TOPOGRAPHIC STADIA SURVEYING A MANUAL WITH REDUCTION TABLES ANrf A NEW TYPE OF REDUCTION DIAGRAM BY C. E. GRUNSKY, ENG.D. ^ MEM. AM. Soc. C.E. 18 ILLUSTRATIONS and A FOLDING PLATE NEW YORK D. VAN NOSTRAND COMPANY 25 PARK PLACE 1917 COPYRIGHT, 1917, BY C. E. GRUNSKY PREFACE THE notes on Stadia Surveying, presented in this manual, were assembled a number of years ago. For the benefit of the surveyor who has occasion to use the telemeter they are now made available in printed form. The method of surveying herein described and the special type of diagram for the reduction of stadia notes, herewith supplied, have been found so satisfactory by the author, and by others who have tried them out, that he considers it a duty to give the profession the benefit of his experience. C. E. GRUNSKY. SAN FRANCISCO, CAL., June 1, 1917. 370008 CONTENTS STADIA SURVEYING HAPTER PAGE I. Introduction and Definitions 1 Theoretical Considerations 3 The Porro Telescope 5 II. The Stadia Formula 9 Derivation of Formula 9 Determination of the Rating Factor 10 General Formulas for Inclined Sights 12 Approximation Formulas 16 Suggestions Relating to the Use of the Formulas 17 III. Diagrams for the Reduction of Stadia Measure- ments. , 19 Diagrammatic Solution of the Stadia Formulas 19 The Diagram Furnished with this Manual 22 IV. The Slide-rule as an Aid in Reducing Stadia Notes 24 Modification of Formulas for Slide-rule Work . . 24 V. Methods of Stadia Surveying 26 Stadia Surveys without the Use of the Magnetic Needle 26 Stadia Surveys with the Use of the Magnetic Needle 28 VI. Practical Suggestions 30 Departures from Ordinary Practice 30 The Stadia Rod 30 The Elimination of the Height of the Telescope above the Instrument Station Plug 35 The Liberal Use of the Magnetic Needle 37 v vi CONTENTS Stadia Notes 38 Note-book Sample Pages 40 Vertical Angles Measured with an Alidade 44 The Amount of Error when the Sighting Point does not Bisect the Intercept 44 Table 1. Corrections for too Large a Ver- cal angle 45 Table 2. Corrections for too Small a Ver- tical angle 46 The Amount of Error Due to Inclined Rod 47 The Accuracy of Telemeter Surveys 48 Table 3. Corrections for Departures cf the Stadia Rod from a True Vertical Posi- tion, etc 49 Table 4. Corrections for Departure of the Stadia Rod From a True Vertical Posi- tion, etc 50 The Effect of Refraction ' 51 VII. The Platting of Stadia Notes 52 VIII. Tables: Table 5. Values of e cos a and e sin a 54 Table 6. Stadia Reduction Table ' 57 Table 7. U. S. Geological Survey Tables for Obtaining Differences in Elevation 63 Conversion of Feet into Miles 91 IX. How to Use the Stadia Diagram 93 INDEX 97 STADIA DIAGRAM IN COVER POCKET TOPOGRAPHIC STADIA SURVEYING CHAPTER I INTRODUCTION AND DEFINITIONS Telescope Cross-hairs, Adjustable or Fixed. The telescope to be used in stadia work is equipped with three horizontal cross-hairs. The spacing of these cross-hairs may be either adjustable or fixed. For general use the fixed cross-hairs are preferred by most engineers and surveyors, though they are not without their disadvantages. When the cross-hairs are adjustable frequent testing of the instrument rating may be necessary. When the cross-hairs are fixed (this term being here use in the sense of permanent in their relative positions, i.e., non- adjustable), the instrument's rating as reported by its maker should be carefully tested before any surveys requiring the limit of attainable accuracy are undertaken. Tachymetry. Tachymetry is that branch of surveying which deals with the rapid measurement of distances, as, for instance, the determination of distance from an instrument by sighting with its telescope to a rod. Telemeter. The term " telemeter " may be applied to any telescope equipped with cross-hairs for measuring dis- tance, or equipped with micrometer screw or other device for accurate determination of the length of rod subtended by an angle of known amplitude. (Only the instruments equipped with cross-hairs are taken into consideration in 2 TOPOGRAPHIC STADIA SURVEYING this discussion, as these alone have come into general use in topographic surveying). Stadia-rod or Telemeter-rod or " The Rod." These designa- tions are applied to the rod which is used in connection with a telemeter for measuring distance. The rod may be equipped with targets, or, as is more common, it may be a self-reading rod; that is to say, a rod on whose face the subdivisions and repetitions of the distance unit are so plainly indicated by markings and figures that the instrument-man can read the rod without recourse to targets. The use of a target-rod is a refine- ment not justified by the accuracy attainable with a telemeter and need not, therefore, receive any special consideration. Intercept. The intercept is the length of that portion of the rod, in stadia units, appearing between two cross-hairs, generally between the lower and the upper hairs. The Anallatic Point. The anallatic point of any instru- ment is that point from which the distance to a rod which is read for distance is proportional to the intercept. For an ordinary telescope the anallatic point lies a principal focal length in front of the object glass. The Telemeter Constant. This is a value to be deter- mined for each telemeter. It is, for an ordinary telescope, the sum of the principal focal distance of the object-glass plus the length of the part of the telescope from the instrument's vertical axis to the object-glass. It is the dis- tance (measured along the collimation axis of the telescope) of the anallatic point from the vertical axis of the instrument. The Rod-reading. The rod-reading, as this expression is used in this manual, is one hundred times the intercept. Unless otherwise noted it is to be understood that an instru- ment rating of 100 is assumed. In other words one stadia unit on the rod is to be read and entered in the notes as 100. The Sighting Point. The sighting point on the rod is that point on the rod to which the sight is taken for vertical angles. It is the point on the rod on which the middle cross-hair is set for the vertical angle. TOPOGRAPHIC STADIA SURVEYING 3 The Rating Factor. The rating factor of any instrument is that factor by which, when sighting horizontally to a vertical rod, the intercept (read in any linear unit as for example in feet), must be multiplied to find the distance to the rod (in the same linear unit), from the anallatic point. The Principal Focal Distance. The expression " principal focal distance " is the distance from a lens at which parallel rays of light passing through it are brought to a focus. The Stadia Unit. The stadia unit is a rod increment of such length that one such unit will be intercepted, when sighting horizontally, for each 100 or 200 or other number of units (depending on the rating factor of the instrument), that the rod is distant from the anallatic point. Theoretical Considerations. The object-glass of the ordinary telescope of a transit or plane-table alidade is a convex lens. For every convex lens: Here B is the distance from the lens to some object whose image appears on the opposite side of the lens at the distance b, and / is the principal focal distance of the lens. A horizontal sight being assumed, let S, Fig. 2, represent the intercept on a rod and s the actual space between the cross-hairs. Then &=* ..... . . . . (2) 4 TOPOGRAPHIC STADIA SURVEYING Combining (1) and (2) (3) FIG. 2. The value of s and the value of / for any telescope are con- stant, therefore, - is a constant, s Make Then B-f=KS. (4) The distance B-f, Fig. 3, is proportional to the inter- cept S. The relation between B /, S, s and / expressed in Eq. (3) appears also from the optical principle illustrated in Fig. 3. TOPOGRAPHIC STADIA SURVEYING 5 The Porro Telescope. It is practicable to construct a telescope in which the anallatic point will coincide with the vertical axis of the instrument. This fact was first demon- strated by an Italian officer, Mr. Porro, who, in 1823, con- structed and described a telescope in which lenses were so combined that all rod-readings were proportional to the dis- tances from the center of the instrument. How this was done will appear by reference to Fig. 4. The object-glass and the auxiliary lens 0' are so placed that the vertical axis L . : i- z> of the instrument, at C, is between them. The object-glass has a longer focal distance than that of the ordinary tele- scope. If the construction is such that the points C and F' are conjugate foci for the lens and the two lenses are rigidly connected, the angle at C will be constant. In other words, the intercept S will be proportional to the distance D, 6 TOPOGRAPHIC STADIA SURVEYING Referring to this type of instrument, which has not come into use in this country, Mr. A. Lietz says:* " Since stadia measurements originate from the outer focus of the objective lens, and not from the center of the instrument, it becomes somewhat troublesome to apply a correction therefor on inclined sights, for, since the corrections remain constant for any distance and vary with the angle of inclination only, it is not practical to incorporate them directly into the tabular values em- ployed in reducing stadia observations. Such tables are usually augmented by placing the corrections due to what is generally termed the constant e at the bottom thereof. To overcome this difficulty, and to make every reading date directly from the center of the instrument, the Italian Porro invented a method in 1823, which is now beginning to be better known. This method has been fre- quently discussed. The Journal of the Franklin Institute contains an article in a number as far back as 1868. The Engineering News of November 8, 1890, has a short discussion by one of our best writers on these subjects, Prof. J. B. Johnson, of Washington Uni- versity, St. Louis. " A convex lens of required focal length is inserted between the objective and the eyepiece, which transfers the anallatic point to the occupied center. Theoretically this is necessary, for the observed vertical angles have their common vertex in the center of the arc, or horizontal axis of the telescope; while the vertex of the dias- timometric angle lies outside of the objective, a distance of 14 ins. from the center of the instrument in the ordinary large .transit. This would cause slight errors in vertical angle and distance, which disappear in the Porro telescope. " There are very substantial reasons, however, why this anallatic lens has not found a more general application in modern surveying instruments, for it is not a new thing with which we are dealing, but a principle that was known and used over half a century ago; and these reasons will now be briefly considered. " By inserting an additional lens the equivalent focal length of the objective is considerably decreased, and the power and capacity are thereby correspondingly lessened. To exemplify this, reference is made to an actual test of which the results were accessible to me. In this case the focal length of the objective equaled 13 \ ins., that of the inserted lens 5 ins. and the distance between them 9f ins. The equivalent focal length of the combination was, therefore, 7f ins. The image of the system lay 2j ins. behind the anallatic lens, and its distance from the objective, therefore, 11 f ins. Here we notice * Journal Assoc. Engrg. Socs., Vol. 19, 1897, p. 256 et seq. TOPOGRAPHIC STADIA SURVEYING 7 that the available focal length has been shortened by the lens com- bination 4| ins., which is a direct loss of nearly 37%. An ordinary telescope with a focus of 11 f ins., possessing an eyepiece with one of 5 in., would have a power of 23, while the Porro telescope under sim- ilar conditions shows only 15, indicating the same percentage of loss in power. There is, however, a slight gain in brightness with the same aperture of objectives, for the reason that the admitted light is concentrated in a smaller space. In order to make up for the loss in power, due to the anallatic lens, a more powerful eyepiece must be made use of. One with an equivalent focal length of T<- in. would about compensate the 37% loss, but the brightness of the image would not then be quite up to that of the ordinary telescope, since the middle lens will cause a slight loss of light by reason of reflection and absorption. This, however, might again be rectified by giving the objective a somewhat larger aperture. " While it is readily seen that a Porro telescope might be con- structed fully up to the capacity of our ordinary transit telescope, it is also apparent that much greater care and refinement would have to be resorted to to reach it, for it is very important that the entire mechanical work should be perfectly in harmony with the greater optical requirements. The tubes must be absolutely straight, the axes of the lenses must be identical and their principal planes normal thereto. Greater care must be exercised in the construction of the objective, it being necessary to correct therein for the aberra- tion due to sphericity and achromatism of the anallatic which is usually a simple convex lens if we would retain a clear and dis- tinct image. "It is a problem for the instrument maker to construct the Porro telescope so that there shall be no complicated parts, and no excess of cost to speak against it. The additional lens, whose focal distance depends upon the length of the telescope and the location of the center of the instrument, is placed in front of and not too far from the cross-hair diaphragm. Its distance from the objective must necessarily remain constant, and any motion of the latter in the tube must be made with the middle lens also. The lenses must move together. "It might be a more advantageous construction to adopt the mov- able eyepiece, and to focus by shifting the cross-hair diaphragm in connection therewith. "This lens combination has one peculiar advantage that must not be left unmentioned, which is that it requires but a very small tele- scopic slide movement to focus from long to short distances and vice versa. A range of half an inch may be sufficient to cover all the required lengths of sight. 8 TOPOGRAPHIC STADIA SURVEYING "In building the tube, provision must also be made for readily removing the inner lens in order to clean it, which would probably be frequently required. The arrangements for this purpose must be so contrived that the lens may be replaced in its proper position and accurately adjusted to the required optical conditions. "Every feature goes to show that the mechanical work of such a telescope must be of the highest order, if it shall meet the demands made upon it. With the cheaper grade of surveying instruments a Porro telescope is an impossibility. "Granted that we have a Porro telescope fully up to the power and capacity of that of the simpler construction, there are the con- stant disadvantages of using a powerful microscope, which must be more or less fatiguing to the eyes of the observer; and the accumu- lation of dust on the inner lens, a difficulty that may lead to consid- erable trouble and annoyance. These reasons have been more than sufficient to prevent the anallatic telescope from being generally introduced and practically used. It is granted, however, that, as a precise instrument, it is perfectly within the reach of the optical and mechanical arts to build one that shall fully accomplish the translation of the anallatic point to the center of the instrument." CHAPTER II THE STADIA FORMULA Derivation of Formula,. The value (Bf) in Eq. (4), for any ordinary telescope arranged as a telemeter is, as has been shown, proportional to the intercept S on a rod held vertically. In other words, sighting horizontally, the par- allel cross-hairs of the telescope will intercept a space on a rod proportional to the distance at which the rod is held FIG. 5. from a point which lies an object-glass principal focal length in front of the object-glass of the telescope. Let c, Fig. 5, represent the distance measured along the tube of the telescope from the vertical axis or center of the instrument to the object-glass. Then for a horizontal sight D=B+c; or From (4) Calling c+f=e, (5) (6) (7) (8) 10 TOPOGRAPHIC STADIA SURVEYING which is allowable because the value c, being affected only by the movement of the object-glass in focusing upon the rod is for practical purposes to be regarded as a constant, Eq. (7) becomes D=e+KS (9) This is the fundamental formula. K is called the rating factor and e may for convenience be called the instrument constant. The values of c and of /, and, therefore, the value of e, can always be directly measured with sufficient precision; / in the instrument of the ordinary type with single objective is the length of that portion of the telescope tube between the objective glass and the cross-hairs, when the telescope has been focused upon a distant object. The value of c may be determined also by measurement when the tele- scope is focused upon some object about 50 ft. distant. Determination of the Rating Factor. When a telescope has fixed cross-hairs and the value of e has been ascertained the instrument's rating factor is determined as follows: Measure from the vertical axis of the instrument as follows: To point Pi at (100 +e) ft.; To point P 2 at (200 +e) ft.; To point P 3 at (300 +e) ft.- etc. etc. To point, Pio at (1000 +e) ft. The selected ground for such a determination must be such that all of the readings can be made with a horizontal telescope otherwise the rod must be held normal to each line of sight and the distance measured on the ground must be parallel with this line of sight. The rod being held at each of the ten points there will be obtained ten rod readings (each foot on the rod being read as 100 ft.). These readings are now divided in their order by 1, 2, by 3, etc., by 10. Each quotient will be an observed TOPOGRAPHIC STADIA SURVEYING 11 value of the instrument's rating-factor. The mean of the observed values is to be accepted as the value of K. No individual observation should vary more than 0.2% from the mean. 100 The stadia unit is then 7- ft. A For example: Suppose K =80 then V / = 1.25 ft., the stadia unit. If now a rod based on the subdivision of 1.25 ft. in- stead of 1 ft. as the unit be prepared for use with the tele- scope whose stadia unit is 1.25, then each such unit may be read as 100 ft. Calling the stadia unit u, its value is but D=e+KS; ....... (9) therefore D=e+100- ....... (11) u The distance in feet, in other words, will be the instru- ment constant plus 100 times the intercept measured in stadia units. Whenever a rod has a stadia-unit other than one foot, some scheme of rod subdivision and marking should be used that will enable an easy identification of the rod, which is in this event to be used only with a particular instrument, and only for stadia and vertical angle work not for any ordinary leveling. When the cross-hairs of the telescope are adjustable they can be set so that the rating of the instrument will be con- venient, usually 1 to 100. To adjust the cross-hairs measure from the center of the instrument to a distance about equal to the average length of a sight making the same some multiple of 100 ft. in- 12 TOPOGRAPHIC STADIA SURVEYING creased by the instrument constant as, for instance (400 -f-e) ft. The cross-hairs are now so adjusted that the intercept between the lower and the upper hairs when sighting with a horizontal telescope will be exactly 4 ft. and that the middle cross-hair will exactly bisect this intercept. The rating of the instrument is thus made 1 to 100. If so convenient a rating factor as 100 is not practical the cross-hairs may, of course, be so adjusted that the intercept will have to be multiplied by some other round number such as 50, 150 or 200 to make the product 400. After the cross-hairs have been adjusted with the rod at some such distance as (400 +e), or (500 -f-e), or (600 +e) ft., readings should be taken at other measured distances, as for example at one-half the distance first selected and at a point at twice this distance, in order to give a check upon the accuracy to be expected. The error in an individual sight for adjustment under assumed favorable atmospheric con- ditions, should not exceed 0.2%, if the instrument is intended for use in ordinary topographic surveying. It may be repeated that, for the instrument with fixed cross-hairs, either the rating factor must be determined, as explained, and used in estimating distances from readings on a rod with the measuring unit (one foot), as the subdi- vision unit, or in the manner already described the stadia unit is calculated from observations and a special rod is constructed for use with that instrument only. The latter is rarely a desirable procedure. General Formulas for Inclined Sights. When the transit, or the alidade of the plane-table are used to measure both distance and difference in elevation, the rod may be held either normal to the line of sight or vertical. In the first case the length of the inclined line from the instrument to the sighting point on the rod is measured. In the second case a reading is obtained from which the horizontal distance to the rod and the difference in elevation may be calculated. The advantages, for all ordinary surveying, of the second TOPOGRAPHIC STADIA SURVEYING 13 method, as illustrated in Fig. 6, are so pronounced that it is not necessary to discuss the use of the inclined rod. In Fig. 6 the intercept on a rod held vertically at the point P is S. The vertical angle, when the middle cross-hair is set on the sighting-point P', is a. It is to be remembered, as already stated, that throughout this manual, except when otherwise noted, instruments rated 1 to 100 are referred to. For such instruments the FIG. 6. rod-reading, as entered in the notes of the surveyor, will be 100 S. When instruments have some other rating the value 'KS may be substituted for the rod-reading (i.e., for 100 S.) Referring again to Fig. 6, it will be seen that if the rod had been held through the point P 7 normal to the axis of the telescope, the intercept would have been HH', instead of S. The length of HH' establishes the length of the inclined line IP', and the line IP' together with the vertical angle 14 TOPOGRAPHIC STADIA SURVEYING a enables a calculation of the horizontal distance D and of the difference of elevation h to be made. HH'=S cos a (very nearly); .... (12) IP' = 100 S cos a+e; (13) D = (100 S cos +e) cos ; . . . (14) and h = (WQS cos <*+e) sine*. . . . (15) Calling the rod reading 100 S=r; (16) will make D=r cos 2 a+e coo a; (17) h=r sin a cos a+e sin ; .... (18) which is h=r(% sin 2a)+e sin a (19) These are the formulas in ordinary and in general use for the determination of distance and difference in elevation with a stadia instrument. They are not strictly correct, because Eq. (12) is not mathematically correct. The line HH' normal to the collimation axis of the telescope is not normal to the two lines IH and IH', between which the inter- cept lies. These lines in the case of an instrument rated at 100 enclose an angle of about 34'. Each of these lines departs from the line of sight by about IT. It follows that while HP' is exactly equal to H'P' the intercept S is not exactly bisected by the middle cross-hair, there being in the small triangle BHP' and B'H'P' (see Fig. 7) an acute angle at H of about 89 43', while at H' in the other small triangle the angle is obtuse, 90 17'. It can readily be shown that the error made in accepting Eq. (12) is so small that it is negligible. In order that this may become apparent the following is presented. Referring TOPOGRAPHIC STADIA SURVEYING 15 to Fig. 7, draw the lines HA and H'A' perpendicular to HH' then HA=H'A'=-sma. (20) FIG. 7. In the triangle HAB the angles will be, for an instrument rated at 100: At//, 17'; At A, 90 -a- AtB, 90+a-17'. In the triangle H'A'B' the angles will be At//', 17'; At A', 90 +a; AtB', 90 -o-17'. Therefore sin 17' . . . (21) 16 TOPOGRAPHIC STADIA SURVEYING A'B>-2a*a-r Slnl7/ (22) 2 sin (89 43' -a) and because ' = (S-A'B'+AB)cosa; .... (23) **^^^:^ (24) and +ecosa. . (25) The error that results in using formula (14) or (17) in place of formula (25) will be Based on this equation it appears that the inaccuracy of Eq. (17) is as follows: For a = 10 the error will be only .00007%; a =20 the error will be only .0003%; a = 30 the error will be only .0008%; a =45 the error will be only .0025%. These errors are, as already stated, too small to be taken into account. Approximation Formulas. The value of e is generally small. It will rarely exceed 2 ft. and will generally be nearer 1 ft. This being the case there will be only a slight error introduced if in formulas (17) and (18) the value e be replaced by e cos a. This substitution is certainly allowable in all ordinary topographic surveying operations, in which dis- tances are required only to the nearest foot. TOPOGRAPHIC STADIA SURVEYING 17 With this modification the formulas (17) and (18) become D = (r +e) cos 2 a (approximate) ; . . . . (27) h = (r+e) sin a cos a (approximate). . . (28) In this form the formulas are very convenient. The expressions (r-\-e] cos 2 a and (r+e) sin a cos a in these equations and the expressions r cos 2 a and r sin a cos a in Eq. (17) and (18) are such that they can conveniently be obtained from diagrams, as will hereinafter be explained. The practice of disregarding entirely the distance incre- ment e cos a in formula (17), and the elevation increment e sin a in formula (18) can not be endorsed. Although, as is well known, the error of the individual moderately long sight is frequently in excess of the value of e, the effect of ignoring the correction altogether would be cumulative, a source of error which is not allowable when locating primary or secondary stations. There is less objection to doing this when side shots for ground elevation only are involved. In this case the author's practice has always been to enter the reduction diagram, hereinafter described, with a value (r+1). One foot is a sufficiently close approximation of the value of e for all ordinary surveying instruments. For unimportant side shots, such as shots for elevation of the ground, the following approximations can therefore be recommended: cos 2 ; ...... (29) sin cos a ...... (30) Suggestions Relating to the Use of the Formulas. In reducing the field observations it will be well to be guided by the following suggestions: 1. Use the correct formulas (17) and (18) in making sur- veys which require the greatest attainable accuracy. 