractor so its center will fall on the station and its edge coincide 
 with the meridian, and with the point of a pin mark the termina- 
 tion of an arc of 66 45' from the north end of the protractor. 
 Then draw the line A B from the station through this point and 
 determine its length by the method explained in Art. 254. Draw
 
 MANUAL OF PLANE SURVEYING. 
 
 141 
 
 B C, C D, and D A in the same manner, and the plot will be com- 
 plete. 
 
 The plot, Fig. 66, is constructed to a scale of 5 chains to the 
 inch. 
 
 In northerly courses the angle or bearing should be read from 
 the north end of the protractor, and in southerly courses from the 
 south end. 
 
 N 
 
 B 
 
 
 D 
 
 fo 
 
 FIG. 66. 
 
 If the last course lack but a little of terminating at the first 
 station, the discrepancy may be the result of the imperfection of 
 the instruments employed; but if the extremities of the lines are 
 a considerable distance apart, it is probable that a mistake has 
 been made somewhere. If it be tested by latitudes and departures, 
 and they balance (Art. 212), the mistake is in the plot, but if they 
 do not balance, the error is in some of the previous work.
 
 142 
 
 MANUAL OP PLANE SURVEYING. 
 
 The descriptions given in Art. 226 may be used as examples in 
 plotting. 
 
 Various other methods are also used in drawing plots, but the 
 one given is, perhaps, the most speedy and simple, and will 
 answer every purpose. 
 
 (259). The pantograph is an instrument used for copying 
 plots, etc., either in a reduced or enlarged form. It consists of 
 four rulers arranged somewhat in the form of a parallelogram. By 
 fastening the instrument on the drawing-board and moving a 
 point on one arm along the plot to be copied, another arm to 
 which a pencil is attached sketches a precise copy on the sheet 
 placed under it. 
 
 (260 ). Buildings, springs, etc., may be located on the plot if 
 their courses from certain points on the boundaries of the tract 
 are known. 
 
 For example, in surveying the west half of a quarter-section, a 
 line from the north-east corner to the north-west corner of a house 
 was found to bear S 45 W, and one from a point 12.00 west of the 
 north-east corner was found to bear S 13 E. While constructing 
 the plot these lines may be laid out from the proper places with 
 the protractor, and the place where they meet will be the north- 
 west corner of the house, as shown in Fig. 67. 
 
 FIG. 67
 
 MANUAL OF PLANE SURVEYING. 143 
 
 ( 261 ). Plots and maps may be colored with crayon pencils or 
 with water-colors; but when water-colors are used care must be 
 taken to keep them from running into one another and injuring 
 the shades. The paper should be dampened preparatory to ap- 
 plying them. For inexperienced persons, crayons will prove the 
 most satisfactory. 
 
 QUESTIONS ON CHAPTER XV. 
 
 1. What is plotting? 
 
 2. Name the instruments used in plotting. 
 
 3. Descr-ibe the diagonal scale. 
 
 4. Describe the method of using the diagonal scale. 
 
 5. Give the length of each of the following lines plotted ta 
 
 scales of 1 chain to an inch, 2 chains to an inch, and 10 
 chains to an inch: 12.50; 15.00; 18.375; 11.25. 
 
 6. Describe the method of using the protractor. 
 
 7. Why should the last course in a plot terminate at the first 
 
 station ? 
 
 8. For what is the pantograph used ? 
 
 9. How may buildings and other objects be located on a plot? 
 
 10. How are plots and maps colored? 
 
 11. Draw plots of the tracts described in Article (226).
 
 CHAPTER XVI. 
 
 SURVEYING WITHOUT A COMPASS. 
 
 (262). A great many surveys can be made without the com- 
 pass, and a few pages will now be devoted to the consideration of 
 the most common cases in which it may be dispensed with. It 
 must be borne in mind, however, that the compass could be ad- 
 vantageously used in nearly all the cases here cited, and that the 
 methods given are intended for use only in emergencies. 
 
 (263). Setting Oorners. Where two witness trees taken to a 
 corner can be found, the corner may be located from them by 
 their distances measured from the sides upon which the blazes are 
 made. Suppose one tree is 15 links from the corner, and the other 
 19 links. Measure off 15 links on one end of a cord and 19 links 
 on the other end, and tie a knot where the two measurements ter- 
 minate. Then have the long end of the cord held against the 
 
 WITNESS 
 
 blaze on the more distant tree, and the short end against the blaze 
 on the other. Stretch both ends of the cord tightly, and the knot 
 will mark the corner, as shown in Fig. 68. 
 
 The corner is always in front of the blazes on the trees. 
 
 The distances of the witness trees from the corner may be found 
 from the field-notes of the tract. 
 
 (144)
 
 OF PLANE SURVEYING. 145 
 
 Where only one witness can be found, the corner can not be 
 located with certainty without a compass. 
 
 This same method may be employed, slightly modified, in lo- 
 cating a corner by the two lines meeting there, when the length of 
 each line and the location of each of the corners at the other end 
 of each, are known. 
 
