I M "■fS" /f-8 SIS! class i n$4£. Book_ .W4-1— Copyright N° COPYRiGHT DEPOSIT. SURVEYING AND TABLES BY G. A. WENTWORTH Author of a Series of Text-Books in Mathematics SECOND REVISED EDITION BOSTON, U.S.A. GINN & COMPANY, PUBLISHERS CI)e SltbcnaE-ttm ^Jress 1903 THE LIBRARY OF CONGRESS. Two Copies Received OT 16 1903 Copyright Entry CLASS Cc XXc. No. S U- k / 3 COPY B. MATHEMATICAL TEXT-BOOKS BY GEORGE A. WENTWORTH Elementary Arithmetic Practical Arithmetic Mental Arithmetic Primary Arithmetic (Wentworth and Reed) Grammar School Arithmetic Advanced Arithmetic Exercises in Arithmetic (wentworth and Hill) First Steps in Algebra School Algebra New School Algebra Higher Algebra Elements of Algebra Complete Algebra Shorter Course in Algebra College Algebra (Revised Edition) Exercises in Algebra (Wentworth and Hill) First Steps in Geometry (Wentworth and Hill) Plane and Solid Geometry (Revised) Plane Geometry (Revised) Solid Geometry (Revised) Plane and Solid Geometry and Plane Trigonometry (Second Revised Edition) _ * Analytic Geometry ' ' , Logarithms and Metric Measures Geometrical Exercises Syllabus of Geometry Examination Manual in Geometry (Wentworth and Hill) Exercise Manual in Geometry (Wentworth and Hill) Plane Trigonometry (Second Revised Edition) Plane Trigonometry and Tables (Second Revised Edition) Plane and Spherical Trigonometry (Second Revised Edition) Plane and Spherical Trigonometry, and Tables (S0c(jn'd Revised Ed'itior) Plane 'pigpaomptry and Surveying, and Tables /'Second Revised Edition) Surveying and Tables (Second Revised Edition) Plane and Spherical Trigonometry and Surveying, and T§.biis t (Seoo c nd Revised Edition) Plaice ard ,'Sphencal Trigonometry, Surveying, and Navigation (Second Revised Edition) Logarithmic and Trigonometric Tables Seven Tables (Wentworth and Hill) Complete Copyright, 1882, 1895, 1896, 1903, by G. A. WENTWORTH ALL EIGHTS RESERVED l-tQ0g(a PREFACE The object of this work on Surveying is to present the subject in a clear and intelligible way, according to the best methods in actual use, and in so small a compass that students in general will find time to acquire a competent knowledge of this important study. The author is under obligation to G. A. Hill, A.M., of Cambridge, Mass. ; to Professor James L. Patterson, of Chestnut Hill, Pa. ; to Dr. F. N. Cole, of New York, N.Y. ; to Professor S. F. Norris, of Baltimore, Md. ; and to Professor B. F. Yanney, of Alliance, Ohio. Professor Yanney has done most of the work on the second revision, and Miss M. Gertrude Cross, of Boston, has furnished the drawings. G. A. WENTWORTH. Exeter, N.H., 1903. CONTENTS SURVEYING [ The numbers refer to the pages.] CHAPTER I. Field Instruments : Definitions, 1 ; classification, 1 ; operations comprised, 2 ; the sur- veyor's chain, 3; the engineer's chain, 3; accompanying pieces, 4; how to chain, 4 ; special constructions by means of the chain, 5 ; obstacles to chaining, 7 ; the tape, 9 ; the compass, 10 ; kinds of compasses, 11 ; bearing of a line, 12 ; checking bearings, 13 ; obsta- cles, 14 ; measurement of horizontal angles, 14 ; measurement of vertical angles, 15 ; verniers, 15 ; uses of the compass vernier, 17 ; magnetic declination, 19 ; surveyor's transit, 23 ; uses, 24 ; measure- ment of horizontal angles, 26 ; measurement of vertical angles, 26 ; stadia measurements, 26 ; the solar compass, 28 ; to establish a true meridian, 32 ; the Y level, 36 ; the leveling rod, 36 ; substitutes for the Y level, 39 ; the plane table, 40 ; to orient the table, 42 ; to plot' any point, 43 ; to plot a field, 43 ; the three-point problem, 44. CHAPTER II. Office Instruments : Definitions, 46 ; the diagonal scale, 46 ; the circular protractor, 47 ; constructions, 48 ; the planimeter, 49 ; the slide rule, 49. CHAPTER III. Land Surveying: Definitions, 50 ; special methods of surveying, and of computing areas, 51 ; rectangular system of co-ordinates, 52 ; general method for farm surveys, 57 ; field notes, 58 ; computation of the area, 58 ; balancing the work, 60 ; supplying omissions, 61 ; to make a plot, 63 ; modification of the latitude and departure method, 66 ; location surveys, 67 ; illustrative problems, 67 ; laying out the public lands, 71 ; reference lines, 71 ; townships, 71 ; subdivision of townships, 73 ; meander lines, 73. vi CONTENTS CHAPTER IV. Triangulation: Definitions, 74 ; classification, 75 ; measurement of base lines, 75 ; measurement of angles, 76. CHAPTER V. Leveling: Definitions, 77 ; corrections for curvature and refraction, 77 ; dif- ferential leveling, 78 ; single setting of the level,' 78 ; several settings of the level, 79 ; profile leveling, 80 ; field work, 81 ; making the profile, 84 ; topographic leveling, 85 ; drainage surveying, 86 ; field work, 86 ; plot and profile, 86. CHAPTER VI. Railroad Surveying : Laying out the route, 89 ; establishing the roadbed, 89 ; excava- tions, 89 ; embankments, 90 ; curves, 91 ; methods of laying out the curve, 92. CHAPTER VII. City Surveying: ■4 Eield-work instruments, 94 ; streets, 94 ; blocks and lots, 96 ; plots, 96 ; records, 96. SURVEYING CHAPTER I FIELD INSTRUMENTS SECTION I DEFINITIONS Definition. Surveying is the art of determining and repre- senting distances, areas, and the relative position of points on the surface of the earth. Classification. Of surveying there are various kinds, depend- ing upon the extent, the purpose, or the method of the survey. The following are the principal divisions : 1. Plane Surveying, in which the part of the earth's surface surveyed is regarded as a plane ; Geodetic Surveying, in which the true figure of the earth is regarded. 2. Land Surveying, in which boundary lines, contents, and outline maps are the chief things aimed at ; Topographic Sur- veying, in which differences in elevation and contour maps are chiefly sought ; Hydrographic Surveying, in which the purpose is to determine the configuration and topography of the bed or basin of a body of water ; Mine Surveying, in which the posi- tion and extent of underground excavations are determined and graphically represented. 3. Rectangular Surveying, in which a system of perpen- dicular lines is used as reference lines ; Triangular Surveying, which proceeds by means of a system of triangles referred to a well established base line. 1 2 SURVEYING Operations Comprised. Surveying commonly comprises the following three distinct operations : 1. The Field Measurements, or the determining certain lines and angles by direct measurement. 2. The Computation of the required parts from the meas- ured lines and angles. 3. The Plotting, or representing on paper the measured and the computed parts in relative extent and position. Historic Note. Surveying is undoubtedly one of the oldest of the arts of civilized man. The Bible contains several admonitions not to remove " the ancient landmark," as in Proverbs xxii. 28. To the Baby- lonians is credited the division of the circle into 360 degrees. The Egyp- tians were known to survey frequently the valley of the Nile, a necessity owing to the periodic overflow of that river. Thence came Geometry. The Egyptians also possessed rules for finding the area of land of various shapes. Moreover, on Egyptian soil the Greek mathematician Eratosthenes made the first attempt at determining the circumference of the earth by meas- uring an arc of the circumference. This was in 276 b.c. Among the Romans Surveying was considered one of the liberal arts, and received impetus in the time of Julius Caesar from his sweeping order that the entire empire should be surveyed for the purpose of equitable adjustment of taxes, and also from the introduction of the more practical parts of Greek Geometry. The works of Roman surveyors served as models for centuries, and much that we have to-day is only improvements on what has been handed down from them. For a brief account of surveying in the United States, see Cajori's " The Teaching and History of Mathematics in the United States," pp. 92, 286. FIELD INSTRUMENTS 3 SECTION II THE CHAIN Surveyor's Chain. The Surveyor's Chain, or G-unter's Chain as it is often called, is made of iron or steel wire and is 4 rods or 66 feet long, composed of 100 links connected by small rings, and provided with a tally mark at the end of every 10 links. A link as a unit of measure includes a link of the chain and half the rings that connect it with adjoining links. Each link is 7.92 inches long. Since a chain is 4 rods long, a square chain contains 16 square rods, and since an acre contains 160 square rods, a square chain is one-tenth of an acre. A square chain contains also 10,000 square links and, therefore, an acre contains 100,000 square links. Hence, if a given area is expressed in square chains, it is reduced to acres by pointing off the last figure, and, if expressed in square links, it is reduced to acres by pointing off the last five figures. The tally marks are appropriately notched to facilitate counting links from either end, the one at the middle of the chain being rounded so as to be distinguished readily from the others. Handles form part of the end links, to which they are so attached as to prevent twisting and to allow lengthening or shortening of the chain. The Surveyor's Chain is used in measuring land. Engineer's Chain. The Engineer's Chain differs from the ordinary Surveyor's Chain chiefly in that it is 100 feet in length, the length of each link being 1 foot. It is used in surveying railroads and canals, and often in other surveys where extensive lines are to be run. Both the Surveyor's Chain and the Engineer's Chain are generally provided with attachments, so that from the full chains half-chains can be made up, to be used in case of rough or hilly country. 