TA 
 
 571 
 LY 
 
 IC-NRLF 
 
 TABLE 
 
 LOVELL 
 
LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Class 
 
I 
 
THE PLANE TABLE 
 
 AND 
 
 ITS USE IN SURVEYING 
 
 BY 
 
 W. H. LOVELL 
 
 Topographer U. S. Geological Survey 
 
 NEW YORK 
 
 McGRAW PUBLISHING COMPANY 
 239 West 39th Street 
 1908 
 
GENERAL 
 
 Copyrighted 1908 
 
 by the 
 
 McGRAW PUBLISHING COMPANY 
 NEW YORK 
 
CONTENTS. 
 
 Introduction 1 
 
 Forms of Plane Tables 3 
 
 Adjustment of the Alidade 5 
 
 Plane Table Triangulation 8 
 
 The Three-Point Problem 12 
 
 The Two-Point Problem 26 
 
 Centering the Plane Table over the Station.*. 31 
 
 Vertical Angulation 32 
 
 Signals 37 
 
 Land Surveys 39 
 
 Plane-Table Traverse 42 
 
 Projections 43 
 
 Conclusion 45 
 
 Index.. 49 
 
 176739 
 
SYMBOLS 
 
 Triangulation point . 
 
 /\ Plane-table station. 
 
 fi Church. 
 
 JE 
 
 jj School house. 
 
 U Factory. 
 
 Q House or shop. 
 
 E3 Barn or shed. 
 
 /} Monument. 
 
 f Windmill. 
 
 T Signal. 
 
 |T] Cemetery. 
 
 Fence Corner, 
 
 f^ Fir Tree. 
 
 j3 Deciduous Tree. 
 
 \ Dead Tree. 
 
 O Hill tops and locations generally. 
 
 IV 
 
UNIVERSITY ) 
 
 OF / 
 
 THE PLANE TABLE 
 
 AND 
 
 Its Use In Surveying 
 
 INTRODUCTION. 
 
 The plane table, one of the oldest of surveying 
 instruments, is, in its simplest form, merely a 
 board for holding the paper or other material upon 
 which a map is drawn with the aid of a rule or 
 straight edge. 
 
 Although the plane table has been known and 
 used in Europe to a greater or less extent for more 
 than three centuries, at the present day, in spite 
 of its obvious advantages as regards speed, economy 
 convenience and adaptability for surveying pur- 
 poses, its use is limited mainly to government sur- 
 veys in the mapping of large areas of country. 
 
 Although a useful and serviceable instrument 
 for railroad and land surveyors, it has never come 
 into general use by them in the United States. 
 
 Why this is so, is hard to explain, unless per- 
 haps because of lack of knowledge of the instru-' 
 ment and its methods, as little has been written 
 on the subject. Of late years it is gradually be- 
 coming better known. All recent text-books on 
 surveying give some space to a description of its 
 use and some instruction is given on the subject 
 in many of the colleges and technical schools 
 throughout the United States. 
 
 1 
 
2 PLANE TABLE. 
 
 The plane table is used extensively in European 
 countries as Gerrna. y Austria, and Italy, etc. on 
 government surveys ad ir> he topographical sur- 
 vey of India by the Jriti . government. 
 
 In the United States ^ has been used for many 
 years by both the Coast and Geological Surveys, 
 and with the increasing demand for the mapping 
 of parks, preserves, municipalities and various 
 tracts of land for public or private purposes there 
 is reason to believe it will gradually come more 
 and more into use as surveyors learn to appreciate 
 the advantages of the instrument. 
 
FORMS OF PLANE 'fABLES. 
 
 A plans- table outfit' msis; " of a drawing-board, 
 mounted on a tripod, t6% r hicn is attached the map 
 or sheet, upon which the' work is to be plotted; 
 a rule or straight edge, called an alidade, either 
 with or without a telescope, used for sighting and 
 drawing lines to objects it is desired to locate; a 
 spirit-level; and sometimes, though not essential, 
 a declinatoire or compass, to aid in approximate 
 orientation of the table. 
 
 An umbrella mounted on a long handle with a 
 sharp iron point to admit of its being firmly 
 driven into the ground is often used to protect the 
 plane table from the glare of the sun. 
 
 Numerous kinds of plane tables have been in- 
 vented and used at different times, most of the 
 variations being in the tripod head or movement. 
 
 This in most cases has been supplied with leveling 
 screws, but in the Johnson and Gurley tables of 
 recent years the screws have been dispensed with 
 and a universal joint motion used for leveling the 
 table. 
 
 The plane table movement or tripod head is 
 made of brass and in the U.S. Coast Survey pattern 
 three leveling screws are used, the horizontal mo- 
 tion is effected by two plates sliding upon each 
 other, and a tangent screw is attached for slow 
 movement in azimuth. 
 
 The Johnson plane table used by the U. S. 
 3 
 
4 PLANE TABLE. 
 
 Geological Survey is much lighter, although suffi- 
 ciently firm and rigid for all practical purposes. 
 
 In this movement there are no leveling screws, 
 both vertical and horizontal movements of the 
 table being effected by a ball and socket joint, and 
 the tangent screw is dispensed with as the table 
 can be moved in azimuth by hand with all suffi- 
 cient accuracy. For triangulation the size of the 
 board commonly used is 24 by 36 inches. 
 
 Folding tables for transportation on horse-back 
 are sometimes used in rough country, and a sketch 
 board made to serve as a plane-table in recon- 
 naissance surveys for military purposes. 
 
 Of alidades there have been many patterns. 
 The earliest type, a flat straight edge with raised 
 sights, called a sight alidade, is still used in running 
 lines of traverse and also to a limited extent in 
 plane table triangulation. 
 
 The form of alidade used by the U. S. Geological 
 Survey consists of a brass or steel rule or straight 
 edge, 18 or 24 inches long, upon which the telescope 
 is mounted on a standard four inches high, the 
 magnifying power of the lens being about 20 
 diameters. 
 
 Telescopic alidades are provided with a striding 
 level and a graduated vertical arc by means of 
 which the altitudes of all located points may be 
 determined, and in addition to the cross-hairs, 
 two more horizontal hairs, called stadia-hairs, are 
 sometimes added for use in stadia work. 
 
ADJUSTMENTS OF THE ALIDADE. 
 
 Parallax: Move the eye-piece until the cross- 
 hairs are distinct and then sight some distant 
 object. If there is no change in position of cross- 
 hairs relative to the object when position of eye is 
 altered, there is no parallax. 
 
 If position of cross-hairs varies, change focus 
 of the eye-piece until both cross-hairs and object 
 can be seen with distinctness and without altera- 
 tion of position, or parallax. 
 
 Collimation: Place intersection of vertical and 
 horizontal lines (cross-hairs) of telescope on some 
 small but distinct object as for instance a nail- 
 head. Revolve the telescope 180 degrees. If the 
 intersection still covers the object sighted, the 
 adjustment is correct. If not, correct one-half 
 of the difference by moving the diaphragm by the 
 adjusting screws, again sight the object, reverse 
 the telescope, and, if there is still an error of 
 collimation, correct one-half by the adjusting 
 screws as before and repeat until adjustment is 
 perfect. 
 