18 TOPOGRAPHIC STADIA SURVEYING 2. Use the approximation formulas (27) and (28) and stadia reduction tables for foresights and backsights and. for sights to reference points. 3. Use the approximation formulas (27) and (28) or (29) and (30) and a slide rule or such diagrams as accompany this manual for all ground heights and general topography. In order that the accuracy attainable by use of the approx- imation formulas (27) and (28) may be correctly gaged, it is to be stated that their use introduces errors as follows: When e = 1.5 ft. the error in distance will be less than 0.1 ft. for all vertical angles less than 20; it will be -0.2 ft. for a vertical angle of 30, and -0.3 ft. for a vertical angle of 45. The error in elevation will be less than 0.1 ft. for all vertical angles less than 30 and it will be 0.3 ft. for a vertical angle of 45. For values of e other than 1.5 ft. the errors can readily be approximated from the foregoing, as they increase or decrease proportionately with e. CHAPTER III DIAGRAMS FOR THE REDUCTION OF STADIA MEASUREMENTS Diagrammatic Solution of Stadia Formulas. The fol- lowing considerations have led to the preparation of diagrams for the determination of values for the expressions r cos 2 a and r sin a cos a in Eq. (17) and (18), (r+e) cos 2 a and (r+e) sin a cos a in the approximation formulas (27) and (28) and for the expressions (r+1) cos 2 a and (r + 1) sin a cos a in the approximation formulas (29) and (30). In any circle whose radius is OP, Fig. 8, there will be /P=7Lcos; IP' =IL cos 2 ; PL=IL sin : PP' =7L sin a cos a. If IL, the diameter of the circle be made equal to r or to (r+e) or to (r + 1), according to the formulas to be used, 19 20 TOPOGRAPHIC STADIA SURVEYING 5 g g S S S si STADIA DIAGRAM For Instruments rated 1 to 1OO Graphical Solution of the Approximation Formolas:- D=(r*OcosV D^r+Ocos 1 h=(r+e) sineccosa * h-(r+l) Where: rereading on a vertical rod -vertical angle. D-feorizontal distance. h=difference in elevation. constant=lhe distance of the outside focal point of the object lens from the instrument axis. Follow the vertical angle ray to the curved line (r-e) or (M) as the case may DC and read D on the horizontal scale and h on the veitical scale. rOo-i-F<-ncr>.-jcDcO oo o oo o o oo TOPOGRAPHIC STADIA SURVEYING 21 the lifte IP' will represent the distance increment and PP' the difference of elevation increment in the above formulas. If, now, for all possible values of r, or of (r+e), or of (r + 1) as the case may be, a series of semicircles be drawn all having a common point I, each circle will be the focus of the points P determined by all possible values of the vertical angle and a value of r, or of (r+e}, or of (r+1), equal to the diameter of each circle. In other words, for any vertical angle the limiting side line of the angle, or the angle ray, will cut the circle at a point P such that the horizontal line IP' or I'P will be the value as the case may be of r cos 2 a, or of (r+e) cos 2 a, or of (r+1) cos 2 a, and that PP' will be the value of r sin a cos a, or of (r+e) sin a cos a, or of (r+1) sin a COS a. Semicircles with diameters increasing by regular amounts 1 ft., or 2 ft., or 5 ft., or 10 ft., according to scale, and hori- zontal lines forming a scale by which to read off difference in elevation and vertical lines by which to read off distance, complete the diagram. To secure accuracy in scaling difference in elevation the unit of the vertical scale may be made larger than the unit of the horizontal scale. The semicircles will then be ellipses. According to the scales adopted any reasonable degree of accuracy can be attained. (See Fig. 9.) For ordinary topographic surveying the stadia diagram accompanying this manual will be found adequate to fill every requirement. This diagram is so arranged that both difference in elevation and correct horizontal distance can be read at the same point. The diagram has been drawn, in the main, to logarithmic scales in order that, for practically all distances the relative accuracy of results obtained by its use will be substantially the same. The distances shown on the diagram are from 100 to 1000 feet. They might have been called 10 to 100 or 1 to 10 feet with a corresponding modification of the difference in elevation. The scale from 22 TOPOGRAPHIC STADIA SURVEYING 100 to 1000 feet was adopted because the largest number of sights will ordinarily fall between these limits. The curved lines in the diagram represent all possible values of r, of r+e, or of r+1. In using the diagram the same care must be exercised in placing the decimal point correctly as in the case of slide rule work. It is to be noted that in any region in which oro- graphic features are pronounced it would be useless to attempt to measure elevations with greater precision than to the nearest foot. They may, of course, be read from the diagram and entered in the notes to tenths, but should in such case appear on the map without fractional feet. The Diagram Furnished with this Manual. The dia- gram for the reduction of stadia notes which accompanies this manual is prepared specifically as a graphic solution at one operation of the approximation formulas. D = 0+e) cos 2 ; (27) and h = (r+e) sin a cos a. . . . (28) But the diagram may also be used in ascertaining- the values of r cos 2 a and r sin a. cos a in the correct formulas Eq. (17) and (18) and for the approximation of (r+1) cos 2 a. and of (r+1) sin a cos a in the approximation formulas (29) and (30). As the formulas (17) and (18) need only be used for sights to turning points and on surveys requiring more than ordinary precision, it would seem advisable to give prefer- ence to reduction tables whenever such approximation for- mulas as (27) and (28) or (29) and (30) will not serve. To Use the Diagram. Follow the ray which corresponds to the angle a of elevation or depression to its intersection with the curved line which corresponds to the value (r+e) in formulas (27) and (28). Holding a needle point at the intersection thus determined read off on the vertical lines the horizontal distance D, that is (r+e) cos 2 a, and on the TOPOGRAPHIC STADIA SURVEYING 23 horizontal lines the difference in elevation h, that is (r-fe) Sin a COS a. Thus when the approximation formulas are to be used, the diagram gives at once the distance and the difference in elevation for any rod-readings and any vertical angles within their scope. Distance should be read to the nearest foot and difference in elevation to the nearest tenth of a foot. When points are located by the intersection of sights from two instrument stations, the horizontal distances from each of these two stations are scaled from the map. The diagram is now entered with each of these distances and needle points are placed at the intersection of these distances with the corresponding angle rays of the measured angles of elevation or depression. If the same difference of elevation is not indicated by both needle points the mean value should be recorded. CHAPTER IV THE SLIDE-RULE AS AN AID IN REDUCING STADIA NOTES Modification of Formulas for Slide-rule Work. It is not always convenient to use a diagram in reducing rod- readings and vertical angles to distance and elevation dif- ference. This is particularly true for plane-table work which requires that the reduction be made in the field. In such cases slide-rules may be used to advantage. Special slide-rules are made for the purpose. These need not receive any special notice. But the ordinary slide-rule can be made a convenient aid as will now be shown. Formulas (17) D =r cos 2 a-\-e cos ; (18) h=r sin a cos + e sin ; and (27) D = (r+e) cos 2 a (approximate); (28) h = (r +e) sin a cos (approximate) ; can be made convenient for solution with the slide-rule by substituting for sin a cos a the trigonometric equivalent sin a cos =| sin 2a (31) For work with the slide-rule only the approximation for- mulas (27) and (28) or (29) and (30) should be used. 24 TOPOGRAPHIC STADIA SURVEYING 25 In combination with (31) the Eqs. (27) and (28) will become : D = (r+e) cos 2 a; (27) h = sin 2a. Both of these equations or similar equations containing the factor (r+1) are readily solved with the ordinary slide- rule. CHAPTER V METHODS OF STADIA SURVEYING Stadia Surveys Without the Use of the Magnetic Needle. When the plane-table or transit are oriented without the use of a magnetic needle, the instrument is to be set up over a starting point of known position and eleva- tion. The height i of the telescope above the bench-mark or station-plug is measured and the table or transit are oriented. The first orientation is adapted to the shape of the area to be covered or to other considerations. It may, of course, be based on a north point determination. At all subsequent settings the plane-table or the lower plate of the transit, as the case may be, must be brought into a position parallel with the first setting. To accomplish this in the case of the transit, after setting the vernier at the azimuth which was read at the last station (when sighting toward the new sta- tion), and reversing the telescope, a sight is taken back toward the last station, whereby the lower plate of the transit is brought into the desired position. In the case of the plane- table the operation is similar, the ruler of the alidade being reversed along the last station sight. At each setting the height i of the telescope above the station plug is measured. This height determines the eleva- tion of the telescope the " height of instrument " in case this should be required. Ordinarily, this will not be required, all sights being taken for vertical angles to the point i on the rod as determined for each instrument setting. Differences in elevation as then determined, regardless of the value of i, are thereupon applied directly to the plug elevation of the 26 TOPOGRAPHIC STADIA SURVEYING 27 instrument station. Only when level sights are taken and the rod is read direct for elevation will it be necessary to apply the readings to the height of instrument, which is, of course, the elevation of the station plug plus i. The rule should be carefully observed to let the last sight recorded at any station be the sight to the next station to be occupied. From each station as occupied there will first be the orien- tation of the transit or plane-table. In sighting back upon the last station occupied the rod should again be read for distance and the vertical angle should be noted. The survey is thus checked. The mean of the two observations, if there be no palpable error, should be used in determining position and elevation of the new station. As a variant of the foregoing the transit may be used at each station to determine the azimuth of all sights taken in their relation to the backsight. In this case the vernier is set at zero when taking the backsight for orientation. Each instrument station should be at such distance from the preceding topographic features being considered that it will command a fair amount of new territory. A foresight of the length of ordinary sights for topographic points would place the new station at the margin of the terri- tory already commanded. In some cases it may be advisable simply to make the foresight as long as consistent with the accuracy required. In other cases it may be of advantage to treat alternate stations as secondary stations using them only for the purpose of locating the next primary station farther on. Referring to stadia surveys, Noble and Casgrain, in the introduction to their tables for horizontal distance and difference of level,* say: "The height of instrument can be determined from the backsight, or the instrument can be set over a point whose height has been determined and the * A. Noble and W. T. Casgrain. Tables for Horizontal Distance , and Difference of Level. Eng. News Pub. Co., 1902. 28 TOPOGRAPHIC STADIA SURVEYING height of the telescope above it is measured directly by a light graduated rod carried for the purpose. The latter is the usual method." Stadia Surveys with the Use of the Magnetic Needle. When the magnetic needle (or a solar compass) is used in orienting the transit or the plane-table, or in determining the azimuth of the sights taken with the transit, a different method of surveying is made possible. The intermediate or secondary stations can be treated as turning-points. The instrument is not set up at all at the secondary stations. But, in this case, the double sighting between stations is no __ k longer possible and recourse should be had to some other method of checking the observations. Probably the best method of accomplishing this is by using two intermediate stations, preferably so selected that the angle between the two foresights to these stations will be at least 30. As all stadia work should be done with two or more rodmen there is usually no difficulty in adopting this double-turning-point method. Two locations and two elevations of each primary station will thus be obtained. Barring gross errors, the mean of the elevations and of the positions of the new instru- ment station thus determined should be accepted. (Correc- tions can be carried back, if desired, to the two secondary stations.) TOPOGRAPHIC STADIA SURVEYING 29 Fig. 10 illustrates a set of sights of this kind. The broken lines show the sights as taken; the full lines as they will appear when corrected. The method of keeping notes for a transit survey by the double-turning-point method is illustrated on page 40. CHAPTER VI PRACTICAL SUGGESTIONS Departures from Ordinary Practice. The author has found several departures from the ordinary methods of stadia surveying advantageous and recommends them to those who have occasion to use the stadia. These depar- tures, including some modifications of methods already alluded to, relate: 1. To the type of rod. 2. To the elimination from the notes of the height of the telescope above a station plug. 3. To the liberal use of the magnetic needle. 4. To the method of keeping field notes. 5. To the use of approximation formulas. 6. To the use of convenient stadia reduction diagrams. The Stadia Rod. The rod which is here described was designed and its markings were devised about 1880 in the office of the State Engineer * of California. No one will be surprised or misled when the author, under whose super- vision the first rod of the kind was made, states that he has found no other self-reading rod equally satisfactory for gen- eral use. The rod is presented on its merits, without prejudice to other self-reading rods of which many more or less satis- factory types are on the market. The rod is shown in Figs. 11 to 16. It is a folding rod, being cut midway of its length, so that, when folded, the painted face of the rod will be protected against injury. * Wm. Hammond Hall was at that time the State Engineer of California. 30 TOPOGRAPHIC STADIA SURVEYING 31 Stiffness when extended is secured by means of a light board, Fig. 11, with projecting overlapping edges. The hinges are relieved of all strain by this arrangement. Into the back of the stiffening board are set two small plates of iron with round holes through which, and through FIG. 11. The stiffen- ing board. FIG 12. I tJ FIG. 13. The folded rod. the board and through the rod, thumb-screws pass to similar plates with threaded holes in the face of the rod. The type of thumb-screw to which preference has been given by the author was turned from a round bar of iron, as shown in Fig. 12. A small bar through the head of the screw gives ample leverage for setting the screws tight, which is a matter of no small importance. The rod when extended 32 TOPOGRAPHIC STADIA SURVEYING FIG. 15. Two types of rod. A. For ordinary use. B. For long sights. FIG. 14. Stadia rod. TOPOGRAPHIC STADIA SURVEYING 33 should have no lost motion at the central joint. Thumb- screws of the type described, cut from about f. in. iron, will stand much rough handling. When folded up the stiffening board is shifted to near the end of the rod, Fig. 13, where there are holes for the free passage of the thumb-screws through one leaf of the folded rod into the threaded holes of two more small iron plates set in the opposing face of the other leaf. The thumb-screws here not only hold the stiffening board securely in place, but clamp the two leaves of the rod, so that there can be no sliding of face against face. In its folded condition the rod is excep- tionally well protected and will stand much handling without injury. The preferred length has always been 11 or 12 ft. but shorter or longer rods may be found convenient. The folded length is just one-half of the full rod length. The top and bottom of the rod should be shod with strips of iron, though in the case of the top, lighter iron than in the case of the bottom may be F IG . 16. A two-tenth used. rod increment. The width of the rod should be at least 3 in. It may, at pleasure and to advantage, be made somewhat wider. Any type of lettering and subdivision may now be used, but one which is not likely ever to be abandoned if once tried, particularly by those who delight in using home-made rods, is the one shown in Figs. 14, 15, and 16. When the rod is wider than 3| ins. the spaces marked f in. Fig. 16, should be increased somewhat. A longer oblique line than shown, for the interpolation of hundredths of a foot, will be found advantageous. The reading is to the nearest hundredth of a foot along the oblique lines of the black triangle. The figures cut by the cross-hair are always read; they stand on the footmarks. 34 TOPOGRAPHIC STADIA SURVEYING The black rectangle of the odd tenths backed by a black triangle, together with the superimposed triangle of the next even tenth make a characteristic design, Fig. 16, which helps the eye to mount from point to point with certainty by two-tenth intervals. The tops of the figures are always three-tenths points. The five- tenth points are indicated by red diamond-shaped marks and the full foot by similar elongated red spear-heads, or half spear-heads, extending across the face of the rod. With telescopes of the ordinary power a rod of this kind with 3| in. face is good for all distances ordinarily entering into stadia work. When sights exceeding 600 ft. are fre- quent, it will be found convenient to use a rod with the sub- divisions of the feet alternately at the left and at the right edge of the rod, as shown in Fig. 15. Any sign painter can paint such a rod. It can be marked in a few minutes. On the white painted surface, after drawing the longitudinal line at the base of the triangles, the foot marks are to be laid off with care, using a tested steel tape. That the foot marks should be correct is of prime importance. The zero point of the rod should preferably be at the top edge of the metal shoe, not at its bottom, which is subject to wear. Using a pattern cut from a sheet of tin or other convenient material, one foot long, the oblique limiting lines of all the black triangles can be drawn prac- tically with a continuous stroke. A stencil may be used in outlining the figures. The red diamonds may now be painted, then all the black on the rod. Sharp outlines of the markings can be secured by using a ruling pen before filling in with the brush. The red diamonds are convenient identification points for short sights. Colors can not be distinguished at long dis- tances, except when light is very favorable.* * A stadia rod in substantial agreement with the foregoing speci- fications has been put on the market by the A. Lietz Co., Instrument Manufacturers, San Francisco, Cal. TOPOGRAPHIC STADIA SURVEYING 35 For work requiring very long sights crosspieces at several points of the rod, projecting beyond its sides, and a slender extension with similar crosspieces, have repeatedly been found to be of great help. The wood used for such a rod should be straight-grain and well seasoned. According to the character of the wood chosen, the thickness of the rod and of the stiffening board may range from about f in. to | in. When the meter is the distance unit instead of the foot, the markings on the rod should be as shown in Fig. 17. Here again the eye recognizes at a glance the even and odd subdivisions. The readings can be made to the nearest tenth of a meter. Such a rod is serviceable for pre- cise leveling. The Elimination of the Height of the Telescope above the Instrument Sta- tion Plug. The ordinary method of doing stadia work requires that sights be taken for vertical angles to some point on the rod determined by the height i of the telescope above the station plug. It will be found much more convenient to disregard the height of the telescope above the instrument point altogether,* and to take all sights to the 5-ft. mark or p IG i7._A metric to some other selected foot mark which is stadia rod. at about the ordinary height of the tele- scope above the ground. That this height need not be the exact height of the telescope above the ground can readily be seen and will be better understood by reference to the * Dr. W. Jordan: Vermessungskunde, p. 630. 