4 SURVEYING Accompanying Pieces. Usually eleven, sometimes ten, Mark- ing pins go with the chain. These are of iron or steel, about 14 inches long, pointed at one end and formed into a ring at the other end. In case eleven pins are used, the first one is placed at the beginning of the line to be measured, and there- after one at the end of each chain. The last pin in the ground is, therefore, not to be counted. In case ten pins are used, the first one is placed at the end of the first chain, and so on, the last pin in the ground being counted. Strips of red cloth should be fastened to the ring ends of the pins so as to make them easily visible. Ranging poles, which are of various lengths, are necessary for alignment. These are commonly made of wood, and are steel shod, graduated to feet, and painted in alternate red and white stripes. How to chain. Ranging poles should be placed, one at each end of the line to be measured, and' at such intermediate points as the necessities of the case require. A head chain- man or leader, and a rear chainman or follower are required. The follower takes one end of the Chain, and one pin, which he thrusts into the ground at the beginning of the line. The leader takes the other end of the chain and the remaining ten pins, and moves forward until the word " Halt " from the fol- lower warns him that he has advanced nearly the. length of the chain. At this signal he stops, and the follower, mean- while having placed his end of the chain against the pin at the beginning of the line, directs the leader by the words " Right" and "Left" until he is exactly in the line. This being accomplished, and' the chain tightly stretched in a hori- zontal position, the follower says, " Down." The leader then puts in a pin at the end. of the chain and answers, "Down" ; after which the follower withdraws the pin at his end of the chain, and the chainmen move forward, repeating the process just described until the end of the line is reached. If the marking pins in the hands of the leader are all placed FIELD INSTRUMENTS 5 before the end. of the line is reached, after putting the last pin in the ground he waits until the follower conies up to him, gives him the ten pins in his hands and records the fact that ten chains have been measured. The measuring then proceeds as before. If the distance from the last pin to the end of the line is less than a chain, the leader places his end of the chain at the end of the line, and the follower stretches tightly such part of the chain as is necessary to reach the last pin, and the number of links is counted. If the ground slopes, one end of the chain must be raised until the horizontal position is attained. By means of a plumb line or a slender staff or, less accurately, in case of the leader by dropping a pin (heavy end downwards), the point vertically under the raised end of the chain may be determined. If the slope is considerable, half a chain or less may be used ; in which case care must be taken that the correct number of full chains and links is found. For instance, if a tally shows 15 half chains and 35 links, the appropriate measure is 7 chains and 85 links, or, as it is usually expressed, 7.85 chains. Special Constructions by Means of the Chain. 1. At a given point in a given line to construct a perpendicular to that line. Let LE (Fig. 1) be the given line, and P the given point. On LE measure off PB = PA = 20 links. Then place one end of the chain at B and the other end at A. Stretch the chain from the middle point, and mark that point, as C. PC is the perpendicular required. (Why ?) Or, make PB = 30 links. Place one E A P B end of the chain at P, and the end of ' Fig. l the 90th link at B. Then, taking the chain at the end of the 40th link from P and stretching both portions tightly, mark that point, as C. Then PC is the perpendicular required. (Why ?) 6 SURVEYING 2. Through a given point without a given line to construct a perpendicular to that line. Let LE (Fig. 1) be the given line, and C the given point. Take any point as B in the line and stretch the chain between C and B ; then swing the chain about C until the point at B is again in the line, as at A. Measure the distance between A and B. Then P, the mid-point of AB, is a second point in the required perpendicular. (Why ?) Or, let the middle of the part of the chain between C and B be held in place, and swing the end at C until it meets the line as at P. PC is the required perpendicular. (Why?) 3. At a given point in a given line to construct an angle equal to a given angle. Let P (Fig. 2) be the given point in the given line LE, and angle A the given angle. Make PD = AB. At D and B, respectively, construct perpendiculars DF and BC. Make DO = BC. Then angle OPD is the angle required. (Why ?) 4. To construct any given angle, as 25° 40'. Find from the tables the tangent of 25° 40', which is 0.4806. Lay off PD (Fig. 2) =100 links. Construct the perpendicular DF and lay off DO = 48.06 links. Then angle OPD is the angle required. (Why ?) 5. Through a given point to construct a line parallel to a given line. Let P (Fig. 3) represent the given point, and LE the given line. Through P lay out any convenient line as BA FIELD INSTRUMENTS 7 intersecting LE. Construct angle BPB = angle PAE. Then the line CD is the required line. (Why ?) E A IT D E Fig. 3 Obstacles to chaining. In general practice various obstacles are encountered in chaining. The circumstances in each case must decide the best method to be used. Only a few sugges- tive cases can be considered in this work. 1. To measure a line when a building, or other object, stands in the way. In Pig. 4 construct the perpendicular AB, the per- -^— pendicular BC, the perpen- dicular CD = AB, then the perpendicular DE, which fig. 4 will be in line LA prolonged. Then, LA + BC + DE = LE. (Why ?) As a check, another series of perpendiculars may be constructed. 2. To measure across a body of water. At A (Fig, 5) lay out AP, making angle ^£ = 60°. This can be done by laying out the equilateral tri- angle ABB. At P range out PC, mak- ing angle APC = 60°. Then measure AP. 8 SURVEYING The line AC is equal to AP. (Why ?) If C is some fixed point in LE, across the stream, accessible or inaccessible, we may proceed as follows : After laying out AP, as already described, with 90 links of the chain stretched in the form of an equilateral triangle, and with one side of this triangle in AP, move the triangle until the point C is in line with the forward side of the triangle. Then proceed as before. 3. To measure a line the end of which is invisible from the beginning, and the intermediate points are unknown. C l d; e B ~~^~-J L R Let LE (Fig. 6) represent the line. Lay out the line LR so that; R shall be beyond E and visible from L. Construct from E the perpendicular EA to LR. Measure LA and AE. LE can then be computed. (How ?) If intermediate points on LE are to be sought, take any point in LA, as B ; construct BC perpendicular to LA ; then measure off BD of such length that BD : AE = LB : LA The line LR is called a random T e line. 4. To measure the dis- tance between two inaccessi- ble points. Let L and E (Fig. 7) be two inaccessible points. Select some point as P from which both L and E are ,' visible. Measure PL and PE by the method in 2. Eange E' FIELD INSTRUMENTS 9 out PL' in line with LP and equal to L,P ; similarly, RE' = ER. Then measure L'E', which is equal to LE. (Why?) EXERCISE I 1. Range out a line which, by estimation, is more than 10 chains long. Then measure it with the chain out and back. 2. Prolong a line beyond a building, or other obstacle which prevents continuous alignment. 3. Find the distance from a point to a line when the dis- tance is more than a chain. 4. Lay out a square field each side of which shall be 5.76 chains long. 5. Find the length of a line by means of a random line. Then, as a check, find its length by direct measurement. SECTION III THE TAPE Kinds of Tape. The tape measure used by the surveyor or engineer consists of a thin ribbon of steel, or of linen with interwoven wires of brass, wound upon a reel, often in a leather or metal case. Tapes vary in length from 25 feet to 500 feet or more. They are variously graduated to links, to feet and inches, to feet and tenths of a foot, to metric units, or to a combination of these. A common combination is feet and tenths of a foot on one side, and links on the reverse side. Uses. The kind of tape determines to a great extent the use to which it is to be put. If 33 feet or 66 feet long and graduated to links, the evident purpose is for land survey- ing. If 50 feet or 100 feet long and graduated to feet and 10 SURVEYING tenths of a foot, the tape is especially designed for city work. Other kinds are employed in bridge, road, or mining work, in very accurate measurements of base lines, or as standards of comparison for other instruments of measurement. SECTION IV THE COMPASS Parts and their Uses. The essentials of the compass, one style of which is shown in Fig. 8, are : the compass circle, graduated to half degrees and figured from 0° to 90° each way Fig. 8. The Surveyor's Compass Note. The letters E and AV on the face of the compass are reversed from their true positions. The reason for this is that if the sights are turned towards the west, the north end of the needle is turned towards the letter W, and if the north end of the needle is turned towards E, the sights are turned towards .the east. If the north end of the needle points exactly towards E or W, the sights range east or west. FIELD INSTRUMENTS 11 from the north and south points, for indicating the directions of lines ; the magnetic needle, pivoted on a pin at the centre of the compass circle, for showing the direction of the mag- netic meridian ; and the sight standards, attached to the ends of the main plate, for alignment. To the main plate are attached two spirit levels at right angles to each other for leveling the instrument; underneath is a needle-lifting screw which, by actuating a concealed spring, lifts the needle from the pivot and presses it against the glass covering of the compass circle when the instrument is not in use ; a tangent screw, and almost directly under it a clamp screw, which operates the vernier; and a small dial plate for keeping tally in chaining. The north end of the needle usually has some ornamentation to distinguish it from the south end, and a coil of fine wire is wound on the south end to prevent the needle from dipping. The sight standards have fine slits nearly their whole length, with circular openings at intervals to facilitate sighting upon an object ; on the edges of the north standard are tangent scales for reading vertical angles, and on the outside of the south standard are two eyepieces at the same distance from the main plate as the zeros of the tangent scales, respectively. The telescopic sight is an attachment to the south standard, now often used. The instrument entire turns horizontally upon the upper end of a ball spindle, the lower end of which rests in a spherical socket in the top of a Jacob's staff, or a tripod, which supports the instrument. The socket of the compass which fits to the ball spindle is provided with a clamp screw and a spring catch. From the centre of the plate at the top of the tripod a plummet is suspended by which the centre of the compass can be placed directly over a definite point on the ground. Kinds of Compasses. The compass described is the vernier compass, or