 ( 264 ). Establishing Lines. When one corner is visible from 
 the coiner at the other end of the line, a stake may be put up, and 
 intermediate points on the line may be marked at pleasure. 
 
 When one corner is not visible from the other, but its direction is 
 approximately known, the line may be " ranged '' from one to the 
 other. To do this, put up a stake or flag at the corner from which 
 the line is ranged, and at a certain distance, say 50 or 100 steps, 
 in the direction of the other corner, set up another stake or flag. 
 Then walk ahead an equal distance and set another stake in line 
 with the first and second. Proceed in the same manner, always 
 setting the stakes at equal distances from one another, and ranging 
 the last one with the two previously put up, until the other corner 
 is reached. The distance that the line misses, either to the right 
 or left, can then be noted, and the stakes corrected in a manner 
 entirely similar to that already explained. 
 
 For instance, if there are 12 stakes on the line, and it termi- 
 nates 30 links to the right of the corner, each stake must be moved 
 to the left. The distance it is to be moved is found by dividing 
 the distance missed by the number of stakes and multiplying the 
 quotient by the number of the stake from the starting point. In 
 
 ( 1 1 'v' ^0 1 
 this case, the llth stake must be moved to the left I ^ ! =27 
 
 links, the 10th [ 10 * 3 ] = 25 links, and so on. 
 
 The stake put down at the corner at starting is not counted, and 
 the next is called the first. 
 
 Of course, the location of the corners must be known before the 
 line can be established. 
 
 ( 265 ). Setting Out Perpendiculars. Almost any kind of a con- 
 trivance with two lines of sight at right angles to one another, 
 will answer for this purpose. It may be a sort of cross-staff with 
 four upright sights provided with slits or threads, two marking 
 each line of sight. The sights need not be more than 18 inches 
 10
 
 146 MANUAL OF PLANE SURVEYING. 
 
 apart, and the apparatus should be made to rest on a staff about 
 4 feet high. It may be rude in construction, but the lines of 
 sight should be exactly at right angles to one another. 
 
 ( 266 ). Rectangular tracts of land may be readily surveyed in 
 many instances with this instrument, but it should be used with 
 care in independent divisions of the section, as they are not often 
 exactly rectangular in form. One of the lines of sight may also 
 be used in sighting lines, and is a good substitute for the method 
 of " ranging " described in the preceding article. 
 
 (267). Measurements. Lines may be measured with a cord, 
 tape-line, or pole, and distances may be given in feet or links, as 
 best suit the case at hand.
 
 APPENDIX. 
 
 ABSTRACT OF DECISIONS, 
 
 (147)
 
 ^ /-.-^~~ 
 
 (rp^^^ju tf r-t 
 
 si^^- 
 
 &^t_ ^ 
 
 ABSTRACT OF DECISIONS 
 
 OF THE 
 
 UNITED STATES AND VARIOUS STATE COURTS 
 
 RELATING TO CONTRACTS, SURVEYS, ETC. 
 
 (Nearly all of the following Decisions have been taken by per- 
 mission from DUNN'S LAND DECISIONS, a valuable book for sur- 
 veyors, published by George H. Frost, New York.) 
 
 BOUNDARIES. 
 
 1. Course and distance must yield to natural and artificial ob- 
 jects of description. Gaveny m. Hinton, 2 Greene (Iowa) 344. 
 
 2. Boundaries marked on the land are to govern courses and 
 distances. Blaisdell vs. Bissell, 6 Barr (Pa.) 478. 
 
 3. The lines marked on the ground constitute the actual sur- 
 vey and control the return of the surveyor, even where a natural 
 or other fixed boundary is called for by the survey, though the 
 space between the two is but twelve perches in breadth. Walker 
 TO. Smith, 2 Barr (Pa.) 43; Hall m Tanner, 4 Barr (Pa.) 244. 
 
 4. A grant called for a certain number of poles " to a stake, 
 crossing the river." Held, that the line must cross the river, 
 though the distance terminated before entering it. Whiteside i. 
 Singleton, 1 Meigs (Tenn.) 207j 
 
 5. A survey must be closed in some way or other. If this can 
 be done only by following the course the proper distance, then it 
 would seem that distance should prevail ; but when distance falls 
 
 (149)
 
 150 APPENDIX. 
 
 short of closing, and the course will do it, the reason for observing 
 distance fails. Doe vs. King, 3 How. (Miss) 125. 
 
 6. Where a deed describes lands by its admeasurements, and, 
 at the same time, by known and visible monuments, these latter 
 shall govern. Mayhew vs. Norton, 17 Peck (Mass.) 357; Massen- 
 gille vs. Boyles, 4 Humph. (Tenn.) 205; Woods vs. Kennedy, 5 
 Monr. (Ky.) 174; Nelson vs. Hall, 1 McLean (U. S.) 518; Camp- 
 bell vs. Clark, 8 Mis. 553. 
 