36 TOPOGRAPHIC STADIA SURVEYING diagram Fig. 18. The difference in elevation between the point B in this diagram and the point C is entirely inde- pendent of the height of the tripod at the point A. It can be calculated from the two sights A B' and AC'. The height of the telescope at A above the ground or above a plug does not have to be known at all, unless the elevation of the ground or of the plug at that point is to be determined. When it happens that the 5-ft. mark is not visible, the cross- hair may be set on some other foot mark, making note thereof, and proper attention must be paid to this fact when elevations are calculated. As the 5-ft. increment of the rod is neither added nor sub- FIG. 18. tracted in note-keeping it follows that all instrument station heights may be entered as ground heights, but that they are in fact fictitious. They are not the real instrument heights nor the exact ground heights at the instrument station, but are elevations 5 ft. lower than the actual height of the instru- ment. It is just the same as though the sights were along the dotted lines A'B and A'C, Fig. 18. In using this method of surveying it is desirable to begin as in ordinary leveling by letting the rod be held at the starting point. It will be found a convenience, and the chance of error in platting will be reduced, if backsights are entered in the notes as though they were sights taken from the rod to the instrument. TOPOGRAPHIC STADIA SURVEYING 37 The Liberal Use of the Magnetic Needle. Before pre- senting a sample page of notes it may be well to explain the method of topographic stadia surveying which led to the foregoing simplification. In difficult country it is often found impracticable to select instrument stations in advance and it is frequently embarrassing to be compelled to occupy stations selected by assistants. The operations of setting up and of orientation consume valuable time. To eliminate these disadvantages of the ordinary method of work it being, of course, assumed that the necessary triangulation work, base-line surveying and precise leveling to establish reference points has been done a start may be made at any point of known position and elevation. The starting point may be called station zero. The rod is held at this point and the instrument is carried to the place from which sights can be taken to best advantage both with a view to getting the topography within reach and to making progress ahead. The azimuth is now determined by magnetic needle. Unless, for some reason, the instrument point is to be pre- served it need not be marked by a plug, neither is it necessary to determine the ground height at the instrument unless required by topographic considerations. The instrument station thus occupied is Station 1. The next turning point located by needle bearing, by stadia reading and by vertical angle is Station 2. The instrument is not set up at Station 2, but is carried on to Station 3, which is again selected with a view to comprehensive work. The position of Station 3 is fixed by direction and distance from 2, and so on. Back- sights for azimuth must, of course, be taken with reversed telescope, or the south end of the magnetic needle must be read. Care must also be taken to give the vertical angle its proper sign. It will be noted that the line becomes a continuous traverse line, the odd-numbered stations being instrument stations, the others turning points. For ground heights and short sights reliance may be had 38 TOPOGRAPHIC STADIA SURVEYING upon the small levels attached to the plate of the transit and perhaps in some cases to the horizontal position of the plane table. For each foresight and for each backsight the vertical circle should be set at zero; the telescope is then pointed toward the rod, the tripod head screws, in the case of a transit, are used to bring the telescope level and then the sight is taken. The accuracy with which such work can be done with a transit and the areas that can be covered are surprising. The author has often had two to three rodmen at work and has found no trouble in the office interpretation of the field notes. The method of occupying with the instrument only the alternate or primary stations is particularly applicable in making surveys of reservoir and dam sites, in taking general topography over large areas and in securing data for topo- graphic maps of mining ground. The foregoing notes relating to the use of the magnetic needle in topographic surveying were written with special reference to surveys made with a transit. They are with slight modification of the text applicable also to plane-table map work. It remains to be said that a magnetic needle 5 ins. long should enable the field work to be done with about the same degree of accuracy at which the data can be platted on a scale of about 200 ft. to the inch feVo)- Longer needles or other methods of work should be used when maps on a very large scale are required and a very high degree of accuracy is demanded. Stadia Notes. It has already been stated that the height at the instrument station, as carried into the notes, if the 5-ft. mark be selected as an arbitrary sighting-point, is a fictitious height 5 ft. lower than the actual height of the instrument. It often happens that many sights can be taken without noting the vertical angle by using the transit as a level. In all such cases the level foresight as made should be recorded, but this rod-reading should not be TOPOGRAPHIC STADIA SURVEYING 39 applied to the fictitous station height used in calculating elevations by vertical angle, but to the real height of the instrument. It will, therefore, be found convenient to insert in a " height of instrument " column the actual height of the instrument (the fictitious station height plus 5 ft.), sub- tracting from this, as in leveling, whenever the transit is used as a level. The fictitious transit station elevation, it will be noted, is carried forward into the column for ground heights and is identified by underlining. To this transit station elevation all differences in elevation, as determined by vertical angles with sights to the 5-ft. mark, are applied to calculate the ground heights. When, in taking a foresight or a sight to any point whose elevation is to be determined, the cross-hair in determining the vertical angle is set on some foot mark n other than the foot mark 5, then subtract (n 5) from the elevation. When a backsight is taken to any mark n on the rod other than the foot mark 5 then add to the new instrument station height (n-5) ft. The backsight which appears in the notes as though taken from an even numbered (secondary) station is, in fact, the first sight taken from the next instrument station. The notes thus become a simple combination of transit and level notes. 40 TOPOGRAPHIC STADIA SURVEYING NOTE-BOOK LEFT-HAND PAGE Rod Read- ing. Dis- tance. Magnetic Course. Vertical Angle. Difference in Elevation. Back- sight. Height of In- stru- ment. Level Sights, Pore- sight. Topog raphic Su rvey of The Eagl e Mine Oct. 17, 1915 Station 362 342 N27 15E + 13.21 +81. 61 Station 1 256 257 S31 35 W -2.52 -12.8 116 371 117 372 S80 SOW S83 25W -3.17 -f-2 00 -6.7 + 13 613 603 N45 OOW +8 14 +87 300 288 N36 10W + 12 05 +61 7 900 831 N3 15E + 16.09 +240.8 950 883 N20 30E + 15.30 -2.0+245.0 428 730 428 717 N85 OOE N60 10E +2.17 +8 07 +3.0+17.1 + 102 23 436 437 Station N40 15E 2 6 17 327 43 3 327 43 925 926 S6 45E 8.3 706 707 N35 05E 3.16 ooc 331 Station N62 30E 4 +9 11 +53 48 TOPOGRAPHIC STADIA SURVEYING 41 SAMPLE PAGES RIGHT-HAND PAGE Remarl Transit No. 36. e = l.l5 ft. All vertical angle sights are to the 5-ft. mark on the rod unless otherwise noted. Odd-numbered points are the instrument stations. Even-numbered points are the turning points. U. S. G. S. Bench, top of iron pipe, located, etc. To Station 1 gentle slope to S. Bottom of gulch. Slope to SW. Bottom of gulch. Bottom of gulch. Slope to W. Top of bluff. To 7 ft. Top of bluff. To 2 ft. Slope to S. To station 2. To Station 3. The fictitious (though approximate) elevation of ground at Station 3, and Station elevation is found by sub- tracting 5 ft. from the H. I. At E. edge of timber. To Station 4. Temporary B. M., etc. To Station 5. 42 TOPOGRAPHIC STADIA SURVEYING NOTE-BOOK Rod Read- ing. Dis- tance. Magnetic Course. Vertical Angle. Difference in Elevation. Back- sight. Height of In- stru- ment. Level Sights, Fore- sight. Station 5 382.75 516 511 Nil 05W 6 18 56 4 5.2 437 438 N36 10W 9.26 Station 6 462 461 N20 OOE 3 56 +3 31 09 Station 7 620 618 N10 OOE +4 12 +45 33 417 417 N51 20E -3.06 -22.57 Station 8A. 516 511 N80 OOE +6.16 +56.13 Station 8B. 565 538 N31 45E +12.56 + 123.51 Station 9 Etc. TOPOGRAPHIC STADIA SURVEYING 43 SAMPLE PAGES Continued Eleva- tions. 377.75 321.4 377.6 373.49 373.49 344.80 390.13 322.23 390.13 446.26 322.23 Remarks. Ground at instrument. To Station 6. To 8 ft. to Station 7. To Station 8A. To Station 8B. To Station 9 To Station 9 44 TOPOGRAPHIC STADIA SURVEYING Vertical Angles Measured with an Alidade. In using the alidade of the plane-table for measuring angles in a vertical plane, two readings on the vertical circle are neces- sary. First, the index error when the telescope, pointed toward the rod, is in a horizontal position; second, the angle when the telescope is depressed or elevated toward the sighting-point. A combination of the two readings gives the angle of depression or elevation. It would be a convenience to have the index arranged movable and pro- vided with a tangent screw, similar to the lower plate of the transit, so that the telescope could be leveled carrying with it the index set at zero. Unclamping and sighting could then be followed, as with a transit, by a reading of the vertical angle freed from index error. The index error here referred to is due to the fact that a plane-table is not expected to have a perfectly true surface and cannot be leveled with the accuracy desirable in measuring vertical angles. The Amount of Error when the Sighting Point does not Bisect the Intercept. The formulas presented in this manual are based on the assumption that the portion of the stadia rod which is read for distance is bisected by the middle cross-hair when the vertical angle is read. As a matter of fact this condition rarely obtains in practice. The lower cross-hair is set upon some foot mark and the intercept is read on the upper cross-hair, thereupon the middle cross-hair is set upon the sighting-point and the rodman is waved off. In order that the topographer may have a clear concep- tion of the error introduced when the rod is read for distance, with the middle cross-hair at some point on the rod other than the sighting-point, Tables 1 and 2 have been prepared. It will be seen from these that for small vertical angles and sights of any length, very little attention need be paid to the portion of the rod used in measuring distance. The impor- tance of having the middle cross-hair near the sighting-point when reading for distance, increases, regardless of the actual TOPOGRAPHIC STADIA SURVEYING 45 distance to the rod, as the angle of elevation or depression increases. TABLE 1 TABLE OF CORRECTIONS TO BE APPLIED WHEN THE ROD IS READ WITH THE TELESCOPE AT A VERTICAL ANGLE OF GREATER AMPLITUDE THAN THE RE- CORDED VERTICAL ANGLE (TO THE SIGHTING- POINT). DECREASE THE DISTANCE AND DECREASE THE DIFFERENCE IN ELEVATION BY THE AMOUNTS NOTED IN THE TABLE II 3.8 If Vert. Angle = 1 Vert. Angle = 5 Vert. Angle = 10 Vert. Angle = 20 Vert. Angle = 30 bib Is* T3 O 3 bo Corrections Corr actions Corrections Corrections Corrections 15 Feet. Feet, Feet. Feet. Feet. P4 ^3 Oj_bB 1 |QGO Dist. Elev Dist. Elev. Dist. Elev. Dist. Elev. Dist. Elev. 100 1 .04 .18 .02 .34 .06 .66 .24 .86 .50 100 2 .13 .41 .04 .70 .13 1.32 .'48 1.72 1.00 100 3 .23 .64 .06 1.07 .20 1.98 .73 2.58 1.50 100 4 .32 .87 .08 1.44 .27 2.65 .97 3.45 2.00 100 5 .42 1.11 .10 1.91 .34 3.32 1.21 4.32 2.50 200 1 .04 .2 .02 .3 .05 .6 .20 .9 .50 200 2 .10 .4 .03 .7 .12 1.3 .45 1.7 1.00 200 3 .17 .6 .05 1.1 .18 1.9 .70 2.6 1.50 200 4 .23 .8 .07 1.5 .25 2.6 .95 3.5 2.00 200 5 .30 1.0 .09 1.9 .32 3.3 1.20 4.3 2.50 500 1 .04 .2 .02 .3 .05 .6 .23 .9 .45 500 2 .08 .3 .03 .7 .11 1.2 .46 1.7 .95 500 3 .13 .5 .05 1.1 .17 1.9 .70 2.6 1.45 500 4 .18 .7 .06 1.5 .23 2.5 .93 3.4 1.95 500 5 .23 .9 .08 1.8 .30 3.2 1.16 4.3 2.45 1000 1 .03 .2 .02 .4 .06 .7 .23 .9 .45 1000 2 .07 .3 .03 .7 .12 1.3 .46 1.7 .95 1000 3 .11 .5 .05 1.0 .18 1.9 .70 2.6 1.40 1000 4 .15 .7 .06 1.3 .24 2.6 .93 3.4 1.90 1000 5 .20 .9 .08 1.7 .30 3.2 1.16 4.3 2.40 The tables are prepared as correction tables, but it will be well to remember that no correction is necessary if the rule be observed requiring the middle cross-hair to be first placed on the sighting-point, and then setting the lower cross-hair 46 TOPOGRAPHIC STADIA SURVEYING upon the foot mark nearest to the lowest cross-hair. The error under observance of this rule will be so small as to be negligible in all surveys, except in special cases where the highest attainable accuracy may be a requirement. Whenever the bisecting point of the intercept is within one foot of the sighting-point the error in distance for any vertical angle less than 30 cannot exceed 1 ft. TABLE 2 TABLE OF CORRECTIONS TO BE APPLIED WHEN THE ROD IS READ WITH THE TELESCOPE AS A VERTICAL ANGLE OF LESS AMPLITUDE THAN THE RECORDED VERTICAL ANGLE (TO THE SIGHTING-POINT). IN- CREASE THE DISTANCE AND INCREASE THE DIF- FERENCE IN ELEVATION BY THE AMOUNTS NOTED IN THE TABLE ll Vert. Anglr- Vert. Anglo Vert. Angle Vert. Angle Vert. Angle *- S = 1 = 5 = 10 = 20 = 30 3lf ob a is* ^ 3 M Corrections Corrections Corrections Corrections Corrections s U-g.2 Feet. Feet. Feet. Feet. Feet. Cd ^ n.'rt ^ o &o 3Qo2 ii Dist. Elev. Dist. Elev. Dist. Elev. Dist. Elev. Dist: Elev. 100 1 .02 .16 .01 .33 .05 .63 .22 .87 .50 100 2 .03 .31 .03 .64 .10 1.25 .44 1.73 1.00 100 3 .02 .44 .04 .94 .16 1.85 .66 2.59 1.50 100 4 -.02 .54 .05 1.22 .21 2.44 .88 3.46 1.95 100 5 -.08 .62 .05 1.49 .26 3.07 1.10 4.32 2.40 200 1 .03 .2 .01 .3 .06 .6 .22 .9 .50 200 2 .05 .3 .03 .7 .12 1.2 .45 1.7 1.00 200 3 .06 .5 .04 1.0 .17 1.9 .67 2.6 1.50 200 4 .06 .6 .05 1.3 .23 2.6 .89 3.4 1.95 200 5 .05 .7 .06 1.6 .28 3.2 1.12 4.3 2.40 500 1 .03 .2 .01 .3 .06 .6 .23 .9 .50 500 2 .05 .3 .03 .7 .12 1.2 .46 1.7 1.00 500 3 .07 .5 .04 1.0 .17 1.9 .68 2.6 1.50 500 4 .09 .7 .06 1.3 .23 2.6 .91 3.4 1.95 500 5 .10 .8 .07 1.6 .28 3.2 1.14 4.3 2.40 1000 1 .03 .2 .01 .4 .06 .6 .23 .9 .50 1000 2 .06 .3 .03 .7 .12 1.3 .46 1.7 1.00 1000 3 .09 .5 .04 1.1 .18 1.9 .70 2.6 1.50 1000 4 .12 .7 .06 1.4 .24 2.6 .93 3.4 1.95 1000 5 .15 .8 .07 1.7 .30 3.2 1.16 4.3 2.40 TOPOGRAPHIC STADIA SURVEYING 47 The columns in the tables bearing the heading " Middle hair departures from the sighting-point " contain the depart- ure of the bisecting point of the intercept from the sighting- point for which the corrections in the succeeding columns have been computed. The sighting can, as stated, always be done in such manner that the use of these tables will not be necessary. Their introduction is mainly for the purpose of showing the errors that will result if proper attention be not paid to the part of the rod read for distance. Amount of Error Due to Inclined Rod. If the stadia rod be not held in a true vertical position, or if, in the case of a sectional rod the face of the rod is in two or more planes, appreciable error may result. All such error should be avoided. Nevertheless in order that the magnitude thereof may not be underestimated attention is called to the following facts. Let it be supposed that a rod is built up of two sections of which the uppermost is fastened to the back of the lower one and that the thickness of the lower section and, therefore, the departure of the upper section from the plane of the lower one is | of an inch or .0875 ft. If now a reading for distance is made on this rod with one cross-hair on the lower and one on the upper section the resulting error in distance will be : For vertical angle + 5 rod reading too small by 0.8 ft. For vertical angle +10 rod reading too small by 1.5 ft. For vertical angle +20 rod reading too small by 3.2 ft. For vertical angle +30 rod reading too small by 5.0 ft. For vertical angle 5 rod reading too large by 0.8 ft. For vertical angle 10 rod reading too large by 1.5 ft. For vertical angle 20 rod reading too large by 3.2 ft. For vertical angle 30 rod reading too large by 5.0 ft. It is to be noted that in the case of short sights the per- centage of error when sighting up or down will be relatively 48 TOPOGRAPHIC STADIA SURVEYING high. The amount of this error is independent of the dis- tance, being dependent solely upon the vertical angle of the sight and the departure of the surface on which one cross- hair is read from that on which the other is read. When due to carelessness or any other cause the stadia rod is inclined forward or backward, and departs from a true vertical plane, the error will be as shown in Tables 3 and 4. The Accuracy of Telemeter Surveys. The accuracy of the survey made with the telemeter and stadia rod is not readily determinable. The error in single readings may vary within considerable limits. The reading is affected not alone by the care with which the telemeter and the rod have been constructed, but also by atmospheric and light conditions and by the personal equation of the observer. Under fair conditions the individual readings, when the distances do not exceed 800 ft. should have a probable error less than 1 in 500. When a survey is under consideration made up of a number of courses, aggregating about a mile in length, the error with ordinary care and with instruments suitable for ordinary good work, should not exceed 1 in 1000. When a still longer distance is measured by many sights, each less than 800 ft., the probable error will be less than this amount. According to the law of least squares, possibly 1 in 2000 when the aggregate length of the survey is about 4 miles. In view of the relatively large possible error in a single sight, it would be useless to note distances other than to the nearest foot, when ordinary topographic surveys are involved. Elevations of temporary reference points, such as turning-points and of permanent bench marks, should be entered in the notes to hundredths. The height of instru- ment, too, should be entered to hundredths of a foot. The elevation of the ground at any point and the differences in elevation for use in determining ground heights should be noted to tenths only. TOPOGRAPHIC STADIA SURVEYING 00 o'Jj ^ CNlC^iN ^t*-^-* O5O5OJ C 1C 1C 000000 OOO lOiOiO XOOOO COCOCO III .S-g TH^JU J.s| "So 02 '3 a 2 2 PH v Q C O. O Tf C5 1C 00 I-H C^ O >1 -^ 1C O5 O5 KXMiC CO 00 CO rH I-H CO CMrt< CoS^HiclS fl < *s M 1 III Ml III Ml >^2 O oj COCOCO Tf ^ -^ (M CN) (N 1C 1C 1C i-H r-l rH 'CiC'C I-II-H^H CT>OiO5 iCiC'C TtirH^ ill > J*- . 5 is g JS| PH o> H a ^ ERTICA CO 1C C^l <** 1C CO (M Tf O i-H ^-1 ^H CO ^> 4 III 1 1 1 III Ml III ^-r^- " H * 3 '^ a O II og | ^ cococo o> O3 os cococo ^ Tj< Tti ic ic ic - T!< CO O I s - Tti t>. 1C (M^H^N ICO5O5 OlMiC O--HTJ< i-HOOiC ^^ fl ^ o a JH oj o T-H CM CMiC -liCO CMOO CO'C^H .2 O-DJ 1-1 "^ 0"S a 33 . ^ - COCOCO OCOt- ^'5 v " -*^ w -*-* -' i-HCO COCO i-I CO CO CMOO ^j>^_3 -*-> < W ^ c!"^ III Ml Ml III Ml O g ?' g a. 04 ^ m'^' a j S.<2* ^ p, "S S S? OOO I-H I-H I-H COCOCO COCOCO OOO 3^3 f_( w S5I rH i-H i-H 5 "^ * B o i "*COiC t^T^r^ (NOC^ iC'fOO (NO O CN T}< I-H 00 CO CO CO CM CO CM * O <-H j 2 |:1 ti Si 1 11 111 Hi 11 11 a | g o a aj.S o s^'g '^0^ | -H ; - l^5c ^"S* rt a &H 82 ^ r a i C O -< CM CO li 11 ^ J< S*-C 50 TOPOGRAPHIC STADIA SURVEYING '30 II si S _T3 Is g s PH H ?i^i * rH CO . IMrHrH lOt~>O OOOr-l ICCOIN h i 1 7 COCOCO 000000 * Tji rj< b-t^t^. "t * Tt< N (N d (N COCOCO rH rH rH b- t^. t>. CO O CO j << o C^rHCO COOOO rHtN-^ tVOOl^ tO'^'CO H g r-ld rH CO rHIOrH d CO b- Tf CO CO III r-. -Hd OlC>O rHrHrH OOOOOO CDCOCO b-t^f^ OOO COCOCO t^t>t^- t^t^t> OOCXDO) o * . . . . . . . - PC H OC^ 1 ^ 1 COCOCO ^OOO b-OOt^- OO^t^* H O i ' i 1 1 t 10 'O 'O o CJ 000 ^^^ 8 3rH J5K.O rH -HIM (MlO rH tO W rHOO K (N(M(M COCOCO OOO rHrHrH OOO OOO rHrHrH COCOCO COCOCO OOO 2C 3 Values of e e cos e sin e cos e sin e cos e sin e cos e sin e cos e sin e cos e sin 0.80 0.80 .01 .80 .07 .79 .14 .77 .21 .75 .27 .69 .40 1.00 1.00 .02 1.00 .09 .98 .17 .97 .26 .94 .34 .87 .50 1.20 1.20 .02 1.19 .10 .18 .21 1.16 .31 1.13 .41 1.04 .60 1.40 1.40 .03 1.39 .12 .38 .24 1.35 .36 1.32 .48 1.21 .70 1.60 1.60 .03 1.59 .14 .57 .28 1.54 .41 1.50 .55 1.39 .80 1.80 1.80 03 1.79 .16 .77 .31 1.74 .47 1.69 .62 1 . 56 .90 2.00 2.00 .03 1.99 .17 .97 .35 1.93 .52 1.88 .68 1.73 1.00 2.50 2.50 .04 2.49 .22 2. 40 .43 2.41 .65 2.35 .85 2.16 1.25 54 TOPOGRAPHIC .STADIA SURVEYING 55 STADIA REDUCTION TABLE Table 6 is a stadia reduction table, checked by Mr. Otto von Geldern, to facilitate the solution of the equations. D=r cos" a+e cos a; .... (17) h =r sin a cos a+e sin ; . . .(18) or sin 2 h=r He sin (19) The tables as here published contain only the increments 100 cos ? a and 100 sin a cos a, In using formulas (17) and (18) the values taken from the tables are to be multiplied by - . In determining dis- luu tance e cos a and in determining difference in elevation e sin a are then to be added to the values found in the tables. In illustrating the use of these tables Mr. von Geldern uses the following figures: For a rod-reading r=285 ft. and a vertical angle 10 12' there will be found in the table in the column " Hor. Dist." 96.86 and in the column "'Diff. Elev." 17.43; in other words 100 cos 2 (10 12') =96.86 ft., and 100 sin (10 12') .IPS (10 12') =17.43 ft. 2jUos( to bo mi 285 Both of these values are to ^multiplied by ^-^ =2.85. J. \)\) Therefore 285 cos 2 (10 12') =2.85x96.86=276.05; 285 sin (10 12') cos (10 12') =2.85x17.43=49.67. 56 TOPOGRAPHIC STADIA SURVEYING If a large ordinary transit has been used the value of e will be about 1.15 ft., and therefore 1.15 cos (10 120=1.13; and 1.15 sin (10 120=0.21, consequently D =276.05+1. 13 =277.18; A =49.67 +0.21 =49.88. The chief value of Table 6 lies in the fact that it is applica- ble to the solution of the approximation formulas which are recommended in this manual for use in stadia surveying. Thus in the case of (27) Z) and (28) h = (r +e) sin a cos a. For the special case (r+e) =285 + 1.15=286.15; 286 15 D =- X96.86 =277.16 ft.; h=-X 17.43 =49.88 ft. Again in the case of (29) D = (r + l) cos 2 ; (30) A = (r + l) sin a cos a. For the special case of (r + 1) =286; 286 D=X96.86 =277.02 ft.; 286 X 17.43 =49.85 ft. 1UU TOPOGRAPHIC STADIA SURVEYING 57 TABLE 6 STADIA REDUCTION TABLE For instruments rated 1 to 100 In the column " Hor. Dist." find: 100 cos 2 a In the column " Diff. Elev." find: 100 sin a cos a Rod Vertical Min. 1 2 3 4 Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. 100.00 .00 P3.97 1.74 99.88 3.49 99.73 5.23 99.51 6.96 2 100.00 .00 09.97 1.80 99.87 3.55 99.72 5.28 99.51 7.C2 4 100.00 .12 ).97 1.86 99 . 87 3 . 60 99.71 5.34 99.50 7.07 G 100.00 .17 39.96 1.92 99.87 3.6C 99.71 5.40 99.49 7.13 8 100.00 .23 99.96 1.98 39.86 3.72 99.70 5.46 99.48 7.19 10 100.00 .29 99.96 2.04 99 .86 3 . 78 99-69 5.52 99.47 7.25 12 100.00 .35 99.96 2.09 99.85 3.84 99.69 5.57 99.46 7.30 14 100.00 .41 99.95 2.15 39.85 3.90 99.68 5.63 99.46 7.36 16 100.00 .47 99.95 2.21 99.84 3.95 99.68 5.69 99.45 7.42 18 100.00 .52 39.95 2.27 99.84 4.01 99.67 5.75 99.44 7.48 20 100.00 .58 39 . 95 2 . 