 Striding level: Place level on alidade and 
 bring bubble to center by means of tangent-screw 
 of the alidade. Reverse the level and if bubble 
 remains in center the adjustment is perfect. If 
 not, correct one-half by tangent-screw and the 
 other half by adjusting screw attached to the 
 level. These adjustments should be made at every 
 
 station. 
 
 5 
 
6 PLANE TABLE. 
 
 Telescopic alidades sometimes have one or more 
 levels attached to the rule or instead a circular 
 level may be carried by the plane-tabler. 
 
 To adjust the attached levels, place the alidade 
 in the center of the table drawing lines to indicate 
 its position and bring the level bubble to the center 
 by leveling the table. Reverse the alidade 180 
 degrees and if the bubble does not remain in the 
 center, correct one-half the difference by adjusting 
 the level screws and one-half by leveling the table. 
 
 These levels, however, are not essential as the 
 striding level can be used instead for leveling the 
 table, as well as for taking vertical angles. 
 
 The alidade rule should be an exact straight 
 edge. To test its fiducial edge draw a line along 
 it, reverse the alidade placing it exactly on the 
 line and draw * another line. If the two lines 
 coincide the edge is true. To ascertain if the sides 
 of the alidade rule are parallel they should be tested 
 by sighting to the same point. If they are not 
 parallel, care should be taken to draw lines on one 
 side only. 
 
 Telescopic alidades are of" various magnifying 
 powers, say from 10 to 24 diameters. 
 
 High power is a disadvantage in hazy weather, 
 as the particles of vapor or dust in the air are mag- 
 nified correspondingly. 
 
 It might be supposed that high magnifying 
 power would be an advantage, but this is not so, 
 beyond a certain limit. 
 
 Only a given amount of light can enter the 
 
THE ALIDADE. 7 
 
 object-glass and the greater the magnifying power 
 the less clear will be the image. 
 
 Two eye-pieces, for high and low power, the 
 former for clear and the latter for hazy weather 
 would be a convenience. 
 
 The magnifying power of a 'telescope is the 
 ratio of the focal length of the eye-piece to that 
 of the object glass. 
 
 To ascertain the magnifying power, point the 
 telescope towards the bright sky holding a slip of 
 thin .white* paper before the eye-piece at the 
 distance at w T hich the image of the object-glass 
 which is projected on it, is well defined. 
 
 Divide the diameter of the object glass by the 
 diameter of the image. 
 
 For instance, if diameter of object glass is two 
 inches and the image 0.1 inch the magnifying power 
 would be 2 *- 0.1 = 20. 
 
PLANE-TABLE TRIANGULATION. 
 
 The plane table is primarily an instrument for 
 graphic triangulation. 
 
 Instead of reading and recording angles, and 
 afterwards computing the resulting triangles, as 
 with a transit or theodolite, the triangles are 
 drawn directly upon the map, or projection, on 
 the plane-table board, thus avoiding possible 
 errors of record, adjustment and plotting. By 
 this method much time is saved, the plane table 
 being the most rapid and economical instrument 
 for the purpose for which it is used, that has yet 
 been devised. It has the additional advantage 
 that any point can usually be tested from different 
 stations in the field at time of survey and any 
 error in its position detected, all plane-table loca- 
 tions being exact to scale employed for the map. 
 It is especially adapted for use in country of con- 
 siderable relief, or open rolling country, in fact, 
 in all regions except heavily-wooded areas and 
 plains and plateaus of low relief. 
 
 Although originally intended for triangulation, 
 the plane table has other uses and properly 
 equipped becomes well-nigh a universal surveying 
 instrument, as, in addition to triangulation, it is 
 used for traverse, topographic sketching and verti- 
 cal angulation, in short, all the processes required 
 for making a complete map. 
 
 In beginning plane-table triangulation a section 
 8 
 
TRIANGULATION. 9 
 
 of country is usually selected in which primary 
 triangulation stations have already been estab- 
 lished. 
 
 The scale and area to be surveyed are decided 
 upon, a spherical projection is made, the poly conic 
 being used on nearly all U. S. Government maps, 
 and upon this projection the primary triangula- 
 tion points are plotted in their relative position in 
 latitude and longitude. 
 
 These, if possible, should be at least three in 
 number. A primary triangulation point is then 
 occupied and the table leveled, either by the strid- 
 ing level attached to the alidade or a round level 
 which can be permanently affixed to the alidade 
 rule or carried in the pocket. 
 
 Place this level in center of table and bring the 
 table to a level by the leveling screws, if any, or 
 by adjusting the legs which can be easily done after 
 a little practice. Unless the table is of more than 
 usual evenness and solidity, it cannot be brought 
 to an exact level anywhere away from the center, 
 but, as is explained later, this is not necessary. 
 After adjusting the alidade for parallax and colli- 
 mation, the table is oriented by sighting some 
 other triangulation point, that is, the projections 
 of these points on the sheet or map upon which the 
 triangulation is to be done, are brought into the 
 same relative positions as the points themselves 
 on the ground. Lines are then drawn to all ob- 
 jects in the landscape, such as signals, church 
 spires, cupolas, chimneys, flag-poles, prominent 
 
10 PLANE TABLE. 
 
 trees, hill- tops, spurs, etc., that may be of use 
 in obtaining proper control for the resulting map. 
 Tangents should also be drawn to all railroads, high- 
 ways, shore lines and other objects in the landscape 
 that it may not be possible to locate by intersection. 
 
 Lines drawn to signals and other points avail- 
 able for plane-table stations are called foresights. 
 
 The points to which foresights have been drawn 
 are occupied and the table again oriented by 
 placing the alidade on the foresight and sighting 
 back to station from which foresight w r as taken. 
 
 Another located point is then observed and the 
 position of point occupied determined by resection. 
 
 A third located point is then sighted and, if the 
 line from this passes through intersection of the 
 lines from the other two points, the table is in 
 position and location of station correctly deter- 
 mined. 
 
 All objects to which lines were drawn from the 
 first station that can be identified, are sighted and 
 located by intersection and lines drawn to other 
 objects that come into view as well, and in this 
 way by the use of foresights an entire sheet may 
 be plane-tabled, but it usually happens sooner 
 or later that resort must be had to the three-point 
 method of location. 
 
 1. It may occur that none of the triangulation 
 points are accessible and in that case it will be 
 necessary to begin plane-tabling with a three- 
 point station. 
 
 2. It may be found on occupying a point to 
 
TRIANGULAT1ON. 11 
 
 which a foresight has been drawn that lines from 
 other located points will not intersect, but form a 
 triangle, the triangle of error caused by an error 
 in the foresight or in identification of point to which 
 foresight was drawn. In that case the table is 
 out of position and must be brought into position 
 by the three-point method. 
 