 7. The rule that monuments control in boundaries is, however, 
 not inflexible ; and in case where no mistake could reasonably be 
 supposed in the courses and distances, the reasons of the rule were 
 held to fail, and the rule itself was not applied. Davis vs. Rains- 
 ford, 17 Mass. 207. 
 
 8. A line is to be extended to reach a boundary in the direc- 
 tion called for, disregarding the distance. Witherspoon vs. Blanks, 
 1 Taylor (N. C.) 110. 
 
 9. If a vendor hold two tracts adjoining, and sell a certain 
 quantity by metes and bounds, though the deeds call for one tract, 
 yet if the metes and bounds run into the other, the purchaser 
 shall hold according to the metes and bounds. Wallace vs. Max- 
 well, 1 J. J. Marsh (Ky.) 447; Mundell vs. Perry, 2 Gill & Johns 
 (Md.) 206. 
 
 10. Posts set up at corners, between adjoining owners of land, 
 control the calls for course and distance and establish the bound- 
 ary where they are mentioned and recognized in the deeds. Al- 
 shire vs. Hulse, 5 Ham. (Ohio) 534. 
 
 11. Where land is described as running a certain distance by 
 admeasurement, to an ascertained line, though without a visible 
 boundary, such line will control the admeasurement and de- 
 termine the extent of the grant. Flagg rs. Thurston, 13 Pick. 
 (N. Y.) 145; Carroll t. Norwood, 5 Har. & J. (Md.) 163. 
 
 12. Where the line or course of an adjoining tract, being suffi- 
 ciently established, are called up in a patent or deed, the lines 
 shall be extended to them without regard to distance. Cherry vs. 
 Slade, 3 Murph. (N. C.) 82. 
 
 13. Where the boundaries of land are fixed, known, and un- 
 questionable monuments, although neither courses, nor distances, 
 nor the computed contents correspond, the monuments must gov- 
 ern. Pernam rs. Wead, 6 Mass. 131 ; Calhoun vs. Wall, 2 Har. & 
 McHen. (Mo.) 416.
 
 APPENDIX. 151 
 
 14. If a deed from the government of the U. S., or an individ- 
 ual, describes land as partly bounded by a river, the river bound- 
 ary will be adhered to, though it does not correspond with estab- 
 lished corners and monuments. Shelton a iis. Mauphin, 16 Mo. 124. 
 
 15. If nothing exists to control the call for courses and dis- 
 tances, the land must be bounded by the course and distances of 
 the grant, according to the magnetic meridian ; but courses and 
 distances must yield to natural objects. 16 Ga. 141. 
 
 17. The corners established by the original surveyors of public 
 lands under the authority of the United States, are conclusive as 
 to the boundaries of sections and divisions thereof, and no error 
 in placing them can be corrected by any survey made by individ- 
 uals or by a state surveyor. Arnier vs. Wallace, 28 Miss. 556. 
 
 18. Whenever natural or permanent objects are embraced in 
 the calls of either a survey or a patent, these have absolute con- 
 trol, and both course and distance must yield to them. Brown vs. 
 Huger, 21 Howard (U. S.) 305. 
 
 19. In determining boundaries under a grant, natural objects, 
 .as landmarks, are to be considered before courses and distances. 
 Daggett vs. Wiley, 6 Fa. 482. 
 
 20. Where adjoining proprietors abut on opposite banks of a 
 stream, their boundary line will follow the natural and imper- 
 ceptible alterations in its course, but not changes caused by arti- 
 ficial means. Halsey vs. McCormick, 3 Kernan (N. Y.) 296. 
 
 21. When lands are described in a deed or grant as bounded by 
 river not navigable, the center of the stream is to be considered 
 the boundary. Claremont vs. Carlton, 2 N. Hamp. 369 ; Palmer 
 DS. Mulligan, 3 Caines (N. Y.) 407, 319; Hayes vs. Bowman, 1 
 -Hand (Va.) 417; Ingraham vs. Wilkinson, 4 Pick. (Mass.) 268; 
 Gavil vs. Chambers, 3 Ham. (Ohio) 496 ; Brown vs. Kennedy, 5 
 Har. & J. (Md.) 195; Arnold vs. Mundy, 1 Halst. (N. J.) 1. 
 
 QUANTITY OF LAND. 
 
 22. A conveyance by metes and bounds will carry all the land 
 contained in them. Belden vs. Seymour, 8 Conn. 19; Jackson vs. 
 Ives, 9 Cow. (N. Y.) 661. Although it be more or less than is 
 stated in the deed. Butler vs. Widger, 7 Cow. (N. Y.) 723. 
 
 23. Where a specified tract of land is sold for a gross sum, the 
 boundaries of the tract control the description of the quantity it 
 contains, and neither party can have a remedy against the other
 
 for an excess or deficiency in the quantity, unless such excess or 
 deficiency is so great as to furnish evidence of fraud or misrepre- 
 sentation. Voorhees vs. De Meyer, 2 Bar. Sup. Ct. Rep. (N. Y.) 87. 
 24. Where a person purchases land by metes and bounds said 
 to contain a certain number of acres, more or less, he is entitled 
 to all the land within the limits, whatever the number of acres 
 may be. Bratton ts. Clawson, 3 Strobh. (S. C.) 127. 
 