33 99.83 4.07 99.66 5.80 99.43 7.53 22 100.00 .64 99.94 2.38 99.83 4.13 99.66 5.86 99.42 7.59 24 100.00 .70 99.94 2.44 39.82 4.18 99.65 5.92 99.41 7.65 26 99.99 .76 99.94 2.50 39.82 4.24 99.64 5.98 99.40 7.71 28 99.99 .81 99.93 2.56 99.81 4.30 99.63 6.04 99.39 7.76 30 99.99 .87 99.93 2.62 99.81 4.36 99.63 6.09 99.38 7.82 32 99.99 .93 99.93 2.67 99.80 4.42 99.62 6.15 99.38 7.88 34 99.99 .99 99.93 2.73 99.80 4.48 99.62 6.21 99.37 7.94 36 99.99 .05 99.92 2.79 99 . 79 4 . 53 99.61 6.27 99.36 7.99 38 99.99 .11 99.92 2.85 99.79 4.59 99.60 6.33 99.35 8.05 40 99.99 .16 99.92 2.91 99.78 4.65 99.59 6.38 99.34 8.11 42 99.98 .22 99.91 2.97 39.78 4.71 99.59 6.44 99.33 8.17 44 99.98 .28 99.91 3.02 39.77 4. 76 99.58 6.50 99.32 8.22 46 99.98 .34 99.90 3.08 99.77 4.8 99.57 6.56 99.31 8.28 48 99.98 1.40 99.90 3.14 39.76 4.88 99.56 6.61 99.30 8.34 50 99.98 1.45 99.90 3.20 99.76 4.94 99 . 56 6 . 67 99 . 29 8 . 40 52 99.98 1.51 99.89 3.26 99.75 4.99 99.55 6.73 99.28 8.45 54 99.98 1.57 39.89 3.31 39.74 5.05 99.54 6.78 99.27 8.51 56 99.97 1.63 99 . 89 3 . 37 99.74 5.11 99.53 6.84 99.26 8.57 58 99.97 1.69 39.88 3.43 99.73 5.17 99.52 6.90 99.25 8.63 60 99.97 1.7499.88 3.49 99.73 5.23 99.51 6.96 99.24 8.68 58 TOPOGRAPHIC STADIA SURVEYING TABLE 6. Continued STADIA REDUCTION TABLE For instruments rated 1 to 100 In the column " Hor. Dist." find: 100 cos 2 a In the column " Diff. Elev." find: 100 sin a cos a Rod Vertical Min. 5 6 7 8 9 Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. 99.24 8.68 98.91 10.40 98.51 12.10 98.06 13.78 97.55 15.45 2 99.23 8.74 98.90 10.45 98.50 12.15 98.05 13.84 97.53 15.51 4 99.22 8.80 98.88 10.51 98.48 12.21 98.03 13.89 97.52 15.56 6 99.21 8.85 98.87 10.57 98.47 12.26 98.01 13.95 97.50 15.62 8 99.20 8.91 98.86 10.62 98.46 12.32 98.00 14.01 97.48 15.67 10 99.19 8.97 98.85 10.68 98.44 12.38 97.98 14.06 97.46 15.73 12 99.18 9.03 98.83 10.74 98.43 12.43 97.97 14.12 97.44 15.78 14 99.17 9.08 98.82 10.79 98.41 12.49 97.95 14.17 97.43 15.84 16 99.16 9.14 98.81 10.85 98.40 12.55 97.93 14.23 97.41 15.89 18 99.15 9.20 98.80 10.91 98.39 12.60 97.92 14.28 97.39 15.95 20 99.14 9.25 98.78 10.96 98.37 12.66 97.90 14.34 97.37 16.00 20 99.13 9.31 98.77 11.02 98.36 12.72 97.88 14.40 97.35 16.06 22 99.11 9.37 98.76 11.08 98.34 12.77 97.87 14.45 97.33 16.11 24 99.10 9.43 98.74 11.13 98.33 12.83 97.85 14.51 97.31 16.17 26 99.09 9.48 98.73 11.19 98.31 12.88 97.83 14.56 97.29 " 16.22 28 99.08 9.54 98.72 11.25 98.29 12.94 97.82 14.62 97.28 16.28 30 99.07 9.60 98.71 11.30 98.28 13.00 97.80 14.67 97.26 16.33 32 99.06 9.65 98.69 11.36 98.27 13.05 97.78 14.73 97.24 16.39 36 99.05 9.71 98.68 11.42 98.25 13.11 97.76 14.79 97.22 16.44 38 99.64 9.77 98.67 11.47 98.24 13.17 97.75 14.84 97.20 16.50 40 99.03 9.83 98.65 11.53 98.22 13.22 97.73 14.90 97.18 16.55 42 99.01 9.88 98.64 11.59 98.20 13.28 97.71 14.95 97.16 16.61 44 99.00 9.94 98.63 11.64 98.19 13.33 97.69 15.01 97.14 16.66 46 98.99 10.00 98.61 11.70 98.17 13.39 97.68 15.06 97.12 16.72 48 98.98 10.05 98.60 11.76 98.16 13.45 97.66 15.12 97.10 16.77 50 98.97 10.11 98.58 11.81 98.14 13.50 97.64 15.17 97.08 16.83 52 98.96 10.17 98.57 11.87 98.13 13.56 97.62 15.23 97.06 16.88 54 98.94 10.22 98.56 11.93 98.11 13.61 97.61 15.28 97.04 16.94 56 98.93 10.28 98.54 11.98 98.10 13.67 97.59 15.34 97.02 16.99 58 60 98.92 10.34 98.91 10.40 98.53 12.04 98.51 12.10 98.08 13.72 98.06 13. 78 97.57 15.40 97.55 15.45 97.00 17.05 96.98 17.10 TOPOGRAPHIC STADIA SURVEYING 59 TABLE 6. Continued STADIA .REDUCTION STABLE For instruments rated 1 to 100 In the column " Hor. Dist." find: 100 cos 2 a In the column " Diff. Elev." find: 100 sin a cos a Rod Vertical Min. 10 11 12 13 14 Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. rlor. Diff. Dist. Elev. 96.98 17.10 96.36 18.73 95.68 20.34 94.94 21.92 94.15 23.47 2 96.96 17.16 96.34 18.78 95.65 20.39 94.91 21.97 94.12 23.52 4 96.94 17.21 96.32 18.84 95.63 20.44 94.89 22.02 94 .09 23 . 58 6 96.92 17.26 96.29 18.89 95.61 20.50 94.86 22.08 94.07 23.63 8 96.90 17.32 96.27 19.85 95.58 20.55 94.84 22.13 94.04 23.68 10 96.88 17.37 96.25 19.00 95.56 20.60 94.81 22.18 94.01 23.73 12 96.86 17.43 96.23 19.05 95.53 20.66 94.79 22.23 93.98 23.78 14 96.84 17.48 96.21 19.11 95.51 20.71 94.77 22.28 93.95 23.83 16 96.82 17.54 96.18 19.16 95.49 20.76 94.73 22.34 93.93 23.88 18 96.80 17.59 96.16 19.21 95.46 20.81 94.71 22.39 93.90 23.93 29 96.78 17.65 96.14 19.27 95.44 20.87 94.68 22.44 93.87 23.99 22 96.76 17.70 96.12 19.32 95.41 20.92 94.66 22.49 93.84 24.04 24 96.74 17.76 96.09 19.38 95.39 20.97 94.63 22.54 93.81 24.09 26 96.72 17.81 96.07 19.43 95.36 21.03 94 .60 22 . 60 93.79 24.14 28 96.70 17.86 96.05 19.48 95.34 21.08 94 .58 22 . 65 93.76 24.19 30 96.68 17.92 36.03 19.54 95.32 21.13 94.55 22.70 93.73 24.24 32 96.66 17.97 96.00 19.59 95.29 21.18 94.52 22.75 93.70 24.29 34 96.64 18.03 35.98 19.64 95.27 21.24 94.50 22.80 93 .67 24 . 34 36 96.62 18.08 35.96 19.70 95.24 21.29 94 .47 22 . 85 93.65 24.39 38 96.60 18.14 95.93 19.75 95.22 21.34 94.44 22.91 93.62 24.44 40 96.57 18.19 35.91 19.80 95.19 21.39 94.42 22.96 93.59 24.49 42 96.55 18.24 95.89 19.86 95.17 21.45 94.39 23.01 93.56 24.55 44 96.53 18.30 95.86 19.91 95.14 21.50 94.36 23.06 93.53 24.60 46 96.51 18.35 95.84 19.96 95.12 21.55 94.34 23.11 93.50 24.65 48 96.49 18.41 95.82 20.02 95.09 21.60 94.31 23. 1C 93.47 24.70 50 96.47 18.46 95.79 20.07 95.07 21.60 94 .28 23 . 22 93.45 24.75 52 96.45 18.51 35.77 20.12 35.04 21.71 34.26 23.27 93 ..42 24 . 80 51 96.42 18:57 35.75 20.18 35.02 21.76 94.23 23.3: 33.39 24.85 56 96.40 18.62 35.72 20.22 34.99 21.81 94 .20 23 . 37 33.. 36 24.90 58 36.38 18.68 35.70 20.28 )4.97 21.87 34.17 23.41 33.33 24.95 60 96.36 18.73 35.68 20.34 )4.94 21.92 34.15 23.47 33.30 25.00 60 TOPOGRAPHIC STADIA SURVEYING TABLE 6 Continued STADIA REDUCTION TABLE] ^ For instruments rated 1 to 100 In the column " Hor. Dist." find 100 cos 2 a In the column " Diff. Elev." find: 100 sin a cos a Rod Vertical Min. 15 16 17 18 19 Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. 93.30 25.00 92.40 26.50 91.45 27.96 90.45 29.39 89.40 30.78 2 93.27 25.05 92.37 26.55 91.42 28.01 90.42 29.44 89.36 30.83 4 93.24 25.10 92.34 26.59 91.39 28.06 90.38 29.48 89.33 30.87 6 93.21 25.15 92.31 26.64 91.35 28.10 90.35 29.53 89.29 30.92 8 93.18 25.20 92.28 26.68 91.32 28.15 90.31 29.58 89.26 30.97 10 93.10 25.25 92.25 26.74 91.29 28.20 90.28 29.62 89.22 31.01 12 93.13 25.30 92.22 26.79 91.26 28.25 90.24 29.67 89.18 31.06 14 93.10 25.35 92.19 26.84 91.22 28.30 90.21 29.72 89.15 31.10 16 93.07 25.40 92.15 26.89 91.19 28.34 90.18 29.76 89.11 31.15 18 93.04 25.45 92.12 26.94 91.16 28.39 90.14 29.81 89.08 31.19 20 93.01 25.50 92.09 26.99 91.12 28.44 90.11 29.86 89.04 31.24 22 92.98 25.55 92 .06 27 . 04 91.09 28.49 90.07 29.90 89.00 31.28 24 92.95 25.60 92.03 27.09 91.06 28.54 90.04 29.95 88.96 31.33 26 92.92 25.65 92.00 27.13 91.02 28. 90.00 30.00 88.93 31.38 28 92.89 25.70 91.97 27.18 90.99 28.63 89.97 30.04 88.89 31.42 30 92.86 25.75 91.93 27.23 90.96 28.68 89.93 30.09 88.86 31.47 32 92.83 25.80 91.90 27.28 90.92 28.73 89.90 30.14 88.82 31.51 34 92.80 25.85 91.87 27. ?3 90.89 28.77 89.86 30.19 88.78 31.56 36 92.77 25.90 91.84 27.38 90.86 28.82 89.83 30.23 88.75 31.60 38 92.74 25.95 91.81 27.43 90.82 28.87 89.79 30.28 88.71 31.65 40 92.71 26.00 91.77 27.48 90.79 28.92 89.76 30.32 88.67 31.69 42 92.68 26.05 91.74 27.52 90.76 28.96 89.72 30.37 88.64 31.74 44 92.65 26.10 91.71 27.57 9Q.72 29.01 89.69 30.41 88.60 31.78 46 92.62 26.15 91.68 27.62 90.69 29.06 89.65 30.46 88.56 31.83 48 92.59 26.20 91.65 27.67 90.66 29.11 89.61 30.51 88.53 31.87 50 92.56 26.25 91.61 27.72 90.62 29.15 89.58 30.55 88.49 31.92 52 92.53 26.30 91.58 27.77 90.59 29.20 89.54 30.60 88.45 31.96 54 92.49 26.35 91.55 27.81 90.55 29.25 89.51 30.65 88.41 32.01 56 92.46 26.40 91.52 27.86 90 .52 29 . 30 89.47 30.69 88.38 32.05 58 92.43 '26.45 91.48 27.91 90.48 29.34 89.44 30.74 88.34 32.09 60 92.40 26.50 91.45 27.96 90.45 29.39 89.40 30.78 88.30 32.14 TOPOGRAPHIC STADIA SURVEYING 61 TABLE 6 Continued STADIA REDUCTION TABLE For instruments rated 1 to 100 In. the column " Hor. Dist." find: 100 cos 2 a In the column " Diff. Elev." find: 100 sin a cos Rod Vertical Min. 20 21 22 23 24 Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. :ior. Diff. Dist. Elev. Hor. Diff. Dist. Elev. Hor. Diff. Dist. Elev. 88.30 32.14 87.16 33.46 85.97 34.73 84.73 35.97 83.46 37.16 2 88.26 32.18 87.12 33.50 85.93 34.77 84.69 36.01 83.41 37.20 1 88.2* 32.23 87.08 33.54 85.89 34.82 84.65 36.05 83.37 37.23 G 88.1-3 32.27 87.04 33.59 85.85 34.86 84.61 36.09 83.33 37.27 8 88.15 32.32 87.00 33.63 85.80 34.90 84.57 36.13 83.28 37.31 13 88.11 32.36 86.96 33.67 85,76 34.94 84.52 36.17 83.24 37.35 12 88.08 32.41 86.92 33.72 85.72 34.98 84.48 36.21 83.20 37.39 14 88.04 32.45 36.88 33.76 85.68 35.02 84.44 36.25 83.15 37.43 16 88.00 32.49 86.84 33.80 85.64 35.07 84.40 36.29 83.11 37.47 18 87.96 32.54 86.80 33.84 85.60 35.11 84.35 36.33 83.07 37.51 20 87.93 32.58 86.77 33.89 85.56 35.15 84.31 36.37 83.02 37.54 22 87.89 32.63 86.73 33.93 85.52 35.19 84.27 36.41 82.98 37.58 24 87.85 32.67 86.69 33.97 85.48 35.23 84.23 36.45 82.93 37.62 26 87.81 32.72 86.65 34.01 85.44 35.27 84.18 36.49 82.89 37.66 28 87.77 32.76 86.61 34.06 85.40 35.31 84.14 36.53 82.85 37.70 30 87.74 32.80 86.57 34.10 85.36 35.36 84.10 36.57 82.80 37.74 32 87.70 32.85 86.53 34.14 85.31 35.40 84.06 36.61 82.76 37.77 34 87.66 32.89 86.49 34.18 85.27 35.44 84.01 36.65 82.72 37.81 36 87.62 32.93 86.45 34.23 85.23 35.48 83.97 36.69 82.67 37.85 38 87.58 32.98 86.41 34.27 85.19 35.52 83.93 36.73 82.63 37.89 40 87.54 33.02 86.37 34.31 85.15 35.56 83.89 36.77 82.58 37.93 42 87.51 33.07 86.33 34.35 85.11 35.60 83.84 36.80 82.54 37.96 44 87.47 33.11 86.29 34.40 85.07 35.64 83.80 36.84 82.49 38.00 46 87.43 33.15 86.25 34.44 85.02 35.68 83.76 36.88 82.45 38.04 48 87 .39 33 . 20 86.21 34.48 84.98 35.72 83.72 36.92 82.41 38.08 50 87.35 33.24 86.17 34.52 84.94 35.76 83.67 36.96 82.36 38.11 52 87.31 33.28 86.13 34.57 84.90 35.80 83.63 37.00 82.32 38.15 54 87.27 33.33 86.09 34.61 84.86 35.85 83.59 37.04 82.27 38.19 56 87.24 33.37 86.05 34.65 84.82 35.89 83.54 37.08 82.23 38.23 58 87.20 33.41 86.01 34.69 84.77 35.93 83.50 37.12 82.18 38.26 60 87.16 33.46 85.97 34.73 84.73 35.97 83.46 37.16 82.14 38.30 62 TOPOGRAPHIC STADIA SURVEYING TABLE 6 Continued STADIA REDUCTION TABLE For instruments rated 1 to 100 In the column " Hor. Dist." find: 100 cos 2 a In the column " Diff. Elev." find: 100 sin a cos a Rod Vertical Mm. 25 26 27 28 29 Hor. Diff. Hor. Diff. Hor. Diff. Hor. Diff. Hor. Diff. Dist. Elev. Dist. Elev. Dist. Elev. Dist. Elev. Dist. Elev. 82.14 38.30 80.78 39.40 79.39 40.45 77.96 41.45 76.50 42.40 2 82.09 38.34 80.74 39.44 79 .34 40 . 49 77.91 41.48 76.45 42.43 4 82.05 38.38 80.69 39.47 79.30 40.52 77.86 41.52 76.40 42.46 6 82.01 38.41 80.65 39.51 79.25 40.55 77.81 41.55 76.35 42.49 8 81.96 38.45 80.60 39.54 79.20 40.59 77.77 41.58 76.30 42.53 10 81.92 38.49 80.55 39.58 79.15 40.62 77.72 41.61 76.25 42.56 12 81.87 38.53 80.51 39.61 79.11 40.66 77.67 41.65 76.20 42.59 14 81.83 38.56 80 46 39.65 79.06 40.69 77.62 41.68 76.15 42.62 16 81.78 38.60 80.41 39.69 79.01 40.72 77.57 41.71 76.10 42.65 18 81.74 38.64 80.37 39.72 78.96 40.76 77.52 41.74 76.05 42.68 20 81.69 38.67 80.32 39.70 78.92 40.79 77.48 41.77 76.00 42.71 22 81.65 38.71 80.28 39.78 78.87 40.82 77.42 41.81 75.95 42.74 24 81.60 38.75 80.23 39.83 78.82 40.86 77.38 41.84 75.90 42.77 26 81.56 38.78 80.18 39. 8C 78.77 40.89 77.33 41.87 75.85 42.80 28 81.51 38.82 80.14 39.90 78.73 40.92 77.28 41.90 75.80 42.83 30 81.47 38. 8G 80.09 39.93 78.68 40.96 77.23 41.93 75.75 42.86 32 81.42 38.89 80.04 39.97 78.63 40.99 77.18 41.97 75.70 42.89 34 81.38 38.93 80.00 40.00 78.58 41.02 77.13 42.00 75.65 42.92 36 81.33 38.97 79.95 40.04 78.54 41.06 77 .09 42 . 03 75. CO 42.95 38 81.28 39.00 79.90 49.07 78.49 41.09 77 .04 42 . 06 75 55 42.98 40 81.24 39.04 79.86 40.11 78.44 41.12 76.99 42.09 75.50 43.01 42 81.19 39.08 79.81 40.14 78.39 41.16 76.94 42.12 75.45 43.04 44 81.15 39.11 79.76 40.18 78.34 41.19 76.89 42.15 75.40 43.07 46 81.10 39.15 79.72 40.21 78.30 41.22 76.84 42.19 75 . 35 43 . 10 48 81.06 39.18 79.67 40.24 78.25 41.26 76.79 42.22 75.30 43.13 50 81.01 39.22 79.62 40.28 78.20 41.29 76.74 42.25 75.25 43.16 52 80.97 39.26 79.58 40.31 78.15 41.32 76.69 42.28 75.20 43.18 54 80.92 39.29 79.53 40.35 78.10 41.35 76.64 42.31 75.15 43.21 56 80.87 39.33 79.48 40.40 78.06 41.39 76.59 42.34 75.10 43.24 58 80.83 39.36 79.44 40.42 78.01 41.42 76.55 42.37 75.05 43.27 60 80.78 39.40 79.39 40.45 77.96 41.45 76.50 42.40 75.00 43.30 TOPOGRAPHIC STADIA SURVEYING 63 ANDERSON'S STADIA REDUCTION TABLE (As prepared and in use by U. S. Geological Survey) Explanation of Table: Table 7 is particularly useful when topographic surveys of large areas are to be made. It was prepared by Mr. C. G. Anderson and has been published by the U. S. Geological Survey in a pamphlet entitled " Tables for Obtaining Differences of Elevation," 1909. It is reprinted here with the permission of the Survey. In the U. S. G. S. pamphlet the table from to 5 angle of elevation includes rod-readings to 3500 ft. though here reproduced to only 2600 ft. The figures in 'the body of the table give " Differences in Elevation " in feet for rod-readings in feet, read on a rod held vertically. The degrees of vertical angle are printed at the top of each page; the minutes in the right or left-hand vertical columns. The figures in the top horizontal line are the rod-readings ( = intercept times rating factor). The figures in the bottom horizontal line are the correct hori- zontal distances based on the middle (30') angle of the page. The horizontal distances were computed by the formula (32) To increase the usefulness of these tables, there has been added, at the bottom of each page, a correction for distance which has been given for each departure of 10' from the angle for which distance is noted in the table. The basic, angle for distance, as already stated, is in each case the half degree. For all vertical angles on any page or in any column less than this basic angle, i.e., above the 30' line, the correction will be positive, it will be added to the distance at the bottom of the page or column ; and for all vertical angles larger than the basic angle, i.e., below the 30' line, the correction is to be sub- tracted. 64 TOPOGRAPHIC STADIA SURVEYING The differences in elevation were computed by the for- mula: h =r sin a cos (33) As elsewhere explained in this manual a somewhat closer approximation, when surveys are made with ordinary instru- ments, can be obtained by entering the table with (r+e) or (r+1) instead of with r. This applies both in the matter of difference in elevation and distance. This table as is seen from the above formulas was pre- pared for use as an approximation table and in this respect ranks with Table 6. When more than ordinary accuracy is required the corrections e cos a and e sin a. can be added to the values taken from the table when entered with the rod- reading r. Tabular values for the omitted columns, viz. : 1000, 2000, and 3000, can be obtained from columns 100, 200 and 300, respectively, by moving the decimal point one place to the right. Tabular values beyond the range of the table can be ob- tained by moving the decimal point to right or left, as shown in the following example: Required the difference in elevation for an angle of 3 16' for a rod-reading of 3644 ft. (i.e., intercept of half stadia interval, 18.22 times 200=3644 ft.). In this case (r + 1) = 3645 ft. For 3000 ft. (from 300 ft. moving the deci- mal to right) 170.7 ft. For 600 ft 34.1 ft. For 40 ft. (from 400 ft. moving the deci- mal point to left) 2.28 ft. For 5 ft. (from 500 ft. moving the deci- mal point two places to left) .28ft. Difference in elevation. . 207.4 ft. TOPOGRAPHIC STADIA SURVEYING 65 The distance in the case of this example is found by the aid of the table to be 3634 ft., as follows: For 3 30' For 3000 ft. (from 300 ft. moving the deci- mal point to right) 2989 ft. For 600 ft 598ft. For 40 ft. (from 400 ft. moving the decimal point to left) 40 ft. For 5 ft. (from 500 ft. moving the deci- mal point two places to left) 5 ft. Distance from table 3632 ft. For 3 16' being 14' less than 3 30' add: 1,4 X36.3 X .035 = 1.78 or 2 ft. Corrected distance is . . 3634 ft. 66 TOPOGRAPHIC STADIA SURVEYING TABLE 7 DIFFERENCES IN ELEVATION ' 100 200 300 400 500 600 700 800 900 1100 1200 1300 ; 03 03 03 0.8 3 5 o 09 o 15 o 29 44 o 6 7 09 1 ?! I ' 3 i 3 i 6 1 4 I 7 '5 ' 9 23 8 9 o 23 26 46 n^ o. 70 o 79 o 87 09 I I 2 i 3 ' 4 I 6 i 6 i 8 ' 9 2 1 i 6 2 9 7 8 3 ' 2 6 .3 o 34 II 3 o 32 o 35 o 38 o 64 o 70 o 77 96 3 '3 I 4 '5 i 6 i 7 ' 9 1-9 2 3 2 3 2 4 2 6 7 6 i 8 3 o 2 9 3 ' 3 4 1:1 4 2 .38 4 2 4 5 4 2 45 4-9 '5 44 o 87 3' 1 7 2 2 2 6 3 I 35 3 9 4 8 52 5- 7 I? 18 '9 49 0.52 o 55 o 99 '05 .48 57 66 2 I 2 5 2 6 3 > 3 5 3-7 4- 4 2 4 4 47 5 4 58 5 9 6 3 66 64 6.8 7 2 20 21 22 '3 0.58 o. 61 0.64 0.67 I. 16 I. 22 1.28 > 34 75 83 92 . 01 24 2.6 3 > 32 1:1 4 3 4-5 47 49 5 ' 5 5 5-8 . 6.7 7 o 7 3 7 7 79 83 5 o 73 J-45 . 18 8 7 94 27 0-79 '57 36 3- ' 39 4- 7 5 5 6 3 7 i 8 6 94 10 2 29 o.8 4 i.6 9 53 3-4 4-2 5 ' 5 9 6 7 7 6 9 3 10 1 II I 3' 32 o. 90 o-93 i. so 1.86 7 79 3-6 3-7 4 5 4-7 54 56 63 6 5 7 2 7 4 8 i 8 4 9 9 10 2 I 1 2 II 7 12 1 34 35 36 s 39 40 4> 42 43 o 99 1 02 05 .08 :ii '9 . 22 :li 1.98 2.04 2.09 2-15 2. 21 2.27 2-33 2.38 2.44 2.50 97 3 5 3- '4 3-23 3-32 3-40 3-49 3-58 3-66 3-75 4.0 4.1 42 4-3 4-4 4-5 4-7 4-8 4-9 5-o 49 5 l 52 54 5-5 5-7 5-8 6.0 6.1 6.2 5 9 6 i 63 65 66 6 8 72 7-3 7-5 6 9 7 > 7 3 75 77 8.0 8 i 1:1 8.8 7 9 8 i 8 4 8 6 8 8 9 ' 93 9-5 9.8 10. 8 9 9 2 9 4 97 9 9 10 2 10.5 10.7 II II 2 10 9 " 5 n 8 '2 5 12 8 '3 ' '3-4 13 8 ii 9 12 2 12 6 12 9 '3 3 '3 6 14 o '43 '4-7 15 o 12 9 '3 -2 '3 6 14.0 14.4 '4-7 '5 ' 15-5 '5-9 16 2 16 6 45 46 31 34 2.62 2.63 3 93 01 5-2 5-4 6-5 6.7 7.8 8.0 9.2 94 10.5 10 7 ii 8 12 14.4 14-7 '5-7 16 i 17 o '74 48 49 50 5 52 53 54 55 56 57 58 $9 .40 42 45 .48 51 54 57 .60 .:8 .69 7.2 2.79 2.85 2.91 2.97 3-02 3-o8 3-14 3-20 3-6 3-32 3-37 3-43 '9 28 36 45 54 4.62 4-7' 4.80 4.88 4-97 5-o6 5- '5 56 5-7 5-8 11 6.2 6-3 6.4 6-5 6.6 6-7 6.9 7-0 7- ' 7-3 7-4 7-6 7-7 78 8.0 8.1 8-3 8-4 8.6 8.4 8.6 8-7 8.9 9- i 9-2 9-4 9.6 9.8 9-9 10. I 10.3 9-8 10 10. 2 10.4 10.8 2 4 6 .8 " ii. a II. 4 ii. 6 II. 9 3 12 6 12.8 '3-3 '35 37 12.6 12 8 13 ' "34 36 3-9 4 i 4-4 4-7 49 5-2 5 4 54 '5-7 16.0 163 16.6 17.0 '73 17 6 '79 18 2 18.6 18 9 16.8 17 ' '74 17.8 18 2 ; 8 .i 19.2 '95 19.9 20. 2 >o 6 18. i .8.5 18 9 '93 '97 20.0 20.4 20.8 21. 2 21 & 21 9 22.3 Horz. Dist. 99-99 99-9 299-9 399-9 499-9 599-9 699.9 7999 899.9 1099.9 1199.9 12999 Hor. dist. Is for 30' point. Add or subtract .005 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 67 TABLE 7 Continued DIFFERENCES IN ELEVATION 1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 2600 f I.O ,., i 8 0.6 0.7 o. 7 0.7 0.8 "5 2 1.6 24 2.8 2.6 3-o 28 33 3-o 3-5 3- ' 3-7 3-3 3-9 3-7 4-3 3-8 4-5 4.0 47 3-5 4- 2 I'l 3-6 4-4 H 3-8 4-S 5-3 5 6 7 g 3-7 3-9 4- 2 4- 4 4-7 5-o l\ it 6.0 6 7 6-3 6.6 6.8 7 6 9 4-5 49 5-3 4.8 5-2 5-7 5- ' 56 6.0 5-4 59 6.4 5-8 63 68 6. i 6.6 7 2 6.7 73 79 7- o 7-7 8.3 7-4 8.0 8.7 77 8.4 9 ' 8.0 8.7 9-4 8-3 K ii 12 3 6. I 6-5 65 7.0 7-4 79 8. 2 9 2 9-8 9.6 10. 2 10. 7 10.5 II. 2 10.9 it. 6 11.3 12. I '5 16 6.9 73 77 8. i 86 9.0 7-4 78 8-3 8.7 H 79 8.4 8.8 9-3 9.8 10. 2 8.9 9-4 10. 10.4 10.9 9-4 9-9 16.5 II 9-9 10. j II. i II 6 II. ii 6 12. 2 12.8 "5 12. 2 12 8 3-4 4- 7 12.7 <3-4 14 '47 5- 4 :;:8 33 14.0 '4-7 |l:t 12-4 ii '5-3 16.0 16.7 12.9 13-6 14.4 I5-I '5-9 16. 6 7-4 17 18 '9 20 21 22 23 9-8 IO. 2 10.6 II II 4 10.9 ;:i 12 2 II 6 13. I 13 6 '30 12.4 12 9 '33 3-8 >3 ' 3-6 '4 I '4 7 13-8 14.4 14-9 '5 5 >5-3 5-9 i6. 6 17 ' 6.0 6.6 7 3 7 9 16.7 17 4 18. i 18.7 7 4 8. 2 18. 8 '9-5 18.2 18.9 19.6 20.4 18.9 19-7 20.4 21. 2 24 25 26 27 28 12 6 '3 ' 13 5 14 o 14. 4 14.8 IS 3 '57 16. 2 16 6 17 i 18 3 18.9 9.2 19.8 20. I 20.9 21 8 22 7 3 13.0 '3 4 14. 14.4 '49 '54 '5-8 ,6.3 16 8 '7 3 18. 2 20. 2 21 I 22 I 23.0 24.0 25.0 33 14 2 14.7 '5 ' 5 5 15-3 '57 16 I 16 6 16.3 16.7 17.2 17-7 '7 3 17 8 '8.3 18 8 18.3 18 8 19. 4 '93 19. 9 20 4 21 4 22 22 6 22 4 23.0 23-7 23-4 24. I 24 7 24.4 III 26.5 25-4 26.2 26.9 27.6 26.5 27 2 28.0 28. 7 35 36 37 38 15 9 16.3 16.7 17 o 17 4 17 9 18 3 18. 2 18.6 19. I 9-3 19.8 20.3 20. 4 20.9 2' 5 22 I 22 7 24.4 25-0 25 6 26.2 26 9 26. I 26.8 27-4 28 I 27.2 27.9 28.6 28.4 29.1 29.8 29-5 30.2 3' o 31. 8 39 40 4> 42 17 5 17 9 18.3 18.7 19 ' 19 5 18. 8 19.2 19.6 20. I 20.5 20 9 20.0 20 5 20. 9 21.4 21 9 22.3 21:2 21.8 22. 2 22.7 23.2 23-7 2?. 5 23. o 23.6 24. 24.6 25 ' 3-8 4-3 4-9 26.5 26.3 26-9 27-5 28.1 28.7 29-3 27-5 28.2 28.8 29-4 30.1 30.7 28.8 29.4 30. I 30.8 3'-4 32- I 32. 8 30.0 30.7 3'-4 32 ' 32.8 33-5 3'. 3 32.0 32-7 33-4 34-2 34-9 35- 6 32-5 33-3 34-o 34-8 35-5 36.3 37-0 43 44 45 46 47 48 49 20.4 20.8 21 8 22 2 23-3 23-7 *4-7 25.2 26.2 26.7 27.6 28.2 28.7 3-5 31-2 3'-8 32.0 32.6 33-3 33-4 Sti 34-9 35-6 36.3 36-4 37- 37-8 37-8 38.6 39-3 50 5 5* 21.6 22 4 22.8 6 24.0 36 4.0 4-4 4-9 5-3 5-7 25. t 25.6 26.1 26.5 27 5 26.7 27-2 27-7 28.2 28.7 29.2 28.3 28.8 29.3 29.8 30.4 3 9 29.8 30-4 30.9 3'-5 32.0 32.6 33-o 33-6 34-2 34-8 35-4 36.0 34-5 35-2 35-8 36 5 37- ' 37-8 s; s? 38.8 39 5 37-7 38-4 39- ' 39-8 40.5 41.2 38.5 39-2 40.7 4'-4 42-2 42-9 40.1 40.8 41.6 42-3 43-' 43 9 44-6 53 54 55 56 5 59 13999 14998 15998 16998 i799- 1899.8 2099-8 2199* 2299.8 2399^ 2499.8 2599-8 Dist. Hor. dist. is for 30' point. Add or subtract .005 ft. to each 100 ft. of distance for each 10' departure. 68 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 1 f 100 200 300 400 500 600 700 800 900 1100 1200 1300 o 2 3 4 5 6 I 9 10 11 12 13 u '5 16 74 77 .80 -83 86 89 9* 95 98 01 04 06 09 12 IS 21 3-49 3 55 3-6r 3-66 3-72 3-78 3-84 3 90 3 96 4.01 4.07 4->3 4- 19 4-^5 4-30 4.36 4-42 5-24 5-32 3-4' 5-50 5-58 5-67 je 5-93 6. 02 6. ii 6.19 6.28 6.37 6.46 6.54 6.63 7.0 7- 8-7 8.9 10.5 10.6 12.2 12.4 14.0 14.2 15-7 16.0 19 2 ' 9 'n 20.9 21 3 22.7 23 i 7-3 7-4 7-6 7-7 7-8 80 8.1 8.3 8-4 8-5 8.6 8.7 8.8 9.2 9-3 11. O 11. 2 12.8 13-0 '4-7 14.9 '65 16.7 20. 1 2 1 22. O 22-3 23 8 J4-2 24 6 24.9 9-6 9-7 9-9 ro. 2 10.3 10.5 10.6 10.8 10. t II. O 11. S 3-4 >5-4 '73 21. I 2 .0 11.9 12.0 12. 2 12.4 12.6 12.7 12.9 13- > '3-3 '38 14.0 14.2 4 4 4-7 14 -9 15-' '.5-3 S-5 >5-7 '5-9 J6. i 6.3 16.5 16.7 16.9 '7-. '5-8 '63 6.5 16.7 17.0 17.2 7-4 7 7 17.9 18. i 18.4 18. 6 18. 8 19. i 9 3 '95 17.8 18. i 18-3 18.6 18.8 19.1 19.4 19.6 19.9 20. 2 2O. 4 20.7 20.9 21.2 21.5 21 7 22. 21.7 22.4 22 7 23 o 23 3 23-7 24.0 24 3 24 6 24 9 25-3 256 25-9 26 2 26 5 26 9 2 7 2 -4 248 25 ' III 26.2 26.5 26 9 27.2 27.6 27 9 28.3 28.6 29.0 29 3 25-7 26. i 26.5 26.8 37.1 27-6 28.0 28.4 28 7 29 ' 29 5 29.9 30.2 30-6 31.0 3' 4 31.8 32 i 32 5 32 9 33 3 18 9 20 21 22 23 24 '5 26 r. 9 30 3i 32 33 34- 35 36 i 39 40 4< 4' 43 44 45 46 47 48 49 5 5' 52 53 54 55 56 8 59 27 3 33 5 41 44 47 5 51 59 62 65 68 70 73 76 79 82 It 9- 94 97 00 .02 3 05 308 3 > 3 M 3 "7 3 20 3 23 3.26 3-29 3-3' 3 34 3 37 3 40 3 43 3 46 4 54 4-59 4 65 4-7" 4- 77 4-83 4.88 4-94 5 oo 5 06 5 12 5 '8 5 23 5 29 5 35 54' 5 47 5 52 5 58 5 64 5 70 5 76 5.8i 5 8'/ 5 93 5 99 6 05 6.80 6.89 6.98 7.07 7 IS 7-24 7 33 74' 7 50 7 59 7.68 7-76 7 85 794 8 02 8 n 8 29 8 37 846 8-55 9 ' 9.2 93 9-4 95 9.6 9.8 9-9 0.0 0. 1 2 4 - 5 07 0.8 o. 9 1 I 3 " 3 "5 11. 6 11.8 11.9 12. 1 12. 2 12. 4 12 5 12.6 12 8 12.9 13-6 '3-8 14.0 14. i 4-3 '4-5 47 14-8 15-0 "S* '54 '55 '75 '7-7 '7 9 20.0 20 5 III 23.0 27i 28 1 30 o 30.3 30-7 '3 2 34 '3 5 ! >4 14 1 '5 9 >6. o 16 2 16 4 16. 6 16 7 16 9 \il 18.9 19 1 '9 3 '95 19.7 21 2 21 4 21 6 21 9 22 1 22 3 22 6 38 4 ' 43 46 24 9 25 ' J5- 4 29. 1 29 4 29. 7 30 1 30 4 30 7 3' o 3' 4 3 8 32 ' il.3 33"' 33 5 338 34 34 4 34 8 35 2 35 5 35 9 36 3 36 7 872 8 81 8 90 8.98 9.07 i 6 '4 5 '7 4 20 3 23 3 26 2 26. 