surveyor's compass, and is the one in general use. If there is no vernier attachment, the compass is called a plain 12 SURVEYING compass and is used in running new lines and the preparation of maps. A railroad compass has all the features of the vernier compass, and has also a vernier plate and graduated limb for measuring horizontal angles. Hints on the Use and Care of Instruments. The instruments described in this work are adjusted by the maker. If they should require readjustment, full directions will be found in the manual furnished with the instruments. Before begin- ning to use any instrument, make a thorough study of its various parts and their uses. In moving or adjusting any part always know what you are doing and why you are doing it. When an instrument is not in use keep it in a place that is free from moisture and dust. Bearing of a Line. The magnetic meridian of a place is the direction which a bar magnet assumes when freely supported in • a horizontal position. The magnetic bearing of a line is the angle it makes with the magnetic merid- ian. To take the bearing of a line proceed as fol- lows : Place the compass so that the Jacob's staff, or plummet of the tripod, is directly over one end of the line, and level by press- ing with the hands on the main plate until the bub- bles are brought to the centres of the spirit levels. Turn the south end of the instrument toward you, and sight at the ranging pole at the other end of the line. Read the bearing from the north end of the needle. First, write N. or S. according as the north end of the needle is nearer N. or S. Fig. 9 FIELD INSTRUMENTS 13 of the compass circle ; secondly, write the number of degrees between the north end of the needle and the nearest zero mark ; thirdly, write E. or W. according as the north end of the needle is nearer E. or W. of the compass circle. Thus, in Fig. 9 (a), the bearing is K 45° W. ; (b), N. 60° E. ; (c), S. 60° W. ; (d), S. 45° E. If the needle coincides with the N.S. or E.W. line, the bearing is N., S., E., or W. according as the north end of the needle is over N., S., E., or W. As the compass circle is divided into half degrees, the bearing may be determined pretty accurately to quarter degrees. It will be noticed that the letters E and W on the face of the compass are reversed from their true positions. These are so placed in order that when the sights are turned towards the west the north end of the needle will point towards the letter W, or if the sights are turned towards the east, the north end of the needle will point towards the letter E. It turns out that if the south sight standard is always turned towards the observer, the reading at the north end of the needle will indicate the true bearing of the line. Should the north sight standard be turned towards the observer, the read- ing at the south end of the needle would then be taken. Checking Bearings. When the bearing of a line has been taken, the instrument should be removed to the other end of the line and the reverse bearing taken. The number of degrees should be the same, but the letters should be reversed. Eor instance, if the direct bearing is N. 35§° W., the reverse bearing should be S. 35f° E. In case the reverse bearing is not what it ought to be, there is some mistake, or some local disturbance, or both. To detect errors a second trial at the direct bearing should be taken. To detect local disturbances take the direct and reverse bearings of other lines ranged out from the beginning of the line whose bearing is sought. If they all show the same difference between their two respective bearings, the evidence of some local disturbance, as iron, 14 SURVEYING iron ore, etc., is pretty conclusive. In this case the true bear- ing of the line can be obtained by making the necessary cor- rection. In all cases, precautions should be taken to have the chain, pins, and other instruments that would affect the direc- tion of the needle sufficiently removed from the compass. Obstacles. When a fence or other obstruction interferes with placing the instrument over the line the instrument may be placed at one side, the ranging pole being correspondingly placed at the other end. If one end of the line cannot be seen from the other end, run a random line. Then (Fig. 6, p. 8) tan EL A = AE -s- LA, whence the angle EL A can be found. This angle combined with the bearing of the random line will give the bearing required. Or some point can be selected from which the ends of the line are visible. The distances to the ends may be measured, and the angle between the two auxiliary lines may also be measured: - Of the triangle thus formed, the angle at the beginning of the given line may be computed, and, when properly combined with the bearing of the first auxiliary line, will give the required bearing. If a single triangle is not sufficient, a series of triangles may be employed until the end of the line is reached. Measurement of Horizontal Angles. To measure a horizontal angle by means of the needle, place the compass over the vertex of the angle, take the bearing of each line separately, and combine these bearings according to the following rules, as suggested by Fig. 10 : 1. If the first letters of the bearings are alike, and also the last letters, find the difference of the bearings. 2. If the first letters are alike, and the last letters unlike, add the bearings. 3. If the first letters are unlike, and the last also unlike, subtract the difference of. the bearings from 180°. 4. If the first letters are unlike, and the last alike, subtract the sum of the bearings from 180°. FIELD INSTRUMENTS 15 Measurement of Vertical Angles. A vertical angle is an angle the sides of which are in a vertical plane. If one side of a vertical angle is horizontal and the other ascends, the angle is called an angle of elevation; if one side is horizontal and the other descends, the angle is called an angle of depres- sion. To measure an angle of elevation by means of the com- pass, sight through the lower eyepiece to a point that is as far above the point whose elevation is sought as the instru- ment is above the point from which the elevation is to be taken. Read off the degrees of the right-hand tangent scale, marked by a card placed squarely across the face of the south standard, the top of the card being in the line of sight. To measure an angle of depression, proceed in the same manner, using the upper eyepiece and the left-hand tangent scale. If the compass is provided with a telescopic sight that has a vertical circle attachment, these should be used instead of the eyepieces and tangent scales. Verniers. A vernier is a contrivance for measuring portions smaller than those into which a line is divided. We shall describe two kinds. Let AB (Fig. 11) be a portion of a line graduated to tenths and hundredths of a foot. VR is the vernier. In (a), nine parts of the line are divided into ten equal parts on the vernier. Hence, a division on the vernier is less than a division on the line by the difference between T i^ of a foot and ^o of T ^ of a foot, or T oV o °^ a f°°t- Now, if the vernier 16 SURVEYING is moved so that 1 of the vernier coincides with 1 of the scale, it has moved over a space equal to T J fT of a foot. If the vernier is moved so that 2 of the vernier coincides with 2 of the scale, it has moved over a space equal to tv %q of a foot ; and so on. In (5), 6 of the vernier coincides with 9 of the scale, which indicates that the zero of the vernier has moved past 3 of the scale a space equal to T q% „ of a foot. The reading, then, is (a) I en ^a ^t- g$ o CiCpfsca^^^^N ^a3Ntoio -4t I II I ! II \R T~1~M , gj 3j •*-* C» B ( c > yi mi -* to 00 I I . I I I \ B Ci Cot^COU^-y-f^©**-! A V J V^ »* <£> 00 N U I i i 1 1 1 1 1 II B (d)\ CiC0>J,«O»OH 1 1 - <0 U5 4 if tne vernier is moved so that 1 of the vernier coincides with 10 FIELD INSTRUMENTS 17 of the scale, i.e., the end of the 6th tenth, the vernier has moved over a space equal to j^q o °^ a foot- ^ the vernier is so moved that 2 of the vernier coincides with 9 of the scale, the vernier has moved over a space equal to t -£qq of a foot ; and so on. In (d), 6 of the vernier coincides with 7 of the scale, which in- dicates that the zero of the vernier has moved past 3 of the scale a space equal to T ^ f of a foot. The reading here is 0.636 foot. - This form of the vernier is known as the retrograde form, since the figuring on the vernier proceeds in the opposite direc- tion from that on the scale. In either form the following rule for using and reading the vernier may be adopted : Move the vernier tintil its zero line, or index, is at the point to which the required measurement is to be taken; read the main scale to the nearest division below the index, and that number of the division line of the vernier which stands opposite a line of the main scale. Fig. 12 Compass Vernier and its Uses. Let LL' (Fig. 12) repre- sent the limb of the compass graduated to half degrees, and VV the vernier divided into thirty equal spaces, equal to twenty -nine spaces of the limb. Then, one space of the vernier is less than one space of the limb by l'(=30' — J^ of 29x30'), and the reading may be obtained to single minutes. 18 SURVEYING In Fig. 12 the index, or zero, of the vernier stands between 32° and 32° 30', and the line of the vernier marked 9 coincides with a line of the limb. Hence, the reading is 32° 9'. When the index moves from the zero line of the limb in a direction opposite to that in which run the numbers of the limb, the number of minutes obtained as above must be sub- tracted from 30' to obtain the minutes required. (Why ?) If, however, the vernier is made double, that is, if it has thirty spaces on each side of the zero line, it is always read directly. The usual form of the double vernier, shown in Fig. 13, has Fig. 13 only fifteen spaces on each side of the zero line. When the vernier is turned to the right less than 15' past a division line of the limb, read the lower figures on the left of the zero line at any coincidence ; if moved more than 15' past a division line of the limb, read the upper figures on the right of the zero line at any coincidence ; and vice versa. In this form of the double vernier it will be observed that the spaces on the vernier are larger than those on the limb, since the 30 equal spaces of the former are equal to 31 half-degree spaces of the latter. FIELD INSTRUMENTS 19 The most important use of the vernier compass is in setting off the variation of the needle explained just below. If the variation of the needle at any place is known, by means of the vernier screw the compass circle may be turned through an arc equal to the variation. If the observer stands at the south end of the instrument, the vernier is turned to the right or left according as the variation is west or east. The compass now gives the bearings of the lines with the time meridian. In order to retrace the lines of an old survey, turn the sights in the direction of a known line and move the vernier until the needle indicates the old bearing. If no line is defi- nitely known, the change of variation from the time of the old survey will give the arc to be set off. Magnetic Declination. The magnetic declination, or varia- tion of the needle, at any place is the angle which the magnetic meridian makes with the true meridian, or north and south line. The variation is east or ivest, according as the north end of the needle lies east or west of the true meridian. Western variation is indicated by the sign +, and eastern by the sign — . The kinds of magnetic declination are put under three heads : 1. Irregular variations, which are sudden deflections of the needle due to magnetic storms or other causes not well understood. 