 3. In a country of great relief where the triangu- 
 lation points are at a considerable elevation above 
 the valleys it will often be found very difficult to 
 recognize objects to which lines have been drawn. 
 In that case it -is often better and more convenient 
 to make three-point stations in the valleys or on 
 the lower hills, the commanding positions of the 
 triangulation points making them easily discernible 
 with the additional advantage that objects to 
 which lines have been drawn can. more easily be 
 identified. 
 
 4. Much time may be saved by the use of three- 
 point stations as fewer signals are necessary, and 
 more stations can be made and more points lo- 
 cated in a given time. 
 
THE THREE-POINT PROBLEM. 
 
 The three-point problem presents no difficulties, 
 and no one can be considered thoroughly compe- 
 tent for plane-table work who does not understand 
 it. 
 
 The rules to be remembered are few and simple. 
 In making a three-point station the plane table 
 is set up in such position that at least three pre- 
 viously located points are visible and in such rela- 
 tion to each other and the point to be determined 
 that lines drawn from them will intersect at large 
 angles, say between 30 and 120. 
 
 The position of the point sought in relation to 
 the three located points from which position of 
 the former is to be determined may be (Fig. 1). 
 
 1. Inside the triangle formed by the three lo- 
 cated points. 
 
 2. Outside the triangle, but inside the great 
 circle (the imaginary circle passing through the 
 three points on the ground). 
 
 3. On the great circle. 
 
 4. Outside the great circle. 
 
 In all cases the point sought is on the same side 
 of line drawn from each located point, that is, if 
 on the right side of one line looking toward the 
 point from which the line is drawn, it is on the 
 right side of the other lines, and distant from the 
 lines drawn from the three points in proportion 
 to its distance from each point. 
 
 12 
 
THREE-POINT PROBLEM. 13 
 
 When the plane table is not in position lines 
 drawn from the fixed points instead of intersecting 
 at one point will form a triangle called the triangle 
 of error, unless the point occupied should chance 
 to be on the circle passing through the three fixed 
 points, in which case the location of the point 
 occupied is indeterminate. 
 
 1. If point sought is within the triangle on the 
 
 FIG. 1. 
 
 ground, in other words, the great triangle, the true 
 point is within the triangle of error and distant 
 from the lines from the three located points in 
 proportion to their distances from the point occu- 
 pied. 
 
 2. When the point sought lies within either of 
 the three segments of the great circle formed by 
 the sides of the great triangle, the true point is 
 without the triangle of error and the line drawn 
 
14 PLANE TABLE. 
 
 from the middle point lies between the true point 
 and the intersection of the lines from the other 
 two points. 
 
 3. When the point sought is on, or very near 
 the great circle, the position is indeterminate. 
 
 4a. When the point sought is without the great 
 circle and the middle point is on the near side of 
 the line joining the other two points, as is the case 
 when the point lies inside of one of the angles 
 formed by the sides of the great triangle produced, 
 the true point is without the triangle of error and 
 the line drawn from the middle point lies between 
 the true point and the intersection of the other 
 two lines. 
 
 46. When the point sought is without the great 
 circle and the middle point is on the far side of 
 the line joining the other two points, the true 
 point is without the triangle of error, and on the 
 same side of the line from the middle point as the 
 intersection of the other two lines. 
 
 The following rule applies to all points outside 
 of the great circle: The point sought is always 
 on the same side of the line from the most distant 
 point as the intersection of the other two lines and 
 distant from each line in proportion to the distance 
 of the point from which it was drawn. In case, as 
 occasionally happens, it is difficult to decide which 
 of the three points is the most distant, the relation 
 of the line from the middle point to the lines from 
 the other two points as described in 4a and 46 will 
 determine on which side of the triangle of erupr 
 the point sought lies. 
 
/ OF THE 
 
 ( UNIVERSITY ) 
 
 A OF / 
 
 X^L'Fo^NV^X 
 THREE-POIN 
 
 REE-POINT PROBLEM. 15 
 
 In the rare case where the three located points 
 are in a straight line the same rule applies as in 
 the case 4a, that is, the line from the middle point 
 lies between the position of point sought and the 
 intersection of the lines from the other two points. 
 
 The above rules for solving the three-point 
 problem form what is commonly called the method 
 by trial and is the one usually employed in the 
 field by practical plane-tablers. 
 
 Other methods will be described later 
 
 In making* a three point station, if the lines 
 drawn from the three fixed points form a triangle 
 of error, showing that the table is not in position, 
 place the alidade on the most distant point, and 
 over the point on the paper, inside or outside of 
 the triangle of error, as the case may be, which as 
 near as can be judged is the location of the point 
 sought. Unclamp the table, turn it in azimuth 
 until the far point is sighted. Clamp the table 
 again, and draw lines from the three fixed points. 
 If these lines intersect in a cohimon point the table 
 is in position. If not, repeat the process, until 
 the intersection is perfect. In short, orient on the 
 most distant point, resect on the nearer points, v. 
 
 The reason for orienting on the most distant 
 point is that any movement of the plane table 
 changes this point more in azimuth than the 
 nearer points, while a slight turning of the table 
 would have but little effect in the position of a 
 nearby point. 
 
 However, in case a foresight has been taken to 
 
16 PLANE TABLE. 
 
 or near the point occupied, it is well to orient by 
 this foresight and resect from the other two points. 
 * If a triangle of error is formed it will usually be 
 small, and then the rules applicable to the three- 
 point problem can be followed. 
 
 After the three point station is made, that is, 
 accurately located, the plane- tabler should sight 
 a fourth well located point such as a signal, lone 
 tree, church spire, etc., if any are visible, as a 
 check on the position, and if a line from this point 
 passes through the station occupied making a 
 good intersection, (an angle between 30 and 120 
 degrees) the station may be considered well de- 
 termined. Other located points may also be 
 sighted as a test of the accuracy of the work. 
 
 Sometimes in making a three-point station a 
 mistake in position of one or more of the located 
 points, from which the station is to be determined, 
 may be made; that is, a point nearby may be 
 mistaken for the signal at the located point. 
 
 In this case it is well to remember that a three- 
 point station can apparently be made, that is, 
 lines from the three points will intersect without 
 forming a triangle of error, although the location 
 on the map will be wrong, and if the true point 
 happens to be very near "the point which is mis- 
 taken for it, the error in location of the three- 
 point station cannot be detected unless a fourth 
 located point, not on the great circle, is visible 
 which may be used to test the location of the 
 station. 
 
THREE-POINT PROBLEM. 17 
 
 In short, the fact that lines supposed to be 
 drawn from three located points intersect without 
 a triangle of error, is no proof of correct location of 
 station, as any three lines will come in. 
 
 Although stations located in the manner may be 
 but slightly out of position, points cut in from such 
 stations may be greatly in error. 
 