 24. Quantity, although the least reliable and last to be resorted 
 to of all descriptions in a deed, in determining the boundaries of 
 the premises conveyed, may sometimes be considered in corrobora- 
 tion of other proof. McClintock vs. Rogers, 11 Ills. 279. 
 
 FIGURE OP TRACTS OF LAND. 
 
 25. If the order for a survey of land do not certainly determine 
 the form in which it should be made, the survey ought to be in a 
 square. Kennedy vs. Paine, Hardin, 10. 
 
 26. "Seventy acres, being and lying in the south-west corner" 
 of a section, is a good description, and the land will be in a 
 square. 2 Ham. (Ohio) 327; Cockrell vs. McQuinn, 4 Monr. 
 (Ky.) 63. 
 
 The rectangular figure will be preserved in preference to 
 any other in fixing locations. Massie is. Watts, 6 Cranch, 148 ; 
 Holmes vs. Trout, 7 Pet. 171. 
 
 ACQUIESCENCE IN BOUNDARIES. 
 
 28. Acquiescence for a long time (e. g. for eighteen years), in 
 an erroneous location, is conclusive on the party making or acqui- 
 escing in such location. Rockwell vs. Adams, 6 Wend. (N. Y.) 469. 
 
 29. Where a boundary is disputed between parties who own ad- 
 joining tracts, and the parties employ a surveyor, who runs out 
 the line, and marks it on a plat in their presence, as a boundary, 
 after twenty years corresponding possession, they are concluded 
 by it. Boyd vs. Graves, 4 Wheat. 513. 
 
 30. An acquiescence for twenty years is, as a general rule, nec- 
 essary to support an implied agreement in respect to a boundary 
 different from that clearly expressed in the title deeds. Ball vs. 
 Cox, 7 Ind. 453. 
 
 31. Where two persons own equal parts of a lot of land in sev- 
 erally, but not divided by visible monuments, if both are in pos- 
 session of their respective parts for fifteen years, acquiescing in an
 
 APPENDIX. 153 
 
 imaginary line of division during that time, that line is thereby 
 established as a divisional line. Beecher vs. Parmele, 9 Ver. 352 ; 
 also 18 Ver. 395. 
 
 32. Maintaining a fence for many years is strong but not con- 
 clusive evidence of limitation of claim to the boundary. Potts tw. 
 Everhart, 26 Pa. 493. 
 
 33. A party is precluded upon principles of public policy, from 
 setting up or insisting upon a boundary line, in opposition to one 
 which has been steadily adhered to upon both sides for more than 
 forty years. Baldwin vs. Brown, 16 N. Y. 359. 
 
 34. A division fence of more than twenty-one years' standing, 
 although crooked, constitutes the line between adjacent land own- 
 ers, even though the deeds of both parties call for a straight line 
 between acknowledged landmarks. McCoy vs. Hance, 28 Tenn. 149. 
 
 35. Where adjoining proprietors, being unable to ascertain the 
 division line, agree verbally upon a certain line, the agreement is 
 binding, and improvements by one up to the line is notice thereof 
 to a purchaser from the other. Houston vs. Sneed, 15 Texas, 307. 
 
 36. An ancient line of division marked on the ground by ad- 
 joining owners, and afterwards acted upon by them, will become 
 the boundary between the lots, although different from the line 
 described in the original deeds. Hathaway vs. Evans, 108 Mass. 267. 
 
 37. A possession for twenty years of a part of the land in dis- 
 pute, in reference to a line conflicting with another tract, of which 
 another party may be also in actual possession, but outside of the 
 disputed territory, may be enough to presume the execution of a 
 deed conveying the land in dispute to the party in possession. 
 Amick vs. Holman, 13 Shobh. (S. C.) 132. 
 
 38. Parties are not bound by a consent to boundaries, which 
 have been fixed under an evident error, unless perhaps by the pre- 
 scription of thirty years. Gray vs. Couvillon, 12 La. Ann. 730.
 
 TABLE OF 
 
 NATURAL SINES AND COSINES. 
 
 (See Articles (88), (207), (208), (209), (210), etc.) 
 
 (155)
 
 156 
 
 TABLE OF NATURAL SINKS AND COSINES.
 
 TABLE OF NATURAL SIXES AND COSINES. 
 
 157 
 
 > M. Sine. 
 <! .0871 
 
 141 33 .99011 
 
 14119 
 
 14148i.98994 
 
 14117 
 
 .!-'.<. I 
 
 14205 .98986 
 
 14234 
 
 14968 
 
 14X98 
 
 14890 
 
 14378 .98961 
 14-107 .98957 
 14436 \989f 
 
 14493 .98944 
 14E22 .9Hi4l 
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 14580 .9893: 
 
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 15069 '.98858 
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 15414 
 
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 15701 
 
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 15758 
 
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 15873 
 15902 
 
 16968 
 
 lr('17 
 10041 
 
 16074 
 
 16103 
 16132 
 Kil(X) 
 16181 
 
 168ft 
 1688 
 
 l,: j ,; 
 n.y,( 
 16411 
 1644' 
 16476 
 16505 
 .16533 
 
 loia 
 16691 
 
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 16763 
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 17250 98501 
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 98652 35 
 98648: 34 
 98643! 33 
 
 98619 28 
 
 !614 27 
 
 98609 26 
 
 98604 25 
 
 18600 24 
 
 98595 28 
 
 OBM
 
 TABLE OF NATURAL SINES AND COSINES.
 