2. Solar-diurnal variations, which in northern latitudes reach their farthest point east about 8 o'clock a.m., and their farthest point west about 2 o'clock p.m., varying from 5' in the winter in some localities to 20' in the summer in other localities. 3. Secular variation, which is a change in the same direction for a period of years, then in the opposite direction for about the same time. It is not accurately known how long it takes a complete secular variation to run its course, but from data already obtained it seems probable that the period of time covered is not less than two and a half or three centuries. 20 SURVEYING ■w »OlN050(NT|l!ONlOQOH!flOO«(NO(0>0»t-H«) ' I— O i-H © © H OdrJrtNNHHOWfNMNN^MMHMmijiidN ! i-i C00'*0>iO<#'*HHO)NNO>O^OOt»00 " r.l o a n in ■* CM i-l i-H i-H i-l .MNt-NOONHiO^CSNOl'^NiOCOtD^IN'XI . i— 1 i— 1 i— 1 r-l i— 1 i— It— ii— li— i » (Mfflr- 1 00 Tt< CO OS CM ■— l INOJiO f~ CO •># (NCOOOlN g t»a©iOOffi01ffiiOlO«lOHffiMHO'*iO!C3!lOiONM'0'-iNMi-i JlNHilr-riHHHHH i-l i-H i-H i-l '*!ociiid'*(NidMH^iM 2 (N I-H t-H r-( r-l i-l l-l i-H ^H r-l i-Hr-l i-H £ OS © OS eo CO CO ffl»Ot> ^iHXCWO © r- i— i (M ■* -* t- g ONOJOfMOCOOOt-aWNXOiffflffiCONXHOlTtlN^iOXH ^©^uirt^indddd^NdxNxdocoTiir-iTiiNi-iMsidNfN Ql— ll— ll— li— ll— ll— li— ll— li— I i-H 1—1 d> 'H « U3 ri a ■* OS LO O t- i— I CO © CO CM OX ©OOIM C05qHNC0M Mx'dc6dddddc6xdoxNdt^io''*(No:dc6iHdoiridrtH IB i-H i—l i-H i-H i-H I ffl ' S CO CO r^ i— l CO CO CM i-*C0 rjH iO CO CM ©H . £ ^XH(M^ci5t-01MI>u3 0NMCBO<0,T)IHTji(NNXiMXM«0'* M^^'«x'dxN^cidididNdNd^coi-iNd«ddddi-id . C0 1-1 1—1 1-1 1—1 II Q ' ' S OOOCOO •* tH tH t- CM . £ a«aiNiotoaHHiiHi>iNt-oioM«5XH!No;©HOHHN cJ'Aoo©i^a6^cDi^cMcd^^^^a6o'^cM©©©'©cM© . M©OOOOOHHHHISIMWMCi5M'*'*iOiOO®OtC«ONNMa q COCOcor-t-f-r-r-^l^t-t^r^t^lr-t-l.^r^r^r^t-t-r^r^t-t-C^r^r— - ©-^oooo©^cMcoco©©cococo©©co©i^cocor~cocococor--iocs i-i TtliOTti©C0©(MCNTtl»O^tli— lcM-*00"*-'#00-<*iiO>OCMi-ii— i i— l >J3 © iO CO (=1 5PrH-*T(((jqoi5CO(NOsr-©CO»0'NCC' q T^^rt*J4 ^§1 ° «--^"£ 5 a 3 £ c^PQ -^S rt * £ £ aO o „ O a 03 ©a CD • • • Q . . aPn>- OJ 03 " 2 3 'S OPiO a, 5 sh =5 a &d a O B fj fl h a c« .-i xj ^= 11,3 ha. J2 b» 1 *Ti(MKlr»r^OrHQOOOiOHCOOHCO « CM 00 CC CM CO IM ■* M -^^^T^iOTti^^CNTfi-^icyciCOCOcCNi— iOOO + !zi O 3 > — — T. =: — y. s 00 - — -r X C: ~1 — X CD 60 CD 3 lO C CM CO lO ^ N « 00 O C CO H H to a O) O CO O © G CO O H O «0 N i- 1 O05^OCMCMrH(MrHHMrtT)iC0C0^«OCMffi»N0000C000CMOt- i i ii i i i i i i i 7 i i i i 777777 CD it - C» JO (M lO >0 CO ■* CM O O OS i— 1 COrt CD CO "* Cv CO CSHOCO© OOO^OCJNLOOJO^CSiOceOCMCBCOClUOiOOOCOOOOlMCMiOCO OC0C0rHCMCMOrHHr4^IM^00'*«3l0iOaNCRC0CO'*CO00CMOt- 1 1 111111111111111777^77 CO & Q CD 60 lO OS 01 CO CM r-- CO -ti O CO CO -* CM -# OS COCOCOOOO"MCCCMQOtHC» ■*^(C5O>OiOCM(10MNrt>OMiO'*»iO'*OrHCMM^i0i0MCM>0CO ONCMCMHCOOOCMCN'OCOi.OTtiU]iOCOOOCOO'MO'*OOOCNCDN 1 1 1 iiiiiiiiii7i7M777 c j"77 CO CO O t~ ?. LO 00 -t N O lO LOCO CM-^t^-^OO-^HlOT-H O t-CSIOlMMXOCOi-OTllcOCOCOt-ONCONCCO'^NrHrH^CMMrH'ctt HHHCOO^OOOO'^'O'litOiOCOCS^NOOOHOOiOCOCOHCON 1 1 IIM ' Ml I'l'llllllll V - 03COCO CBM't^lH CO Ir~ O CO O) t- CM OrH»0)COOOOiOO)0'*'*N ■OHIO ■ -COr-CM • -co •■*© coo'd^dcdcNH^iodLO i>'co • r-^ cd ad ' 'cmoo " *cm" ■ 10 cd 1 1 1 1 1 .1 1 1 1 1 1 1 : 1 1 1 : 1777 : 17, ."77 CO So -4.05 '-■6.39 -4.7 -1.4 -6.86 -2.84 -1.1 -4.99 -5.0 -6.7 -7.50 -6.1 -6.71 -7.96 -12.6 -9.8 -11.79 -14.54 -16.0 CD So 50 -4.55 -6.46 -1.8 -3.1 -0.5 -4.89 -6.84 -5.81 -7.12 -10.69 -13.6 -15.1 -a a a 3 ft c oi CD - OHiaiOCM»COOiOM»'*Ot-M«OiOCD^NCO'*XO'#^OI^* ■0000-*-*OCMCMi— i-liiOr- 1 CO »£> O O 1— iO-^O-^CMOOt— icMCMCM C:OOHHrHCOT)('*©COCONNNOOOOCM'*inNWiOHNfMCMTl< l^XXXXCCCCCC»CO»CX3CCCX)XCCO;0102ffl©05050>HHCMCMCM q NCOaiOOCOHOCCLOOOOHO^CMOOOCOCCCONNlOCOCMCOCOCO iiOJOOMCONWOOOiiOliOO^ttJCOitHrtHOJ^-liiiCO^M CMOCMCMHiJNOOWCDHOHMOCJCOCOCJHOttOOCMt^t-O CO^^CO^C^l-rtl^CO^CO^COTt<-*COCMCO-^ICM-^C0cMCO-*C0-^C0-* J Charleston, S.C. . Pittsburg, Pa. . Erie, Pa Savannah, Ga. . . Cleveland, 0. . . Key West, Fla. Detroit, Mich. . . Sault Ste. Marie, Mich Cincinnati, 0. . Grand Haven, Mich. Nashville, Tenn. . Michigan City, Ind. Pensacola, Fla. . . Chicago, 111. . . . Milwaukee, Wis. . Mobile, Ala. . . New Orleans, La. . St. Louis, Mo. . . Duluth, Minn. . . Galveston, Tex. Omaha, Neb. . . . Austin, Tex. . . San Antonio, Tex. Denver, Col. Salt Lake City, Utah San Diego, Cal. Seattle, Wash. . . San Francisco, Cal. C. Mendocino, Cal. 22 SURVEYING The agonic line, or line of no variation, is a line joining those places at which the magnetic meridian coincides with the true meridian. At the beginning of the present century this line crossed the United States in an irregular way from Michigan to South Carolina. It is gradually moving west- ward, so that the variation is increasing at places east of this line, and decreasing at places west of the line. East of this line the variation is westerly, and west of this line the varia- tion is easterly. Lines that join places of equal magnetic declination are called isogonic lines. Table of Magnetic Declination. On pp. 20, 21 will be found a table showing the variation in magnetic declination at different places in the United States and contiguous territory during the nineteenth century ; also the annual change for the epoch of 1900. EXERCISE H 1. Lay out a field of five sides and take the bearings and measures of the sides in order, beginning at the most westerly point and going about the field clockwise. 2. From the bearings obtained in Example 1 find the value of each of the interior angles. What is their sum ? 3. Lay out the field the bearings and distances of whose sides are given in Example 1 of Exercise VI, p. 64. 4. Eange out a line whose bearing is N. 38° 30' W., and at some point in this line range out another line making a right angle with it. What is the bearing of the second line ? 5. Set up the compass at a spot near which there is known to be some local disturbance, as iron in a building, or an iron fence, and find the variation of the needle due to such disturbance. FIELD INSTKUMENTS 23 SECTION V THE TRANSIT Surveyor's Transit. The transit is the most important instrument used in surveying. There are many modifications of it, each adapted to its own particular use. All, however, have about the same essential features. The one described here, and shown in Fig. 14, is the surveyor's transit, the one of most general use. The essential parts are the telescope with its axis and two standards, the circular plates with their attachments, the sockets upon which the plates revolve, the leveling head, and the tripod. Within the telescope are two fine cross wires, at right angles to each other, whose intersection determines the optical axis, or line of collimation, of the tele- scope. Under the telescope, and attached to it, is a spirit level by which horizontal lines may be run, or the difference of level between two stations be found. The axis of the tele- scope carries a vertical circle which measures vertical angles to single minutes by means of a vernier. The vernier plate, which carries the telescope and also the compass circle, has two verniers diametrically opposite to each other, and it moves entirely around the graduated limb of the main plate. The sockets are compound ; the interior spindle attached to the vernier plate turning in the exterior socket, when an angle is taken on the limb, but when the plates are clamped together the exterior socket itself, and with it the whole instrument, revolves in the socket of the leveling head. The transit is leveled by four leveling screws which pass through a plate firmly fastened to the ball spindle and rest in small sockets, these resting in turn on the upper side of the tripod plate. On the underside of this lower or tripod plate is an arrange- ment called a shifting centre, which enables the surveyor to change the position of the vertical axis horizontally without 24 SURVEYING moving the tripod ; besides this there is, if specially ordered, a device called a quick-leveling attachment to bring the transit quickly to an approximately level position by the pressure of the hands after which the leveling screws are used. Uses. The transit may be used for all the purposes for which the compass may be used, but with much greater precision. The principal use, however, is in measuring hori- zontal angles by means of the graduated limb and verniers. It may be used, furthermore, in obtaining differences of level ; also, provided there is the attachment to the telescope known as the stadia, in measuring distances, especially over broken ground. A still further use, when the transit is supplied with what is known as a gradienter attachment, is in fixing grades as well as measuring distances. Getting the Transit Ready. The instrument should be set up so as to be firm, the tripod legs- being pressed into the ground until the plates are as nearly level as can conveniently be done by this means. For the subsequent leveling turn the instrument until the spirit levels on the vernier plate are parallel to the vertical planes passing through opposite pairs of the leveling screws. Take hold of opposite screw heads with the thumb and forefinger of each hand, and turn both thumbs in or out as is necessary to bring the bubble to its proper place, the left thumb always moving in the direction that the bubble is to move. For precise work, in addition to leveling by the leveling screws, it is advisable to level the plates by the telescope level, as this