4 26.7 27. o 3" 7 32 3 32 6 32 9 33 3 33 6 33 9 34-2 34 5 34-8 35 2 35 5 35 8 36-1 36.4 36-8 37 37-4 37-7 380 34 5 34 9 35 * 35 6 35 9 36 3 36 6 37 o 37-3 37 7 38.0 38-4 387 39-' 39 4 39-8 40.1 40 5 40.8 41 2 4' 5 37 4 37 8 3& ' 386 38 9 39 3 39 7 40. i 40.4 40 8 4' 2 41 6 41 9 42-3 42 7 43 ' 43 4 43 8 44 .2 44 6 45 ' 9 2 1 zi >5 o 15 ' 17.8 18.0 20.8 21.0 23-7 24 o 6. 16 6 22 6.28 6-34 6.40 [?, 6-57 6.63 6 68 6.74 6.80 6.86 6.92 9.24 9-33 9.42 9 50 9 59 9.68 9 77 9 85 9 94 10. 20 10.29 .0.38 2 3 24 2 6 2-7 12.8 12.9 13 ' '32 3 4 13 5 '36 "3-7 38 Si 5 7 '58 16. o 16. 1 >6.3 16 4 16 6 16.7 16.9 17.0 17.2 7 3 8-5 18.7 18 8 19.0 19.2 '94 '95 19.7 19.9 20. I 2O. 2 20.6 20.7 21 6 21.8 22. 2 22.4 22.6 22 8 23.0 23-2 23-4 23-6 23-8 24.0 2 4 .2 2 4 6 24.9 25 ' 25-3 25 6 25 8 26.0 26.3 26.5 26.7 27.0 27 2 27 4 27 7 27 5 27.7 28.0 28.3 28.5 28.8 29.0 29 3 29.6 29.8 30.1 303 30 6 30 9 3' ' Horz. i".!. 99-93 199.9 2998 399-7 499-6 599 699 799 899 1099 "99 1299 Hor. dist. is for 30' point. Add or subtract .015 ft. to each 100 ft. distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 69 TABLE 7 Continued DIFFERENCES IN ELEVATION 1 1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 2600 f 24. 4 26.2 27.9 29-7 3> 4 33-2 36.6 38.4 40. i 41.9 43 6 45-4 24 8 26.6 28.4 30.2 3' 9 33-7 37-2 39 o 40.8 42.6 44- 4 46.1 i 25 2 27.0 28.8 30.6 32.4 34-3 37-9 39 7 4' 5 43-3 45 ' 46.9 2 25 6 27-5 29-3 3' ' 33-o 34-8 38.5 4-3 42. i 44-o 45 8 47.6 3 26. i 27.9 29.8 3' 6 33-5 35-4 39- i 40.9 42.8 44-7 46.5 48.4 4 26.5 28.4 30.2 32- ' 34 o 35-9 39-7 4.. 6 43-5 45-4 47-3 49 ' 5 20. 8 28.8 3 7 32.6 34- S 36.5 40.3 42.2 44- ' 46. i 48.0 49-9 6 27 3 29.2 3' 2 33 ' 35- 37 o 40.9 42.9 44 8 46.7 48.7 50.6 7 27 7 29.7 3'- 6 33-6 35-6 37-6 4'- 5 43 5 45 5 47-5 49- 4 5'-4 8 28. I 30. i 32- I 34- ' 36.1 38. 44- ' 46.1 48.2 50. 2 52.2 9 28.5 30.5 32-6 34-6 36.6 38.7 42 7 44- 8 46.8 48.8 50.9 52.9 10 289 3' o 33 o 35- 37 2 39 * 43 3 45-4 47-5 49 5 5' 6 53-7 ,, 29-3 3>-4 33-5 35 6 37-7 398 44.0 46.1 48.2 50 3 52.4 54-4 12 29-7 31-8 34-0 36.1 38-2 4 3 44 6 46.7 48.8 5-9 53 ' 55-2 '3 3 ' 3*-3 34 4 36.6 38.7 40.9. 45-2 47 3 49 5 5> 6 53 8 55 9 14 30-5 3* 7 34 9 37 i 39 3 41 4 458 48 50.2 52 3 54 5 56.7 '5 3 9 33 2 35 4 37-6 398 42 o 46.4 48.6 50.8 53 o 55 2 57-5 16 3 1 - 3 33 6 35-8 38.1 40.3 42 5 47 49-3 5' 5 53 7 56 o 58.2 '7 3 7 36.3 38.6 40.8 43 ' 47 6 49 9 52 2 54-4. 56.7 59 o 18 32 2 34 5 36.8 39 o 4' 3 43 6 48.2 50.5 52.8 55.' 57 4 59 7 '9 32 .6 34 9 37-2 39-6 41.9 44 2 48.9 5' 2 53 5 55 8 58 3 60 5 20 33 35 3 37 7 40.0 42. 4 44.8 49 5 5-8 54 2 56 5 58 9 61. 2 2I 33 4 35 8 j 40.5 42.9 45 3 5 I 5* 5 54 8 57 2 59 6 60 i 62 62 8 22 33 8 34 2 36 2 36 6 39 ' 4' 5 44.0 46.4 5 7 5' 3 53 ' 53 7 55- 5 56.2 57 9 58 6 oo 3 61 i 63 5 23 24 34 6 37 i 39 5 44 5 47 o 5' 9 54 4 56 8 59-3 6. 8 64 3 25 35 37 5 40. o 42 5 45 o 47 5 52 5 55 -o 57 5 60.0 62 5 65 o 26 35 4 37 9 40 5 43 45 5 53 ' 55 6 58.2 60 7 6 3 2 65 8 27 35 8 38 4 40.9 43 5 46 48 6 53 7 56.3 58.8 61 4 64 66 5 28 36 2 388 41 4 46.6 49 2 54-3 56 9 59 5 62 i 64 7 67 3 29 366 39 3 41 9 44 5 47 i 49 7 55 o 57 6 60 2 62 8 65 4 68 o 3 J? o 39 7 42 3 45 47 6 5 3 55 6 58 2 60 9 63 5 66 2 68 8 3' 37 4 42 8 45 5 48 2 50 8 56.2 58 8 61 5 64 2 66.9 69.6 32 37 9 40 b 43 3 48 7 5" 4 56 8 59 5 62 2 64.9 67 6 70 3 33 3 3 41 o 43 7 46 5 49 2 5' 9 57 4 58 o 60. I 60. 8 62 9 6l e 65 6 66 i 68.3 7' ' 71 8 34 39 > 41 y 44 7 47 4 50 2 53 o 58 6 61 4 3 5 64 2 oo. 3 67 o 698 72 6 35 36 39 5 4? 3 45 ' 47 9 50 8 53 6 59 2 64 9 67 7 70 5 73 3 37 39 9 42 7 45 6 48 4 5' 3 54 i 598 62 7 65 5 68.4 71 2 74 ' 38 40 3 43 * 46 48 9 5' 8 54 7 60.4 63 3 66.2 69.1 72 74 8 39 40 7 43 & 46.5 49 4 52 3 55 2 64.0 66.9 69 8 72 7 75 6 40 4> 44 47 o 49 9 52 9 55 8 61 7 64 6 67 S 70.5 73 4 76 3 4> 4 1 5 4> 9 44 9 47 9 5 9 53 9 56 3 56 9 62 3 62 9 65 9 68.9 71.9 74 9 77 9 43 42 3 45 3 48 4 5' 4 54 4 57 4 63 5 66.5 69 5 72 6 75 6 78 6 44 42 7 45 8 488 5' 9 54 9 580 64 i 67.2 70.2 73 3 76.3 79 4 45 43 ' 40 i 49 3 S 2 4 55 5 58 5 64-7 67 8 70 9 74 o 77 80. i 46 43 5 46 7 49 8 52 9 56 o 59 ' 65-3 68 4 71.5 74 6 77 8 80.9 47 43 9 47 ' 5 2 53 4 56 5 59 7 65.9 69.1 72 2 75 3 78 5 81 6 48 44 4 47 5 50 7 53 9 57 o 60 2 66.5 69 7 72 9 76 o 79-2 82.4 49 44 48 51 2 54 4 57 6 60 8 67 ' 70.3 73 5 76 7 80.0 83 ' SO 45 2 4 4 5' 54 58.1 6i.3 67 8 . 74 2 77 4 80.7 83.9 5' 45 6 48.8 52 i 55 3 58.6 61.8 68 4 . 6 74-9 78.1 81 4 84 6 52 46 49 3 52 6 55 8 59 ' 62.4 69. o 3 75 5 78 8 82. i 85 4 53 46.4 49 7 53 56 3 59 6 63 o 69 6 9 76 2 79 5 82.8 86 2 54 46.8 50.1 S3 5 56.8 60. 2 63 5 70 2 3 5 76 9 80.2 836 86.9 55 4? 2 47 6 50 6 53 9 57 3 60.7 64 i 70 8 74 * 77 6 80 9 84 J Q- .. 7 7 88 4 56 48 o 5' 5 54 4 54 9 57 " 58 3 61 7 65 2 72 o 75 5 78 9 82 j Ill 8 9 1 5 $ 8 48 4 5' 9 55 3 58-8 62 3 65 ? 72 6 76 i 79 6 83 o 86 5 89 9 59 '399 '499 '599 1699 '799 199 2098 2,98 2298 2398 2498 25?8 Horz Dist. Hor. dist. is for 30' ppint. Add or subtract .015 ft. to each 100 ft. of distance for each 10' departure. 70 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 3 f 100 200 300 400 500 600 700 800 900 1100 1200 1300 3 49 6 98 10 46 14 O I? 4 20.9 24.4 27 9 31 4 38.4 41 9 45-3 1 3 52 7 03 10 55 14 1 17 6 21 1 24.6 28. i 31 7 38 7 42 2 45-7 2 3 3 55 3 58 7 09 10. 64 "4 2 17 7 21 3 24.8 28.4 3' 9 32.2 39-0 39 3 42.6 42 9 46.1 46.5 4 S 360 3 63 7 21 7 '7 .0.81 10.90 14 5 18 2 21 8 25 4 29. I 32 4 32 7 396 40.0 43 2 43 6 46.8 47- 6 3 66 7 32 10 99 14.6 18 3 22. O 25 6 29 3 33 o 40 3 43 9 47-6 7 3 69 7 38 u 07 14.8 18 5 22 1 25,8 29 5 33-2 44 3 48.0 8 3 72 7 44 11 16 14.9 18 6 22 3 26.0 29.8 33 5 40.9 446 48.4 9 3 75 75 u 25 15.0 18.7 22 5 26. 2 30.0 33 7 41 2 45 -o 48.7 3 78 7 5 ii 33 15 I 18 9 22-7 26.4 30.2 34- 41 6 45-3 49-1 it 3 81 7 61 li 42 5 2 19. o 22 8 26.6 3 S 34 3 41.9 45 7 49-5 1 3 384 7 67 II Si 15 3 19 2 23 o 26 8 30.7 34 5 42 2 460 49 9 13 3 86 7 73 11 60 IS 5 19 3 23 2 27 i 30.9 34 8 42 5 46.4 50.2 >4 3 89 7 79 11.68 15 6 19 5 23 4 7'3 3 i 35 -o 42.8 46 7 50.6 '5 3 92 7.85 ii 77 15-7 19.6 23 5 27 5 3 4 35 3 43 47 i 51 16 3-95 79 II 86 58 19.8 3 7 27 7 36 35 6 43 5 47 4 5 4 I? 3-98 7 96 u 94 15 9 19 9 23 9 27.9 3 8 35-8 36 i 43 8 44. i 47 8 48.1 5 -7 5 ' >9 4.04 4.07 8.08 8.14 12 20 16.3 20.3 24-4 28.3 28.5 3 -3 3 -5 36-3 36.6 44 4 44 7 48 5 488 S -5 5 9 21 4 10 8.19 12 29 16.4 20. 24 6 28 7 32 8 36.9 45 49 2 S3 3 22 4 U 8 25 .2.38 16.5 20. 24.8 28.9 33-0 37 i 45 4 49 5 53-6 3 4 16 8 31 12 46 16 6 20. 24.9 29. i 33-2 37-4 45-7 49 9 54-o 24 4. ,8 837 12 55 16 7 20. 25 i 29 3 33-5 37 7 46. o JO. 2 54 4 25 4.21 8-43 12 6 4 16.8 21. 25-3 29-5 33 7 37-9 46 3 506 54-8 6 4 24 848 12.73 17 o 21 25 4 29 7 33-9 38.2 46 7 50 9 55 j 4 27 8 54 12 8l 17 i 21. 25 .6 29 9 34 2 38 4 47 o 51-2 55-5 26 4 30 8 60 12 90 72 21 25 8 30. l 34-4 38.7 47 3 51 6 55-9 30 4 33 4 36 8 716 13 07 7 4 21 26. I ,A , 30. 3 30-5 34- 6 34-9 39- 39 2 47 6 47 9 48 3 5 1 9 52 3 5 2 6 56- 3 3* 33 4 42 4 44 8 831 8 889 13 25 3 33 77 7.8 22 20. 3 26 5 26.7 3- 7 3 9 31- i 35- ' 35-3 35-6 39- 5 39-7 40. o 48 6 48 9 53 o 53 3 57.4 57.8 34 4-47 8947 13 42 79 22 26 8 31-3 35 8 40.3 49 2 53 7 58 2 35 4-50 9.005 13-51 8.0 22. 27.0 3i 5 36.0 40-5 49 5 54 -0 585 36 4 53 9.063 3 59 8.1 22 27 2 31 7 36.2 40.8 49 8 54-4 58-9 37 4-56 9. 121 1368 8.2 22. 27 4 3i 9 36 5 41. o 50.2 54-7 59 3 38 4 59 9- 179 13-77 8.4 22. 27-5 32-1 36.7 41.3 50.5 55- I 59-7 39 4.62 9-237 13- 86 8.5 23- 27-7 32.3 36.9 41 6 50.8 55-4 60.0 40 4-65 9-295 13-94 8.6 23- 27.9 32.5 37 41.8 51 I 55-8 60.4 41 4.68 9 353 14-03 8-7 3- 28.1 32 7 37-4 42 > 51 4 56.1 60.8 42 4-71 9.411 14. 12 8.8 23- 28.2 32.9 37 6 42 3 56.5 61.2 43 4 73 9-469 14. 20 8-9 23 28.4 33 i 37 9 42.6 42. 9 52 I 56-8 57 2 61 5 61 9 45 4-79 9-585 14.38 9-2 24- 28.8 33-5 38^3 43 I 52 7 57-5 62.3 46 4.82 9.642 I 4 46 9-3 j 4 28.9 33 7 38.6 43-4 53 o 578 62.7 47 4-85 9.700 M 55 9-4 24- 29. i 34 o 38.8 43 -6 53-4 58-2 63.0 48 4.88 9.758 14.64 95 24- 29-3 34- i 39 o 43 9 53 7 58.5 63-4 49 4.91 9.816 14 72 9-6 24- 29.4 34-4 39-3 44-2 54-0 58.9 63-8 50 4-94 9-874 14-81 9-7 24- 29.6 34-6 39-5 44-4 54-3 59-2 64.2 Si 4-97 9-932 14.90 19.9 24- 29.8 34.8 39 7 44 7 54-6 596 64.6 52 S-oo 9.990 14.98 20.0 25- 30.0 35-0 40.0 45 o 54-9 59 9 64.9 53 5-02 10. 048 15-07 20. I 25 , 30. i 35-2 40.2 45-2 55-3 60.3 65-3 54 5-5 10. 106 15-16 20.2 25- 30-3 35-4 40.4 45-5 55-6 60.6 65.7 55 5-o8 10. 164 15-25 20.3 25- 3 5 35-6 40-7 45-7 55-9 61.0 66. i 56 5 ii 10. 222 IS 33 20. 4 25- 3 7 35-8 40.9 46.0 56.2 61.3 66.4 57 5-14 5-17 0.280 15-42 15-5' 20.6 20.7 25- 30.8 31-0 36.0 36.2 41. i 4 3 46-3 46.5 3ti 61.7 62.0 66.8 67.2 59 5 20 0.396 >5 59 20.8 26.0 31-2 36-4 41.6 46.8 57-2 62.4 67.6 Horz. Dist. 99-8i 199-6 299.4 399-2 499.0 599 699 798 898 1098 1198 1297 Hor. dlst. Is for 30' point. Add or subtract .025 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 71 TABLE 7 Continued DIFFERENCES IN ELEVATION 2 1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 2600 t 48.8 52.3 55.8 59-3 62.8 66.3 73-* 76.7 80.2 83-7 87.2 90.7 o 9- 2 56.3 59-8 63.3 66.8 73-9 77-4 80. 9 84-4 87-9 91.4 i <;. 6 53- 2 56.7 60.3 63.8 67.4 74-5 78.0 8'i.6 85-1 88.6 92.2 1 53-6 57-2 60.8 64-4 67.9 75- ' 78.6 82.2 85.8 89-4 93-0 3 5- 5 54- i 57-7 61.3 64. 9 68.8 75-7 79-3 82.9 86.5 90. i 93-7 4 50.9 54-5 5 S.I 61.8 65.4 69.0 76.3 79-9 83.6 87.2 90.8 94-5 S 5 -3 54-9 58-6 62.2 65.9 69.6 76.9 80.6 84.' 2 87-9 91.6 95-2 6 5 -7 55-4 59- ' 62.7 66.4 70. l 77-5 81.2 84.9 88.6 92-3 96.0 7 5 55-8 59-5 63.2 67.0 70.7 78.1 81.8 8 5 .6 89-3 93-0 96.7 8 5 5 56.2 60.0 63-7 67.5 71-2 78.7 82.5 86.2 90.0 93-7 97-5 9 5 9 56.7 60.4 64.2 68.0 71.8 79-3 83.1 86.9 90.7 94-5 98.2 10 53-3 57 i 60. 9 64-7 68.5 72-3 79-9 83.7 87.6 91.4 95-2 99.0 ii 53-7 57-5 61.4 65.2 69.0 72.9 80.6 84.4 88.2 92.0 95-9 99-7 12 54- ' 58.0 61.8 65.7 69-6 73-4 81.2 85.0 88.9 92.8 96.6 100.5 13 54- S 58.4 62.3 66.2 70.1 74.0 81.8 85-7 89.6 93-5 97-4 101. 2 >4 54-9 5 8.8 62.8 66.7 70.6 74-5 82.4 86.3 90.2 94- ' 98.1 102. O IS 55-3 59-3 63.2 67.2 , , 75- I 83.0 86.9 90.9 94-8 98.8 02.7 16 55-7 59-7 63.7 67-7 I- 7 75-6 83.6 87.6 91.6 95-5 99-5 03.5 17 56. I 56.5 6a6 64.6 68.7 2.7 76.7 84.8 88.9 92.9 96.9 IOI.O 05 o '9 56.9 61.0 65.1 69.2 3-2 77-3 85.4 89-5 93-6 97-6 101.7 05.8 20 57-4 61.5 65.6 69.6 3-7 77-8 86.0 90.1 94.2 98.3 102.4 06.5' 21 57.8 61.9 66.0 70. I 4-3 78.4 86.6 90.8 94-9 99-o 103.2 07 3 . 22 58.2 62.3 66.5 70. 6 4.8 78.9 87.3 91.4 95-6 99-7 '03 9 08.0 3 58.6 62.8 66.9 71. I 5-3 79-5 87.9 92.0 96.2 100.4 104.6 08.8 24 59-0 63.2 67-4 71.6 75-8 80.0 88.5 92.7 96.9 101. I 105. 3 09.5 25 59-4 63.6 67.9 72. I 76.4 80.6 89.1 93-3 97-6 101.8 1 06.0 10.3 26 59-8 64-1 68.3 72.6 76.9 81. i 89.7 94.0 98.2 102. 5 106.8 27 60.2 64.5 68.8 73- i 77-4 81.7 9-3 94.6 98.9 103. 2 107.5 it. 8 28 60.6 64-9 69-3 73-6 77-9 82.2 90. 9 95-3 99-6 103-9 108. 2 12.5 29 61 65.4 69-7 74-t 78.4 82.8 9'- 5 95-9 100. 2 104.6 109.0 '3-3 3 61 4 65.8 70.2 74-6 79-0 83-3 92.1 96-5 00.9 '05. 3 109.7 14. i 31 61.8 66.2 70.6 75- I 79-5 83-9 92-7 97- 01.6 106.0 10.4 14.8 3* 62. 2 66.7 71. I 75-6 80.0 84. 4 93-3 97-8 O2. 2 106.7 II. I 15-6 33 62.6 67 I 71.6 76.0 80.5 85-0 93-9 98.4 02.9 107.4 ii. 8 16.3 34 63.0 67.5 72.0 76.5 81.0 85-5 94.6 99- l 03.6 108. I 12.6 17.1 35 63.4 68.0 72.5 77-' 81.6 86. I 95-2 99-7 04.2 108.8 13-3 17.8 3* 63.8 68.4 73-0 77-5 86.7 95-8 100. 3 04.9 109-5 14.0 18.6 37 6 4 .2 68.8 73-4 78.0 82 6 87.2 96.4 IOI.O 05.6 I 0. I 4-7 "9-3 38 64.7 69-3 73-9 78.5 83.1 87.8 97.0 toi.6 06.2 i 0.9 '5-5 20. I 39 6 5 .' 69-7 74-4 79.0 83.7 88.3 97-6 102.2 06.9 i 1.5 16. 2 20. 8 4P 65.5 70. I 74-8 79-5 84.2 88.9 98.2 102. 9' 07.6 I 2. 2 16.9 21.6 4' 65.9 70.6 75-3 80.0 84-7 89.4 98.8 103.5 08.2 I 2.9 17.6 22.3 42 66.3 71.0 75-8 80.5 85.2 90.0 99-4 104.2 08.9 i 3-6 18.4 ts 43 66. 7 6 7 1 7'. 4 71-9 76. 3 76.7 8i'. 5 85- 7 86.3 9- 5 91.1 100.6 105.4 10. 2 I 5-0 19.8 24.6 45 67.5 67. 9 72.3 72.8 77 > 77-6 82.0 82.4 as. s 87.3 91.6 92.2 101. 2 101.8 I06.I 106.7 0.9 ' 5-7 20.5 25-3 26.1 46 47 68.3 68.7 73-2 73-6 78., 78-5 82.9 83.4 8 7 .8 88.3 92.7 93-2 103. I 107.3 108.0 2-9 I 7-8 22. 7 26.8 27.6 48 49 69.1 74-1 79.0" 83-9, 88.9 93-8 103-7 108.6 3-6 118. 5 23-4 28. 4 : 50 69.5 74-5 79-5 84-4 89.4 94-3 104.3 109.3 4-2 ii9. 24.2 29. 1 j S 69 9 74-9 79-9 84.9 89.9 94-9 104.9 109.9 4-9 119.9 24-9 29.9 5* 70.3 75-4 80.4 85.4 90.4 <*' 105.5 II0.5 5-6 120.6 25-6 30.6; t*l A S3 70. 7 71- I 75- 8 76.2 8K 3 85-9 86.4 90.9 9-5 96.6 106.7 in. 8 6^9 121.3 122. O 26. 3 27.0 3~- 4 ' 32.1 54 55 71-5 76.7 81.8 86.9 92.0 97-1 107.3 112.4 7-5 122.6 27.8 32.9 56 71.9 77- I 82.2 87.4 92.5 97-7 107.9 113.1 8.2 >23-3 28.5 33-6 57 7*-4 77-5 82. 7 87.9 93-0 98.2 108.5 "3-7 8.9 124.0 29.2 34-4 S 72.8 78.0 83-2 88.4 93-6 98.7 109.1 "4-3 9-5 124-7 29-9 35-' 59 1397 1497 "597 1697 1797 1896 2096 210 2296 2395 2495 2595 Hon. Dist. Hor. dist. is for 30' point. Add or subtract .025 ft. to each 100 ft. of distance for each 10' departure. 72 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 3 t 100 200 300 400 500 600 700 800 900 1100 1200 1300 5-23 10.46 15-68 20.9 26.1 3-4 36.6 4' 47.0 57-5 62.7 67-9 5.^6 10.51 15-77 21.0 26.3 31-5 36.8 42- 47-3 57-8 63.1 68.3 5-^9 10. 57 15-85 'll. I 26.4 31-7 37-o 42. 47-6 58.1 63-4 68.7 5-31 10. 63 15-94 21.3 26.6 3'-9 37-2 42. 47 8 58.4 63.8 69.1 5-34 10.68 16.03 21.4 26.7 32.0 37 4 42 48.1 58-7 64.1 69.4 5-37 I ' 74 i6..u 31.5 26.9 32.2 37 6 43- 48.3 59- i 64.4 69.8 5-40 19.80 16.20 ti 6 27.0 3*-4 378 43-2 48.6 59-4 64.8 70.2 5-43 10. 86 16.29 21.7 27 i 32-6 38.0 43-4 48.9 59-7 65.1 70.6 5.46 10.92 16-37 21.8 27-3 32 7 38.2 43-7 49-1 60.0 65-5 71.0 5-49 10.97 16.46 21 .9 27-4 32 9 384 43-9 49-4 60.4 65-8 7i. 3 1 5-5* 11.03 16-55 22. 1 27.6 33- 38.6 44- I 49-6 60.7 66.2 71.7 ,1 5-54 II IO 16.63 22. 2 27-7 33-3 38.8 44-4 49-9 61 o 66.5 72. i 1} 5 58 11.15 16.72 22-3 27 9 33-4 39 o 44-6 50.2 61.3 66.9 72.5 3 5.60 It. 2O 16. 81 22 4 28.0 336 39-2 44-8 50 4 61.6 67.2 72.8 4 5 63 11.26 16.89 22-5 28.2 33-8 39 4 45 o 50 7 61 9 67.6 73-2 5 5-66 11.32 16.98 22.6 28.3 34 o 39-6 45 3 50.9 62.3 679 73-6 6 5.69 ..38 17 07 22.8 28.4 34 l 398 45-5 Si 2 62.6 68 3 74 o 7 5-72 11.44 '7-iS 22 9 28.6 34-3 40 o 45-7 5" 5 62 9 68.6 74-3 8 5-75 11.49 17.24 23.0 28.7 34-5 40.2 46 o Si 7 63.2 69.0 74 7 9 5-77 "55 '7-33 23- 1 28.9 34 7 40. 4 46 2 52-0 63.5 693 75 ' JO 5.8o 11.61 17.41 23.2 29.0 34-8 40 6 46.4 52.2 63.8 69.6 75 5 21 5-83 11.67 17 SO 23 3 29- J 35 o 40.8 46.7 52 5 64.2 70 o 75 8 22 5-86 11.72 "7-59 23-4 29-3 35 2 4 46.9 52.8 64-5 70.4 76.2 23 5 89 n 78 17 67 23.6 29 5 35-3 4 2 47 i 53 o 64.8 70.7 76 6 24 5 9J it 84 17 76 23 7 296 35 5 4 4 47 4 53-3 65.1 71 o 77 25 5 95 11.90 17 85 238 29 7 35 7 4 6 47 6 53 5 654 71 4 77 3 26 598 n 96 '7 93 23 9 29 9 35 9 4 8 478 53-8 65.8 71 7 77 7 27 6 01 12 Ol 18.02 24.0 30 o 36.0 4 48.1 54- l 66.1 72 1 7.i 28 6.04 12 O7 18. n 24 i 30 2 36 2 4 2 483 54 3 66.4 72 4 73-5 29 6.06 12. 13 18 19 24 3 30 3 36 4 4 4 48 5 54 6 66 7 72 8 78.8 30 6 09 12 19 18 28 24 4 30 5 36 6 4 7 48.7 54-8 67 o 73- 79- 3 6 12 12 24 18.37 4 5 306 367 42 9 49 o 55- 67 3 73-5 79-6 3* 6.15 12 30 18.45 24 6 308 36 9 43 ' 49 2 55 4 67 7 73-8 80.0 33 6 18 12 36 18.54 24 7 30 9 37 i 43 3 49 4 55 6 68 o 74-2 80.3 34 6 21 12.42 .863 24.8 3' o 37 2 43 5 49 7 55-9 68 3 74-5 80.7 35 6 24 12.48 187' 25.0 31 2 37 4 43 7 49 9 56 i 68.6 74--9 81 l 36 6.27 12.53 18 80 25 ' 3' 3 376 43 9 50. i 56-4 689 75-'2 81.5 37 6.30 12.59 18 89 25.2 3i 5 37 8 44- i 50 4 56.7 69.2 75 5 81.8 38 6 32 12 6 5 1897 25 3 3' 6 37 9 44 3 506 56 9 69.6 75-9 82.2 39 6-35 12.71 19.06 25 4 3' 8 38.1 44 5 50 8 57 2 69.9 76.2 82.6 40 6.38 12 7 6 19- 15 25-5 3 9 38.3 44-7 5' i 57 4 70 2 76.6 83-0 4' 6.41 12.82 19-23 25 6 32.1 38 5 44 9 5' 3 57 7 70 5 769 83-3 42 6.44 12 88 19 32 25.8 32-2 386 45 i 5' 5 580 70.8 77 3 83-7 43 647 12.94 19.41 25 9 32-3 38.8 45 3 5' 7 58 2 7' i 77 6 84.1 44 6 50 13.00 19 49 26.0 32.5 39-o 45 5 52.0 58.5 7' 5 78.0 84-5 45 6.53 13.05 958 26.1 32.6 39-2 45 7 52 2 58.7 7i 8 78.3 84.8 46 6.56 13 11 19.66 26 2 32 8 39 3 45 9 52 4 59 o 72 i 78 7 85.2 47 6.59 '3 7 "9-75 26 3 32 9 39 5 46 i 52 7 59-3 72 4 79-o 85.6 48 6.61 3 23 19.84 26.4 33-1 39-7 46.3 52.9 59-5 72 7 79-4 86 o 49 6.64 3-28 19.92 26.6 33-2 39.8 465 53- i 59-8 73- ' 79-7 86.3 50 6.67 3-34 20.01 26.7 33 4 40.0 46.7 53 4 60.0 73 4 80.0 86 7 5' 6.70 '3-40 2O. IO 26.8 33-5 40.2 46.9 53 6, 60.3 73 7 804 87.1 52 6 73 '3-46 20. 1 8 26.9 33-6 40.4 47 > 53 8 60.6 74 o 80 7 87 5 53 6.76 '3 5' 20. 27 27 o 33-8 40 5 47 3 54 i 60.8 74 3 81 i 87.8 54 6.79 '3-57 20.36 27 i 33-9 40.7 47 5 54-3 61. i 74.6 81 4 88.2 55 6.81 >3-63 20.44 27 3 34- 40.9 47 7 54-5 61 3 75 o 81 8 88.6 56 7 6.85 6. 88 3-69 20.53 27-4 34-2 41. i 47 9 54 7 61 6 75 3 7C f\ 82.1 g 2 5 89-0 flrt i 58 6^90 13-80 20.70 27 6 1 34 5 41 4 48 3 55 2 62 i 75 75 9 82 8 *9- 3 89-7 59 6.93 13.86 20.79 27-7 34 6 41.6 48.5 55-4 62.4 76.2 83-2 90. i Horz. Dist. 99-63 '99-3 298.9 398.5 498.2 598 697 797 897 1096 1196 1295 Hor. dist. is for 30' point. Add or subtract .035 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 73 TABLE 7 Continued DIFFERENCES IN ELEVATION 3 1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 2600 f 73-2 78.4 83.6 88.8 94.1 99-3 09.8 "5-o I2O 2 125-4 130.7 35-9 O 73-6 74.0 78.8 79-3 84.. 84.6 SI 94.6 95-1 99-9 loo. 4 10.4 "5.6 16.3 120.9 121. 5 126.1 126.8 131-4 132.1 136.6, 137-4 2 74-4 74. 8 79-7 80. i 85-0 85. 5 90.4 90.8 95-6 100.9 ii. 6 16.9 122. 2 127-5 132. 8 138. . 138.9 3 4 75- 2 75-6 80.6 81 o 85.9 86.4 91-3 91.8 96.7 97.1 O2. 6 13-4 18. 8 124.3 128.9 129.6 134-3 '35-o 39-6 140.4 5 6 76.0 81.4 86.9 92.3 97-7 03.2 14.0 19.4 124.9 '30-3 '35-7 141.2 7 76.4 81.9 87 3 92.8 98.2 03-7 14.6 .25-5 131-0' 136.4 141-9 8 76. 8 77 * 82.3 82 7 88.2 93-8 99-3 04-9 15.8 21.3 126.9 132-4 "37-9 "43-4 10 77 6 83.2 88.7 94- 3 99-8 05-3 16.4 22. O '27-5 '33- i 138,6 144.2 i 78.0 83.6 89.2 94-7 100. 3 05-9 22.6 128.2 33-8 139-3 144.9 2 78.4 84.0 89.6 95-2 loo. 8 06.4 17^6 23-3 128.9 '34-5 140. i '45-7 J 78.8 84-5 90. i 95-7 01. 4 07.0 18.3 23.9 '29-5 135-2 140.8 146-4 4 79.2 84.9 90.6 96.2 01.9 07.5 18.9 24-5 130.2 '35-8 141-5 147-2 5 79 .6 8S-3 91 o 96.7 02.4 08. I '9-5 25-2 130.8 136.5 142. 2 147-9 6 80.0 862 9"-5 97-2 02. 9 08.6 20. I 25-8 '3'-5 137.2 143-0 148.7 7 18 80.5 80. 9 86^6 92 o 92.4 9 8 2 04.0 09.7 21-3 27.1 132-9 137. 9 138.6 '43- 7 144.4 150.2 '9 81.3 87 i 92 9 98.7 04.4 to. 3 21.9 27-7 133-5 '39- 3 '45-1 150-9 20 8. 7 87 5 93 3 99 2 05.0 10.8 22.5 28.3 134-2 140.0 145.8 5'-7 21 82 i 82 5 III 93-8 94 3 99-7 05 5 06.0 II. 4 "9 23. ' 23.7 29.0 2 9 .6 '34-9 '35-5 140.7 146.6 52-4 22 82 9 83 3 88.8 89 2 94 7 95 2 100.6 07 ' '3 o 24.9 30.9 136.8 142.7 148.7 '53-9 '54-7 24 25 837 84 I 89 7 90 i 95 & 96. 1 ioi 6 102 I 07 6 08 i '36 25.5 3' 5 '37 5 '43- 5 149.4 155-4 26 27 28 84 5 84 9 85 3 90 5 91 4 96 6 97 5 IO2 6 103. 6 09.7 5-8 33-4 34- i 138. 8 '39-5 140.2 144. 8 '45 5 146.2 '5- 9 151 6 152-3 156- 9 '57 7 '584 29 30 85 7 9. 8 98.0 104 I 2 63 28.6 34-7 140.8 146.9 1 53- i '59-2 3' 86 i 92 3 98.4 104. 6 07 6.9 29. 2 35 3 14' 5 147 6 '53.8 '59-9 1 60. 7 32 33 86. 5 86.9 Q_ , 92 7 93 ' 98. 9 99 3 nn 8 105. 6 i 8 8.0 30 4 366 142 8 149.0 155-2 156. o 161.4 l62. 2 34 35 B 7 3 87 7 93- 6 94 o 99- " oo. 3 106 5 2 8 '9 ' 3' 6 37 9 '43* 5 144- 1 '5-4 156 7 162.9 36 88. i 94 4 00.7 107.0 3 3 19.6 32 2 38.5 144.8 IS'-' 157-4 163 7 37 88 5 94 8 01 2 '07 5 38 20 2 32-8 39 i 145-5 5'. 8 158-1 164.4 38 889 95-3 01 6 108.0 4- 4 20. 7 33-4 39-8 146.1 152.5 158.8 .65.2 39 89.4 95 7 02 1 108.5 49 21 3 34-0 40.4 146.8 153-2 59-6 165-9 40 89.7 96 2 02 6 109.0' 5-4 21 8 34-6 41.0 147-4 '53-9 160.3 166.7 4' 90 2 96.6 03.0 '09-5 5-9 22 4 35-2 4i 7 148.1 154.6 161.0 167.4 4* 90.6 97 o 03-5 I !0 64 22 9 35-8 42.3 148.8 155-2 161.7 168.2 43 97 5 04.0 MO 5 7 o 23 5 36.4 42.9 ., f. 149.4 I55.9 T*j6 6 162.4 I f, I 2 168.9 169. 7 44 45 91 4 9 , 8 97 9 98 3 04. 4 04.9 III 4 80 24 5 37- i 37 7 43- 44- 2 150. i 150.8 157 3 lOj. 2 163.9 170.4 46 92 2 98 8 05 3 in 9 85 25- ' 38.3 44-8 151-4 158.0 164. 6 171.2 47 92 6 99 2 05 8 112 4 9 o 25.6 38.9 45-5 152.1 158-7 165.3 171.9 48 93 99 6 06 3 112 9 9 5 26 2 39-5 46.1 152-7 '59-4 166.0 172.7 49 93 4 100. 1 06.7 "3-4 I 26.7 40.1 46.8 153-4 160. i 166.8 73-4 5 93 oo 5 07 2 "39 o 6 27 3 40 7 47-4 '54- i 160.8 67-5 174.2 5 94 2 07 6 "44 i i 27 8 4' 3 48.0 '54-7 161.5 168.2 174-9 5* 94-6 01 4 08 i 114.9 i 6 28 4 41.9 48.6 '55-4 162.2 168.9 175-7 53 95-0 01 8 08 6 "5-4 2. I 28.9 42.5 49-3 156.1 162.9 169.6 176.4 54 95 4 02 I 09.0 "5.8 2 7 29-5 43- ' 49-9 156.7 '63.5 170.4 177.2 55 05.8 02 6 09.5 U6. 3 3-2 30.0 43-7 50.6 157-4 164.2 171. I 177.9 56 96 2 03 1 09. 9 116.8 3-7 30.6 44-3 5'-2 158.1 164.9 171.8 178.7 57 96.6 3 5 10 4 "73 4-2 3' ' 44-9 5'. 8 58.7 165.6 172.5 179-4 5 97 O 04.0 10. 9 117.8 4-7 3' 7 45-5 52.5 '59-4 166.3 173 3 1 80. 2 59 '395 1494 '594 1694 '793 893 2092 Horz. Disc Hor. dist. is for 30' point. Add or subtract .035 ft. to each 100 ft. of distance for each 10' departure. 74 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 4 / 100 200 300 400 500 600 700 800 900 1100 1200 1300 6.96 '3- 92 20.87 27 8 34-8 41.8 48-7 55-7 62.6 76-5 83.5 90-5 6.99 13-98 20.96 28.0 34-9 41.9 48.9 55-9 62.9 76.9 83-8 90.8 3 "4-03 21.05 28. i 35- i 42.1 49- ' 56.1 56. 4 63. i 77- 2 84.2 84- 5 91-2 91. 6 3 4 7- 5 7.08 14. 09 I4-15 21. 22 28.3 35-4 42. 4 49-5 56.6 63-7 77-8 84.9 92.0 S 7.10 14.21 21.31 28.4 35-5 42.6 49-7 56.8 63-9 78.1 85.2 92-3 6 "3 14. 26- 21-39 28.5 35-7 42.8 49-9 57-1 64. 2 78.4 85.6 92-7 7 . 16 14.32 21.48 28.6 35-8 43-0 50- i 57-3 64. 4 78.8 85-9 93- I 8 19 I4-38 21-57 28.8 35-9 43- i 50-3 57-5 64-7 79- I 86.3 93-5 9 14.44 21.65 28.9 36-1 43-3 50-5 57-7 65. o 79-4 86.6 93-8 10 25 14.49 21-74 29.0 36.2 43-5 50-7 58.0 65. 2 79-7 87.0 94-2 II .28 '4- 55 21.83 29. I 36-4 43-7 50-9 58-2 65-5 80.0 87-3 94-6 12 3 14.61 21.91 29.2 36-5 43-8 5'- i 58-4 65. 7 80.3 87.6 95-0 13 33 14.67 22.00 29-3 36.7 44-0 51-3 58.7 66.0 80.7 88.0 95-3 14 .36 I4-72 22.08 29.4 36-8 44-2 Si-5 58-9 66.3 81.0 88.3 95-7 '5 39 14.78 22.17 29.6 37-o 44-3 51-7 59- i 66. 5 81.3 88.7 96.1 16 42 14.84 22.26 29.7 37-1 44-5 51-9 59-4 66.8 81.6 89.0 96.4 06 8 17 18 :Ji 14. 90 14-95 22. 34 22.43 29. 8 29-9 37- 2 37-4 44-9 52-3 59-8 67-3 82. 2 89.7 90. o 97-2 >9 7.51 i5-<" 22. 52 30.0 37-5 45-0 52-5 60. o 67-5 82.6 90. i 97-6 20 7-53 15-07 22.60 30.1 37-7 45-2 52-7 60.3 67.8 82.9 90.4 97-9 2 , 7-56 I5-I3 22.69 30-3 37.8 45-4 52-9 60.5 68. i 83-2 90.8 98-3 22 7-59 I5--8 22.78 30.4 38-0 45-6 53-1 60.7 68.3 83-5 91. i 98.7 23 7.62 "5-24 22.86 30-5 38.1 45-7 53-3 .0 68.6 83-8 91. 4 99- I 24 7.65 '5-3 22.95 30.6 38-2 45-9 53-5 . 2 68.8 8 4 .I 91.8 99-4 25 7.68 15-36 23-03 30-7 38-4 46.1 53-7 4 69. i 84-5 92. i 99-8 26 7.71 15-4I 23.12 30-8 38.5 6.2 53-9 7 69.4 84.8 92.5 100. 2 27 7-74 '5-47 23.21 30- 9 38-7 6.4 54- i . 9 69. 6 85-1 92.8 ioo. 6 28 7.76 15-53 23-29 3 -i 38-8 6.6 54-4 2. 1 69.9 85-4 93-2 100.9 29 7-79 15-59 23-38 3 -2 39-0 6.8 54-6 2-3 70. i 85-7 93-5 101.3 3 7.82 15-64 23-46 3 -3 39- I 6-9 54-8 2.6 70.4 86.0 93-9 101.7 31 7.85 15-70 23-55 3 -4 39-3 7- i 55-o 62.8 70.7 86.4 94-2 102. I 32 7.88 15-76 23-64 3 -5 39-4 7-3 55-2 63.0 70.9 86.7 94-5 102.4 33 7.91 15- 82 23-72 3 -6 39-5 7-4 55-4 63.3 71. 2 87.0 94-9 102.8 34 7-94 15-87 23.81 3 -7 39-7 47.6 55-6 63.5 71-4 87-3 95-2 103. 2 35 7-97 15-93 23.90 3 -9 39-8 47-8 55-8 63.7 71-7 87.6 95-6 103. 6 36 7-99 15-99 23-98 3 -o 40. o 48.0 56.0 64.0 7-9 87-9 95-9 103.9 37 8.02 16.05 24.07 3 i 40. i 48.1 56.2 64.2 72- 2 88.2 96-3 104.3 38 8.05 8.08 16. 10 24-15 3 -2 40.3 48-3 A Q c 56-4 56 6 64.4 64. 6 72.5 88.6 88 9 96. 6 104. 7 39 40 8. ii 16.22 24- 33 3 -4 40.5 40- 5 48.7 .0 O 56^8 64.9 Ar i 73-o s 9 : 2 gg e 97-3 "05-4 105.8 42 43 8.17 8.20 6.33 16.39 24-50 24.58 1:1 40.8 41.0 40. o 49.0 49.2 57- o 57-2 57-4 05. 1 65-3 65.6 73- 2 73-5 73-8 89^8 90. 1 98! o 98-3 106.2 106.5 44 8.22 16-45 24.67 3 -9 41. i 49-3 57-6 65.8 74-o 90-5 98-7 106.9 45 8.25 .6.50 24-76 33-o 4i-3 49-5 57-8 66.0 74-3 90.8 99.0 107.3 46 8.28 16.56 24.84 33-' 41.4 49-7 58.0 66.2 74-5 91.1 99-4 107-7 47 8.31 16.62 24- 93 33- 2 1.6 49-9 58-2 66.5 74-8 91.4 99-7 48 8-34 16.68 25.02 33-4 i-7 50.0 58-4 66.7 75-o 91-7 00. I I08.' 