 However, if the three points are well located 
 and there is no doubt about their identification, a 
 well determined three-point station can be made 
 from them, and afterwards when still another 
 point has been located from the three initial points 
 the accuracy of the work can be tested as although 
 any three points will come in, lines from four 
 points can not meet in the same intersection, unless 
 they are correctly located in reference to each 
 other. Although they may appear to do so, if 
 two of the points lie in nearly the same direction 
 from the station occupied. In the selection of a 
 position for a three-point station, care should be 
 taken that the point chosen, if inside the triangle, 
 is not nearly in line between two of the three points, 
 or, if outside the triangle, is not on nor very near 
 the great circle, nor so far outside, that lines from 
 the three points intersect at such angles, less than 
 25 or 30 degrees, that the intersection is indefinite, 
 unless a fourth point is discovered that will serve 
 as a check. 
 
 Sometimes the plane-tabler may find himself 
 in a region of limited view where only short sights 
 can be obtained. In this case, when orienting 
 
18 PLANE TABLE. 
 
 from a short foresight, great care must be taken 
 to sight back to the exact point from which the 
 foresight was taken, some slender object as a pole 
 having been left there to indicate the precise spot 
 occupied, and the points that are used for resection 
 should also be small and sighted with extreme care. 
 
 If great care is not exercised in this respect, on 
 developing the triangulation until some distant 
 point before located is sighted, it will probably 
 fail to come in, that is, the location of the point 
 occupied, will be found to be in error, although 
 the locations made by the short sights were ap- 
 parently correct in themselves. 
 
 This illustrates the extreme hazard of carrying 
 on a system of plane-table triangulation, based 
 entirely on three points, and emphasizes the 
 necessity of always having four well located and 
 distributed points in view from every station, if 
 possible. 
 
 In plane-table work, as in primary triangulation 
 a system of quadrilaterals is to be preferred to that 
 composed of plane triangles. In making three- 
 point stations a compass will be found a conven- 
 ience in orienting the table approximately. 
 
 In conjunction with the stadia or telemeter, the 
 plane-table may be used in locating nearby points 
 by radiation, so called. 
 
 In this manner with one or more rodmen a large 
 number of points can often be located from one 
 station. 
 
 It is a most convenient and satisfactory method 
 
THREE-POINT PROBLEM. 19 
 
 for the survey of lakes and rivers, which are often 
 so situated as to be very difficult or impossible to 
 locate by triangulation. The stadia-rod can also 
 be advantageously used in a survey on a large 
 scale, where it is desirable to locate many points 
 within a small area. 
 
 To make a stadia-rod, take a strip of smooth 
 unpainted board, from four to six inches wide, 
 and ten to fifteen feet long. Mark off the board 
 into sections six inches in length and paint each 
 alternate section black. 
 
 Set up the plane table and sight the rod remov- 
 ing it to such distance that two adjacent stadia- 
 hairs will cover one division on the rod. Measure 
 distance between telescope and rod carefully, with 
 tape or chain. In most telescopes the stadia-hairs 
 intercept one six-inch division on the rod for every 
 hundred feet. If this should not prove to be the 
 case, whatever distance is intercepted should be 
 taken for the unit of distance. For more exact 
 work stadia-rods can be procured of makers of 
 engineering instruments graduated to any re- 
 quired fineness. 
 
 To locate a station by the tracing paper method 
 attach the paper to the board and mark a point 
 upon the paper or cloth for the point sought. From 
 this point sight and draw lines to the three known 
 points from which the station is to be determined. 
 Then shift the tracing paper until each of the three 
 lines passes through the plotted point correspond- 
 ing to the point toward which it was drawn. Posi- 
 
20 PLANE TABLE. 
 
 tion of the point sought will be at the intersection 
 of these lines, which can be pricked through the 
 paper on to the plane-table sheet. This method is 
 quite often used, but is apt to be inaccurate unless 
 great pains are taken in drawing the lines to the 
 sighted points, and is impracticable in windy 
 weather. 
 
 The three-point problem may be solved geo- 
 metrically with the aid of compasses as follows: 
 
 Let a, b, and c be the projections on the plane- 
 table sheet of the three located stations on the 
 ground from which the point occupied is to be 
 determined. 
 
 Draw a circle through a, b and the intersection 
 of the lines from these points which form one angle 
 of the triangle of error; also draw a circle through 
 b, c and the corresponding intersection. A third 
 circle, as a check on the work can be drawn through 
 a, c and the intersection of the lines from these 
 points. 
 
 The intersection of these circles is the location 
 of the true point. 
 
 Place the alidade on this point, orient, or bring 
 table into position, by sighting one of the fixed 
 points and verify the position by resecting on the 
 other located points. This method is inconven- 
 ient in the field, but is useful in the office as an aid 
 to the proper understanding of the three-point 
 problem. 
 
 BesseVs method by inscribed quadrilateral, or the 
 exact method so-called, another solution of the 
 
THREE-POINT PROBLEM. 
 
 21 
 
 three-point problem, may be employed when 
 practicable, which is not always the case, as it 
 often happens that the intersection' of the construc- 
 tion lines comes off the board. 
 
 FIG. 2. 
 
 In Figs. 2 and 3, a b c are points on the plane- 
 table sheet corresponding to the located points 
 ABC on the ground. Set up the table at the 
 point to be determined. Place the alidade on the 
 points c a and revolve the table until point A on 
 the ground is sighted. Clamp the table, and, 
 
22 
 
 PLANE TABLE. 
 
 with the alidade on c, sight the middle point B 
 and draw a line c e along the edge of the alidade 
 rule. Then, with the alidade on the line a c 
 revolve the table until the point C is sighted. 
 
 Clamp the table, place the alidade on a, sight 
 the middle point B and draw the line a e along the 
 edge of the rule. A line drawn through e and the 
 middle point b will pass through the point sought 
 
 Set the alidade on this line, revolve table until 
 point B is sighted and table will be in position. 
 
 Place the alidade on a and direct to A and draw 
 a line along the alidade rule. 
 
 The intersection of this line with the line b e is 
 location of point sought. 
 
 Verify the position by placing the alidade on c 
 and resecting on C. 
 
THREE-POINT PROBLEM. 23 
 
 The following analytic solution of the three- 
 point problem is adapted from Chambers' Practical 
 Mathematics. 
 
 Given the distances between any three points 
 and the angles subtended by them at a station to 
 find the relative position of the station and its 
 distance from each of the three points. 
 
 CASE I. When the station is outside the triangle 
 
 formed by lines joining the given points and the 
 middle point is beyond the line joining the other 
 two points (Fig. 4). 
 
 Let A, B, C be the three points, E the station 
 occupied and m, n the angles read from E. 
 
 Make the angle A, B, D = m' and the angle 
 DAB = n'. 
 
 In the triangle ABC the three sides are given 
 hence angle A can be found. In the triangle 
 
24 
 
 PLANE TABLE. 
 
 A D B, the angles and side A B are given; hence 
 A D can be found. 
 
 In triangle A D C, A C and A D are given, and 
 angle A = C A B DAB; consequently angle 
 A C D can be found. 
 