is much more sensitive than the levels on the plate. • In this operation the position of the level on the telescope must be observed over both sets of leveling screws, one half the correction being made by the axis tangent screw, the other half by the leveling screws. Before an observation is made with the telescope, the eye- piece should be focused by its pinion until the cross wires appear distinct ; the object glass is then focused by its pinion FIELD INSTRUMENTS 25 Fig. 14. The Surveyor's Transit 26 SURVEYING until the object to be observed appears well defined. This latter process must be repeated when the distance to the object is changed. Measurement of Horizontal Angles. Place the instrument directly over the vertex of the angle, and level. Set the limb at zero by the tangent screw of the plates, and turn the telescope in the direction of one of the sides of the angle, directing it to the object by the tangent screw of the leveling head. Then unclamp the main plate and turn the telescope until it is in the direction' of the other side of the angle, and read the angle by the verniers. The object of the two verniers. on the vernier plate is to correct any mistakes that might arise from the want either of exact coincidence in the centres of the verniers and the limb or of exact graduations on the limb. The correct reading may be obtained by adding to the reading of one vernier the supplement of the reading of the other, and taking half their sum. Measurement of Vertical Angles. Direct the telescope to the object ; clamp, and read the angle indicated on the vertical circle by the vernier. The angle read will be an angle of elevation or depression as the case may be, the horizontal line being the line of collimation of the telescope when in a hori- zontal position. Stadia Measurements. As already stated on page 24, the stadia is an attachment to the telescope used in measuring distances, especially over rough ground. It consists essen- tially of two horizontal wires fastened to small movable slides, and so adjusted as. to include a given space, say one foot on a rod 100 feet distant. These wires will then include, two feet on a rod 200 feet away, or a half-foot at a distance of 50 feet, and so on. Usually the instrument is so adjusted that the zero of the indicated distance is in front of the centre of the instrument; hence, the true distance is the indicated distance plus the distance of this zero from FIELD INSTRUMENTS 27 the centre of the instrument. This latter distance is deter- mined for each instrument by the maker, and noted on a card placed on the inside of the instrument box. It is known as the constant of the instrument. The readings are taken on a rod, specially designed for the purpose, known as the stadia rod. This is graduated to feet, and tenths and hundredths of a foot. Any ordinary leveling rod, if similarly graduated, will answer the same purpose. Obviously in taking stadia meas- urements the rod must always be held at right angles to the line of sight. This statement has special reference to measurements taken up or down hill-slopes. In this case, if horizontal distance is required, the measured distance must be multiplied by the cosine of the angle of elevation or depression. (Why ?) EXERCISE m 1. By means of the transit, measure the interior angles of the field of Example 1, Exercise II, p. 22, and compare with the results obtained in Example 2 of the same exercise. 2. Lay out the entire angular magnitude about some point into four or more angles, and measure each one of them. What should the sum of them equal ? 3. If the constant of a transit adjusted to one foot 100 feet away is 3.8 inches, what is the true length of a line when the indication on the rod is 2.35 feet ? 4. Measure a line by the stadia, and compare with measure- ments taken by the chain and also by the tape. 5. Compute the height of a tall object, as a tree or steeple, by first measuring its distance from some convenient point and measuring the angle of elevation at that point. 6. Lay out a square field containing just one acre. 28 SURVEYING SECTION VI THE SOLAR COMPASS Description and Uses. A full description of the solar com- pass, or Burt's solar compass, as it is often called from its inventor, with its principles, adjustments and uses, forms the subject of a considerable volume, which should be in the hands of the surveyor who uses this instrument. The limits of our space will allow only a brief reference to its principal features. Fig. 15 exhibits the instrument by itself; Fig. 16, p. 31, is a graphical illustration of the solar apparatus as an attachment to the transit, the circles shown being intended to represent those supposed to be drawn upon the concave surface of the heavens. The form of the solar compass shown in Fig. 15 has the arrangement of its sockets and plates -similar to that of the transit, the standards similar to those of the compass, the solar apparatus being placed on the upper vernier plate and taking the place of the needle, for which it operates as a substitute in the field. The solar compass consists mainly of three arcs of circles, a the latitude arc, by which is set off the latitude of the place, b the declination arc, by which is set off the declination of the sun, and c the hour arc, by which is set off the hour of the day. The arm h is movable about a point at the extremity of the piece containing the declination arc, there being at each end a solar lens having its focus on a silvered plate on the other end. The arc of the declination limb turns on an axis, and one or the other solar lens is used, according as the sun is north or south of the equator. Fig. 15 shows the position of the decli- nation arc when the sun is south; Fig. 16, when it is north. The needle box is moved about its centre by a slow-motion screw. It contains a magnetic needle, and is furnished with a graduated arc about 36° in extent. FIELD INSTRUMENTS 29 Fig. 15. Burt's Solar Compass FIELD INSTRUMENTS 31 Fig. 16. Transit with Solak Attachment The circles shown in the cut are intended to represent in miniature circles supposed to be drawn upon the concave surface of the heavens. 32 SURVEYING The solar compass may be used for most of the purposes of a compass or transit. Its most important use, however, is to run north and south lines, especially in laying out the public lands. It may be used also in determining the latitude of a place. To establish a True Meridian. Set off on the latitude arc the latitude of the place. Set off on the declination arc the declination of the sun, corrected for refraction. Set the instrument over the station ; level, and turn the sights in a north and south direction by the needle. The surveyor then turns the solar lens to the sun, and with one hand on the instrument and the other on the revolving arm, moves both from side to side until the sun's image is made to appear on the silvered plate, precisely between the equatorial lines. The line of sights then indicates the true meridian. The bearing of any line from the meridian may be read by the verniers of the horizontal limb. • ^When a due east and west line is to be run, these verniers are set at 90°, and the sun's image is kept between the lines as before. Other Methods. By North Star at Culmination. The North Star, or Polaris, at present revolves about the north pole of the heavens at the distance of about li° ; hence, it is on the meridian twice in 23 h. 56 m. 4 s. (a sidereal day), once above the pole, called the upper culmination, and 11 h. 58 m. 2 s. later below the pole, called the lower culmination. The time of the upper culmination of Polaris may be found by means of the star Mizar, the middle one of the three stars in the handle of the Dipper (in the constellation of the Great Bear). It crosses the meridian at nearly the same time as Polaris. Suspend a plumb line, placing the bob in a pail of water to lessen its vibrations. South of the plumb line, upon a horizontal board firmly supported, place a compass sight, or any upright with a small, opening or slit, fastened to a board a few inches square. At night, when Mizar by estimation approaches the meridian, place the compass sight in line with FIELD INSTRUMENTS 33 Cassiopeiae Polaris Polaris and the plumb line, and move it so as to keep it in this line until the plumb line falls also on Mizar (Fig. 17). Note the time ; then (1903) 3 m. 39 s. later Polaris will be on the meridian. If then Polaris, the plumb line and the com- pass sight are brought into line, the plumb line and compass sight will give two points in the meridian ; or if the telescope of the transit is brought to bear on Polaris, and a light is held near to make the wires visible if necessary, the telescope will then lie in the plane of the meridian, which may be marked by bringing the telescope to a horizontal position. For each year subsequent to 1903 add 21 s. to 3 m. 39 s. If the lower culmina- tion takes place at night, the time may be found in a similar manner. When Mizar cannot conveniently be used, 8 Cassiopeiae (Fig. 17) may be employed, the method being the same as in the case of Mizar. The interval, however (1903), is 4 m. 24 s. and the annual increase of the interval '•■'■■ ■<■ about 20 s. By North Star at Greatest 'Elongation. When Polaris is at its greatest apparent angular distance east or west of the pole, it is said to be at greatest elongation. It attains its greatest eastern elongation and western elongation, respectively, 5 h. 59 m. 1 s. after lower and upper culmination. The azimuth of a star is the angle which the meridian plane makes with the vertical circle passing through the star and the zenith of the observer. If now we know the time of either extreme elongation and also the azimuth of Polaris at an extreme elongation, we can from these data establish a true meridian. The latter of these Pole Great Bear Fig. 17 34 SURVEYING data is given for various latitudes and for years to come in tables, to which the surveyor is supposed to have access. To obtain a line in the direction of Polaris at greatest elongation, we may proceed as follows : A few minutes before the time of greatest elongation, place the compass sight in line with the plumb line and Polaris, keeping it in line with these until the star begins to recede. At this moment the sight and plumb line are in the required line. Or bring the telescope of the transit to bear on the star, and follow it keeping the vertical wire over the star until it begins to recede. The telescope will then be in the required line. In either case, after having the transit sighted in the