4 49 8.37 16-73 25.10 33-5 1.8 50.2 58-6 66.9 75-3 92.0 00.4 108.8 SO 8.40 16.79 25- 19 33-6 2.0 50.4 58.8 67.2 75-6 92-4 00.8 109.1 5> 8-43 16.85 25-27 33-7 2. I 50.5 59-0 67-4 75-8 92.7 01. I 109-5 52 8-45 16.91 25-36 33-8 '.3 50-7 59-2 67.6 76.1 93-o 01. 4 109.9 53 8.48 16.96 25-45 33-9 2.4 50-9 59-4 67-9 76-3 93-3 01. 8 110.3 54 8.51 17.02 25- 53 34-0 2.6 51- ' 59-6 68. I 76.6 93-6 02. i 1 10. 6 55 8-54 .7.08 25-62 34-2 42.7 51-2 59-8 68.3 76.9 94-9 02.5 III.O 56 8-57 17.14 25-70 34-3 42.8 51-4 60.0 68.5 77-1 94.2 02.8 1 1 1. 4 57 8.60 17. 19 25-79 34-4 43-o 51-6 60. 2 68.8 77-4 94-6 03.2 in. 8 58 8.63 17-26 25-87 34-5 43-1 5 -8 60.4 69.0 77.6 94-9 03-5 1 12. I 59 8.65 I7-3I 25.96 34-6 43-3 5i-9 60.6 69-2 77-9 95-2 03.8 112.5 Horz. Dist. 99-38 98.8 298. I 397-5 496.9 596 696 mj 894 1093 "93 1292 Hor. dist. is for 30' point. Add or subtract .045 ft. to each ioo ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 75 TABLE 7 Continued DIFFERENCES IN ELEVATION 1400 1500 1600 1700 1800 1900 2100 2200 2300 2500 2600 f 97- 04.4 1-3 18.3 125.2 32-2 146.1 153-1 1 60. o 167.0 174.0 ,80.9 O 97- 04.8 1.8 18.8 125.8 32.8 146.7 153-7 160.7 167-7 174-7 181.7 1 98. 05.2 2-3 19-3 126.3 33' 3 147-3 154-4 161.4 168.4 175-4 ,82.4 1 98. 05-7 2- 7 19.8 126.8 33-9 '47-9 155-0 162. o 169. i 176.1 183.2 3 99- 06. i 3-2 20. 3 127-3 34-4 148.6 155-6 162.7 169.8 176.8 83-9 4 99- 06.5 3-6 20.7 127.8 34-9 149-2 156.3 163.4 170-5 177.6 184.7 5 99- 07.0 4.1 21. 2 128.4 35-5 149-8 156.9 164.0 171.2 78-3 185.4 6 00. 07.4 4-6 21. 7 128.9 36.0 150.4 157-5 164.7 171.8 179.0 186.2 7 oo. 07.8 5-o 22. 2 129.4 36.6 151-0 58.2 165.3 I72-5 "79-7 186.9 8 01. 08.3 5-5 22. 7 129.9 37-1 15'- 6 158.8 166.0 173-2 1 80. 4 9 01. 08.7 5-9 23-2 130.4 37-7 152.2 159-4 1 66. 7 '73-9 181.2 \88. 4 01. 09. i 6.4 23-7 131-0 38-2 152.8 160. I 167-3 174.6 181.9 189.2 ,, 02. 09.6 6.9 24.2 131-5 38.8 '53-4 160.7 168.0 175-3 182.6 189.9 12 02. IO. O 7-3 24.7 132-0 39-3 "54-0 161. 3 168.7 176. o 183-3 190.7 3 OJ. 10.4 7.8 25- ' 132-5 39-9 154-6 162.0 169-3 176.7 ,84.0 191.4 4 03-5 10. 9 8.2 2 5 .6 '33-0 40.4 155- 2 162.6 470. o 177-4 184.7 192.2 5 03-9 "3 8.7 26. 1 I33-S 41.0 155-8 .6-3.2 170. 6 178. i 185-5 192.9 6 4-3 11.7 2 26.6 "34- i 1-5 156-4 163.9 i i-3 178.8 186.2 193- 6 7 04.7 12. 2 6 27. I 134-6 2. I 157-0 164.5 i 2.9 179-4 186.9 194.4 18 05. I 12.6 I 2 7 .6 '35- ' 2.6 57.6 165. i 1 2.6 1 80. i 187.6 195- i 19 05-5 13-0 6 '35-6 3-2 158.2 165.8 i 3-3 180.8 . 188.4 '95-9 05-9 '3-4 o 28.6 136.1 3-7 158.8 166.4 i 3-9 181.5 189., 196. 6 21 06.3 "3-9 5 29. I '36.7 4-2 159-4 167.0 i 4.6 182. 2 189.8 '97-4 22 06.7 '4-3 9 29-5 137.2 4.8 160.0 167.6 i 5-3 182.9 190.5 23 O?. 1 14.7 4 30.0 137-7 5-3 160. 6 168.3 i 5-9 83.6 191. 2 198.9 24 07-5 '5-2 8 3-5 138.2 5-9 161.2 168.9 176.6 184-3 I92.O 199.6 25 07.9 nft l 15-6 3 g 31-0 138-7 6.4 161.8 169.6 177-3 185. o ,Q C ~, 192.7 200. 4 26 os. 3 08.7 i6! 5 2 31* 5 32.0 J39-8 7-5 163-1 170. 8 178.6 105. 7 186.3 193- 4 194- 1 201. 9 28 09. 1 16.9 7 32-5 MO 3 163-7 171.4 179. 2 187. o 194-8 2O2. 6 29 09-5 17-3 1 33-o 140. 8 8^6 164-3 172. i 189.9 187.7 195-5 203.4 30 09.9 17.8 25-6 33-5 I4I-3 49-2 164.9 172.7 180.6 188.4 196.3 204. 1 3' 10.3 18. 2 26. i 33-9 141.8 49-7 I&5-5 173-3 181. 2 189. i 197.0 204.9 32 10. 7 18.6. 26.5 34-4 142-3 50-3 1 66. I 174. o 181.9 .89.8 97-7 205. 6 33 u. I 19. o 27.0 34-9 142.9 50. 8 166.7 174. 6 182.5 '90.5 198.4 206. 3 34 '1-5 '9-5 27-4 35-4 '43-4 5'.3 167-3 175-2 183.2 . Q, 199. I ion ft 207. i 35 16 12-3 12.7 20.3 20. 8 2! 4 28.8 35- 9 36.4 36-9 144.4 144.9 52-4 53 o 168.5 169. i 175- 9 176- 5 177. i '3- 9 184-5 185. 2 192. 6 193-2 199. o 200. 6 201.3 208. 6 209-3 3 37 38 13- i 2 . 2 29-3 37-4 "45-4 53-5 169.7 177-8 185-8 193-9 2IO. 1 39 "3-5 2 .6 29.7 37-9 146.9 54- ' 170.3 178.4 I86. 5 194-6 202. 7 210. 8 40 '3-9 2 . I 30.2 38.3 146.5 54-6 170.9 179.0 187.2 195-3 203.4 211. 6 4' '4-3 2 -5 30-7 38.8 147.0 55- 2 I7L5 179.7 187.8 ,96.0 204. 2 212.3 42 '4-7 2 .9 31- l 39-3 '47-5 55-7 172.1 1 80. 3 188.5 196.7 204.9 213. 1 43 '5- ' 23-4 31-6 39-8 148.0 56.2 172.7 1 80. 9 189.1 197-4 205. 6 213. 8 44 "5-5 23-8 32.0 40.3 '48.5 56.8 173-3 181.6 I8 9 .8 198., tnft 7 206. 3 214.6 45 46 15. 9 16.3 16.7 24-7 25.1 33-9 33-4 4'-3 41-8 149.6 150. i 57-9 58-4 174-5 175- 182.8 183-4 190. 5 191. i 191.8 190. 7 199.4 200. 1 207. 8 208. 5 216' I 216.8 H 17. i 25-5 33-9 42. 2 150.6 59-0 75-7 184.1 192.4 200. 8 209. 2 217-5 49 '7-5 25-9 34-3 42.7 151-1 59-5 176.3 184.7 193- T _. o 201. 5 209.9 218.3 50 17. 9 8.3 18.7 26. 4 26.8 27.2 35-2 35-7 43- 2 43-7 44.2 151. 6 152.2 .152.7 60.6 61.2 176- 9 '77-5 178.1 \S6o 186.6 193- 8 194. 4 195- i 202.9 203.6 211.3 219. 8 220. 5 52 5. 19. i 27.7 36.2 44-7 '53- 2 61. 7 178.7 187.2 195-7 204. 2 212. 8 221.3 54 '9-5 28.1 36.6 45-2 '53-7 62.2 179-3 87.9 196.4 204. 9 213-5 222 55 20.0 28.5 37- I 45-7 '54-2 62.8 179-9 188.5 197-1 205. 6 214. 2 222.8 56 20.4 28.9 37-5 46.1 54-7 63-3 1 80. 5 189. i 97-7 206. 3 214. 9 223-5 57 20.8 29-4 38-0 46.6 155-2 63-9 181.1 189.8 198-4 207. o 215. 6 224-3 58 21. 2 29. 8 38-5 47- i J55-8 64.4 181. 7 190.4 199.0 207. 7 216.4 225.0 59 1391 1491 '590 1689 789 ,888 2087 2186 2286 2385 2484 2584 Horr. Dist. Hor. dist. is for 3 7 8.88 7-77 26.65 35-5 44-4 53-3 62. 2 71. r 79-9 97-7 106.6 15-5 8 8.9: 7.82 26.73 35-6 44-5 53-5 62.4 7'-3 80.2 98.0 106.9 15-8 9 8.94 7.88 26.82 35-8 44-7" 53 6 62.6 7i-5 80.5 98-3 107-3 16. 2 10 8.97 7-94 26. 90 35-9 44-8 53-8 62.8 71.8 80.7 98-7 107.6 16.6 12 9. oo 9.03 Is. 05 26. 99 27.08 36. o 36-1 44- 9 45-" 54- 54-2 63.2 2. 2 81.2 99-3 108.3 17-3 13 9.06 18. 11 27.16 36-2 45-3 54-3 63-4 2.4 81.5 99-6 108.7 17-7 14 9.08 18.17 27.25 36-3 45-4 54-5 63-6 2-7 81.7 99-9 109.0 18. i 15 9.11 l8. 22 7-33 36-4 45-6 54-7 63-8 2-9 82.0 100. 2 109-3 18.5 16 9.14 18.28 27-42 36.6 457 54-8 64.0 73-' 82.3 100.5 109.7 18.8 17 9- '7 18.34 27-51 36.7 45-8 55-o 64.2 73-4 82.5 100.9 110.0 19.2 18 9.20 18-39 27-59 36.8 46.0 55-2 64.4 73-6 82.8 IOI. I 1 10. 4 19.6 9 9-23 18-45 i7.68 36-9 46.1 55-3 6 4 .6 73-8 83.0 101.5 110.7 19.9 9.25 I8. 5 I 27-76 37-0 46.3 55-5 64.8 74.0 83-3 ioi. 8 III.O 20.3 91 9.28 18-57 27-85 37-1 46.4 55-7 65.0 74-3 83-6 102. I ill. 4 20.7 22 9-3' 18.62 27-94 37-2 46.6 55-9 65.2 74-5 83-8 102.4 111.7 23 9-34 18.68 28.02 37-4 46.7 56.0 65-4 74-7 84.1 102. 7 21.4 24 9-37 18.74 28.11 37-5 46.8 56.2 65-6 75-0 84-3 103. 1 112.4 21.8 25 9.40 18.80 28. 19 37-6 47-0 56.4 6 5 .8 75-2 84.6 103-4 112.8 22.2 26 9-43 18.85 28.28 37-7 47-1 56-5 66.0 75-4 84.8 103.7 113. 1 22-5 27 9/46 18. 91 28.37 37-8 47-3 56-7 66.2 75-6 85-1 104.0 "3-5 22.9 28 9.48 18.97 28.. 45 37-9 47-4 56-9 66.4 75-9 85-4 104.3 113-8 23-3 89 9-51 28.54 38.0 47.6 57- i 66.6 76.1 85-6 104.6 114.1 *3-7 30 9-54 19.08 28.62 38-2 47-7 57-2 66.8 76.3 85-9 104.9 1 14- 5 24.0 3' 9-57 19.14 28.71 38-3 47-8 57-4 67.0 76.6 86. I 105-3 114-8 24-4 32 9.60 19.20 28.79 38-4 48.0 57-6 67.2 76.8 86.4 105.6 115-2 24.8 33 9-63 "9-25 28.88 38-5 48.1 57-8 67.4 77-0 86.6 105.9 "5- 5 25. 1 34 9.65 '9-3' 28.96 38-6 48-3 57-9 67.6 77-2 86.9 106.2 "5-9 25-5 35 9.68 J9-37 29.05 38-7 48.4 58-1 67.8 77-5 87.2 106.5 116.2 25-9 36 9-71 19.42 29- >3 38-8 48.6 58.3 68.0 77-7 87-4 106.8 116.5 26.2 37 9-74 19.48 29. 22 39-0 48.7 58.5 68.2 77-9 87.7 107. 1 116.9 26.6 38 9-77 "9-54 29-3' 39- 48.9 58-6 68.4 78.2 87.9 107-5 117.2 27.0 39 9.80 19.60 29-39 39-2 49-0 58-8 68.6 78-4 88.2 107.8 117.6 27-4 4 9-83 9-65 29.48 39-3 49-2 59-o 68.8 78.6 88.5 108.1 118. o 27-7 4< 9.86 19.71 29.56 39-4 49-3 59-2 69.0 78.8 88.7 108.4 118.3 28.1 42 9. 88 '9-77 29.65 39-5 49-4 59-3 69.2 79- i 89.0 108. 7 1 1 8. 6 28.5 43 9.91 19.81 29-73 39-7 49-6 59-5 69.4 79-3 89.2 109. o 118.9 28.8 44 9-94 29.82 39-8 49-7 59-6 69.6 79-5 89-5 109-3 H9-3 29.2 45 9-97 19.94 29.90 39-9 49-8 59-8 69.8 79.8 89-7 109.7 119.6 29-6 46 O. 00 19.99 29.99 40.0 50.0 60. o 70.0 80.0 90.0 IIO.O 120.0 30.0 47 0.02 20. 05 30.08 40. i 50.1 60.2 70. 2 80.2 90.2 110.3 120.3 30-3 48 0.05 20. 11 30.16 40.2 50-3 60.3 70.4 80.4 9-5 1 10. 6 120.6 30-7 49 0.08 20. 1 6 30.25 40.3 50-4 60.5 70.6 80.7 90.8 1 10. 9 121. 3-' 50 0. II 20.22 30.33 40.4 50.6 60.7 70.8 80.9 91.0 III. 2 121.3 i'-4 5' 5 a o. 14 20. 28 30.42 40.6 50.7 60.8 7 -o 8 .1 9-3 in.5 I2I.7 31-8 53 0.20 20. 34 20. 40 3- 5 30-59 40. 7 40.8 50. 8 51-0 6 . 7 -4 8 .6 9 1 - 5 91.8 111-9 112. 2 122.4 32. 2 32.6 54 55 0. 22 20.45 30.68 0-9 5 6 . 7 -6 8 .8 92.0 \\l:l 122.7 32-9 56 o. 25 0.28 20. 51 20.57 30.84 f J 5 -4 6 . 72.0 82.2 9 2 - 3 92- 5 113. i 123; o 123.4 33- 3 33.6 57 0.31 20.63 30-93 I. 2 5 -6 6 . 72. 2 82,5 92.8 "3-4 123.7 58 >0- 34 20.68 1.4 5 -7 62. 72.4 82.7 93-0 "3-7 124. 1 34-4 59 10.37 62. 72.6 82.9 93-3 114.0 124.4 34-8 Horz. Dist. 99.08 98.2 297-2 396.3 495-4 594 694 793 892 1090 1-89 | 1288 Hor, dist. Is for 30' point. Add or subtract .055 ft. to each 100 ft. of distance for each 19' deoarture. TOPOGRAPHIC STADIA SURVEYING 77 TABLE 7 Continued DIFFERENCES IN ELEVATION 1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 2600 / 21.6 22.0 22.4 22.8 23-2 30. 2 30.7 31- 31-5 32.0 138-9 "39-4 "39-8 140.3 140. 8 147.6 148. i 148.6 149. i 149-5 156.3 156.8 157-3 57.8 158.3 65- 65- 66. 66. 67 182.3 182.9 183-5 184! 7 191.0 191.6 192.3 192.9 193-5 200.0 200. 4 201. 201. 7 202. 3 208. 4 209. I 209.7 210. 5 211. I 2 7- i 2 7 .8 2 8. 5 29-2 2 9.9 225-7 226.5 227.2 228.0 228. 7 O 2 3 4 24.0 24.4 24.8 25.2 32.8 33-2 33-7 34- ' 141.7 142.1 142.6 143.0 150.5 151.0 151-5 152.0 159-4 159 9 160.4 1 60. 9 68.2 69^3 69.9 185-9 186.5 187^7 194-8 195-4 196.0 196.7 203. 6 204.3 205.0 205.6 212.5 "213.2 213-9 214.6 2 1-4 2 2. I 2 2.8 23-5 230. 2 231.0 23'-7 232-4 6 8 9 26.0 35-0 144.0 '53-o 162.0 7f.o 188.9 197.9 206.9 215.9 2 4. 9 233-9 26.8 35.8 144.9 153-9 163.0 72. o 190. i 199. 2 208. 3 217.3 26.4 235-4 13 27.6 27.9 28. 4 28.8 36.7 37- ' & 145.8 146. 2 M 6.7 154.9 155.4 155-9 164. o 164.5 165.0 73- I 73-7 74- 2 74.8 19I-4 192.0 192-5 193- l 200.5 201. 1 202 3 209. 6 210. 2 211.5 218.7 219-4 220. 7 2 78 2 8.5 2 9.9 236.9 237-7 238.4 239-1 15 16 17 29.S 29.6 30.0 30.4 30.8 31-2 3'.6 32.0 32-4 32-8 33-2 33-6 34-0 38.4 38.8 39-3 39-7 40. i 40-5 41.0 41.4 41.9 42.3 42-7 43- > 43-6 147. 6 148.1 148.5 149.0 149.4 "59 9 150.4 I50-9 I5I-3 l5>-7 152-2 152-6 '53-1 156-8 157-3 .57.8 158-3 158.8 59-3 159-8 160.2 1 60. 7 161.2 161.7 162. 3 162.7 1 66. I 166.6 167. 1 167. 6 168. i 168.6 169.2 169-7 170.2 170.7 171. 2 171 7 172.2 75-3 75-8 76.4 76.9 77-5 78.0 78.6 79 I 79 7 So. 2 80.7 81.3 81.8 193.7 194.3 195-0 '95 6 196.2 196.7 197.3 197.9 198.6 199-2 199-7 200.' 3 200. 9 204.2 204.9 205. 5 206. i 206.7 207.4 268.0 208.6 209.3 209.9 210. 5 213.5 214.2 214. 8 215.5 216. I 216.8 217.5 218. i 218.8 219.4 220. I 222. 8 223-5 224.2 224.9 225-5 226.2 226. 9 227.6 228. 3 229.0 229.7 232.1 232.8 233-5 234-2 234-9 235.6 236.4 237-1 237-8 238-5 239-2 239 9 241.4 242. i 242.9 243-6 244-3 245.1 245-8 246.6 247-3 248. o 248.8 19 20 21 22 23 24 25 26 27 28 29 30 3 34-8 35-2 44-4 44-8 154-0 154-5 163.6 164.1 173.8 83 4 202.7 212.4 222. 1 231 7 241.4 251.0 33 34 36.0 36.4 36.8 45-7 46.1 46.5 155-4 155-8 156-3 156 8 165.1 165.6 166. i 174-8 175-3 175 8 84-5 85.1 85 6 203-9 204. 5 205. i 2 3-7 2 4-3 2 4.9 223.4 224. o 224.7 233- i 233-8 234-5 242. 8 243-5 244. 2 252 5 253-3 254 .0 36 1 37-6 38.0 47-4 47-8 157-2 157.7 167. o 167. 5 176.9 177-4 86.7 87.2 206. 3 206.9 2 6. 2 2 6. 8 226.0 226. 7 235-8 236. 5 245-6 246-4 255-5 256. 2 40 41 38.8 39 2 48.7 49- 1 158-6 "59-0 168.5 169.0 178.4 178 9 88.3 89.9 208. i 208.7 280 2 8.7 227.9 228.6 237 9 238.6 247.8 248.5 257-7 258.4 43 44 40. 4 40.8 50.0 5-4 50.8 160.0 160.4 160.9 169.9 170. 4 170.9 179-9 .80.5 89.9 90. 5 209. 9 210. 5 299 229.9 230. 6 239-9 240. 6 249.9 250. 6 259-9 260. 7 261.4 46 47 48 4 .6 ,61.8 263.6 50 51 4 -4 4 -8 52.5 52-9 162. 7 163.1 173-3 183-5 93-7 2 4- i 224-3 234-5 244-7 254-2 254.9 264.4 265.1 52 53 43-6 53-8 164.1 174-3 184.6 94.8 2 5-3 225-6 235.8 246.1 256.3 266.6 55 44-3 44.8 45-1 54-6 55- ' 55-5 165. o 165-4 165. 9 175.3 175-8 176.2 185.6 186.1 186.6 95-9 96.4 2 6. 5 2 7. 1 226. 8 227.4 UK 247.4 248.1 2578 258-5 268. i 268.8 269.5 12 59 1387 1486 1585 1684 1783 1882 2081 Horz. Dist. Hot. dist. is for 30' point. Add or subtract .055 ft. to each 100 ft. of distance for each 10' departure. 78 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 6 f too 200 3QO 400 500 600 700 800 900 1100 1200 1300 0.40 20.79 3'- 19 41.6 52.0 62.4 72.8 83.2 93-6 114.4 124.7 135- 1 0.42 20. 85 3I-27 41-7 S 2 - i 62.5 73-o 83.4 93-8 14-7 25- i 135-5 0-45 20.90 3'- 36 41.8 52-3 62.7 73-2 83.6 94-1 15-0 25-4 135-9 o. 48 20.96 3<-44 41.9 52-4 62.9 73-4 83.8 94-3 '5-3 25-8 136-2 0.51 21.02 31-53 42.0 52-5 63-1 73-6 84.1 94-6 15-6 26.1 36.6 0-54 21. 08 31-6. 42.2 52-7 63.2 73-8 84-3 94-8 15-9 26.5 137-0 o.57 21.13 31-69 42.3 52.8 63-4 74.0 84.5 95- i 16. 2 26.8 137-4 o.59 19 3L78 42-4 53-o 63.6 74-2 84.8 95-4 '6.5 27.1 137-7 o. 62 .25 3'- 87 42-5 53-1 63.7 74-4 85.0 95-6 16. 8 27-5 138-1 0.65 30 31-95 42.6 53-3 63-9 74-6 85-2 95-9 17.2 27.8 138.5 1 0.68 .36 32-04 42. 7 53-4 64.1 74-8 85-4 96.1 17-5 28.2 138-8 II 6.71 42 32.12 42.8 53-5 53- 7 64.3 64. 4 75-o 85.7 85. 9 96.4 96 6 17.8 18 I 28.5 28. 8 139-2 39- 6 13 o. 76 53 32-30 43- i 53-8 64^6 75-4 86. i yu. v 96.9 ,8.4 29. 2 139-9 14 0.79 59 32.38 43-2 54-0 64.8 75-6 86.3 97- > 18.7 29 5 140-3 15 0.82 64 32.47 43-3 54-1 64.9 75-8 86.6 97-4 19.0 29-9 140.7 16 0.85 .70 32.55 43-4 54-2 65.1 76. o 86.8 97.6 19.4 30.2 141.1 17 0.88 -76 32-64 43-5 54-4 65-3 76.2 87.0 97-9 '9-7 30.5 141.4 18 o. 91 .81 32.72 43-6 54-5 65.4 76.3 87-3 98.2 20.0 30-9 141.8 19 0.94 -87 32-8, 43-7 54-7 76.5 87.5 98.4 20.3 3'- 2 142.2 20 0.96 93 32-89 43-9 54-8 65.8 76.7 87-7 98.7 20.6 31.6 142-5 21 0-99" .98 32.98 44-0 55-0 66.0 76.9 87.9 98.9 20.9 31.9 142.9 22 04 33-06 44. i 55- 1 66.1 77-1 88.2 99-2 21. 2 32.2 143-3 23 1.05 . 10 33-15 44.2 55-2 66.3 77-3 88.4 99-4 21-5 32.6 M3-6 24 i. off . 16 33-23 44-3 55-4 66.5 66. 6 77-5 88.6 88.8 99-7 21.8 32.9 144.0 26 11.13 27 33-40 44-5 55- 5 55-7 66.8 77-9 89.1 OO. 2 22.5 33.6 144-7 27 33 33-49 44-6 55-8 67.0 78.1 89-3 00.5 22.8 34-0 I4S-I 28 it. 19 38 33-57 44.8 56.0 67.1 78.3 89-5 00.7 23-1 34-3 H5-5 29 II. 22 44 33-66 44-9 56.1 c6 2 67-3 67 c 78-5 78. 7 89.7 01. 23-4 34-6 ,45.8 3 31 1 1. 25 11.28 49 55 33.83 45-1 50. Z 56.4 07. 5 67.7 78.9 90.2 01.5 24.0 35-3 146.6 32 11.30 .61 33-91 45-2 56-5 67.8 79- 90.4 01.7 24-3 35-6 147.0 33 11.32 .66 34-oo 45-3 56.7 68.0 79-3 90.7 02.0 24.7 36.0 M7- 3 34 11.36 .72 34.08 45-4 56.8 68.2 79-5 90.9 O2. 2 25-0 36.3 147-7 35 "39 .78 34-17 45-6 56-9 68.3 79-7 91. i 02-5 25-3 36.7 148.1 36 11.42 .84 34-25 45-7 57- I 68. 5 79-9 91-3 02.8 2 5 .6 37-0 148.4 37 11-45 89 34-34 45-8 57-2 68.7 80. i 91.6 03.0 25-9 37-4 148.8 38 1 1 -.47 95 34-42 45-9 57-4 68.8 80.3 91.8 03-3 26.2 37-7 149-2 39 11-50 .00 34-51 46.0 57-5 69.0 80.5 92.0 03.5 26.5 38.0 149-5 40 .06 34-59 46.1 57-6 69.2 80.7 92.2 03-8 26.8 38-4 149-9 41 11-56 . 12 34-68 46.2 57-8 69.4 80.9 92-5 04-0 27.1 38.7 I50.3 42 11-59 . 18 34-76 46-4 57-9 69-5 81. 92.7 04-3 27-5 39-0 150-6 43 11.62 23 34-84 46-5 58.. 69-7 81. 92.9 04-5 27.8 39-4 I .0 44 11.64 .29 34-93 46.6 58.2 69.9 81. 93-2 4 .8 28. i 39-7 i 4 45 11.67 3-34 35-02 46.7 58-4 70.0 81. 93-4 05.0 28.4 40.1 I -7 46 11.70 3-40 35-10 46.8 58.5 70- 81. 93-6 05-3 28.7 40.4 I . L 47 it-73 3.46 35-19 46.9 58.6 70. 82. 93-8 05.6 29.0 40.7 I -5 40 11.76 3-5" 35-27 47-0 58.8 70. 82. 94-1 05.8 29-3 I. I i .8 49 II-79 3-57 35-36 47- I 58-9 70. 82. 94-3 06. I 29.6 1-4 153-2 50 1 1. 8.1 3-63 35-44 47-3 59-1 70. 82. 94-5 06.3 29-9 1.8 1536 51 11.84 3-68 35-53 47-4 59-2 82. 94-7 06.6 30.3 2. I 153-9 52 11.87 3-74 35-6i 47-5 59-4 83- 95-o 06.8 30.6 2-4 154-3 53 11.90 3.8o 35-70 47-6 59-5 83-3 95-2 07-1 30-9 42.8 54.7 54 "93 3-85 35.78 47-7 59-6 83.5 95-4 07-3 3'- 43- ' 155-0 55 11.96 3-91 35-86 47-8 59-8 83-7 95-6 07-6 3'- 43-5 '55-4 56- 11.98 3-97 35-95 47-9 59-9 7'. 83-9 95-9 7 .8 31- 43-8 155-8 57 12.01 4.02 36-03 48.0 60. i 72. 84.1 96.1 08. I 32- 44-1 156-1 58 59 12.04 12.07 24.08 24- "4 36. 20 48.2 48-3 60.2 60.3 72. 72. 84.3 84-5 96-3 96.5 08.4 08.7 32- 32- 44-5 44-8 156.5 156.9 Horz. Dist. 98.72 '97-4 296.2 394-9 493-6 592 691 790 888 1086 1185 1283 Hor. dist. Is for 30' point. Add or subtract .065 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 79 TABLE 7 Continued DIFFERENCES IN ELEVATION 7 100 200 300 400 500 600 700 800 900 1100 1200 1300 r 2. 10 24. 19 36.29 48.4 60.5 72.6 84.7 96.8 08. 9 <33-' 145-2 157-2 1. 12 24-25 36.37 48-5 60.6 72.7 84.9 97-o 09. i 133.4 145-5 157-6 ' IS 24-30 36.46 48.6 60.8 72.9 85.1 97-2 09.4 133-7 45-8 158.0 2.18 24. 36 36-54 48.7 60.9 73-1 85-3 97-4 09. 6 134-0 146. 2 158.4 2. 21 24.42 36-63 48.8 61. I 73-2 85-5 -97-7 09. 9 >34-3 M6.5 158.7 2.24 24-47 36.71 48.9 61.2 73-4 85.7 W-9 10. I 134-6 146.8 I59-I 12.27 24-53 36.80 49.1 61.3 73-6 85.9 98.1 10.4 134-9 147-2 159.4 12.29 24-59 36.88 49-2 61.5 73-8 86.0 98.3 10. 6 135-2 147-5 159.8 12.32 24-64 36.97 49-3 61.6 73-9 86.2 98. 6 10. 9 135-5 147-9 I&0..2 "2-35 24.70 37- 05 49-4 61.8 74- i 86.4 98.8 II. 2 135.8 I 4 8.2 I60.6 .2.38 24-76 37- i J 49-5 61. 9 74-3 86.6 99-o II.4 136.2 148.6 160.9 i 12.41 24.81 37- 22 49.6 62.0 74-4 86.8 99.2 n-7 136.5 148.9 I6I.3 ,, 12-43 24.87 37-30 49-7 2. 2 74-6 87.0 99-5 11.9 136.8 149.2 161.6 1 2 12.46 24. 92 37-39 49-8 2-3 74-8 87-2 99-7 12. 2 '37- i 149.6 162.0 13 12.49 24.98 37-47 50.0 2-5 74-9 87-4 99-9 12.4 137-4 149. 9 162.4 M 12.52 25 04 37-56 50. I 2.6 75-' 87.6 100. 2 12.7 '37-7 150.2 162.7 15 iz-55 25-09 37.64 50.2 2.7 75-3 87.8 00.4 12.9 138.0 150. 6 163.1 16 2-58 25- 15 37-73 50.3 2-9 75-4 oo. 6 '3-2 138.3 i ifi A '50-9 163-5 163. 8 17 18 12-63 25.26 37.89 50-5 63.2 75-8 88.4 01. '3- 4 '3-7 130. o 138.9 151. 2 151.6 164.2 9 12.66 25-32 37.98 50.6 63.3 76.0 88^6 01.3 13-9 '39-3 15'.9 164.6 20 12.69 25-38 38.06 50.8 63.4 76.1 88.8 01.5 14.2 139-6 152.3 164.9 21 12.72 25-43 38.15 50.9 63.6 76.3 89.0 01.7 14.4 139-9 152.6 165-3 22 2-74 25-49 38.23 S'.o 63.7 76-5 89.2 02. 4-7 140.2 I52.9 165-7 23 12.77 25-54 38-32 51-1 63.9 76.6 89.4 1O2. 2 15.0 140.5 153-3 166.0 24 12.80 25.60 38.40 5'-2 64.0 76.8 89.6 102.4 "5-2 140.8 '53-6 166.4 25 12.83 25-66 38.49 Si-3 64.1 77-0 90.0 IO2. 6 "5-5 14 .1 153-9 166.8 26 12.86 25-71 38.57 5'-4 64.3 77- I 90.0 102. 8 15-7 14 .4 154-3 167.1 27 12.88 25-77 38.65 51-5 64.4 77-3 90.2 103. I 14 7 54.6 167.4 12. 91 12. 94 25. 83 25.88 38. 74 38.82 51.8 64.7 77-6 90.6 103.5 16.5 14 .4 155-3 168.2 30 12.97 25-94 38-91 51-9 64.8 77.8 90.8 103.8 16.7 42.7 155-6 168.6 31 13-00 25-99 38.99 52. o 65.0 78.0 91.0 104.0 17.0 143.0 156.0 169.0 32 13. 02 26.05 26. ii 39.08 52. i 52. 2 65.1 65 3 78.1 91.2 04.2 17.2 143-3 156.3 156. 6 169.3 169. 7 33 I3-08 26. 16 39-24 52-3 65.4 72-5 91.6 04.6 '7-7 143-9 157-0 170.0 35 13 'I 26.22 39-33 52.4 65.5 r a - 7 91.8 104.9 18.0 144.2 >57-3 170.4 36 13- '4 26.28 39-41 52-6 65.7 78.8 92.0 105.1 18. 2 144-5 157-6 170.8 37 13- '7 26.33 39-50 52.7 65.8 79.0 92.2 105.3 18.5 M4.8 58.0 171.2 38 13-20 26.40 39.60 52-8 66.0 79.2 92.4 105.6 18.8 145-2 158. 4 171.6 39 13-22 26.44 39-66 52.9 66.1 79-3 92.6 105.8 19. o 145.4 158.7 17.1.9 40 3-25 13-28 26. 50 26.56 39-75 39-83 53-o 53- t 66.2 66.4 79-5 79-7 92.8 92-9 106. o 106.2 19.2 19-5 a: "59-0 159.3 172.2 172.6 41 4 13-3" 26.61 39-92 53-2 66.5 79-8 93- i 106.4 19.8 146.4 159-7 173-0 43 '3-33 26.67 40.00 53-3 66.7 80.0 93-3 106.7 20.0 146.7 160. o 173-3 44 '3-36 26. 72 40.09 53-4 66.8 80.2 93-5 106.9 20.3 147.0 t6o. 3 173-7 45 '3-39 26.78 40.17 53-6 67-0 8o.7 93-7 107.1 20. 5 147'. 2 160.6 174.0 46 ! 3* 4 2 '3-45 26^9 40. 25 40-34 53- 7 53.8 67. I 67.2 80. 5 80.7 93-9 94- ' i7- 3 107. 6 21.0 147-9 161.4 174. 4 174.8 47 4 8 '3-47 26.94 40.42 53-9 67-4 80.8 94-3 107.8 21-3 148.2 161.7 175-2 49 13-50 27.00 40.50 54-0 67.5 81.0 94-5 108.0 21.5 148.6 162.0 75-5 50 13-53 ^7-o6 40.59 54-' 67.7 8 .2 94-7 108.2 21.8 148.8 162.4 "75-9 51 13.56 27. 12 40-67 54-2 67.8 8 -3 94-9 108.5 22. O 149.1 162.7 176,2 52 3-59 27.17 40.76 54-3 67.9 8 .5 95- 108.7 22.3 149.4 163.0 176.6 53 13-61 27.23 40.84 54- 5 68. I 8 .7 95-3 108.9 22.5 149-8 '63.4 177.0 54 13-64 27-28 40.93 54-6 68.2 8 .8 95-5 109.1 22.8 I50.I '63-7 '77-3 55 13-67 27-34 41. 01 54-7 68.4 82.0 95-7 109.4 23.0 '50-4 164.0 177-7 5* 13-70 27.40 41.09 54-8 68.5 82.2 95-9 109.6 23-3 150.7 164-4 78.1 57 '3-73 13-75 27-45 27.5I 41.18 41.26 54-9 55-0 68.6 68.8 82.4 82.5 96.1 96.3 109-8 tio. o 23.5 23-8 151-0 5i-3 164.7 165.0 178.4 178.8 58 59 98.29 196.6 294.9 393-2 491.4 590 688 786 885 1081 1179 1278 Horz. Dist. Hor. dist. is for 30' ppint. Add or subtract .075 ft. to each 100 ft. of distance for each 10' departure. 80 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 8 / 100 200 300 400 500 600 700 800 000 1100 t o 13.78 27-56 4-35 55- ' 68.9 82.7 96.5 10.3 124.0 151.6 O I 13-81 27.62 41-43 55-2 69.0 82.9 96-7 10.5 124.3 151-9 2 13-84 27.68 4i-5i. 55-4 69.2 83.0 96.9 10.7 124- 5 152. 2 2 3 13-87 27-73 41. 60 55-5 69-3 83-2 97-i 10. 9 124.8 152. 5 3 4 13-89 27.78 41-68 55-6 69-5 83-4 97-3 II. 2 125.0 152.8 4 5 13.92 27-84 41-76 55-7 69.6 83-5 97-4 II- 4 125-3 153- i 5 6 13-95 27.90 41-85 55-8 69.8 83-7 97.6 ii. 6 125.6 153-4 6. 7 13-98- 27-96 41-93 55-9 69-9 83-9 97-8 n. 8 125.8 153-8 7 8_ 14.01 28.01 42.02 56.0 70.0 84.0 98.0 12.0 126.0 154-1 8 9 '4-03 28.07 42.10 56.1 70.2 84.2 98.2 12.3 126.3 154- 4 9 to 14.06 28.12 42.18 56.2 70.3 84.4 98.4 12-5 126.6 154-7 Ii 14.09 28.18 42.27 56.4 cA e 70.4 ?r> ft 84-5 98.6 08 8 12.7 126.8 155-0 ii 13 14. 14 28.29 42-44 5- 5 56.6 70. o 70.7 84. 7 84-9 90. 8 99-o 12. 9 13-2 127.3 155- 3 155-6 13 14 14-17 28.35 42-52 56.7 70.9 85.0 99.2 13.4 ,27.6 155-9 14 5 14. 20 28.40 42. 60 5 6.8 71.0 85.2 99-4 13.6 127.8 156-2 15 16- 14-23 28.46 42.68 56.9 . I 85-4 99-6 13.8 128.0 156.5 6 17 14.26 28.51 42.77 57-0 3 85-5 99.8 14.0 128.3 156.8 7 18 14.28 28.57 42.85 57- 1 . 4 85-7 14.3 128.6 157-1 8 >9 14- 3 28.62 42.94 57-2 .6 85-9 00. 2 14-5 128.8 157-4 9 20 14-34 28.68 43-02 57-4 7 86.0 00.4 4-7 129.1 157-7 o 21 M-37 28.74 43- 10 57-5 71-8 86.2 oo. 6 14.9 129.3 158.0 i 22 14.40 28.79 43- '9 57-6 72.0 86.4 oo. 8 IS- * ,29.6 .58.4 2 23 14.42 28.95 43-27 57-7 72.1 86.5 01. 15-4 129-8 158.7 3 24 "4-45 28.90 43-36 57-8 72-3 86.7 OI. 2 15-6 130.1 159.0 24 *5 14-48 29.96 43-44 57-9 72-4 86.9 01.4 5-8 I30-3 159-3 25 26 '4-5' 29.02 43-52 58.0 72.5 87,0 o .6 16. i 130.6 159-6 26 27 14-54 29.07 43- 60 58-1 72-7 87.2 o -7 6-3 130.8 159-9 27 28 14-56 29- 13 43-69 58.2 72.8 87.4 o .9 16.5 131-1 160.2 28 29 14-59 29.18 43-77 58-4 73-o 87.6 16.7 131-3 160.5 29 3 14.62 29.24 43-85 58.5 73- i 87.7 o .3 16.9 131-6 160.8 30 31 .4-65 29.29 43-94 58.6 73-2 87.9 o . 5 17.2 131-8 16 .1 31 32 14-67 29-35 44.02 58.7 73-4 88.0 o -7 17-4 132- i 16 .4 32 33 14.70 29.40 44- " 58.8 73-5 88.2 o .9 17.6 132-3 16 .7 33 34 35 !t* 29. 46 29-52 44- '9 44-27 58. 9 59-o 73- 6 73-8 88.6 o -3 18. i 132. 8 16 .3 34 35 36 14-79 29-57 44-36 59-1 73-9 88.7 03.5 18.3 133-1 16 .6 36 37 i 4 .8i 29-63 44-44 59-2 74- I 88.9 03.7 18.5 133-3 16 .9 37 38 14.84 29.68 44-52 59-4 74-2 89.0 03.9 18.7 133-6 163.2 38 39 14.87 29-74 44.61 59-5 74-3 89.2 04. 1 19.0 '33-8 163.6 39 4<> 14.90 29.78 44.69 59-6 74-5 89.4 04.3 19.2 '34- 163-9 40 41 14.92 29-85 44-77 59-7 74-6 89.6 04.5 19-4 134-3 164.2 41 42 14-95 29.90 44.86 59-8 74-8 89.7 04.7 19.6 134-6 164-5 42 43 14.98 29.96 44-94 59-9 74-9 89.9 04.9 19.8 134-8 164.8 43 44 15.01 30. 02 45-02 60.0 75-o 90.0 05.0 135-1 165.1 44 45 5-4 30-07 45- li 60. i 75-2 90.2 05.2 20.3 135-3 165-4 45 46 15.06 30-13 45-18 60.2 75-3 90.4 05.4 20.5 35-6 165.7 46 47 '5-09 30. 1 8 45-27 60.4 75-5 90.6 05.6 20.7 135-8 166.0 47 48 15-12 30-24 45-36 60.5 75-6 90.7 05.8 21.0 136-1 166.3 48 49 IS- '5 30-29 45-44 60.6 75-7 90.9 06. o 2 . 2 136.3 166.6 49 5 15- 7 30-35 45-52 60.7 75-9 9 .0 06.2 2 -4 136.6 166.9 y> -5 15-20 30.40 45- 60 60.8 76.0 06.4 2 .6 136.8 167.2 51 52 5-23 30-46 45-69 6o.-9 76.2 06.6 2 .8 I37-I <6?-5 52 53 54 15. 26 15-28 30.51 30.57 45-77 45-86 .0 . i 76-3 76.4 . 