 In triangle ACE the angles and side A C are 
 known; therefore the sides A E and C E can be 
 found. 
 
 Then in triangle A B E the sides A B, A E and 
 
 the angles being known the side B E can be ob- 
 tained. 
 
 CASE II. When the station occupied is without 
 the triangle, and the middle point is on the near 
 side of the line joining the other two points (Fig. 5). 
 
 Let the middle point C be between the station E 
 and the line A B then the point E and D will be 
 both without the triangle ABC and on opposite 
 sides of it, and the solution will be analogous to 
 that of the first case. 
 
THREE-POINT PROBLEM. 25 
 
 CASE III. When the station is within the 
 triangle (Fig. 6). 
 
 Let D be the station then, the angles A D C, 
 B D C being given their supplements are known. 
 
 Make angles A B E, B A E, respectively = 
 A D E and B D E. 
 
 Angle C A E = C A B +E A B. 
 
 Angle C AD = 180 -(AC D + AD C} and 
 
 angle BAD. = CAB-C AD. 
 
 In the triangle A C D the angles CAD and 
 ADC are known and the side C, from which the 
 sides A D arid C D can be found. 
 
 In the triangle BCD the angle C and the sides 
 B C and C D are known from which the remaining 
 side B D can be found. 
 
 *An original and ingenious graphic solution of the 
 three-point problem is given by Prof. Llano in the Engi- 
 neering News for December 29, 1904. 
 
THE TWO-POINT PROBLEM. 
 
 It may sometimes be desirable to place the table 
 in position at a point from which only two located 
 inaccessible points can be seen. 
 
 The following solution of this problem is taken 
 from the U. S. Coast and Geodetic- Survey Report 
 for 1897-98: Fig. 7. 
 
 To put the plane table in position at a third 
 point C by resection from two located points A 
 and B, whose projections on the sheet are repre- 
 sented by a and 6, select a fourth point D so that 
 intersections from C and D upon A and B will 
 make angles sufficiently large for good determina- 
 tions. 
 
 Put the table approximately in position at D, 
 by estimation or compass, and draw lines A a, 
 B b, intersecting in d. Through d draw a line 
 directed to C. Then set up at C, and assuming 
 the point c on the line d C at an estimated distance 
 from d, and putting the table in a position parallel 
 to that which is occupied at D, by means of the 
 line c d, draw lines from c to A and from c to B. 
 
 These will intersect the lines d A , d B at points 
 a' and 6', which form with c and d a quadrilateral 
 similar to the true one, but erroneous in size and 
 position. The angles which a b and a' b' make 
 with each other is the error in position. 
 
 By constructing through c a line c d' making the 
 same angle with c d as that which a b makes with 
 
 26 
 
TWO-POINT PROBLEM. 27 
 
 a 'b', and directing this line c d' to 77, the table 
 will be brought into position and th true point c 
 can be found by the intersections of a A and b B. 
 Instead of constructing with drawing instru- 
 ments, the angle of error in the position of the 
 table, that is the angle of the line a' b' makes 
 with the line a 6, which is not always convenient, 
 the following expedient may be adopted. 
 
 a r b' is now parallel to A B and to bring the table 
 into position it must be turned until a b is parallel 
 to A B. 
 
 To do this set up a pole or other mark in the 
 direction a' b' \ set alidade on a b and revolve the 
 plane table until a b points to the mark. 
 
 Then a b is parallel to A B and the table is 
 oriented. 
 
28 PLANE TABLE. 
 
 Another solution of the two-point problem is as 
 follows (Fig. 8) : 
 
 After the table has been placed in position by 
 estimation, resect upon A and B, the two lines 
 intersecting at c. The angle a b c is the angle sub- 
 tended by A B at C and the position of the point 
 occupied (C) must be on the circle passing through 
 a b c. 
 
 Select a fourth point D nearly at right angles 
 
 to b c. Sight the signal D and draw line c d. 
 
 Occupy D, place the alidade on the line c d and 
 sight C, thereby bringing the table into a position 
 parallel to its position when at C. With the 
 alidade on d observe the signal at B and draw 
 the line d e intersecting c b. c e is the distance of 
 C from B. Lay this distance off from b in the 
 direction of c as a chord of the circle drawn 
 through a b c. 
 
TWO-POINT PROBLEM. 29 
 
 The intersection of the chord with the circle at / 
 is the true location of station C. 
 
 The two point problem can also be solved with 
 tracing paper as follows: 
 
 The two located points A and B are plotted on 
 the plane-table sheet as a and b (Fig. 7). It is 
 desired to find the position of a third point C. 
 Occupy a fourth point D, so placed that lines drawn 
 from the other points will intersect at sufficiently 
 large angles. Orient the table by estimation or 
 with the compass. 
 
 On the tracing paper which is fastened to the 
 board, indicate a point to represent the location 
 of D. Draw lines from this point towards the sta- 
 tions A B and C. Lay off the line d c the estimated 
 distance to scale between d and c. Occupy the 
 station C and bring the table into a position parallel 
 to that at D by sighting back to D on the line c d. 
 
 Draw lines from c to A and B, intersecting the 
 lines drawn to the same points from D, in a' and 
 b'. The angle which the lines a b and a' b' make 
 with each other is the error in position of the table. 
 Move the tracing paper until the line a' b' is 
 brought over the line a 6, thereby bringing the 
 table into position. Sight and draw a line from, 
 in other words resect on A and B. The intersec- 
 tion of these lines will give the position of C which 
 can be pricked through with a needle to the sheet. 
 
 When possible to get in line with two located 
 points a two-point stati n may be made in the 
 following manner. Set the plane table up any- 
 
30 PLANE TABLE. 
 
 where in line with, and bring into position by sight- 
 ing on, the located points. Sight the point where 
 a station is to be made, which should be at some 
 point affording angles large enough for good inter- 
 sections, drawing the line at the most convenient 
 place on the sheet. 
 
 Occupy the point to which the line is drawn, 
 and bring the table into position by placing the 
 alidade on the line and sighting back to the point 
 just left from which the line was drawn. 
 
 The table will now be in orientation and the 
 position of the station can be determined by resec- 
 tion on the two located points. Frequently sta- 
 tions can be made by ranging in between, or 
 lining up, that is, getting in line outside of two 
 located points. A foresight may be taken over a 
 chimney, or a tree on a hillside, and a station made 
 on the hilltop back of the same. 
 
CENTERING THE PLANE TABLE OVER THE STATION. 
 
 In regard to placing the plane table directly 
 over a primary triangulation station, or other lo- 
 cated point to be used as a station, it is well to 
 remember that exact centering of the table is only 
 necessary on maps of very large scale. 
 
 For instance on scale of 1 : 45,000, 75 feet on 
 the ground is represented by 1/50 of an inch on 
 the map and as 1/150, or at the extreme 1/200, 
 of an inch is about the limit of human vision, if 
 the plane-table is set within few feet of the exact 
 point there can be no appreciable error. 
 