direction of the line just found, turn it in the proper direction through an angle equal to the azimuth as found from the tables. The accompanying table * gives the Washington mean time of each tenth transit of Polaris (upper culmination) at the meridian of Washington, D.C. The last column contains the variation per day, to facilitate the interpolation of the time for any intermediate transit. The transit which occurs October 17 is the tenth transit following that which occurs on October 8. This is because two transits occur on October 13 ; the interval separating them being 23 h. 56 m. 4 s. of mean time. These two transits are introduced in the table for greater convenience, and as a safe- guard against error respecting the particular day of transits in that vicinity. The double lines merely call attention to the break thus caused in the series. By interpolation we may, by taking account of the longitude of any given station, find the local mean time of transit of Polaris at that station for any particular day. Thus, to find the Cincinnati mean time of the upper culmination of Polaris at Cincinnati, on May 15, 1902, we have (p. 36) : * Furnished by the Director of the Nautical Almanac Office, Wash- ington, D.C. FIELD INSTRUMENTS 35 Day of Local Mean Time Change in the Year of Every 10th Transit 1 Day 1902 (Civil Time.) Jan. 1 Qh 41m igs PM . - 3™ 56*.8 11 6 1 51 " 56.9 21 5 22 22 " 56.9 31 4 42 53 " 56.9 Feb. 10 4 3 24 " 56.8 20 3 23 56 " 56.7 Mar. 2 2 44 29 " 56.6 12 2 5 4" 56.4 22 1 25 41 " 56.2 Apr. 1 12 46 20 " 56.0 11 12 7 1 " 55.8 21 11 27 44 a.m. 55.7 May 1 10 48 28 " 55.7 11 10 9 14 " 55.3 21 9 30 2 " 55.1 31 8 50 51 " 55.0 June 10 8 11 41 " 55.0 20 7 32 31 " 54.9 30 6 53 22 " 54.9 July 10 6 14 13 " 54.8 20 5 35 5 " 54.9 30 4 55 56 " 54.9 Aug. 9 4 16 47 " 55.0 19 3 37 37 " 55.1 29 2 58 26 " 55.2 Sept. 8 2 19 14 " 55.3 18 1 40 1 " 55.4 28 1 46 " 55.5 Oct. 8 12 21 30 " 55.7 Oct. 13 12 1 51 A.M. Oct. 13 11 57 55 p.m. Oct. 17 11 42 12 p.m. 55.8 27 11 2 53 " 56.0 Nov. 6 10 23 32 " 56.1 16 9 44 10 " 56.3 26 9 4 46 " 56.4 Dec. 6 8 25 21 " 56.5 16 7 45 55 " 56.7 26 7 6 27 " 56.8 36 6 26 58 " - 3 56 .9 36 SURVEYING Local mean time of transit at Washington, May 11, 1902 = 10 h 9 m 14 s a.m. Longitude of Cincinnati ivest of Washington = + h 29 m 40 s = + d .021. May 15 d + d 021 = May 15 d 021. Preceding tabular date == May 11. Therefore, interval = 4 d .021. Daily variation = - 3 m 55 s . 3 = - 235 s . 3. Total change = 4.021 x (- 235 s .3) = - 15 m 46 s . 10 h 9 m 14 s a.m. -15 46 9 h 53 m 28 s a.m. Therefore, the required time is 9 h 53 m 28 s a.m., May 15, 1902. SECTION VII THE Y LEVEL Description. The essential parts of the Y level (Fig. 18) are, the telescope, which is of various lengths, usually about 20 inches, and rests on supports called Y's, from their shape ; the spirit level, which is under the telescope and attached to it ; and the leveling head and tripod, which are similar to the same parts of the transit. Leveling Rod. There are several kinds of leveling rods, each possessing some merit peculiar to its purpose. The one shown in Fig. 19 is known as the Philadelphia leveling rod, and is the one in most common use. It is made of two pieces of wood, sliding upon each other, and held in position by a clamp. The front surface of each piece is graduated to hun- dredths of a foot up to 7 feet ; the back surface of the rear piece is figured from 7 to 13 feet, reading from the top down, FIELD INSTRUMENTS 37 Fig. 18. The Y Level 38 SURVEYING and it also has a scale by which the rod is read to half hun- dredths of a foot as it is extended. The target slides along the front of the rod and is held in place by two springs which press upon the sides of the rod. It has a square opening at the centre, through which the division line of the rod oppo- site to the horizontal line of the target may be seen. It also carries a scale by which heights may be read to half hundredths of a foot. For heights not greater than 7 feet, the target is moved up or down the front surface, the rod being closed and clamped; but when a greater height is required the target is fixed at 7 feet and the rear half of the rod extended to the required height. The rod thus becomes a self- reading rod 13 feet long* How to use Level and Rod. When the leveling instrument is used, the tripod should be set firm ; the spirit level should then be brought succes- sively over each opposite pair of leveling screws and leveled in each position, the operation being repeated until the bubble remains in the middle of the tube through an entire rotation of the tele- scope. Each time before taking an observation the instrument should be examined to see if it is still level. Care should be taken to bring the cross wires of the telescope precisely in focus and the object into such perfect view that the wires will appear, to be fastened to the surface, how- ever the eye is moved. For very accurate work the instrument should be shielded from the direct rays of the sun. FlG 19 The leveling rod should be held in a truly vertical position, the rodman standing squarely behind it. 9i 5i FIELD INSTRUMENTS 39 The target is then raised or lowered at the signal of the leveler until its horizontal line is cut by the intersection of the cross wires of the telescope. The reading is done by the leveler or the rodraan according to the kind of rod used. Substitutes for the Y Level. For ordinary work, the Sur- veyors or Engineer's Transit is often used. The plumb level (Fig. 20) consists of two pieces of wood joined at right angles. A straight line is drawn on the upright perpendicular to the upper edge of the crosshead. The instru- ment is fastened to a support by a screw through the centre of the crosshead. The upper edge of the crosshead is brought to a level by making the line on the upright coincide with a plumb line. — £ 9 Fig. 20 Fig. 21 Fig. 22 A carpenters square can be made into a level by being supported by a post (Fig. 21), the top of which is split or sawed so as to receive the longer arm. The shorter arm is made vertical by a plumb line, which brings the longer arm to a level. The water level, as shown in Fig. 22, consists of two upright glass tubes cemented into a connecting tube of any material. The whole is nearly filled with water and sup- ported at a convenient height. The surface of the water in the uprights determines the level. The water should be colored. 40 SURVEYING A level line may be obtained by sighting along the upper surface of the block in which an ordinary spirit level is mounted. For many purposes not requiring great accuracy, any of the foregoing simple instruments in connection with any graduated rod will be sufficient. EXERCISE IV 1. Set up the level and take the readings on the leveling rod at two stations equally distant from the instrument. What does the difference of these readings indicate ? 2. Set up the level successively at the two stations in Example 1, taking the readings on the leveling rod placed where the instrument was first. What does the difference of these readings indicate ? Ought this difference to be the same as that in Example 1? Explain. 3. In the field of Example 1, Exercise II, p. 22, set up the level successively at the middle of each of the five sides, taking the readings on the rod each time at both adjacent stations of the field. Find the difference between the sum of the hind- sights and the sum of the foresights. What should this difference equal ? SECTION VIII THE PLANE TABLE Description and Uses. The plane table, an approved form of which is shown in Fig. 23, consists mainly of a drawing board made of well-seasoned wood, arranged in sections to pre- vent warping, and supported at a convenient height by a tripod and leveling head, with attachments for horizontal movement. FIELD INSTRUMENTS 41 Fig. 23. The Plane Table 42 SURVEYING The board is provided with rollers or clamps or both, for keeping the paper secure and even. The plumbing arm has its end brought to a point which, however placed on the paper, is directly above the corresponding point on the ground determined by the plummet. The alidade is a ruler of brass or steel supporting a telescope with stadia or sight standards, whose line of sight is in or parallel to the same vertical plane with the beveled edge of the ruler. A compass with two spirit levels serves both to level the table and, when applied by the edges parallel to the zero line of the compass circle, to determine the magnetic bearing of the lines drawn on the paper, or the direction of the table itself. After the principal lines of a survey have been determined and plotted, the details of the plot may be filled in by means of the plane table ; or, when a plot only of a tract of land is desired and extreme accuracy is not required, this instrument affords the most expeditious means of obtaining it. There is little use for it outside of the United States Coast and Geodetic Survey and the United States Geological Survey. To orient the Table. This operation consists in placing the table so that the lines of the plot shall be parallel to the corresponding lines on the ground. This may be accomplished .approximately by turning the table until the needle of the compass indicates the same bear- ing as at a previous station, the edge of the compass coinciding with the same line on the paper at both stations. If, however, the line connecting the station at which the instrument is placed with another station is already plotted, the table may be placed in position accurately by placing it over the station so that the plotted line is by estimation over and in the direction of the line on the ground ; then making the edge of the ruler coincide with the plotted line, and turn- ing the board until the line of sight bisects the signal at the other end of the line on the ground. FIELD INSTRUMENTS 43 To plot any Point. Let ab on the paper represent the line AB on the ground; it is required to plot c, representing C on the ground. 