 TABLE OF NATURAL SIXES AND COSINES. 
 
 Oin. 
 
 95iu7; 
 
 159 
 
 M. 
 
 .94552 60 
 
 '.4542 
 
 ..",1040 
 
 95061 
 
 3X694 
 
 .31068 
 
 B6069 
 
 89799 
 
 .31095 
 
 96048 
 
 32749 
 
 .81198 
 
 96088 
 
 89771 
 
 .31151 
 
 95094 
 
 32804 
 
 
 9:(nr, 
 
 8988S 
 
 ! 8190(1 
 
 
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 114997 
 
 89867 
 
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 94970 
 
 32%9 
 
 .81344 
 
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 .32997 
 
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 94969 
 
 
 
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 [88061 
 
 '.3i':i"7 
 
 9J933 
 
 48079 
 
 .31454 
 
 .'.M924 
 
 88106 
 
 .31482 
 
 .'.'1915 
 
 48184 
 
 
 .94908 
 
 48161 
 
 181685 
 
 .94897 
 
 
 .81666 
 
 .94888 
 
 48911 
 
 .81693 
 
 .94878 
 
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 .88844 
 
 32227 
 
 94666 
 
 .88874 
 
 89964 
 
 94- M 
 
 .88901 
 
 32282 
 
 MM, 
 
 88928 
 
 89801 
 
 
 88961 
 
 89881 
 
 94627 
 
 88981 
 
 89864 
 
 
 84011 
 
 88883 
 
 .33419 
 
 94599 
 
 '.'. \( l >it- 
 
 .32447 
 
 94690 
 
 840M 
 
 .32474 
 
 915-n 
 
 .34120 
 
 .89609 
 
 94571 
 
 34147 
 
 .32529 
 
 94661 
 
 31175 
 
 .89667 
 
 94669 
 
 34202 
 
 1 Co>ln. | Sine. 
 
 71" 
 
 0in. | 
 
 TO
 
 TABLE OF NATURAL SINES AND COSINES. 
 
 91355 tt) ) 
 
 mm . 
 
 93:253 
 30133 .93243 
 3616 2 
 36 190 i. 93222 
 36-217 .93211 
 30244 .93^)1
 
 TABLE OF NATURAL SINES AND COSINES. 
 
 161 
 
 .42473 
 .42400 .90530 .44072 
 ..,2525 '.90507 .14-10-1 
 .42-552 .9049.-) .44124 
 .42578'. 9048V '.44151 
 .43604 .90470 .44177 
 .42631 .90458 ,.44203 
 .42037 .901 IK .44220 
 
 28 
 
 29 i 
 
 Sine. 
 
 Cwin 
 
 TBST 
 
 c',-r,:\ 
 
 4>i047 
 
 88295 
 
 48481 
 
 vt-tm 
 
 4',! 173 
 
 88281 
 
 1 s -:' t; 
 
 b744s 
 
 J'i'f'.*'.* 
 
 47n24 
 
 S "*',!()" 
 
 8B8M 
 
 16689 
 
 .48557 
 
 >7-io I 
 87420 
 
 47060 
 
 .8BMI 
 
 48688 
 
 87406 
 
 47076 
 
 .88994 
 
 48606 
 
 87891 
 
 .47101 
 
 .88213 
 
 (6684 
 
 87:-:77 
 
 47127 
 
 .88191 
 
 486M 
 
 S7: f,3 
 
 47168 
 
 .8818C 
 
 .4W184 
 
 .S7340 
 
 4717,s 
 
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 .48710 
 
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 .47204 
 
 .88168 
 
 487% 
 
 xmm 
 
 47999 
 
 >.-H4 
 
 .48761 
 
 .87806 
 
 47966 
 
 >.-!:-;< 
 
 .4b78H 
 
 .87999 
 
 .47281 
 
 >Hr 
 
 .48811 
 
 .>7i7x 
 
 .47306 
 
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 .^72C4 
 
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 8806! 
 