06.8 07.0 2 . I 2 -3 137-3 137-6 167.8 168.1 53 54 55 5-3 30. 62 45-94 . 2 76.6 07.2 2 -5 37-8 168.4 55 56 15-34 30.68 46.02 4 76.7 07.4 122.7 138.1 168.7 56 57 15-37 30.74 46. 10 J 76.8 07.6 122-9 138.3 169.0 57 58 15-40 30.79 46.19 .6 77-o 07.8 123.2 .38-6 169-4 58 59 15-42 30.85 46. 27 7 77- i 08.0 123-4 138.8 169. 6 59 Horz. Dist. 97.82 195-6 293; 5 391-3 489. I 587 685 783 880 1076 Horz. Dist. Hor. dist. is for 30' point. Add or subtract .085 ft. to each ipo ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 81 TABLE 7 Continued DIFFERENCES IN ELEVATION 9 f 100 200 300 400 500 600 700 800 900 1100 f 15-45 30.90 46.35 .8 77-3 92.7 08.2 123.6 139. i 170.0 O 15-48 30.96 46.44 9 77-4 92.9 08.4 .23.8 39-3 170. 3 I5-5I 31-01 46.52 . o 77-5 93-o 08.5 124.0 139-6 170.6 2 15-53 31-07 46.60 . i 77-7 93-2 08.7 124.3 139-8 170. 9 ^ 15-56 31.12 46.68 . 2 77-8 93-4 108.9 124-5 140.0 171.2 4 15-59 31-18 46.77 4 77-9 93-5 09. i 124.7 140.3 171-5 5 15-62 31-23 46.85 2-5 78.1 93-7 09-3 124.9 140.6 171.8 6 15-64 31-29 46.93 2.6 78.2 93-9 09-5 125. 2 140.8 172. i 7 15-67 3'-34 47-02 2-7 78.4 09-7 125.4 141.0 172-4 8 15-70 47- 10 2.8 78.5 94 2 09-9 125.6 141-3 172.7 9 10 15-73 31-45 47-18 62.9 78.6 94-4 10. I 125.8 141-5 173-0 10 II 15-76 3i 5' 47.26 63.0 78.8 94-5 0.3 126.0 141.8 173-3 ir 12 15-78 31-' 56 47-35 63.1 78.9 94-7 o. 5 126.3 142.0 173-6 12 13 15-8. 31.62 47-43 63.2 79.0 "94-9 0.7 126.5 142.3 173- 9 13 M 15-84 31.68 47-51 63.4 79-2 95-o a 9 126-7 174- 2 ! 4 15 15.86 3'-73 47.60 63.5 79-3 95-2 i. i- 126-9 142*8 174.5 IS 16 15-89 31-79 47.68 63.6 79-5 95-4 . 2 127. I 143-0 174- 8 16 7 15-92 47-76 63.7 79-6 95-5 . 4 27.4 143-3 75- i 17 18 15-95 31-90 47- 84 63.8 79-7 95-7 .6 127. 6 143-5 175-4 18 19 i 15.98 31-95 47-93 63.9 79-9 95-8 8 127.8 143-8 75- 7 19 20 16.00 32.01 48.01 64.0 80.0 96.0 .O 128.0 144.0 176.0 20 21 16.03 32.06 48-09 64.1 80.2 96.2 .2 128.2 144-3 176.3 21 22 16.06 32.12 48.17 64.2 80.3 96-4 4 128.5 144-5 176.6 22 23 16.09 32-17 48.26 64-3 80.4 96-5 .6 128.7 144.8 176.9 23 24 16. n 32-23 48.34 64.4 80.6 96.7 .8 128.9 45-0 177. 2 24 25 16.14 32.28 48.42 64.6 80.7 96.8 3-0 129.1 145-3 177.6 25 26 16.17 32.34 48.51 64.7 80.8 97- o 3-2 129.4 145-5 177.8 26 27 1 6. 20 32-39 48.59 64.8 81. o 97-2 3-4 129.6 145-8 178.2 27 28 16. 22 32.45 48.67 64.9 81.1 97-3 3-6 146.0 78.5 28 29 6.25 32-50 48.75 65.0 81.3 97-5 8 130.0 146.3 I 7 8.8 29 3 16.28 32.56 48.84 65.1 81.4 97-7 130.2 I79.I 30 31 16.31 32.61 48.92 65.2 81.5 97-8 , 130.4 146.8 179 4 31 32 16.33 32-67 49.00 65.3 81. 7 98.0 3 130.7 147.0 179-7 3* 33 6.36 32.72 49.08 65.4 81.8 98.2 5 130.9 147.2 180.0 33 34 i6.39 32.78 49-17 65.6 81.9 98-3 7 131. i 147-5 180.3 34 35 16.42 32-83 49-25 65.7 82.1 98.5 9 147.7 180.6 35 36 16.44 32-89 49-33 65.8 82.2 98.7 5- i 131-6 148.0 180.9 36 37 16.47 32-94 49-41 65.9 82.4 5-3 i3'-8 148.2 181.2 37 38 1 6. 50 33-oo 49- 50 66.0 82.5 99-0 5-5 132.0 148.5 181.5 3 39 16-53 33-05 49- 58 66.1 82.6 99.2 5-7 132-2 148.7 181.8 39 40 i- 55 33-11 49.66 66.2 82.8 99-3 5-9 132-4 149.0 182. i 41 16.58 33-16 49-74 66.3 82.9 99-5 6.1 132-6 149.2 182.4 41 42 16.61 33-22 49.82 66.4 83.0 99- 6 6-3 132.9 149-5 182.7 42 43 16.64 33-27 49.91 66.5 83.2 99.8 6.4 I33-I 149-7 183.0 43 44 45 16.66 16.69 33-33 33-38 50.00 50.07 66.6 66.8 83-3 83-4 00.0 6.6 6.8 33-3 133-5 150.0 150 2 183-3 183-6 44 45 46 16.72 33-44 50-15 66.9 83.6 00.3 133-7 150.5 183-9 46 47 16.74 33-49 50.24 67.0 83.7 oo. 5 2 150.7 184.2 47 48 16.77 33-54 50.32 67.1 83-9 00.6 4 134-2 151. o 184.5 48 49 1 6. 80 33- 60 50.40 67.2 84.0 00.8 6 134-4 151-2 ,84.8 49 50 16.83 33-66 50.-48 67-3 84.1 OI. O 8 .34-6 151-4 185.1 50 51 16.86 33-71 50-56 67-4 84-3 I 8.0 134-8 151-7 185.4 5 52 16.88 33-76 50-65 67-5 84.4 o -3 8. 2 135- i 151.9 185.7 5* 53 16.91 33-82 50.73 67.6 84.6 o -5 8.4 135-3 152.2 186.0 53 54 16.94 33- 87 50.81. 67.8 84.7 8.6 135-5 152.4 186.3 54 55 16.96 33-93 50.89 67-9 84-8 o .8 8.8 35-7 186.6 55 56 16.99 33-98 50.98 68.0 85-0 03.0 8.9 "35-9 152.9 186.9 56 Si 17.02 17.05 34-04 34-09 51-06 51.14 68.1 68.2 85.1 85-2 02. 1 02.3 9.1 9-3 36.2 136.4 153.2 153-4 187.2 87.5 57 58 59 ,7-08 34-16 51-24 68.3 85-4 02.5 9-5 136.6 153-7 ,87.9 59 Horz. 97-28 194.6 291-9 389-2 486.4 584 68 1 778 876 1070 Horz. Dist. DisU Hor. dist. is for 30' point. Add or subtract .095 ft. to each 100 ft. of distance for each 10' departure. 82 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 10 f 100 200 300 400 500 600 700 800 900 1100 t 17. 10 34-20 5 -30 68.4 85- 102.6 9-7 36.8 !53- 9 1 88. i I 17- 13 34-26 5 -39 68.5 85- 102. 8 19.9 37-o 154-2 188.4 2 17.16 34-3' 5 -47 68.6 85- 102. 9 20. 1 37-2 154- 4 188.7 3 17.18 34-37 5 -55 68.7 85- 103.1 20.3 37-5 154-6 189.0 4 17.21 34-42 5 -63 68.8 86. 103.3 20.5 37-7 154.9 189-3 5 17-24 34-48 5 -7i 69. o 86. 103.4 20.7 37-9 155- 189.6 6 17.26 34-53 5 80 69.1 86.3 103.6 20.9 38.1 155-4 189.9 7 17.29 34-58 5 ^88 69.2 86.5 103.8 2 .0 38.3 155-6 190. 2 8 17-32 34-64 5 -96 69.3 86.6 103.9 2 .2 38.6 155- 9 190- 5 9 17-35 34-69 5 -04 69-4 86.7 104.1 2 -4 38-8 156-1 190.8 c 17-37 34-75 5 -12 69-5 60 6 86.9 Q- n 104.2 2 .6 39-o 156.4 191. i 1 12 17. 4 17-43 34^86 5 * 20 5 -29 6 9 : 7 07. o 87.1 104.6 2 .0 39-4 156.6 156-9 191. 4 191.7 1 13 17-46 34-91 5 -37 69.8 87.3 104.7 2 . 2 39-6 157- I 192. P 3 17-48 34-97 5 -45 69.9 87.4 104.9 2 .4 39-9 157-4 192.3 4 '5 17-51 35-02 5 -53 70.0 87.6 105.1 2 .6 40. i 157-6 192.6 5 16 17-54 35-o8 5 -61 70.2 87.7 105- 2 22.8 40-3 157-8 192.9 6 '7 7-56 35 13 5 -70 70.3 87.8 105.4 23. o 40-5 158. l '93- 2 7 18 19 17-59 17.62 35-18 35-24 5 -78 5 -86 70.4 70.5 88.0 88.1 105.6 105.7 23.1 23-3 40.7 41.0 Si 193-5 193-8 18 9 20 17-65 35-29 52-94 70.6 88.2 105.9 23-5 41.2 158.8 194.1 20 21 17-67 35-35 53-02 70.7 88.4 106.0 23-7 41.4 159.' 194-4 2I 22 17.70 35-40 53- 10 70.8 88.5 106.2 23-9 1.6 159-3 194- 7 22 23 17-73 35.46 53-18 70.9 88.6 106.4 24.1 1.8 159-6 195-0 23 24 17-76 35-51 53-27 71.0 88.8 106.5 24-3 2.0 159.8 95-3 24 25 17.78 35.56 53-35 jri.l 88.9 106.7 24-5 2-3 160.0 195-6 25 26 f 7 .8i 17 84 35-62 35- 67 53-43 71.2 89. o 106. 9 24-7 2.5 160.3 '95-9 26' 28 17' 86 35-73 53- 51 53-59 71-5 89-3 107.2 25.0 42.9 1 60. 5 160, 8 196. 2 196.5 2 7 28 29 17-89 35.78 53-67 71.6 89-5 107.4 25-2 43- i 16 .0 196.8 29 30 17.92 35.84 53-76 7i-7 89.6 107-5 25-4 43-4 16 .3 197. I 30 31 17-95 35.89 53- 84 71-8 89-7 107.7 25.6 43-6 16 .5 197-4 31 32 17-97 35-94 53-92 7i-9 89.9 107.8 25.8 43-8 16 .8 197- 7 32 33 18.00 36.00 54.00 72.0 90.0 108. o 26.0 44-0 16 . o 198.0 33 34 18.03 36-05 54.08 72- i 90. i 108. 2 26.2 44-2 162.2 198.3 34 35 18.05 36.11 54- -6 72-2 90-3 108.3 26.4 44-4 162.5 198.6 35 36 18.08 36. 6 54-24 72-3 90.4 108.5 26.6 44-6 162.7 198.9 36 37 1 8. II 36. 2 54-33 72. 4 90.5 108. 6 26.8 44-9 163.0 199.2 38 18.14 36. 7 54-41 72.5 90.7 108.8 27.0 45- i 163.2 199-5 38 39 18. 16 36. 2 54-49 72.6 90.8 109.0 27. i 45-3 163.5 ,99.8 39 40 18.19 36. 8 54-57 72.8 109. I 27-3 45-5 .63.7 200. I 40 41 18. 22 36. 3 54-65 72.9 ., 109-3 27-5 45-7 164.0 200.4 41 42 18.24 36. 9 54-73 73-0 , 2 109. 5 27-7 46. o 164.2 200. 7 42 43 18.27 36.54 54-81 73- i 4 109. 6 27-9 46.2 164-4 201.0 43 44 18.30 36.60 54-89 73-2 5 109.8 28. i 46.4 164.7 201. 3 44 45 46 18.32 36.65 54-98 55- 06 73-3 .6 28.3 46.6 164.9 201.6 45 47 48 Is: 38 18. 41 36^76 36-81 55-14 55-22 73-5 73-6 9 2.0 110.3 110.4 28.6 28.8 47-2 165. 4 165.6 202. 2 2O2. 5 47 48 49 18.43 36.87 55-30 73-7 92.2 29.0 47-5 165-9 49 50 18.46 36.92 55-38 73-8 92-3 no. S 29.2 47-7 166.1 203.1 50 51 18.49 36.98 55.46 74-0 92.4 no. 9 29.4 47-9 166.4 203.4 51 52 18.51 37-03 55-54 74- i 9 2.6 in. i 29.6 48.1 1 66. 6 203.7 52 53 18.54 37-oS 55-62 74-2 92.7 III. 2 29.8 48.3 166.9 204.0 53 54 18.57 37-14 55-71 74-3 92.8 111^4 30.0 48.6 167.1 204. 2 54 55 18. 60 37-19 55-79 74-4 93- in. 6 30.2 48.8 167.4 204.6 55 56 18.62 37-24 55-87 74-5 93-1 in. 7 30.4 49.0 167.6 204.8 56 57 18.65 37-30 55-95 74-6 93-2 111.9 30. 6 49-2 167.8 205. I 57 58 18.68 37-35 56-03 74-7 93-4 112. I 30.7 49-4 1 68. i 205.4 58 59 18.70 37-41 56-11 74-8 93-5 112. 2 30.9 49-6 168.3 205.7 59 Horz. t)ist. 96.68 93-4 290.0 386.7 483.4 580 677 773 . 870 106 4 Horz. Dist. Hor. dist. is for 30' point. Add or subtract .105 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA. SURVEYING S3 TABLE 7 Continued DIFFERENCES IN ELEVATION 11 f 100 200 300 400 500 600 700 800 900 1100 f o i8.73 37-46 56.19 74-9 93-6 12.4 i3- 149.8 168.6 206.0 O I 18.76 37-52 56.27 75-0 93-8 12.6 I3I-3 150. i 168.8 206. 3 I 1 18.78 37-57 56.36 75- ' 93-9 12.7 13'- 5 150.3 169.1 206.6 a- 3 18. 81 37.62 56.43 75-2 94- i 12.9 3'.7 150.5 169.3 206.9 3 4 18.84 37.68 56-5. 75-4 94.2 13.0 131-9 150-7 169.5 207. 2 4 5 1 8. 86 37-73 56.60 75-5 94-3 13-2 132.1 i5 -9 169.8 207.5 5 6 18.89 37-78 56.68 75-6 94-5 '3-4 132-2 '5 ' 170.0 207.8 6 7 18.92 37-84 56.76 75-7 94.6 '3-5 132.4 15 4 170.3 2Q8.I 7 8 .8.95 37-89 56.84 75-8 94-7 13.7 132-6 15 6 170.5 208.4 8 9 18.97 37-95 56.92 75-9 94-9 13-8 132-8 15 8 170.8 208.7 9- 10 19.00 38.00 57-oo 76.0 95-o 14.0 33-o 15 o 171.0 209.0 to II '9-03 38-05 57.08 76.1 95- 1 14.2 133-2 15 2 171.2 209.3 ii 2 '9-5 38.11 57-16 76.2 95-3 14-3 133-4 15 4 i7i-5 209. 6 12 3 4 19.08 19. u 38. 1 6 38.22 57-24 57-32 76.3 76.4 95-4 95-5 '4-5 14-6 J33-6 133-8 15 6 171.7 269.9 13 14 5 6 19-13 19. 6 38.27 38.32 57-40 57-48 76:5 76.6 95-7 95-8 14.8 15.0 133-9 134-1 153-3 172-4 2 0.8 15 16 7 19. 9 38.38 57-56 76.8 95-9 '5- ' 134-3 153-5 172-7 2 I. I 7 18 19. 2 38.43 57-64 76- 9 96.1 '5-3 134-5 153-7 172.9 2 1.4 18 9 19. 4 38.48 57-72 77-o 96.2 15-4 134-7 153-9 173-2 2 I. 7 19 30 19. 7 38.54 57-81 77- ' 96.3 J5-6 134-9 154-2 173-4 2 2.0 20 31 I9.30 38.59 57-89 77. a 96-5 06 6 15-8 '35-1 154-4 173-7 2 2. 2 21 3 19. 32 19-35 38. 64 38.70 57- 97 58-05 77- 3 77-4 9^8 \6.i 135-4 54-8 174. i 2 2.8 23 24 19.38 38.75 &;? 77-5 96.9 16.3 135-6 155-0 174-4 2 3-1 24 25 36 19. 40 '9-43 38. 8O 38.86 5. 21 58.29 77- 6 77-7 97.0 97.2 16.4 16. 6 135- 8 136.0 155-4 174-9 2 3-7 26' 27 19.46 38.91 58.37 77-8 97-3 16.7 136.2 155-6 i75-i 2 4.0 27 28 19.48 38.97 58- 45 77-9 97-4 16.9 136.4 155-9 175-4 2 4-3 28 29 i9-5> 39-02 58-53 97- 6 17. i 136.6 i6. i 175-6 2 4 .6 29 30 '9-54 39-07 58.61 7^2 97-7 17.2 136-8 156-3 175-8 2 4-9 30 3i 19.56 39- '3 58.69 78.2 97-8 17-4 136-9 IS6.5 176.1 2 5. 2 3 32 '9-59 39- "8 58.77 78.4 98.0 '7-5 137- i 156.7 176.3 2 5-5 32 33 19.62 39-23 58.85 78.5 98.1 17-7 137-3 156.9 176.6 2 5-8 33 34 19.64 39-29 58.93 78.6 98.2 J7-9 137-5 157-2 176.8 2 6. I 34 35 19.67 39-34 59-01 78.7 98-4 137-7 57-4 i77-o 2 6.4 35 36 19.70 39-39 59-09 78.8 98.5 1 8. a 137-9 157-6 177-3 2 6. 7 36 37 19.72 39-45 59- '7 78.9 98. 6 18.3 138.1 157-8 177-5 2 7. O 37 38 "9-75 39-50 59- 25 79.0 98.8 18.5 138.2 158.0 177.8 2 7-3 38 39 19.78 39-56 59-33 79.1 98.9 18.7 138.4 158-2 178.0 2 7 .6 39 40 19. 80 39-61 59-4' 79-2 99.0 1 8. 8 138.6 158-4 178.2 2 7.8 40 4 19.83 39-66 59-49 79-3 99.2 19.0 138.8 .58.6 178-5 2 8. 1 4> 42 .9.86 39-72 59-57 79-4 99-3 19.2 139-0 158.9 178-7 3 8. 4 42 19.88 39-77 59-65 79-5 99-4 19-3 139-2 159-1 179.0 2 8. 7 43 44 19. 91 39-82 59-73 79-6 99-6 19-5 139-4 159-3 179.2 2 9.0 44 45 19.94 39.88 59-81 79-8 99-7 19.6 139-6 159-5 179-4 2 9-3 45 46 19.96 39-93 59-89 79-9 iS'o 19-8 .39-8 159-7 179-7 2 9 . 6 46 47 19.99 39-98 59-97 80.0 20. o 139-9 159-9 179.9 2 9-9 47 48 20.02 40-04 60. 05 80. I 100. I 20. I 140.1 160. i 180.2 2 0. 2 48 50 2O.O7 40.14 60.21 80.3 100.4 20. 4 140.5 160.6 180.6 50 5' 20. IO 40.20 60. 29 80.4 100.5 20.6 140.7 160.8 ,80.9 2 I. I 5 5 20. 12 40.25 60. 37 80.5 loo. 6 20. 7 140.9 16 .0 18 .1 2 I. 4 52 53 20.15 40.30 60.45 80.6 loo. 8 20.9 141.0 16 .2- 18 . 4 2 1.7 53 54 20.18 40.36 60.53 80.7 100.9 2 . I 14 .2 16 .4 18 .6 2 2.0 54 55 2O. 2O 40.41 60. 6 1 Rr n 18 1 55 cfi 56 57 2O. 23 20. 26 40. 46 4- 5 1 60. 77 oo. 9 8l.O 101.3 2 5 14 -8 16 .1 is : 3 222! 8 5 57 58 . 59 30.28 20. 31 40-57 40. 62 60.85 60.93 81. I '.6 2 -7 14 .0 14 .2 16 .3 16 .5 18 .6 18 .8 223. I 223.4 58 59 Horz. Dist 96.03 192. i 288., 384-' 480.2 576 6 7 2 768 864 I0 5 6 Horz. Dist. Hor. dist. is for 30' point. Add or subtract .113 ft. to each TOO ft. of distance for each 10' departure. 84 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 12 f 100 200 300 400 500 600 700 800 900 1100 / - 20-34 40.67 61 . 01 8 -3 101.7 122.0 142. 162.7 183.0 2 3-7 I 20.36 40-73 40. 78 6 .09 4 101.8 122. 2 142.. 162.9 163. I 183.3 2 4.0 3 20' 42 40.83 6 .25 7 102. I 122-5 142. 163-3 183^7 2 4^6 4 20.44 40.89 6-33 .8 102. 2 122.7 MS- 163-5 184.0 2 4.9 "5 20.47 40.94 6 .41 9 102-4 122.8 MS- 163.8 184.2 2 5. 2 6 20.50 40.99 6 .49 8 .0 102.5 123.0 M3- :6 4 .o 184, 5 225-5 7 20. 52 41.04 6.57 8 .1 102.6 I23.I 143- 164.2 184.7 .0. n "5.8 9 20. 58 41- 15 6 .73 8 -3 102.9 123. 3 123-4 M3- 144. 164. 4 164.6 104.9 185. 2 226. 3 10 20. 60 41.20 6 .81 82.4 IO3.O 123.6 144. 164.8 85.4 226.6 I ,, 20.63 41.26 6 .89 82.5 103. I 123.8 144. 165.0 185.7 226.9 i 12 20.66 4I-31 6 . 97 82.6 o3-3 123-9 144. 165.2 185.9 227.2 i 13 20.68 4I-36 6 .04 82.7 .103- 4 124.1 144. 165.4 186.1 227-5 I < >4 20.71 41.42 6 .12 82.8 Q~ 103- 5 124.2 MS- 165.7 186.4 1; '5 16 20. 73 20.76 41. 47 41-52 62.28 02. 9 83.0 103. 8 124.6 MS- 3 166. i 1 86. 8 228.4 16 7 20.79 41-58 62.36 83.2 103.9 124.7 MS- 5 166.3 187.1 228. 7 17 18 20.81 41.63 62.44 83.3" 104.1 124.9 MS- 7 166.5 187-3 229.9 18 >9 20.84 4.. 68 62.52 83- 4~ 104.2 125.0 1 45- 9 166.7 187.6 229. 2 19 20 20.87 4'-73 62.60 83-5 104.3 125.2 146-1 166.9 187.8 229-5 20 21 20. 89 41.79 62.68 83-6 104-5 .125-4 146.2 167.2 188.0 229.8 21 22 20.92 41.84 62.76 83-7 104.6 125-5 146.4 167-4 188.3 230.1 22 23 20.95 41.89 62. 84 -83-8 104.7 125-7 r46.6 167.6 .88.5 230.4 23 24 20.97 41.94 62.92 83-9 104.9 125.8 146.8 167.8 188.8 230.7 24 26 2 .03 42.05 63.08 84.1 105.1 126.2 lift i M7-2 168.2 1 68 4 189.2 | n r III 26 38 2.08 42. j 6 63-23 84-3 105. 3 J05-4 120. 3 126.5 147-4 147-6 168.6 109- 5 189-7 23 . o 23 -9 27 29 2 . 10 42.21 63-31 84.4 105.5 126.6 M7- 7 168.8 189.9 23 .2 29 3 2 .13 4.2J6 63-39 84-5 105-7 126.8 M7-9 169.0 190.2 23 -4 30 31 21.16 42. 32 63-47 84.6 105.8 127.0 148.1 169.3 190.4 232.7 3 32 2I.I8 42-37 63-55 84-7 105.9 127. 1 M8.3 169-5 190.6 233-0 32 33 21.21 42.42 63-63 6l 71 84.8 S5 o 106.0 127.3 148.5 169.7 190.9 233-3 33 35 21^26 42.52 03- /' 63.79 85.0 106.3 127.6 148.8 170.1 191.4 233-9 .34 35 36 37 21. 9 21.32 42- 5- 42.63 63.87 63-95 85.2 85-3 106.4 106.6 127.7 127-9 149.0 149.2 170.3 170.5 191-6 191.8 234-2 234-5 36 37 38 21-34 42.68 64.02 85.4 106.7 128.0 149.4 170.7 192.1 234-8 38 39 21-37 42.74 64. 10 ft* iR 85.5 o e f. 106.8 149-6 170.9 192.3 235-0 39 41 21. 39 21.42 42. 79 42.84 04. IB 64.26 05. O 85-7 107. l 128.5 149-9 171. 192.6 192.8 235-3 235-6 4O- 41 42 21-45 42-89 64.34 85.8 107.2 128.7 150. i 171. 193-0 235-9 42 43 21.47 42-95 64.42 85-9 107.4 128. 8 150-3 171. 193-3 236.2 43 44 21.50 43.00 64.50 86.0 107-5 129.0 150.5 I?2. 193-5 236.5 44 45 21-53 43-05 64.58 86.1 107.6 129.2 150.7 172. 193-7 236.8 45 46 21-55 43- JO 64.66 86.2 107.8 129-3 150-9 172. 194-0 237-1 46 47 21.58 43-16 64-73 86.3 107-9 129-5 i5'-o 172. 194.2 237-4 47 48 21.60 43-21 64.81 86.4 108.0 129.6 151. 2 172. 194.4 237 6 48 '49 21.63 43-26 64.89 86.5 108.2 129. 8 15I-4 173- 194-7 237-9 49 50 21.66 43-31 64.97 86.6 108.3 129-9 I51-6 173- 194.9 238. 2 50 51 21.68 43-37 65.05 86.7 108.4 130.1 .51.8 173- 195-2 238.5 5' 5* 21.71 43-42 65.13 86.8 108.6 130-2 152.0 173- 195-4 238.8 52 53 21-74 43-47 65.21 86.9 108.7 130.4 152.2 173- 195.6 239-1 53 54 21.76 43-52 65-28 87.0 1 08. 8 130.6 152.3 174- 195-8 239-4 54 55 2J-79 43-58 65.36 87.2 108.9 130.7 152.5 74- 196.1 239-7 55 56 21.81 43-63 65.44 87-3 109.1 130.9 152.7 174-5 196.3 240.0 56 57 21.84 43-68 65.52 87-4 109.2 131.0 152.9 174-7 196.6 240.2 57 58 21.87 43-73 65.60 87-5 109-3 131-2 I53-I 174-9 196.8 240.5 5 59 21.89 43-78 65. 68 87.6 109-5 I3I-4 153-2 I75-I 197-0 240. 8 59 Horz. Dist. 95-32 190.6 286.0 381.3 476.6 572 66 7 763 858 1048 Hon. Dist. Hor. dist. is for 30' point. Add or subtract .123 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 85 TABLE 7 Continued DIFFERENCES IN ELEVATION 13 f 100 200 300 400 500 600 700 800 900 1100 / o 21.92 43-84 65.76 87.7 109.6 131-5 153-4 175-4 197-3 241.1 x 21.94 43-89 65-83 87.8 109.7 131-7 153-6 175-6 197.5 241.4 2 21. 97 43-94 65.91 87.9 09.9 131-8 153-8 75-8 197-7 241.7 3 22.00 43-99 65-99 10. 132-0 154.0 176.0 198.0 242.0 4 22.02 44-05 66.07 88. i 1O. 1 132-1 154-2 176.2 198.2 242.2 5 22.05 44.10 66.15 88.2 10. 2 132-3 154-3 176.4 198.4 242.5 6 .22.08 44- >5 66.23 88.3 10-4 132-4 154-5 176.6 198.7 242.8 7 22. 10 44-20 66.30 88.4 10-5 132-6 154-7 176.8 198.9 243. 1 8 22.13 44.26 66.38 88.5 132.8 154-9 177. 199. 2 243.4 8 9 22. 15 44-3' 66.46 88.6 10. 8 132.9 155-1 177.2 199.4 243.7 9 22. 18 44-3* 66.54 88.7 10.9 "33-1 155.3 177-4 199.6 10 , 22. 21 44.41 66.62 88.8 II. O >33-2 155-4 177.6 199.8 244.3 n 2 22.23 44- 46 66.70 88. 9 1 1. 2 133-4 155-6 177-9 2OO. I 244.6 12 3 22. 26 44-52 66.77 89. o "3 133.6 155-8 178. i 200-3 244.8 J3 4 22.28 44-57 66. 85 89.1 11.4 133-7 156.0 178-3 200. 6 245.1 U 5 22.31 44.62 66.93 89.2 n. 6 133-9 156-2 178-5 200. 8 245.4 15 6 22.34 44.67 67.01 89.3 11.7 134.0 156.4 178.7 201.0 245.7 16 7 22. 36 44-72 67.09 - 89.4 n. 8 134-2 156-5 178.9 201.3 246.0 17 18 22.39 44-78 67. 1 6 89.6 u.g 134-3 156.7 179. i 201.5 246.3 18 19 22.41 44.83 67.24 89.7 12. I 134-5 156.9 179-3 201. 7 246.6 19 20 22.44 44-88 67-32 89.8 12. 2 "34-6 57- 1 179-5 202.0 246.8 20 21 22.47 44-93 67.40 89.9 12-3 134-8 157-3 179-7 202. 2 247. 1 21 22 22-49 44.98 67.48 90.0 12-5 135-0 157-4 179.9 2O2. 4 247.4 22 23 22.52 45-04 67-55 90.1 12.6 135-1 157-6 1 80. i 202-7 247.7 23 24 22.54 45-09 67.63 9- 2. I2. 7 135-3 157.8 180.4 202.9 248.0 24 25 22-57 45- '4 67.71 9-3 12.8 135-4 .158-0 180.6 203. I 248.3 25 26 22.60 45- "9 67.79 90.4 13.0 135-6 158.2 180.8 203.4 248.6 26 27 22.62 45-24 67.86 90.5 13. I 135-7 158.4 181.0 203. 6 248.8 27 28 22. 65 45-30 67. 94 90. 6 13.2 135-9 158-5 181.2 203.8 249. 1 28 29 22.67 45-35 68.02 90.7 '3-4 136.0 158.7 181.4 204. i 249.4 29 30 22. 70 45-40 68. 10 90.8 '3-5 136-2 158.9 181.6 204.3 249-7 30 31 22-73 45-45 68.18 90.9 13-6 136.4 I59-I 181.8 204.5 250.0 31 32 22.75 45-50 68. 25 9 -0 13-8 136.5 159-3 182.0 204. 8 250.3 32 33 22.78 45-55 68-33 9 i "3-9 136.7 136. 8 159-4 l82. 2 205.0 250. 6 33 34 35 22.83 45.66 68.49 9 -3 14.1 137-0 159' 8 182^6 205.5 251. i 35 36 22.86 45- 7 1 68.56 9 -4 '4-3 137-1 160.0 182.8 205.7 25I-4 36 37 22.88 45-76 68.64 9 -5 14.4 137-3 160. 2 183.0 205.9 251-7 37 38 22.91 45.8i 68.72 9 -6 14.5 137-4 160.4 183.2 206. 2 252.0 38 39 22.94 45.88 68.81 9 -8 14. 7 137-6 160. 6 183.5 206.4 252-3 39 40 22.96 45-92 68.88 9 -8 14-8 137-8 160.7 I83-7 206.6 252-5 40 4i 22. 98 45-97 68.95 fiQ ni 91.9 14-9 137-9 1181 160.9 161. i 183.9 ISA I 206.9 252-8 41 43 23-04 46.07 09. 03 69.11 92. i 15. o "5-2 130. i 138-2 161.2 1840 207-3 253. i 253-4 43 44 23.06 46.12 69. 1 8 92.2 15.3 138.4 161.4 184.5 207:6 253-7 44 45 23-09 46.18 69-26 92-4 15.4 '38.5 161.6 18 4 .7 207. 8 254-0 45 46 47 23.11 23- '4 46-23 46.28 69-34 69.42 92.4 92.6 '5.6 "5-7 138-7 .38.8 161.8 162.0 184.9 I85-I 208.0 208.2 254-2 254-5 46 47 48 23- '5 46.30 69.46 92.6 138.9 162. i 185.2 208.4 254-7 48 49 23- '9 46.38 69.57 92.8 16. o I39-I 162.3 185-5 208.7 255-1 49 50 23-22 46.43 69.65 92.9 16. i 139-3 162.5 185.7 209.0 255-4 5 Si 23-24 46.48 69-73 93-o 16. 2 139-4 162.7 185.9 209.2 255-7 5' 52 23-27 46.54 69.81 93-1 16.3 I39. 6 162.9 209.4 256.0 52 53 23.29 46.59 69.88 93-2 16.5 139.8 163.0 186.4 209.6 256.2 53 54 23-32 46.64 .69.96 93-3 16. 6 139-9 163.2 186.6 209.9 256.5 54 55 56 23 34 46.69 46. 74 70.04 93-4 16.7 ifi o 163-4 186.8 2 5 6.8 55 56 57 58' 23-40 23-42 46.79 46.84 70. 19 70.37 93- 5 93-6 93-7 10. 9 17.0 17. I 140.4 140.5 163-8 164.0 187. 2 187.4 210.6 210.8 257-4 257.6 57 5 59 23-45 46. 90 70.34 93-8 17. 2 140. 7 164.1 I8 7 .6 211. 257-9 59 Horz 94-55 189.1 283.6 378.2 472.8 567 662 756 851 1040 Horz. Dist. Dist. Hor. dist. is for 30' point. Add or subtract .132 ft. to each 100 ft. of distance for each 10' departure- 86 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 14 / 100 200 300 400 500 600. 700 800 900 1100 f 23-47 47.00 70. 42 93-9 J'7-4 140.8 164-3 187.8 211.3. 258.2 4, 23-50 47-00 70. 50 94-0 117-5 141.0 164.5 188.0 211.5 258.5 , C Q Q 1 3 23- 52 23-55 47.05 47.10 70.58 70. 65 94- l 94.2 "7! a I4J-3 164.8 188.4 212.0 250. o 259.' 3 4 5 23- 58 23.60 47- '5 47.20 70. 73 70.81 94- 3 94-4 I 7- 9 llS.O 141. 5 141.6 165.2 188.8 212.4 259.6 4 5 6 23-63 47.25 70.88 94-5 118. i . ,0 , ,41.* 165-4 ,/ - A 189.0 212.6 259.9 6 I 2 3- 65 23.68 47- 3* 47-36 70. 96 71.04 94- 6 94-7 I lo. 3 142.1 105. D 165.8 189.4 213. I 260.5 8 9 23.70 47- 4' 71. ii 94.8 1 1 8. 5 142.2 165.9 189.6 213-3 260.8 9 10 23-73 47.46 71.19 94-9 118.6 142.4 166.1 189.8 213.6 261.0 10 II 23-76 47- 5 71.27 95-0 1 1 8. 8 142.5 166.3 190.0 .213.8 261.3 |i 12 23-78 47.56 71-34 95- ' 118.9 142-7 166.5 190.2 214.0 261.6 12 >3 23.81 47.6i 71.42 95-2 119.0 142.8 166.6 190.5 214-3 261.9 I* >4 23-83 47.66 7I-50 95-3 119.2 143.0 166.8 190.7 2 4-5 262.4 14 15 23.86 47-7* 71-57 95-4 i 9-3 143-2 167.0 190.9 214-7 262.4 15 16 23.88 47-77 71-65 95-5 119.4 143-3 167.2 19 .1 215.0 262.7 16 17 23-91 47-82 71-73 95-6 119.6 143-4 167.4 19 -3 215-2 263.0 17 18 '9 23-94 23-96 47-87 47-92 71.80 71.88 95 'Z 95-8 119.7 119.8 143.6 143-8 167.5 167.7 19 -5 19 .7 215-4 215-6 SI 18 19 20 23-98 47-97 72.00 95-9 119.9 143-9 167.9 19 -9 215-9 263.8 2O 31 24.01 48.02 72-03 96.0 120. I 144.1 I68.I 19 .1 216. i 264.1 21 22 24.04 48.07 72.11 96.2 1 20. ? 144.2 168.3 19 -3 216.3 264.4 it 23 24.06 48.12 72.19 96.2 120.3 144.4 168.4 192-5 216.6 264. 7 3 24 24.09 48.18 72.26 96.4 1 20. 4 144-5 168.6 192-7 216.8 265.0 24 25 24.11 48-23 72-34 96.4 120.6 J44-7 168.8 192.9 217.0 265.2 15 26 24.14 48.28 72.42 96.6 120.7 144.8 169.0 193-' 217.2 265.5 *6 27 24. i 48.33 72.49 96.7 120. 8 '45-0 169.2 193-3 217-5 265.8 27 28 24.1 48.38 72.57 96.8 121.0 MS- i 169-3 193-5 217. 7 266.1 28 9 24:2 48.43 72.64 96-9 121. I 145-3 169-5 193-7 217-9 266.4 29 30 24. 2 48.48 72.72 97-o 121. 2 M5-4 169-7 193-9 218.2 266.6 3 3> 24.2 48.53 72.80 97-1 121. 3 145-6 169-9 194.1 218.4 266.9 3 32 24. 2 48.58 72.88 97-2 I2I.5 145-8 170. o 194-3 218.6 267.2 3 33 24-3 48.63 72.95 97-3 121.6 145-9 170. 2 194-5 218.8 267.5 33 . 34 24-34 48.68 73-03 97-4 121. 7 146.0 170.4 194.7 219. i 267.8 34 35 24-37 48.74 73-io 97-5 121. 8 146.2 170.6 194-9 219-3 268.0 35 36 24-39 48.79 73-18 97-6 122.0 146.4 170.8 195-' 219-5 268.3 36 37 24.42 48.84 73-26 97-7 122. I 146-5 170.9 195-4 219.8 268.6 37 38 24.44 48.89 73-33 97-8 122.2 146.7 I71.I 195-6 220.0 268.9 38 39 24.47 48.94 73-4' 97-9 122.4 146.8 I7I-3 195.8 220. 2 269.2 39 .40 4-5<> 48.99 73.48 98.0 122-5 147.0 I7I-5 196.0 220.4 269.4 40 4> 24.52 49.04 73-56 98.1 122.6 147.1 I7I.6 196.2 220.7 269.7 4> 42 24-54 49.09 73.64 98.2 122.7 1 47,- 3 171.8 196-4 220.9 270.0 42 43 24-57 49.14 73-71 98.3 122.8 147-4 172.0 196.6 221. I 270.3 43 44 24.60 49.19 73-79 98.4 123.0 147.6 172.2 196,8 221.4 270. 6 44 45 24-62 49.24 73.86 98.5 I23.I 147-7 172. 4 197.0 221.6 270.8 45 46 24-65 49-29 73- 94 98-6 23.2 147.9 172.5 197.2 221.8 271.1 46 47 24.67 49-34 74-02 98.7 23-4 148.0 172.7 197-4 222. I 271.4 47 48 24.70 49-39 74.09 98.8 23-5 148. 2 172.9 197-6 222-3 271.7 48 49 24.72 49-44 74-17 98.9 23.6 148.3 I73-I 197.8 222.5 272.0 49 50 24-75 49-50 74-24 99.0 23-7 148.5 173-2 198.0 222.7 272.2 5 5' 24.77 49-55 74-32 99.1 23-9 148.6 173-4 '1 9 8. 2 23-0 272.5 Si 52 24.80 49.60 74-39 99.2 24-0 148.8 173-6 198.4 23.2 272.8 52 53 24.82 49-65 74-47 99-3 24-1 148.9 173-8 I 9 8.6 23-4 273-1 53 54 24-85 49.70 74-55 99-4 24.2 149.1 173-9 198.8 23.6 273-3 54 55 24.87 49-75 74.62 99-5 24.4 149.2 174.1 199.0 23-9 273.6 55 cfi S 6 58 24.90 24.92 24.95 49- 80 49-85 49- 9 74.70 74-77 74.85 99- 6 99-7 99-8 124.6 ' 49- 6 149-7 174-5 174-6 199.4 199.6 224.3 224.6 274- 3 274-4 5 57 58 59 24.98 49-95 74.92 99-9 124.9 1 49- 8 174.8 199-8 224-8 274-7 59 Horz Dist. 93-73 J87.5 374-9 468.6 562 656 750 844 1031 Horz. Dist. Hor. dist. is for 30' point. Add or subtract .141 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 87 TABLE 7 Continued DIFFERENCES IN ELEVATION 15 t 100 200 300 400 500 600 700 800 900 1100 f o I 2 3 25-00 25.02 25-05 25.08 50.00 50.05 50.10 75-oo 75-08 75-15 100.0 100. 