1. By intersection. Place the table in position at A (Fig. 24), plumbing a over A, and making the fiducial edge of the ruler pass through a ; turn the alidade about a until the line of sight bisects the signal at C, and draw a line along the fiducial edge of the ruler. Place the table in position at B, plumbing b over B, and repeat the operation just described. Then c is the intersec- tion of the two lines thus drawn. FlG ^ 2. By resection. Place the table in position at A (Fig. 25), and draw a line in the direc- tion of C, as in the former case ; then remove the instrument to C, place it in position by the line drawn from a, make the edge of the ruler pass through b, and turn the alidade about b until B.is in the line of sight. A line drawn along the edge of the ruler will intersect the line from a in c. 3. By radiation. Place the table in position at A (Fig. 26), and draw a line from a toward C, as in the former cases. Measure AC, and lay off ac to the same scale as ab. To plot a Field ABCD • • • By radiation. Set up the table at any point P, and mark p on the paper over P. Draw indefinite lines from p / •> v 1 1 \ 1 X b ^a B Fig. 25 44 SURVEYING toward A, B, C, ■ ■ ■ Measure PA, PB, • • • , and lay off pa, pb, suitable scale, and join a and b, b and c, c and d, ■ ■ ■ to a t» ^a B By progression. Set up the table at A, and draw a line from a toward B. Measure AB, and plot ab to a suitable scale. Set up the table in position at B, and in like manner deter- mine and plot be ; and so on. Fig. 27 By intersection. Plot one side as a base line. Plot the other corners by the method of intersection, and join these points in proper order by straight lines. By resection. Plot one side as a base line. Plot the other corners by the method of resection, and join these points in proper order by straight lines. The Three-Point Problem. Let A, B, C represent three field stations plotted as a, b, c, respectively (Fig. 28) ; it is required fig. 2s to plot d representing a fourth field station D, from which A, B, and C are visible. Place the table over D, level and orient approximately by the compass. Determine d by resection as follows : Make the FIELD INSTRUMENTS 45 edge of the ruler pass through a and lie in the direction a A, and draw a line along the edge of the ruler. In like manner, draw lines through b toward B and through c toward C. If the table is oriented perfectly, these lines meet at the required point d, but ordinarily they will form the triangle of error, ab, ac, be. In this case, through a, b, and ab ; a, c, and ac ; and b, e, and be, respectively, draw circles ; these circles will inter- sect in the required point d. For at the required point the sides ab, ac, be must subtend the same angle as at the points ab, ac, be, respectively. Hence, the required point d lies at the intersection of the three circles mentioned. The plane table may now be oriented accurately. The three-point problem may also be solved by fastening on the board a piece of tracing paper and marking the point d representing _D, after which lines are drawn from d toward A, B, and C. The tracing paper is then moved until the lines thus drawn pass through a, b, c, respectively, when by pricking through d the point is determined on the plot below. This method, however, is impracticable in case the wind blows. CHAPTER II OFFICE INSTRUMENTS SECTION IX PLOTTING INSTRUMENTS Definitions. A map is a representation by means of points, lines, and conventional signs on a plane surface, as on paper of a surveyed portion of the earth's surface, including objects upon it. If only the boundary lines- are drawn, the repre- sentation is called an outline map, or plot. The plot is a figure similar to the original, and the ratio of a line of the field to the corresponding line of the plot is called the scale. In surveying it is customary to designate the scale as so many chains to the inch. Principal Minor Instruments. The principal minor instru- ments used in plotting are a' ruler, pencil, straight-line pen, hair-spring dividers, compasses, a right triangle of wood or hard rubber, a T-square, and a parallel ruler. The Diagonal Scale. A portion of this scale is shown in Fig. 29. AB is the unit. AB and A'B' are divided into ten equal parts, and B is joined with h, the first division point to the left of B'; the first division point to the left of B is joined with the second to the left of B', and so on. The part of the horizontal line numbered 1 intercepted between BB' and Bh is evidently t l of J^ = T ^ of the unit ; the part of the hori- zontal line numbered 2 intercepted between BB' and Bh is T f „ of the unit, and so on. 46 OFFICE INSTRUMENTS 47 The method of using this scale is as follows : Let it be required to lay off the distance 1.43. Fig. 29 Place one foot of the dividers at the intersection of the horizontal line numbered 3 and the diagonal numbered 4, and place the other foot at the intersection of the vertical line numbered 1 (CC) and the horizontal line numbered 3 ; the distance between the feet of the dividers will be the distance required. For, measuring along the horizontal line num- bered 3, from CC to BB' is 1 ; from BB' to Bh is 0.03 ; and from Bh to the diagonal numbered 4 is 0.4 ; and 1 + 0.03 + 0.4 = 1.43. The Circular Protractor. This instrument (Fig. 30) usually consists of a semicircular piece of brass or german silver, with its arc divided into degrees and its centre marked. Some protractors have an arm which carries a vernier, by which angles may be constructed to single minutes. Still others embrace an entire circle and have several arms with verniers. A rectangular protractor, having the degrees marked off on three sides of a plane scale, is sometimes used. Often this form of the protractor is found on the reverse side of the diagonal scale. 48 SURVEYING Constructions. 1. To lay off an angle with the circular protractor. Place the centre over the vertex of the angle, and make the diameter coincide with the given side of the angle. Mark off the number of degrees in the given angle, and draw a line through this point and the vertex. Fig. 30 2. To draiv through a given point a line parallel to a given line with a right triangle and ruler. Make one of the sides of the triangle coincide with the given line, and, placing the ruler against one of the other sides, move the triangle along the ruler until the first side passes through the given point; then draw a line along this side. 3. To draw through a given point a line perpendicular to a given line with a right triangle and ruler. Make the hypotenuse of the right triangle coincide with the given line, and' placing a ruler against one of the other sides of the triangle, revolve the triangle about the vertex of the right angle as a centre until its other perpendicular side is against the ruler ; then move the triangle along the ruler until the hypotenuse passes through the given point, and draw a line along the hypotenuse. OFFICE INSTRUMENTS 49 SECTION X COMPUTING INSTRUMENTS The Planimeter. This is an instrument for measuring the area of any irregular field, by applying it to a plot of the field drawn accurately to scale. The form in most common use is that known as the polar planimeter. The essential parts are two arms, one fixed in length, the other adjustable, and a rolling wheel mounted on an axis parallel to the adjust- able arm. The outer end of the arm of fixed length is made fast to the plot by means of a needle point, and the free end of the other arm is made to trace the perimeter of the figure to be measured. A disk records the area in the unit for which the instrument is set. The Slide Rule. This is an instrument for effecting the processes of multiplication, division, involution, and evolution by means of logarithms. It consists of a series of scales so arranged that by sliding one upon the other the addition or subtraction of logarithms is mechanically performed. For a full description of this labor-saving device in its various forms, the student is referred to some treatise on the subject. CHAPTER III LAND SURVEYING SECTION XI DEFINITIONS Land Surveying is the art of measuring, laying out, and dividing land, computing parts and areas from measured parts, and preparing a plot. An original survey includes laying out the boundary lines and establishing the corners. A resurvey is the retracing of old boundary lines -and the finding of corner monuments, or the relocating of them when lost. Rules for Areas. The unit of land measure is the acre = 10 square chains = 4 roods = 160 square rods, perches, or poles. Areas are referred to the horizontal plane, no allowance being made for inequalities of surface. Let A, B, and C be the angles of a triangle, and a, b, and c the opposite sides, respectively, and let s = %(a + b + c). Area of triangle ABC = \ base x altitude = ^ be sin A a 2 sin B sin C ~ 2 sin (B + C) = y/s (s — a)(s — b) (s — c). Area of rectangle = base x altitude. Area of trapezoid = ^ sum of parallel sides x altitude. Note. Spanish American units are in use in Texas, California, and Mexico. In this system the vara is the unit of length, which in Texas is 50 LAND SURVEYING 51 reckoned 33£ inches, in California 33 inches, in Mexico 32.9927 inches. The area of a square 1000 varas on a side is called a labor, and of a square 5000 varas on a side is called a league. SECTION XII SPECIAL METHODS OF SURVEYING, AND COMPUTING AREAS Triangular Fields. Measure, as may be most convenient, the three sides, two sides and the included angle, two angles and the included side, or a side and the altitude upon that side, and compute the area by the appropriate formula. Fields having More than Three Straight Sides. Divide the field into triangles and take the sum of the areas of the triangles. Or, run a diagonal and perpendiculars to it from the opposite vertices ; take the sum of the areas of the right triangles, rectangles, and trapezoids thus formed. A third method is as follows : Let ABCD (Fig. 31) repre- sent a field, and P and P' two stations within it. (They may be without the field.) Measure D PP' with great exactness. Meas- ure the angles • between PP' and the lines from P and P' to the corners of the field. In the triangle P'PD, PP' and the angles PP'D and P'PD are known ; hence, PD may be found. In like manner, PC may be found. Then, in the triangle PDC, PD, PC, and the angle DPC are known ; hence, the area of PDC may be computed. In like manner, the areas of all the trian- gles about P or P' may be determined. Area ABCD = PAD + PDC + PCB + PBA; also, area ABCD = P'AD + P'DC + P'CB + P'BA. 52 SURVEYING Fields having Irregular Boundary Lines. Let A GBCD (Fig. 32) represent a field having a stream AEFGHKB as a boundary line. Run the line AB. From E, F, G, H, K, prominent points on the bank of the stream, let fall perpendiculars EE', FF', GG', etc., upon AB. Regarding AE, EF, etc., as straight Fig. 32 Fig. 33 lines, the portion of the field cut off by AB is divided into right triangles, rectangles, and trapezoids, the necessary ele- ments of which can be measured and the areas computed. The sum of these areas added to the area of ABCD gives the area required. If the offsets are at regular intervals, then the area of the part cut off by AB may be found by adding the offsets and multiplying by the common distance between them. When the irregular boundary line crosses the straight line that joins its extremities, as in Fig. 33, the areas of AEFH and HGB may be found separately, as in the preceding case. Then, the area required = ABCD + HGB — AEFH. Rectangular System of Co-ordinates. Let XX' and YY' (Fig. 34) be two fixed perpendicular lines intersecting at the point O. Let the four parts into which these lines divide the plane be called Quadrants, as in Trigonometry, and be distinguished by naming them, respectively, first, second, third, and fourth quadrants. Suppose the position of a point is described by saying that its distance from YY', expressed in terms of some chosen unit LAND SURVEYING 53 II N III ?