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 >N ?A 
 
 .48064 
 
 >71!tH 
 
 47460 
 
 .86091 
 
 .48988 
 
 .KI178 
 
 .47488 
 
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 .41.014 
 
 .87164 
 
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 .49C40 
 
 .87150 
 
 .47681 
 
 .87971 
 
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 .H7136 
 
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 .8796E 
 
 .49090 
 
 .87121 
 
 .47588 
 
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 .49116 
 
 .87107 
 
 .47014 
 
 .87937 
 
 .49141 
 
 .87093 
 
 .47639 
 
 .87925 
 
 .49166 
 
 .87079 
 
 .47660 
 
 .87901 
 
 .49192 
 
 .87064 
 
 .47690 
 
 .87891 
 
 .49217 
 
 .87060 
 
 .47716 
 
 JOOK 
 
 .49242 
 
 .87036 
 
 .47741 
 
 .87868 
 
 .49268 
 
 .87021 
 
 .47767 
 
 .87864 
 
 .49898 
 
 .8T007 
 
 .47793 
 
 .878* 
 
 .49316 
 
 >f.'.,!.3 
 
 47818 
 
 .67891 
 
 .49344 
 
 .6978 
 
 47844 
 
 jtnstii 
 
 .49869 
 
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 47860 
 
 .87798 
 
 49804 
 
 .86949 
 
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 48078 
 48080 
 
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 .49647 
 
 66805 
 
 481CO 
 
 .87645 
 
 49672 
 
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 .87631 
 
 49697 
 
 K,777 
 
 48901 
 
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 49799 
 
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 49748 
 
 80748 
 
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 40699 
 
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 49960 
 
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 48466 
 
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 87462 
 
 50000 
 
 80608 
 
 Colin. Sine. 
 
 Cosin. | Sine. 
 
 J 
 
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 50 
 58 
 57 
 56 
 55 
 54 
 
 I 
 
 10 
 
 9 ? 
 8 
 
 1 / 
 6 
 6 ? 
 
 i : - 
 
 i 
 
 '
 
 TABLE OF NATVRAL SINES AND COSINES. 
 
 Sine. 
 
 50000 
 
 50025 
 
 50126 .86530 
 501511.86515 
 86501 
 
 30 
 
 50503 
 50588 
 
 50553 
 50578 
 501103 
 501128 
 50654 
 5')'179 
 
 50S-29 
 5IK5! 
 50879 
 
 51104 
 51129 
 
 5122!) 
 51854 
 
 51304 
 51329 .85821 
 
 31 C 
 
 85926 
 85! ID 
 
 51504 
 
 51690 
 
 51551 
 
 5i 5; '.) 
 51(104 
 51028 
 51653 
 51678 
 517(1:! 
 51728 
 
 518,03 
 51X28 
 5185-2 
 51877 
 
 51902 
 
 51! I. '7 
 51(15-' 
 
 51977 
 
 52002 
 53088 
 
 5-2-2 10 
 52225 
 .52250 
 5-2275 
 
 52291) 
 
 52!>t 
 
 5284U 
 
 52 I IS 
 
 59* i 
 
 528 I I 
 
 Cosi 
 
 .a5717 
 .85702 
 .85687 
 .85672 
 .85657 
 .85ti J2 
 
 85597 
 
 S558-2 
 
 , 
 ,85506 
 
 ,851; 11 
 s.Mlti 
 ,85431 
 
 85370 
 
 .S5325 
 
 ,85310 
 
 .-(KM 
 
 53189 
 58314 
 
 53-2H3 
 53288 
 
 53730 
 53754 
 
 53779 
 
 510-21 
 5404'.) 
 
 5 I .' 1 1 
 5l'2(i!t 
 542: 13 
 54317 
 ,5434-2 
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 5I115 
 
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 .84417 
 
 .' I -2! 1-2 
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 33 
 
 34 
 
 Sine 
 
 Cosin 
 
 Sine. 
 
 fV^TI. 
 
 .54464 
 
 83807 
 
 55919 
 
 82904 
 
 5 1-188 
 
 83851 
 
 559 13 
 
 82887 
 
 51513 
 
 83835 
 
 55968 
 
 82871 
 
 54537 
 
 83S19 
 
 50992 
 
 .82855 
 
 54561 
 
 83804 
 
 56016 
 
 .82839 
 
 5458i 1 
 
 83788 
 
 5601(1 
 
 
 54610 
 
 .83772 
 
 
 .8-J8I 6 
 
 54635 
 
 .8:1756 
 
 '56088 
 
 .82790 
 
 5-165!) 
 
 .837-10 
 
 5611-2 
 
 .82773 
 
 51683 
 
 .83; 21 
 
 .56136 
 
 .82757 
 
 .54708 
 
 ..-3708 
 
 .56160 
 
 .82741 
 
 517::-2 
 
 .83(15)2 
 
 .56184 
 
 .82721 
 
 51756 
 
 >:;o:r 
 
 
 .8-2 ;i>- 
 
 .54781 
 
 
 '.56232 
 
 .82692 
 
 5-18(15 
 
 '.8SMI 
 
 ..-(1256 
 
 .82675 
 
 .54829 
 
 .83629 
 
 .56280 
 
 .82659 
 
 .54854 
 
 .83613 
 
 .56305 
 
 .82643 
 
 .5-1878 
 
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 .56377 
 
 
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 !&354 
 
 .56101 
 
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 .82661 
 
 .54999 
 
 .83517 
 
 .561-19 
 
 .8251 1 
 
 .55(124 
 
 .83501 
 
 .5617:, 
 
 .8V52X 
 
 .55048 
 
 
 .56497 
 
 .82511 
 
 .55072 
 
 !8. : i-l(i! 
 