2 125.0 125.2 125.2 150.0 150-2 150.3 175-0 175-2 175-4 200.0 200.4 225-3 225-5 275.0 275-3 275-6 4 5 6 I 9 10 ii. 25. 10 25- '3 *5-i5 25.18 25. 20 25-23 25.25 S5-28 50. 20 50.25 50.30 50-35 50. 40 50-45 50.50 50.55 75-30 75.38 75-45 75- 53 75.60 75-68 75- 76 75-83 100. 4 100.5 100.6 100.7 100. 9 IOI.O 101. I J25-5 125.* 1*5-8 "e'o 126.1 126.3 126.4 150.6 150.8 150.9 15 IS 15 15 15 - 175-7 175-9 176.0 176.2 176.4 176.6 176.8 176. 9 200.8 201.0 201. 2 201.4 201. 6 202.0 225.9 226.1 226.4 226. 6 226.8 227. o 227.3 276. i 276-4 276.6 276.9 277.2 277-5 277.8 4 5 6 7 8 9 10 3 14 25-30 25-33 25-35 50. 60 50- 6 5 . 50.70 75-90 75-98 76.06 101. 4 101. 3 101.4 126.5 126.6 126.8 15 15 15 177.1 177-3 177-5 202.6 227.9 278.3 278.6 278-9 13 4 15 16 17 18 "9 20 21 22 25-38 25-40 25-43 25-45 25-48 25-50 25-53 25- 55 50.75 JO. 80 50.85 50.90 50-95 5I-05 "76.13 76.21 76.28 76.36 76-43 76.51 76.58 76. 66 101.5 101.6 \l\.l 101.9 102. 1 102. 2 126.9 127.0 127. I 127.3 127.4 127.5 127.6 127. 8 15 15 15 15 15 153- 153-2 153-3 177.6 177-8 178.0 178^ 178.5 178.7 203.2 23-4 203.6 203.8 204.0 204.2 228.6 228.8 229.1 229.3 229-5 229-7 279. 4- 279.7 280.0 280.2 280. 5 280.8 28 .1 15 16 17 18 19 20 21 22 24 25 26 27 28 29 25-58 25.60 25-63 25.65 25.68 25.70 25-73 5'- '5 51- .0 51-25 51-30 5>-35 5'-40 5'-45 76.73 76.81 76.88 76.95 77-03 77.11 77.18 102.3 102.4 102.5 : I02. 6 102.7 102. 9 127-9 128.0 128.1 128.3 128.4 128.5 128.6 153-5 153-6 153-8 153-9 154- i 154-2 154-4 179.0 179.2 179-4 179-6 179-7 179-9 180. i 204.8 205. 2 205.4 205. 6 205.8 230.4 230.6 230.9 23 i 23 -3 23 -5 28 .6 28 .9 28 : 4 28.7 283.0 24 25 26" 27 38 2 9 3' 32 33 34 35 25-78 25. 80 25-83 25-85 25 88 51-55 51-60 5'-65 -51.70 77-33 77-41 77.48 77-56 103.1 103.3 103.4 128.9 129.0 129.1 "29-3 ' '54-7 154-8 "55-0 155-1 180.4 180.6 180.8 206.2 206.4 206.6 206.8 23 .0 23 -2 23 -4 23 -7 283.6 283.8 284.1 284.4 3" 32 33 34 36 37 38 25-90 25-93 51-80 51-85 77-70 77-78 103.6 \ll:l 129-5 129.6 155-4 155-6 i -3 i -5 207. 2 207.4 233-1 233-3 284.9 285.2 36 * 39 40 25.98 51-95 77-93 103. 129.9 >55-9 i . 8 207. 8 233- 8 285.7 39 4> 4- 26.02 52-05 78.08 104. 130-2 156-2 1 . 2 208. 2 234-3 286.3 4 43 44 45 46 47 48 49 50 5" 52 53 54 55 56 26.08 26. 10 26.12 26.15 26.18 26. 20 26.22 26. 25 26. 27 26. 30 26.32 26.35 26. 37 52. 15 52. 20 52.25 52.30 52-35 52.40 52.45 52.50 52.55 52.60 52-65 52.70 52-74 78.23 78.3 78.38 78.45 78.52 78.60 78.67 78-75 78.82 78.90 78.97 79.04 79.12 104. 104. 104. 104. 104. 104. 104. 105. 105. 105. 105. 105. 105. 130.4 130.5 130-6 130-8 130.9 13 -o 13 -i 13 -2 13 -4 13 -5 13 -6 '3 -7 13 -9 156.4 156.6 156.8 156.9 157-0 157-2 157-3 157-5 '57-6 "57-8 157-9 158-1 158.2 182.5 ,82.7 182.9 183.0 183.2 183-4 183.6 183-7 183-9 184.1 184-3 184.4 184.6 208.6 208.8 209.0 209.2 209.4 209.6 209.8 2 0.0 0. 2 0-4 0.8 1.0 234-7 234-9 235-1 235-4 235-6 235-8 236.0 236.2 236.5 236- 7 236-9 237-1 237-4 286.8 287.1 287.4 287.6 287.9 288. 2 288.5 288.7 289.0 289.3 28 9 .6 289.8 290.1 43 44 45 46 47 48 49 50 51 52 53 54 55 57 58 59 26.42 26.45 26.47 52.84 52.8 9 52-94 79.27 79-34 79.42 105.7 105.8 105.9 132.1 132.2 132-4 158-5 158.7 158.8 185.0 .85.1 185-3 211.4 211. 6 211.8 237-8 238.0 238.2 2.90.6 290.9 291.2 57 58 59 Horz. Dist. 92.86 185-7 278.6 371.4 464-3 557 650 743 836 1022 Dist.' Hor. dist. is for 30' point. Add or subtract .150 ft. to each 100 ft. of distance for each 10' departure. 88 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Continued DIFFERENCES IN ELEVATION 16 t 100 200 300 400 500 600 700 800 900 1100 1 o 26. 50 5 2 - 99 79- 45 106. o 185 5 26. 52 53-04 79-56 106. I 32' 6 '59- i 185.6 212. 2 238.7 291.7 2 26.55 53-09 79.64 106.2 32-7 '59-3 185.8 212.4 238-9 292.0 3 26.57 26. 60 53-14 79-71 79- 78 106.3 106. 4 32-8 '59-4 186.0 212.6 239- i 292.3 5 26.62 53-24 79-86 106.5 33- l '59-7 186.3 213.0 239-6 292. 5 292.8 6 26.64 53-29 79-90 106.6 33-2 '59-9 186.5 213-2 239-8 293-1 6 7 26.67 53-34 80.01 106.7 33-3 160.0 186.7 213-4 240.0 293-4 7 8 26.69 53-39 80.08 106.8 33-5 160.2 186.8 213-5 240. 2 293-6 8 9 10 26. 72 26.74 53-44 53.48 80.15 8o.,23 106. 9 107.0 33-6 33-7 160.3 160.4 187.0 187.2 213-7 213-9 240.5 240.7 293-9 294.2 9 10 II 26.77 53-53 80.30 107. I 33-8 160.6 187.4 214. I 240.9 294.4 ii 12 26.79 53.58 80.38 107.2 34-0 160.8 187. 5 24-3 241.1 294-7 3 26.82 53-63 80.45 >07- 3 34- i 160. 9 187.7 214-5 24I-3 295.0 13 4 26.84 53-68 80.52 107.4 34-2 16 .0 187.9 214. 7 2 4 ,.6 295-2 >4 15 26.86 53-73 80.60 107-5 34-3 16 .2 188. i 214.9 241.8 295-5 5 16 26.89 53-78 80.67 107. 6 34-4 16 .3 188.2 215. i 242.0 295-8 16 17 26. 91 53-83 80.74 107. 7 34-6 16 .5 188.4 215-3 242.2 296.0 17 18 26.94 53-88 80.82 107. 8 34-7 16 .6 188.6 215.5 242.4 296.3 18 19 26.96 53-93 80.89 107.8 34-8 16 .8 188.7 215 7 242.7 296.6 19 JO 26.99 53-98 80.96 108.0 34-9 16 .9 188.9 215-9 242.9 296-9 20 Ji 27.01 54-02 04 108.0 35- i 162. I 189. I 216. i 243- I 297-1 21 22 27.04 54- 07 . ii 08.2 35-2 162.2 189-3 216.3 243-3 297-4 22 23 27.06 54- '2 . 18 108.2 35-3 162.4 189.4 216.5 243-6 297-7 23 24 27.09 54- '7 .26 08.3 35-4 162. 5 189.6 216. 7 243.8 297.9 24 25 27. ii 54-22 33 108.4 35-6 162.7 189.8 216.9 244-0 298.2 25 26 37 27- 3 27. 16 54 26 54- 3 2 .40 48 108.5 108 6 35-6 35- 8 162.8 163. o 189.9 217.0 244.2 298.4 26 2 7 28 27. 1 8 54-37 55 08.7 35-9 163.1 190.3 217-5 244.6 299.0 28 29 27. 21 54-4" .62 108.8 36.0 163. 2 190.4 217-7 244.9 299.3 29 30 27-23 54 46 70 108.9 36.2 if) 1 163.4 iftl C 190.6 ton K 217.9 245- 1 299.6 -30 31 32 33 27.28 27. 30 54' 56 54 6 1 54- 66 ^84 .92 109. I 109.2 3- 3 36.4 36.5 IO 3- 5 163.7 63.8 190. o 19 .0 19 .1 218.2 218.4 245-5 245-8 3o. i 300.4 32 33 34 35 if, 27.35 27. 38 54-71 54- 76 .10 109. 3 109.4 3^8 lt\ 164.1 *f*A 1 19 -5 218.8 246.2 300.9 35 76 3 37 38 27.40 27-43 54- 80 54-85 '3 . 21 .28 109. 5 109.6 109.7 3". 9 37-0 37-' 104. 3 164.4 164. 6 !!: 192.0 219.2 19.4 246.6 246.8 3O1- 2 301.4 301.7 3 11 39 27-45 54-90 35 109.8 37-3 164.7 192.2 19.6 247-1 302.0 39 40 27.48 54-95 2-43 109.9 37-4 164.8 192.3 19.8 247-3 302. 2 40 41 27-50 55-00 82.50 I 37-5 165.0 192.5 20.0 247-5 302.5 41 42 27-52 55-05 82-57 i i 37-6 165.1 192.7 20. 2 247-7 302.8 42 43 27-55 55- 'o 82.60 I 2 37-7 165.3 192.8 20.4 247-9 303.0 43 44 45 27- 57 27.60 55- '4 55- '9 82. 72 82.79 I 3 i 4 37-9 38-0 165. 4 165.6 193-2 220. 8 248.4 303.3 303.6 44 45 46 27.62 55-24 82.86 i 5 38.1 165.7 193-4 221.0 248.6 303.8 46 47 27- 65 55-29 82.94 38-2 165.9 193-5 221. 2 2 4 8.8 304. 1 47 48 27.67 55-34 83.01 1 7 38-4 1 66. 193-7 221.4 249.0 304 4 48 49 27-69 55-39 83.08 i 8 38-5 166.2 193-9 221.6 249. 2 304. 6 49 50 27-72 55-44 83-15 i 9 38.6 166.3 194-0 221.7 249-5 304- 9 50 51 27-74 55-48 83-23 I O 38.7 166.4 194.2 221.9 249-7 305-2 5' 52 27-77 55-53 83-30 i i 38-8 166.6 194.4 222. I 249.9 305-4 52 S3 27.79 55-58 83-37 I 2 39-0 166.7 194.5 222.3 250. I 305.7 53 54 27.82 55-63 83-44 i 3 39- i 166.9 194.7 222.5 250.3 306.0 54 55 27-84 55-68 83-52 i 4 39-2 167.0 194.9 222.7 250.6 306.2 55 5 Z7-86 55-73 83-59 I 4 39-3 167.2 195-0 222.9 250.8 306.5 56 57 27-89 55-78 83.66 i 6 39-4 167-3 195-2 223-1 251.0 306.8 57 58 27.91 55-82 83-74 i 6 39-6 .67-5 195-4 223-3 251.2 307.0 58 59 27.04 -55- 87 83-8, i 7 39-7 167.6 195.6 223-5 25I-4 307.3 59 Horz. Dist. 91-93 183-9 275- 8' 367-7 459-7 552 644 735 827 ion Horz. Dist. Hor. rtist. is for 30' point. Add or subtract .158 ft. to each 100 ft. of distance for each 10' departure. TOPOGRAPHIC STADIA SURVEYING 89 TABLE 7 Continued DIFFERENCES IN ELEVATION 17 to 23 t 17 ;s 19 20 21 22 23 ; t o 27. 96 29-39 30.78 32. 14 33-46 34-73 35-97 o I 27-99 29.42 30.81 32.16 33-48 34-75 35-99 1 a 28. 01 29-44 30.83 32.18 33-50 34-77 36.01 X 3 28.04 29.47 30.85 32.21 33-52 34-80 36.03 S 4 28.06 29.49 30.87 32.23 33-54 34-82 36-05 * 5 28.08 29-51 30.90 32.25 33 57 34.84 36.07 5 6 28. 10 29-53 30. 92 32-27 33.,'59 34-86 36.09 6 7 28.13 29.56 30.94 32.30 33; 6l 34-88 36.11 7 8 28.15 29-58 30.97 32.32 33-63 34.90 36. 13 8 9 28. 18 . 29. 60 30.99 32-34 33- 6 5 34-92 36. 15 9 10 28. 20 29.62 31-01 32.36 3,3-67 34-94 36- 17 IO ii '28.22 29-65 31-04 ; 32. 39 33-70 34-96 36- '9 It 12 28.25 29. 67 31-06 32.41 33-72 34-98 36.21 12 '3 28. 27 29.69 3-o8 32.43 ,33-74 35-oo 36-23 13 4 28.30 29.72 31. 10 32.45 33-76 35-02 36-25 I* 5 28.32 29-74 3i- '3 32-47 33.78 35- 05 36-27 15 16 28.34 29. 76 31-15 32.49 33.8o 35-07 36.29 16 7 28. 37 29.79 3 -*7 32.51 33-82 35 09 36.31 17 18 '28.39 29.81 3 -19 32.54 33-84 35- ii 36.33 18 >9 28.42 29-83 3 -22 32-56 33-87 35-13 36-35 9 20 28.44 29.86 3 -24 32-58 33-89 35 15 36.37 20 21 28.47 29.88 3 -26 32. 61 33-91 35- 17 36.39 21 22 28.49 29.90 3 -28 32.63 33-93 35-19 36-41 22 23 28.51 29-93 3'-3o 32.65 33-95 35-21 36.43 23 24 28.54 29-95 31-33 32.67 33-97 35-23 36.45 24 35 28.56 29 97 31-35 32.70 33-99 35-25 36.47 25 26 28.58 30.00 3'-38 32.72 34-oi 35-27 36.49 26 37 28.61 30.02 3'-40 32.74 34-04 .35- 29 36.51 27 28 28.63 30.04 3"-42 32-76 34.06 35-31 36.53 28 29 28.66 30.07 3'- 43 32-78 34.08 35-34 36.55 29 30 28.68 30. 09 3'-47 32.80 34- 10 35-36 36 57 jo 31 28.70 30. n 31-49 32-83 34- 12 35 38 36.59 31 32 28.73 30- '4 3 -51 32.8 5 34- 14 35-40 36.61 32 33 28.75 30.16 31-54 32.87 34-16 35-42 36.63 33 34 28.77 3- 1 9 3 -56 32.89 34- 1 8 35-44 36.65 34 35 28.80 30.21 31-58 32-91 34-21 35 46 36.67 35 36 28.82 00-23 3 -60 32-93 34-23 35-48 36.69 36 37 28.85 30. 26 31-63 32.96 34-25 35-50 36.71 37 38 28.87 30. 28 31-65 32.98 34- 27 35-52 36.73 3* 39 28.89 30.30 31-67 33-oo 34-29 35-54 36.75 39 40 28.92 30.32 31.69 33-02 34 3i 35.56 36.77 40 41 28.94 30.36 31-72 33-05 34-33 35-58 36.79 4 42 28.96 30.37 31-74 33-07 34-35 35-6o 36.80 42 43 28.99 30.39 31-76 33-09 34-38 35-62 36.82 43 44 29.01 30.41 3'-78 33 1 1 34.40 35 64 36.84 44 45 29-04 30-44 33- 13 34-42 35-66 36.86 45 46 29.06 30.46 31-83 33- 1 5 34-44 35-68 36.88 46 47 29.08 30-49 31-85 33-18 34.46 35-70 36. 90 47 48 29. ii 30.5> 31-87 33-20 34-48 35-72 36.92 48 49 =9- '3 30.53 3 -90 33-32 34-50 35-74 36.94 49 50 29- '5 30.55 31-92 33-24 34-52 35.76 36.96 50 S" 29. 1 8 30.58 31-94 33-26 34-54 35-78 36.98 5 52 29.20 30. 60 3L96 33, 28 34-57 35-80 37.00 52 53 29-23 30.62 3'-99 33-31 34 59 35-83 37-02 53 54 29.25 30-65 32.01 33-33 34-61 35-85 37-04 54 55 29-27 30.67 32-03 33- 35 34-63 35-87 37-o6 55 56 29.30 30.69 32-05 33-37 34.65 35.89 37-oS S& 57 29.32 30.72 32.07 33 39 34.67 35-91 37-1 57 58 29-34 30.74 32.09 33-41 34.69 35-93 37-12 5* 59 29-37 30.76 32-12 33-44 34.71 35-95 37-14 59 Horz. 90.96 89-93 88.86 87.74 86-57 85-36 84-10 Hon. Dist. Dist. Horz. Corr. '6 7 3 .182 .191 .198 .206 1 3 Horz. Con. 90 TOPOGRAPHIC STADIA SURVEYING TABLE 7 Concluded DIFFERENCES IN ELEVATION 34 to 29 * 24 25 26* 27 28 29", '. o 37-16 38.30 39-49 4-45 41-45 42.40 1 37.18 38-32 39-42 40.47 4'-47 42.42 i 2 ^57-20 .38.34 39-44 40. 49 41.48 42-43 i 3 37- 22 38-36 39-46 40. 5' 4'- 50 42-45 3 4 37-23 38-38 39-47 40-52 4 -52 42.46 4 5 37-25 38.40 39-49 40-54 4' -54 42.48 5 6 37-27 38.41 39-51 40-55 41-55 42-49 6 7 37-29 38.43 39-5' 40-57 4>-57 42-5" 7 8 37.31 38.45 39-55 40.59 41.58 42-53 8 9 37-33 38.47 39-56 40. 6 1 41.60 42.54 9* 10 37-35 38.49 40. 62 41.61 42.56 10 ,, 37-37 38.52 39.60 40.64 41.63 42.58 it 12 37-39 38.53 39-61 40.66 41-65 42-59 12. 13 37-41 38.55 ' 39- 63 40.68 41.67 42. 60 1J M- 37-43 38-56 39-65 40.69 41.68 42.62 I* 15 37-45 35-58 39-67 40.71 41.70 42.64 15 16 37- 47 38 Bo 39-69 40.72 41.71 42-65 16 17 37-49 38^62 39-7' 40. 74 4'-73 42.66 17 18 37- 5 38. 64 39-72 40.76 41-74 42.68 IS '9 37-53 38.66 39-74 40.78 41.76 42.70 '9 30 37-54 .38-67 39- 76 40. 79 41-77 42.71 20 21 37-56 .38.69 39-78 40. 8 1 41-79 42.72 2, 22 39-79 40.82 41.8! 42-74 22 23 37.60 38.73 39-82 40.84 41.83 42-76 23 24 37-62 38.75 39-83 40.86 1.84 42-77 24. 25 37-64 38.76 39-85 40.88 1.86 42.78 25 26 37-66 38.78 *39- 86 40.89 1.87 42. 80 26 27 37-68 38.80 39-88 40.91 1.89 42.82 27 28 37-70 38.82 39-90 40.92 1.90 42.83 28 29 37-72 38.84 39-92 20. 94 41.92 2.85 29 30 37-74 38..S6 39-93 40.96 41 93 2.86 30 31 37-76 38.88 39-95 40.98 41-95 2.88 3 32 37-77 38.89 39-97 40.99 41-97 2.89 32 33 37-79 38-9' 39-99 .01 41.99 2.91 33- 34 37-8i 38.93 40. oo . 02 2.00 2.92 34 35 37-83 40.02 .04 2.02 2.94 35 36 37.85 38.97 40.04 .06 2.03 2-95 36 37 37-87 38.99 40.06 .08 2.05 2.97 37 38 37-89 39.00 40.07 .09 2.06 2.98 3 39 37-9' 39-02 40.09 . 1 1 2.08 43.00 39 40 37-93 39-04 40.11 . 12 42.09 43-01 40 41 42 43 37-95 37- 96 37-98 39- 06 39.08 39- >o 40.14 40. 1 6 .16 42. 4 43-04 43.06 4* 43 44 38.00 39-" 40.18 >9 2- 5 43-07 44 45 45 46 38. 02 38.04 39- '5 40.21 .22 2.19 43- '0- 43- 12 46 47 48 38.08 39- "8 40.24 .26 2.22 43- >3 49 38. 10 39-20 40.26 .28 2. 24 43- "5 49 50 3 8... 39-2? 40.28 29 42.25 43-16 50 5 38.13 39-24 40.30 31 42. 26 43-'7 5 52 38.15 39-26 40.31 32 42.28 43.18 5 53 38.17 39-27 40-33 34 42.30 43-20 53 54 38-19 39-29 40.35 35 42. 31 43-21 54 55 . 38-21 39-31 40.37 37 42-33 43-23 55 56 57 38-23 38.25 39-33 39- 35. 40.38 40.40 39 .41 42.34 42.36 43-24 43-26 56 57 58 38.26 39 ; .36 40.42 .42 42.37 43-27 58 59 38.28 40.44 43 42.39 43-29 59 'Horz. Dist, 82.80 8I-.47 80.09 78.68 .77-23 75-75 Horz. Dist. Horz. Corr. .219 .226 233 .238 .344 .250 Horz., Corr; TOPOGRAPHIC STADIA SURVEYING 91 Conversion of Feet to Decimals of a Mile. Table 8 is a table for the conversion of feet to decimals of a mile. A table of this character will be found convenient when the mile is the unit for platting. This table is repro- duced by permission from publications of the U. S. Geological Survey. For any distance expressed in feet which is likely to come into consideration in making a stadia survey the equivalent fraction of a mile is noted. 92 TOPOGRAPHIC STADIA SURVEYING TABLE 8 CONVERSION OP FEET TO DECIMALS OP A MILE (By permission of the U. S. Geological Survey) Feet. Mile. Feet. Mile. Feet. Mile. Feet. Mile Feet. Mile. Feet. Mile. Feet. Mile. 100 0.019 600 0.114 1 100 o. 208 1600 0.303 2100 0-398 2600 0.492 3100 0.587 10 .021 10 . 116 10 . 210 10 305 10 .400 10 494 589 20 .023 20 .118 20 . 212 20 37 20 .402 20 .496 20 59" 30 .025 30 . 120 3> .214 3 .309 30 404 30 .498 30 593 4O .026 40 . 122 40 .216 40 3" 40 405 40 500 40 595 SO .028 50 '24 50 .218 5 3'3 50 .407 50 502 50 596 60 .030 60 '25 60 .219 60 3"4 60 .409 60 54 60 598 70 .032 70 .127 70 . 221 70 3'6 70 .411 70 506 70 .600 So O34 80 .129 So .223 80 .318 80 4'3 So 508 80 .602 90 .036 90 .I3 90 .225 90 .320 90 4'5 90 509 90 .604 200 .038 7 00 133 1 200 .227 1700 .322 22OO .417 2700 5>i 3200 10 .606 . 608 20 . 040 .042 20 .136 20 23' 20 .326 20 .420 20 515 .610 30 .044 3 .138 30 233 30 .328 30 .422 30 5'7 30 .612 40 .046 40 .140 40 235 40 330 40 .424 40 519 40 .614 50 47 SO .142 50 .236 50 33' 5 .426 50 521 50 .616 60 .049 60 .144 60 -238 60 333 60 .428 60 523 60 .617 70 .051 70 .146 70 .240 70 335 70 43 7 525 70 .619 80 053 80 .148 So .242 80 337 80 432 80 527 So . 621 90 055 90 .150 90 .244 90 339 90 434 90 529 90 -623 300 057 800 152 1300 .246 1800 . -34' 2300 436 A 19. 2300 530 3300 .625 627 20 059 .061 10 20 '53 '55 20 .250 20 345 2O 43 439 20 53 2 534 20 .629 3O .062 3 157 3 .252 30 347 30 .441 3 536 30 631 40 .064 40 159 40 254 40 349 40 443 40 .538 40 633 5 .066 5 .161 50 .2 5 6 50 350 50 445 5 540 50 .644 60 .068 60 -163 60 257 60 352 60 447 60 542 60 . 666 .070 .072 70 80 .165 .167 70 80 259 .26l 70 80 354 356 70 80 449 45" 70 80 544 546 70 So .688 ..640 90 -074 90 .169 90 .263 90 .358 90 453 90 547 90 .642 400 10 . 076 .078 900 10 .170 .172 1400 10 .265 .267 1900 10 360 -362 2400 10 455 456 2900 549 55" 3400 10 644 .646 080 20 ! 74 20 .269 20 364 20 458 20 553 ao ' " .648 3 .082 3 .176 30 .271 30 366 3 .460 30 555 3 650 40 50 60 084 .086 . 088 40 50 60 .178 .180 .181 40 50 60 -273 275 .276 40 5 60 367 369 37 1 40 50 60 .462 .464 .466 40 50 60 557 559 56' 40 50 6ft .652 653 655 70 80 .089 091 70 80 :S 70 So .278 70 80 373 375 70 80 .468 .470 70 80 .562 564 ' -657 659 90 093 90 .187 90 .'282 90 377 90 .472 90 -566 90 .661 500 10 095 .097 1000 10 .189 '9' 1500 .284 .286 2000 10 379 381 2500 10 474 475 3000 568 570 3500 10 .663 .665 20 098 20 193 20 .288 20 383 20 477 20 572 20 .667 30 40 5 60 . 00 . 62 . 04 . 06 3 40 5 60 >95 .197 '99 . 200 30 40 5 60 .290 .292 294 295 3" 40 50 60 384 386 388 390 30 40 5 60 479 .481 -483 485 3 40 50 60 574 576 578 ' -580 30 40 50 60 .669 .670 .672 .674 70 80 90 . 12 70 80 90 ' .202 .204 .206 7 80 90 .297 .299 .301 70 So 90 392 394 396 70 80 90 .487 489 .491 70 So 90 .58' 583 585 70 So 90 .676 .678 .680 CHAPTER IX HOW TO USE THE STADIA DIAGRAM Formulas and the Diagram. The diagram for the reduc- tion of stadia notes which accompanies this manual, is pre- pared specifically as a graphic solution at one operation of the approximation formulas: Z) = (r+e) cos 2 ; (27) and h = (r +e) sin a cos a (28) But the diagram may also be used in ascertaining the values of r cos 2 a and r sin a cos a in the correct formulas (Eq. 17) and (18) and for the approximation of (r+1) cos 2 a and (r + 1) sin a cos a in formulas (29) and (30). As the formulas (17) and (18) need only be used for sights to turning points and on surveys requiring more than ordinary precision, it would seem advisable to give preference to reduction tables when- ever such approximation formulas as (27) and (28), or (29) and (30) will not serve. To Use the Diagram: Follow the angle ray which corre- sponds to the angle a of elevation or depression, to its inter- section with the curved line which corresponds to the value (r+e) in formulas (27) and (28). Holding a needle point at the intersection thus determined read off by the aid of the vertical lines the horizontal distance D, that is (r -\-e) cos 2 a. and by the aid of the horizontal lines the difference in eleva- tion h, that is (r+e) sin a cos a. Or make the more convenient determination sufficiently 94 TOPOGRAPHIC STADIA SURVEYING close in all ordinary cases, by entering the diagram with (r+1) instead of (r+e). Whenever the use of the approximation formulse are per- missible, as in the determination of topography, the diagram gives, at once, the distance and the difference in elevation, for any rod-readings and any vertical angles within their scope. Distance should be read to the nearest foot and differ- ence in elevation to the nearest tenth of a foot. When points are located by the intersection of sights from two instrument stations, the horizontal distances from each of these two stations are scaled from the map. The diagram js now entered with each of these distances and needle points are placed at the intersections of these distances with the corresponding angle rays of the measured angles of elevation or depression. If the same difference in elevation is not indicated by both needle points the mean value should be jecorded. The author, early in his experience on topographic surveys, constructed a diagram as here described based on the funda- mental approximation formulse (27) and (28) and has found the same a great convenience, fulfilling every requirement both as to minimizing mental effort, reducing the chance of error and insuring accuracy of results. It eliminates the undesirable features of many of the other diagrams at various times suggested for use, which do not give final results with- out additions or subtractions. The explanatory notes for the use of the diagram are as follows: TOPOGRAPHIC STADIA SURVEYING '95 STADIA DIAGRAM For Instruments rated 1 to 100 Graphical Solution of the Approximation Formulas: D = (r +e) cos 2 f D = (r +1) cos 2 a or \ h = (r +e] sin a cos a [ h = (r+l) sin a cos a Where r = reading on a vertical rod. a = vertical angle. D = horizontal distance. h = difference in elevation. e= instrument constant = the distance of the outside focal point of the object lens from the instrument axis. Directions : Follow the vertical angle ray to the curved line (r-\-e) or (r + 1), as the case may be, and read D on the horizontal scale and h on the vertical scale. NOTE. The diagram can also be used to find the value of r cos 2 a and of r sin a cos a. INDEX Accuracy of stadia surveys 48 Alidade, vertical angles measured with 44 Anallatic point, defined 2 Anderson's stadia reduction table, explanation 63 Approximation formulas for distance and difference in elevation 16 Casgrain, W. T., and A. Noble, publication by, referred to. . 27 Corrections, tables of, for departure of the stadia rod from a true vertical position 49, 50 Corrections, tables of, when sighting point does not bisect the intercept 41, 46 Cross-hairs, adjustable or fixed 1 Departures from ordinary practice in stadia surveying 30 Diagrams for stadia reduction 19, 22, 93 Diagram furnished with manual 22 Diagrammatic solution of stadia formulas 19 Diagram with manual, how to use 22, 93 Error, due to inclined rod 47 Error, when sighting point does not bisect the intercept. ... 44 Feet, conversion into miles, table 91 Focal distance, principal, defined 3 Formula, the stadia 9 Formulas, basic 3 Formulas for inclined sights 12 Formulas for inclined sights, approximation 16 Formulas, modification of, for slide-rule work 24 Formulas, use of 17 Hall, Wm. Hammond, referred to 30 Height of telescope above station plug can be eliminated from notes 35 Inclined sights, approximation formulas 16 Inclined sights, formulas 12 Instrument constant 2, 10 97 98 INDEX PAGE Intercept, defined 2 Lietz, A. Co., referred to . 34 Lietz, A., paper on the Porro telescope 6 Magnetic needle, surveys with use of 28, 37 Magnetic needle, surveys without use of 26 Methods of stadia surveying. 26 Miles, conversion into feet 91 Noble, A., and W. T. Casgrain, publication by, referred to . 27 Porro telescope 5 Porro telescope, described by A. Lietz 6 Rating factor 10 Rating factor, defined 3 Rating factor, determination of 10 Refraction, the effect of 51 Rod reading, defined 2 Rod, special type of 30 Rod, the target 2 Rod, the telemeter or stadia, defined 2 Sighting point, defined 2 Slide-rule as an aid in reducing stadia work 24 Stadia formula. 9 Stadia formulas, diagrammatic solution 19 Stadia field notes 38 Stadia field notes, sample pages : . . 40 Stadia notes, the platting of 52 Stadia reduction diagrams 19, 22, 93 Stadia reduction diagram, special type of, how to use. ... 22, 93 Stadia reduction table, Anderson's, by permission of U. S. Geol. Survey, explanation 63 Stadia reduction table, for readings of 100 feet and instru- ments rated 1 to 100, explanation of 55 Stadia reduction with aid of slide-rule 24 Stadia rod, defined 2 Stadia surveying, methods of 26 Stadia surveying, with use of magnetic needle 28, 37 Stadia surveying, without use of magnetic needle 26 Stadia surveys, accuracy of 48 Stadia surveys, reference to Noble and Casgrain 27 Stadia unit, defined 3 INDEX 99 TABLES 1. Corrections for too large a vertical angle 45 2. Corrections for too small a vertical angle 46 3-4. Corrections for departure of rod from a true vertical. 49, 50 5. Values of e cos a. and e sin a 54 6. Stadia reduction table for a rod reading of 100 ft 55 7. Stadia reduction table, U. S. Geol. Survey (Anderson). 63 8. Conversion of feet into miles 91 Tachymetry, defined 1 Telemeter constant, defined 2 Telemeter, defined 1 Telemeter or instrument constant 10 Telemeter rod 2 Telemeter rod, special type of 30 Telemeter surveys, accuracy of 48 U. S. Geological Survey, reduction table 63 Vertical angles, measured with alidade 44 Von Geldern, Otto, referred to 55 RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (415)642-6233 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW YB 10993