 Plane- tablers have sometimes taken a great 
 deal of time and trouble to remove and afterwards 
 replace a signal in order to set directly over the 
 station when the scale of. the map was so small as 
 to render such care entirely unnecessary. 
 
 In regard to errors arising from imperfect level- 
 ing of table, it has been shown by Josiah Pierce in 
 his essay on the " Economic Use of the Plane 
 table," that errors from this cause amount to 
 practically nothing unless the inclination of the 
 board is very great. 
 
 A plane table may be 15 degrees out of level 
 before the maximum error in the measurement of a 
 horizontal angle will amount to one degree. 
 
 31 
 
VERTICAL ANGULATION. 
 
 The process of obtaining altitudes by vertical 
 or dip angles is peculiarly adapted to the plane 
 table. The vertical angle between the station 
 occupied and any located point, of which it is 
 desired to ascertain the elevation, is read, the 
 distance between the two points is carefully mea- 
 sured on the map and from this data, after the 
 correction for curvature and refraction is made, the 
 difference in height of the two stations is deter- 
 mined. 
 
 Differences in altitude or elevation may be com- 
 puted from a table of natural tangents, but, as 
 this is a rather tedious operation when a large 
 number of angles are to be calculated, vertical 
 angle tables adapted to the scale of the map and 
 containing corrections for curvature and refraction 
 are generally used. 
 
 Every point whose elevation it is desired to 
 ascertain with any degree of precision should be 
 observed from two or more stations whose heights 
 are well determined, and the stations from which 
 elevations of other points are to be obtained should 
 be determined by a series of vertical angles from 
 two or more stations. Reciprocal angles are not 
 checks and elevations should not depend upon them 
 alone. 
 
 Any datum can be assumed, but if it is desired 
 to connect the results obtained from vertical angles 
 
 32 
 
VERTICAL ANGULATION. 33 
 
 with any special datum, as sea-level, a line of levels 
 can be run from some convenient bench mark to 
 one or more signals or other exact and well deter- 
 mined point on the map. 
 
 To obtain the best results with vertical angles 
 exact points must be sighted, as for instance a 
 cross-piece attached to a signal, the height of 
 which above the ground is known. 
 
 The height of the telescope above the station 
 occupied must also be measured. This will be 
 found to be ordinarily about 4.5 feet. 
 
 The correction for curvature of xthe earth is 
 0.667 of a foot for the first mile, increasing as the 
 square of the distance, or two- thirds the square of 
 the distance in miles equals the curvature in feet. 
 
 The usual formula for computing the combined 
 curvature and refraction is 0.574 into square of 
 distance in miles equals curvature and refraction 
 in feet. In making allowance for refraction it is 
 usually reckoned as one-seventh of the curvature, 
 but may vary greatly from this, although for 
 distances of 8 or 10 miles the variation of the re- 
 fraction would not be the cause of any large error 
 that might occur. 
 
 Large errors in vertical angles at these distances 
 are caused by too coarse .or imperfect graduation 
 of the vertical arc, imperfect adjustment of alidade, 
 difficulty in leveling the alidade because of windy 
 weather, error in location of point, or mistakes 
 in reading the angles. With an arc reading to 
 One minute, and by estimation to one- half minute, 
 
34 PLANE TABLE. 
 
 at a distance of 5 miles, angles taken to exact 
 points as signals, lone trees or houses should check 
 out within 5 feet under favorable conditions of 
 weather. Up to distances of seven or eight miles, 
 elevations of even wooded summits should be 
 obtained with no greater error than half a 20 ft. 
 contour interval, say ten feet. In careful vertical 
 angle work it is w^ell after reading an angle to invert 
 the telescope and observe again, taking the mean 
 of the observations and thereby eliminating the 
 errors of adjustment. 
 
 The following illustration taken from the U. S. 
 Coast and Geodetic Survey Report for 1880 will 
 best show how this is done: 
 
 Telescope direct: 
 
 Level direct, reading +0 1 ' 
 
 Level reversed . . 0' 
 
 Mean +0 0' .5 
 
 Angle to point +2 17' 
 
 Elevation (difference) 2 16' . 5 
 
 Telescope inverted: 
 
 Level direct, reading 2' 
 
 Level reversed 1 ' 
 
 Mean I' .5 
 
 Point.. .+2 12' 
 
 Elevation (difference) 2 13' . 5 
 
 Mean , 2 15' 
 
VERTICAL ANGULATION. 35 
 
 It will be seen that the level was one-half 
 minute out of adjustment, the horizontal wire one 
 and one-half minutes, and that revolving the 
 telescope about itself changed its relation to the 
 index on the vernier by 1'. 
 
 The mean is free from all errors of adjustment. 
 
 Before reading the vertical angles the adjustment 
 of the striding-level should be tested, and the 
 index-error of the vertical arc, if any, noted. If 
 the zeros on the arc and vernier coincide when the 
 telescope is level, there is no index-error. If 
 they do not, the reading must be noted and the 
 correction applied to the angles. 
 
 Most alidades of recent make have an adjust- 
 able vernier thus eliminating the index-error. 
 
 An example of a vertical angle computation 
 follows : 
 
 Elevation of station above sea 250 ft. Distance 
 of summit, whose height is to be obtained, 1.5 
 miles. Vertical angle +1 50'. 1.5 miles = 7920 
 ft. Tangent of 1 50' = 0.03201. 7920X0.03201 
 = 253.5 ft. 1.3 = correction for curvature and 
 refraction and 4.5 ft. -height of telescope above 
 ground at station. 
 
 253.5+1.3 + 4.5 = 259.3ft. 
 
 250 + 259.3 = 509.3 ft. height of summit. 
 
 Angles of elevation are called + angles, of de- 
 pression, angles. 
 
 Although, as before stated, refraction is usually 
 estimated as one-seventh of the curvature, it 
 
36 PLANE TABLE. 
 
 varies greatly to an indefinite amount, increasing 
 with the distance between the stations observed. 
 
 The best time for measuring vertical angles is 
 between 9 a.m. and 3 p.m., as between these hours 
 the vertical refraction is less variable than earlier 
 or later in the day. 
 
 A book should be used in which to record vertical 
 angles as well as such descriptions of the foresights, 
 lines, and locations as may be desirable as an aid 
 to identification, but at the same time it is well to 
 put everything on the plane-table sheet, as num- 
 bers, graphic sketches, and written descriptions, 
 that will tend to make the work legible to others 
 than the plane-tabler in case of loss of record book, 
 or the plane-tabling were to be completed by 
 another. The Roman numerals may be used for 
 numbering stations, the Arabic figures for fore- 
 sights, locations, etc., and the altitudes should be 
 placed on the sheet in red. 
 
SIGNALS. 
 
 Unbleached cotton cloth is best for signal flags. 
 It wears better and is bleached by exposure to the 
 air in a few days. Flags should not be over five 
 or six feet in length, as longer flags will not blow 
 out in light winds. If a large flag is desired, put 
 up two flags, one under the other. 
 
 White is better than black or colored flags. 
 