 .56521 
 
 .82495 
 
 .55(197 
 
 .83-15: 
 
 .565 15 
 
 .82-178 
 
 .55121 
 
 .83437 
 
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 .82462 
 
 .5ii.- 
 
 .8:121 
 
 .5, 15! 13 
 
 .82416 
 
 
 .83-10: 
 
 .56617 
 
 .82-129 
 
 !55UM 
 
 .83369 
 
 .56641 
 
 .82113 
 
 .55218 
 
 .83373 
 
 .566(15 
 
 .82396 
 
 .66842 
 
 .88361 
 
 .56689 
 
 .82380 
 
 .66801 
 
 .8334C 
 
 .56713 
 
 .82363 
 
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 .6786 
 
 .82347 
 
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 .56976 
 
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 .55581 
 
 .83131 
 
 .57024 
 
 .82148 
 
 .55605 
 
 .83115 
 
 .57047 
 
 .82132 
 
 556:! i 
 
 >3i 63 
 
 .57071 
 
 .57(195 
 
 .82115 
 .82098 
 
 55678 
 
 
 .57119 
 
 .82182 
 
 55702 
 
 ieaoeo 
 
 .57143 
 
 .82065 
 
 55726 
 
 .83034 
 
 .57167 
 
 .8201-- 
 
 55750 
 
 .83017 
 
 .57191 
 
 .82032 
 
 .55775 
 
 .83001 
 
 .57215 
 
 .82'115 
 
 5579!) 
 
 .82985 
 
 ,57238 
 
 .819!)!) 
 
 .55823 
 
 .82969 
 
 TM "Tl'' 
 
 .81982 
 
 5-8 17 
 
 82963 
 
 .57286 
 
 .819(15 
 
 .55871 
 
 >->!<:i6 
 
 .5731(1 
 
 .81919 
 
 .55*95 
 
 .82920 
 
 .57334 
 
 .81932 
 
 .55919 
 
 .82901 
 
 .57358 
 
 .81915 
 
 Cosin. 
 
 Sine. 
 
 Cosin. Mne. 
 
 66 
 
 55 
 
 19 ( 
 18 > 
 17 ) 
 16 b 
 15 ) 
 14 \ 
 13 ( 
 12 ( 
 11 } 
 
 10 5 

 
 TABLE OF NATURAL SINKS AND COSINES. 
 
 773^9 
 
 .77310 38 
 87 
 
 .77273: 36 
 
 .77255! 35 
 
 .77236 34 
 
 .77218 33 
 
 .77199 32 
 
 .771811 31 
 
 .77102: 30
 
 164 
 
 TABLE OF NATURAL SINKS AND COSINSS.
 
 BY 5. U. (SOOMBS. 
 
 PRICE, 
 
 .25. 
 
 CONTENTS OF THE NORMAL READER. 
 
 INTRODUCTION. 
 
 PART I. 
 How to teach a child to read. 
 
 PART II. 
 Dictionary Work. 
 
 1. Pronunciation. 
 
 1. Key to Pronunciation. 
 
 3. Elementary Sounds. 
 
 4. Principles of Pronunciation. 
 
 5. Articulation. 
 
 6. Words Often Mispronounced. 
 
 1. How to Teach Reading. 
 
 2. Examples for Practice. 
 
 PART IV. 
 
 Elocution. 
 Art of Delivery. 
 Outline of Elocution. 
 Plan of Studies. 
 Elements. 
 Respiration. 
 Breathing. 
 Formulas. 
 Articulation. 
 Orthoepy. 
 Vocal Culture. 
 Exercises for Drill. 
 Quality 
 Vocal 
 Volume. 
 Rate. 
 Gesture. 
 Su 
 
 1. 
 
 2. 
 
 To Ministers. 
 To Lawyers. 
 
 PART V. 
 
 One Hundred and Twelve of the best 
 Selections of Prose and Poetry 
 from the Best English and Amer- 
 can Authors. 
 
 Liberal terms for first introduction by the 
 quantity. Sample copy sent for $1.00 to those 
 who desire to examine with a view to an adop- 
 tion. No free copies. Please don't ask for 
 them. Address, 
 
 J. E. SHERR1LL, Pub., 
 
 DANVILLE, IND.
 
 - ): DALE'S :( - 
 
 OUTLINE OF ELOCUTION. 
 
 BY G. WALTER 
 
 The purpose of this book is to afford a complete and philosoph- 
 ical treatment of all the principles underlying the art of human 
 expression. It is designed to. analyze the art into its elements, and 
 discuss these elements in such a manner as that students who do 
 not have the advantage of aid from the living teacher may suc- 
 cessfully acquaint themselves in a practical manner with this fine 
 art. Its scope is bounded only by the possibilities of the subject, 
 which makes it a work of extraordinary value, in that it contains 
 the entire subject, logically treated. The definitions, discussions 
 and exercises are concise, explicit and pertinent. They are 
 adapted to students in any grade, from the primary to the high 
 school, seminary or college. The twelve appended Essays cover 
 ground discussed in no other similar work, and involve, among 
 others, " Care of the Voice," " Primary Teaching," and a multi- 
 tude of ;< Hints and Suggestions." It is an elocutionary library 
 in itself, as it represents the science and art of expression by voice 
 and action. As a book of reference it is standard literature, and 
 a classic of its kind. A student of ordinary intelligence can take 
 this book and study elocution without the aid of an instructor, 
 which he can not do by the aid of any other book. This is be- 
 cause the subject is placed before the student with such clearness, 
 in such minuteness of detail, that there is no room for misunder- 
 standing. It is the most popular book published on the subject 
 of Elocution. 
 
 IT CONTAINS ESSAYS ON : 
 
 1. Emphasis. 2. Projection of Sound. 3. Timbre. 4. 
 Care of the Toice. o. A Course of Reading. 6. Dramatic 
 Reading and Recitations. 7. Impersonation of Old Age. 
 8. Primary Teaching. 9. Hints and Suggestions, etc., etc. 
 
 The last 200 pages are filled with the best collection of selections 
 for reading ever embodied in a book of this kind. 
 
 The matter is new, the selections abundant and fresh, and the 
 tone of the book immeasurably above that of the ordinary reading 
 book. It is the work of one of the most successful teachers of 
 reading, who is himself a living example of the high class of in- 
 struction he gives in his book. Liberal terms for introduction. 
 Agents wanted all over the world. The most favorable induce- 
 ments offered. Write for terms. 
 
 Address, J. E. SHERRILL, Pub., 
 
 IPUD.
 
 THE 
 
 Iijdiarja 
 
 This is an entirely new and original departure in 
 books of this class, and can not fail to be a happy hit 
 and meet with warm approval and a hearty welcome 
 from the public in general. As its name indicates, it 
 is made up of selections from the very best productions 
 of the very best authors in Indiana. We mean no 
 offense to authors in limiting the work to this State ; 
 neither do we think it necessary to offer any apologies, 
 for her bright galaxy of distinguished writers has al- 
 ready placed the " Hoosier State " in the front rank 
 of the literary world. The book contains writings of 
 much merit from almost every class of our educated 
 people, comprising new, original, attractive and patri- 
 otic recitations' and declamations for every grade of 
 pupils. This book will displace the old and hack- 
 neyed pieces in our school rooms by supplying orig- 
 inal and the brightest and best thoughts and speeches 
 of our own people. Send for a copy at once. 
 
 Address, 
 
 J.E.S^e 
 
 Qa^ville, Jrjdiarja.
 
 THF XORJI.VI. 
 
 DIALOGUE BOOK. 
 
 PRICE, FIFTY CENTS. 
 
 Arranged with a Tien to giving something highly entertaining, and at the 
 same time something suit able and practicable for the school exhibition. 
 
 CONTENTS OF THE NORMAL DIALOGUE BOOK. 
 Miscellaneous. 
 
 Another Arrangement. 
 
 Aunt Betsy's Beau. 
 
 Which Will You Choose? 
 
 Maud's Command ; or, Yielding to Temptation. 
 
 The Smoke Fiend. 
 
 Charade. Phan-Tom. 
 
 Fourth of July Oration. 
 
 A Woman's Business Meeting. 
 
 Boarding School Accomplishments. 
 
 Leap Year in the Village with One Gentleman. 
 
 Too Greedy by Half. 
 
 The Way to Wyndham. 
 
 Little Folks' Department. 
 
 Vacation Fun. The Old Maid. 
 
 The Secret. Little Mischief. 
 
 An Interrupted Recitation. A Stitch in Time Saves Nine. 
 
 How He Had Him. The Stolen Pets. 
 
 Tableaux. 
 
 Tableau 1. Little Jack Homer. 
 
 " 2. The Old Woman who Lived in a Shoe. 
 
 3 ) 4 f 5. When I was a Bachelor. 
 
 " 6. Cinderella. 
 
 ?. Mischief in School. 
 
 " 8. The Four Seasons. 
 
 " 9. The Witches in Macbeth. 
 
 Shadow Acts and Pantomimes. 
 
 Box and Cox. 
 
 Courting Under Difficulties. 
 
 Hospital Practice. 
 
 Chapter of Instructions. 
 
 Great Inducements to Agents. Liberal Terms to the Trade. 
 
 Address, J. G, SffEJWfcfc, Pub,, 
 
 DANVILJUE, IND.
 
 UNIVERSITY OF CALIFORNIA AT LOS ANGELES 
 THE UNIVERSITY LIBRARY 
 
 This book is DUE on the last date stamped below 
 
 AUG 1 
 
 Form L-9-15m-3,'34 
 
 UNIVERSITY of CALIFORNIA 
 
 AT 
 LOS ANGELES
 
 545 Bagot - 
 
 U4m A manual of 
 plane 
 ing. 
 
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