 Color can not be distinguished at a distance of a 
 few miles and a black flag will not show plainly, 
 if at all, against a dark background, while a white 
 flag appears black against a bright sky. 
 
 The signal pole may be from fifteen to forty 
 feet in length, according to circumstances, but 
 should at least rise high enough above the ground 
 to allow the flag to blow out freely, and may be 
 nailed to a tree, or fence, or set firmly in the 
 ground, 2.5 to 3 feet, by tamping, as on occupying 
 the point with the plane table it will not be neces- 
 sary to remove the signal unless the work is on a 
 very large scale as perfectly accurate results can 
 be obtained by setting the table by the side of and 
 within a few feet of the pole. On ledges or rocky 
 hills props may be necessary to support the signal 
 pole. These should be eight feet or more in 
 length according to height of pole and at least three 
 in number, four are preferable, set 120 degrees 
 apart and nailed to the pole at different heights, a 
 foot apart if possible, to prevent the pole " kick- 
 
 37 
 
38 PLANE TABLE. 
 
 ing out " in high winds. The lower ends of the 
 props should be driven firmly into the ground or 
 else weighted down and held in place by heavy 
 stones. 
 
LAND SURVEYS. 
 
 The plane table is well adapted to the survey 
 of large or small tracts of land, as farms, parks, 
 et cetera, on any scale desired, except in heavily 
 wooded areas, and in many ways is more con- 
 venient and efficient than the trasit or Jacob-staff, 
 as the work is plotted directly upon the sheet in 
 the field at time of survey, thereby saving possible 
 errors of recording and plotting. 
 
 In beginning the survey of a tract of land of 
 which a map or plat is to be made, two intervisible 
 points as nearly as possible on a level should be 
 selected and the distance between them measured 
 by chain or tape. 
 
 This distance will serve as a base-line. These 
 points should be plotted on the map or plan at 
 such distance apart as is required by the scale. 
 Signals should be erected at each end of the base 
 line and also at as many other prominent points 
 as is desirable to insure proper control. 
 
 Set up the table at one end of base line, place 
 alidade on the plotted points on the sheet which 
 represent the stations at end of base-line, and re- 
 volve table until signal at other end of base-line 
 is sighted. The table is now in position. 
 
 Sight and draw lines along the edge of the 
 alidade rule to all the visible signals as- well as 
 other prominent points it may be desired to locate 
 as trees, fence corners, houses, sheds, etc, 
 
 39 
 
40 PLANE TABLE. 
 
 Then occupy the other end of base line and 
 after bringing the table into the same position as 
 at first station by sighting back to same, draw 
 lines to all visible points to which lines were drawn 
 from first station, whose positions are such that 
 the intersections will form sufficiently large angles 
 for good determinations. After completing work 
 at this station, occupy a third point to which a line 
 or foresight has been drawn and locate same by 
 resection as it is called, that is, by sighting the 
 first station occupied at end of base line. 
 
 From this last station other points can be inter- 
 sected and lines drawn to new points that come 
 into view. 
 
 In this manner the work can be carried on until 
 the entire area is surveyed. 
 
 The position of points that can not be located 
 by intersection, not being visible from any two 
 stations, may be found by stadia, tape, or chain 
 measurements, or even by pacing if the distance is 
 not great. At every station, sight all previous 
 stations and locations, as each location should be 
 sighted from at least three stations as a check 
 upon the accuracy of the work. 
 
 Altitudes can be determined by vertical angles, 
 if the alidade has a vertical arc; and the configura- 
 tion of the ground shown by contour lines drawn 
 at any desired vertical interval. 
 
 In surveys on a large scale care must be taken to 
 set the plane table over the exact point repre- 
 senting the station. In government surveys the 
 
LAND SURVEYS. 41 
 
 locations of primary triangulation points are usually 
 indicated by a copper bolt, metal tablet, or iron 
 or stone post; but, for temporary purposes, a 
 chisel mark on a rock, or a wooden pin, is sufficient. 
 
 On a scale of 100 feet to 1 inch, 0.01 of an inch 
 on the map represents 1 foot on the ground. In 
 such cases to insure accuracy in the plane-table 
 work, it is necessary to place the point on the 
 table, corresponding to the station on the ground, 
 very nearly over the pin marking the station, and, 
 in order to do this properly, a plumb-line should 
 be used and the table carefully plumbed over the 
 station. ' 
 
 On maps of large scale the signal poles should 
 be placed directly over the pin marking the point 
 on ground and great care taken in sighting and 
 drawing lines to signals and other objects so that 
 the exact point may be intersected from each sta- 
 tion. 
 
 The larger the scale, the more care is required 
 in this respect. 
 
 In order that the plane table may be placed 
 directly over the station, signals should be built 
 so that they can be easily removed and replaced, 
 or else the signal pole placed .high enough from 
 the ground to clear the head of the operator. 
 
 The magnetic meridian should be drawn on the 
 sheet and if desired the true meridian can be ob- 
 tained by a north star observation. 
 
PLANE-TABLE TRAVERSE. 
 
 -On the U. S. Geological Survey the plane table 
 is used largely as a traverse instrument. 
 
 That is, in surveying or traversing roads, trails, 
 'Streams, and valley ways, the table being oriented 
 by compass, and distances obtained by wheel 
 revolutions, stadia, tape, or pacing. 
 
 Used in this way, it is the most satisfactory 
 and expeditious method of filling in the details 
 of a map. 
 
 For this purpose a smaller and lighter plane- 
 table is used with a sight alidade made especially 
 for the purpose. 
 
 This alidade is a brass rule six inches in length 
 and fitted with a front and back sight instead of a 
 telescope, the short distances measured in traverse 
 rendering a magnifying glass unnecessary. 
 
 42 
 
PROJECTIONS. 
 
 A map projection is an approximately rectangu- 
 lar diagram on which are plotted the parallels of 
 latitude and meridians of longitude according to 
 the scale of the map. Many different projections 
 have been invented and employed from time to 
 time, but the polyconic is considered the most 
 satisfactory, as it involves less distortion of the 
 earth's surface, and is the projection now used 
 by all U. S. Government Surveys. 
 
 The U. S. Coast and Geodetic Survey publishes 
 tables of this projection which can be used for any 
 scale, and 
 
 Bulletin No. 234 of the U. S. Geological Survey 
 contains tables adapted to several different scales 
 with directions for laying-off or plotting the pro- 
 jection. 
 
 The paper used for the field sheet must be of 
 the very best quality as it is a substance very sus- 
 ceptible to changes of weather, nor can fine delicate 
 lines be drawn on poor paper. 
 
 Even the best paper of ordinary thickness has 
 been found to be subject to considerable distortion 
 from expansion and contraction caused by changes 
 in the weather and to obviate this, two sheets of 
 heavy paragon paper, so arranged that the grain 
 of the sheets is at right angles, are pasted together 
 with muslin between. 
 
 It has been found that the slight changes that 
 43 
 
44 PLANE TABLE. 
 
 occur in paper prepared in this manner are dis- 
 tributed uniformly in all directions, thus reducing 
 the distortion to a negligible quantity. 
 
 Celluloid sheets are sometimes used in very 
 rainy regions, but with proper care double-mounted 
 paragon eggshell paper can be used in almost any 
 climate with satisfactory results. 
 
 Sheets of this double thick paper can not be 
 rolled, but must be transported in flat tin or 
 wooden boxes, or while in use in the field perma- 
 nently attached to the plane-table board, both 
 when not in use being kept in a wooden or sole- 
 leather case. 
 
 Single thick paragon paper, properly seasoned, 
 can be used for plane-table work with good results, 
 if care is taken to protect it from the weather, and 
 the field work does not take a great length of time. 
 
 Various appliances have been used, for fastening 
 the plane-table sheet, or map, to the board, as 
 clamps, screws, and thumbtacks. 
 
 Clamps are objectionable as they take up con- 
 siderable space on the board, thereby interfering 
 with the use of the alidade, are liable to slip, and 
 do not hold the paper firmly in place. 
 
 Decidedly the most satisfactory contrivance 
 for this purpose is a brass, flat-topped screw which 
 is screwed by hand into a cylindrical brass screw, 
 with an inside thread, set permanently into the 
 board, flush with the surface of the table. This 
 arrangement holds the paper firmly in position and 
 is in every way satisfactory. 
 
CONCLUSION. 
 
 Two pencils should be used in plane-table work, 
 one with a chisel edge for drawing lines along the 
 edge of the alidade rule, and the other with a 
 cone shaped point for drawing symbols, numbers, 
 etc., on the map. These pencils should be very 
 hard, 6 or 7 H at least and of the best quality. 
 
 For recording vertical angles etc., a softer pencil 
 may be used. Sandpaper pads for sharpening the 
 pencils and rubber pencil tips, for erasing pencil 
 marks are a great convenience. 
 
 A fine needle with a large head made by melting 
 sealing wax, should be used for marking with a 
 small needle-hole the exact intersection of the 
 lines determining the position of a station "or other 
 located point. 
 
 Before beginning the plane-table work, it is a 
 good plan to ride over a considerable portion of 
 the area to be surveyed in order to get a general 
 idea of the " lay of the land," position and 
 distribution of the commanding points, and amount 
 of control needed. 
 
 During this reconnaissance the main stations 
 can be selected and signals erected, leaving minor 
 stations to be chosen as occasion arises during the 
 prosecution of the work. 
 
 In this way the progress of the work can be 
 facilitated and an estimate made of the time re- 
 quired to complete the triangulation. 
 
 45 
 
46 PLANE TABLE. 
 
 Sometimes it will be found necessary to return 
 to a station a second, or even a third time, because 
 of details at first overlooked or observations pre- 
 vented by bad weather. 
 
 The amount of control, that is, the number and 
 distribution of the stations, intersections and other 
 located points, necessar to insure the required 
 accuracy in the map, varies according to the 
 character of the land surface and amount of detail, 
 and must largely be left to the judgment of the 
 plane-tabler; but, in general, it may be said, if 
 the plane-table locations are properly distributed, 
 and in sufficient number to insure that all details 
 are shown without appreciable error to scale, the 
 map is practically perfect. 
 
 One great advantage the plane table possesses 
 over other surveying instruments is, that the map 
 is made directly in the field and at every station 
 all visible points previously located can be tested 
 and any error discovered and corrected at once, and 
 not as sometimes happens in transit work, remain 
 undetected until long after when the angle is 
 plotted in the office, where it is often impossible 
 to rectify the error. 
 
 In short the plane-table method is the most 
 rapid, economical and satisfactory way of making 
 a map yet discovered. It is accurate to scale, 
 detects and corrects error during the continuance 
 of the field work and as before remarked is well- 
 nigh a universal surveying instrument for all the 
 purposes for which a map is intended, as has been 
 
CONCLUSION. 47 
 
 thoroughly proven by many years use on the 
 Government surveys in all kinds of country. 
 
 Mr. Gannett, Geographer, U. S. Geological 
 Survey, in his manual of Topographic Methods 
 says, " For making a map the plane table is a 
 universal instrument. It is applicable to all 
 kinds of country to all methods of work, and to 
 all scales. For making a map, it is the most simple, 
 direct and economic instrument; its use render 
 possible the making of the map directly from the 
 country as copy, and renders unnecessary the 
 taking of elaborate notes, sketches, photographs, 
 etc., which is not only more expensive, but pro- 
 duces inferior results." 
 
 In conclusion, the following extract from Pierce 
 on the " Use of the Plane Table " well expresses its 
 merits as a surveying instrument: 
 
 " Recent results and improvements show, be- 
 yond a doubt, that a far greater degree of precision 
 can be obtained from simple graphic triangulation 
 than is commonly supposed, amply sufficient for 
 purposes of mapping, and with a degree of economy 
 unequalled by other systems. 
 
 " The engineer, or student, can not afford to lose 
 sight of a valuable and simple instrument, with 
 which he can, even alone and unassisted, construct 
 a topographical map of any scale, with a degree of 
 precision only limited by the scale, and in the 
 same time that he would occupy in taking observa- 
 tions with other instruments " 
 
INDEX. 
 
 Alidade, adjustments of 5 
 
 telescopic 4,6 
 
 sight 42 
 
 Angulation, vertical 32 
 
 Collination 5 
 
 Control 46 
 
 Curvature 33 
 
 Declination 3 
 
 Land surveys 39 
 
 Leveling the plane table 9,31 
 
 Map projections 43 
 
 Paper 43 
 
 Parallax 5 
 
 Pencils 45 
 
 Plane table, advantages of 8, 46, 47 
 
 centering over station 31 
 
 forms of 3 
 
 traverse 42 
 
 triangulation 8 
 
 Radiation 18 
 
 Record book 36 
 
 Reciprocal angles 32 
 
 Refraction 33 
 
 Signals 37 
 
 Stadia-rod 19 
 
 Striding- level 5 
 
 Telemeter 18 
 
 Telescope, magnifying power of 7 
 
 Three-point problem 12, 19 
 
 analytical solution 23 
 
 Bcssel's method 21 
 
 Geometrical solution 20 
 
 tracing-paper method 19 
 
 Traverse, plane table 42 
 
 Triangle of error 11 
 
 Two-point problem 26 
 
 Vertical angulation 32 
 
 49 
 
THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WILL INCREASE TO 5O CENTS ON THE FOURTH 
 DAY AND TO $1.OO ON THE SEVENTH DAY 
 OVERDUE. 
 
 / :. 
 
 16 1961 
 
 2 1936 
 
 Ftb 27 1938 
 
 KtC'D L.Q 
 
 JULXSWI 
 
 MAB lg 1940 
 
 T ~ 
 
 101943 
 
 MAR 01 1942 
 
 LD 21- 
 
YB 10999 
 
 / 
 
 x /^^^^7 
 
 TA 
 176739