-F IV M -II Y Fig. 34 of length, is 3, and its distance from XX' is 4. Then there is in each quadrant one point and only one which will satisfy these conditions. The position of the point in each quadrant may be found by drawing parallels to YY' at the distance 3 from YY', and parallels to XX' at the distance 4 from XX' ; E~ then the intersections P v P 2 , P 3 , and P 4 satisfy the given condi- tions. X rrt k !-- X In order to determine which one of the four points, Pi, P 2 , P s , P 4 , is meant, we adopt the rule G- that distances measured from YY' to the right are positive; to the left, negative. Distances measured from XX' upward are positive ; downward, negative. Then, the position of P 1 will be denoted by + 3, + 4 ; of P 2 , by - 3, + 4 ; of P 3 , by — 3, - 4; of P 4 , by + 3, - 4. The fixed lines XX' and YY' are called the Axes of Co-ordi- nates ; XX' is called the Axis of Abscissas, or Axis of x ; YY', the Axis of Ordinates, or Axis of y. The intersection is called the Origin. The two distances (with signs prefixed) which determine the position of a point are called the Co-ordinates of the point ; the distance of the point from YY' is called its Abscissa ; and the distance from XX', its Ordinate. Abscissas are usually denoted by x, and ordinates by y, and a point is represented algebraically by simply writing the values of its co-ordinates within parentheses, that of the abscissa being always written first. Thus, P x (Fig. 34) is the point (3, 4), P 2 the point (— 3, 4), P, the point (— 3, — 4), and P 4 the point (3, — 4). In general the point whose co-ordinates are x and y is the point (x, y). 54 SURVEYING This system of co-ordinates may be applied to the determi- nation of areas in the following manner : Suppose the field to be ABODE (Fig. 35). Lay out the two axes so that the field shall lie wholly within the first quad- rant. Then measure the co-ordinates of each of the vertices and designate them as follows : for A, (x 1} yd ; for B, (x 2 , y 2 ) ; for C, (x 3 , y 3 ) ; for D, (x±, y 4 ) ; for E, (x 5 , yd- Evidently each of these co-ordinates is positive. Then, area ABODE = area LABM + area MBCP + area PCDR — area NEDR — area LA EN; or, in terms of the co-ordinates, area ABODE = %(y x + yd (x % — x x ) + \ (y 2 + y s ) (x 3 — x 2 ) + £ (y» + yd ( x i - » 8 ) - iO'+ yd («4 - *s) = h\ x i (ys — yd + x* (yi - yd + * 3 (y* - yd + %i (y s - yd + * 5 (>4 -yd\- This method can be put in the form of a general rule : Take one-half the algebraic sum of the products obtained by multiplying the abscissa of each vertex by the difference between the ordinates of the two adjacent vertices, taken in the clockwise order. LAND SURVEYING 55 EXERCISE V 1. Required the area of a triangular field whose sides are 13 chains, 14 chains, and 15 chains. 2. Required the area of a triangular field if it has two angles 48° 30' and 71° 45', and the included side 20 chains. 3. Required the area of a triangular field whose base is 12..60 chains, and altitude 6.40 chains. 4. Required the area of a triangular field which has two sides 4.50 chains and 3.70 chains, and the included angle 60°. 5. Required the area of a field in the form of a trapezium, one of whose diagonals is 9 chains, and the two perpendicu- lars upon this diagonal from the oppo- site vertices 4.50 chains and 3.25 chains. 6. Required the area of the field ABCDEF (Fig. 36), if A E = 9.25 chains, FF' = 6.40 chains, BE = 13.75 chains, DD' = 7 chains, -DB = 10 chains, CC = 4 chains, and A A' = 4.75 chains. fig. 36 7. Determine the area of the field ABCD from two interior stations P and P', if PP' = 1.50 chains, PP'C= 89° 35', PP'D = 349° 45', P'PB = 3° 35', P'PA = 113° 45', PP'B = 185° 30', PP'A = 309° 15', 8. Required the area of the field ABCDEF (Fig. 37), if AF' = 4 chains, FF' = 6 chains, A EE' = 6.50 chains, AE' = 9 chains, AD = 14 chains, AC" = 10 chains, AB' = 6.50 chains, BB' = 7 chains, CC = 6.75 chains. P'PD = 165° 40', P'PC = 303° 15'. 56 SURVEYING 9. Kequired the area of the field AGBCD (Fig. 32, p. 52), if the diagonal A C = 5, BB' (the perpendicular from B to AC) = 1, DD' (the perpendicular from D to A C) = 1.60, EE' = 0.25, PP' = 0.25, GG> = 0.60, ##' = 0.52, KK'= 0.54, .4P' = 0.2, E'F' = 0.50, F'G' = 0.45, £'#' = 0.45, H'K' = 0.60, and K'B = 0.40. 10. Eequired the area of the field AGBCD (Fig. 33, p. 52), if AD = 3, AC '= 5, .45 = 6, angle £U C = 45°, angle BA C = 30°, J1.E' = 0.75, AF' = 2.25, AH = 2.53, .1G-" = 3.15, EE' = 0.60, FF' = 0.40, and GG' = 0.75. 11. Determine the area of the field A BCD from two exterior stations P and P', if PP' = 1.50 chains, P'PB = 41° 10', P'PP = 104° 45', PP'B = 132° 15', P'p.4 = 55° 45', PP'D = 66° 45', +PP'A = 103° 0'. p'PC = 77° 20', PP'C = 95° 40', 12. Find the area of the field ABCDE (Fig. 35, p. 54), if the co-ordinates, in chains, of the vertices taken in order are (1.40, 6.75), (4.60, 8.32), (9.00, 9.05), (12.15, 5.58), and (5.27, 1.16). 13. Find the area of the field ABCDE (Fig. 35, p. 54), by measuring distances as follows : AL = 400 feet ; BM = 700 feet ; CP = 680 feet ; DR = 380 feet ; EN = 200 feet; LM = 150 feet ; MN = 250 feet; NP = 200 feet ; PR = 220 feet. 14. Lay out a field of four sides, and find its area by the method of triangles and also by the method of rectangular co-ordinates. 15. Lay out a field of six sides, and find its area by the method of triangles and also by the method of rectangular co-ordinates. LAND SURVEYING 57 SECTION XIII GENERAL METHOD FOR FARM SURVEYS Definitions. A course is the bearing and length of a line. The latitude of a course is the distance between the parallels through its extremities, and is called a northing or a southing, as the course is northward or southward. The departure of a course is the distance between the meridians through its extremities, and is' called an easting or a westing, as the course is eastward or westward. The meridian dis- tance of a point is its distance from a meridian. The double meridian distance of a course is double the meridian distance of its mid-point, and therefore equal to the sum of the meridian distances of the extremities of the M course. Let AB (Fig. 38) represent a line, whose bearing and length are known. Let MN be a reference meridian ; and let j) and^' be parallels through A and B, and m and m' meridians through the same points. Then, N angle mAB represents the bearing FlG " 38 of line AB. The latitude of the course AB is AE, and its departure EB. The meridian distance of the point B is BC and of A, AD. Evidently, the double meridian distance of the course AB is ±(BC + AD). Again, in the triangle AEB, A E = AB x cos EAB, and EB = AB x sin EAB. Hence, latitude = distance x cos of bearing, and departure = distance x sin of bearing. From these formulas, the latitude and departure of any course may be found by means of a table of natural sines and cosines. They may be found also 58 SURVEYING from the Traverse Table, which is merely the tabulated results of the foregoing method for given courses. Field Notes. The field notes are kept in a book provided for the purpose. The page is commonly ruled in three col- umns, in the first of which is written the number of the station ; in the second, the bearing of the side ; and in the third, the length of the side. Field Notes N 1 N. 20° E. 8.66 2 S. 70° E. 5.00 3 S. 10° E. 10.00 4 N. 70° W. 10.00 Fig. 39 To obtain the field notes, say of field ABCD (Fig. .30), place the compass at A, the first station, and take the bearing of AB (p. 12) ; suppose it to be N. 20° E. Write the result in 'D the^cond column of the field notes opposite the number of the station. Measure AB = 8.66 chains, and write the result in the third column of the field notes. Place the compass at B, and, after testing the bearing of A B (p. 13), take the bear- ing of BC, measure BC, and write the results in the field notes ; and so continue until the bearing and length of each side have been recorded. Computation of the Area. The survey may begin at any corner of the field ; but, for computing the area, the field notes should be arranged so that the most eastern or the most western station shall stand first. For the sake of uniformity, we shall always begin with the most western station and keep the field on the right in passing around it. LAND SURVEYING 59 The field notes occupy the first three of the eleven columns in the tablet below. Columns IV, V, VI, and VII contain the latitudes and departures corresponding to the sides, taken from the Traverse Table. The line represented by each number is indicated immediately above that number. Column VIII contains the meridian distances of the points B, C, D, and A, taken in order. Column IX contains the double meridian distances I II HI IV V VI VII VIII IX X XI Side Beaking DlST. N, S. E. W. M.B. B.M.D.. N.A. S.A. AB BC CD DA N.20°E. S.70°E. S. 10° E. N.70°"W. 8.66 5.00 10.00 10.00 AB 1 8.14 D'A 3.42 B'C 1.71 CD' 9.85 BB' 2.96 C"C 4.70 D'D 1.74 DD' 9.40 BB' 2.96 CC 7.66 DD' 9.40 BB' 2.96 BB' + CC 10.62 CC'+DD' 17.06 DD' 9.40 2 ABB' 24.0944 2 ADD' 32.1480 2 C'CBB' 18.1602 2 D'DCC 168.0410 33.66 11.56 11.56 9.40 9.40 56.2424 186.2012 (186.2012 sq. ch. - 56.2424 sq. ch.) + 2 = 64.98 sq. ch. = 6.50 acres. of the courses. Their composition is indicated by the letters immedi- ately above the numbers. Column X contains the products of the double meridian distances by the northings in the same line. The first number, 24.0944 = 2.96 x 8.14 = BB' x AB' = twice area of triangle ABB' ; "32.1480 = 9.40 x 3.42 = DD' x AD' = twice area of triangle ABB'. Column XI contains the products of the double meridian distances by the southings in the same line. The first number, 18.1602 = 10.62 x 1.71 = (BB' +-CC) x B'C — twice area of trapezoid C'CBB' ; 168.0410 = 17.06 x 9.85 = (CC + DD') x D'C" = twice area of trapezoid D'DCC. The sum of the north areas in column X = 56.2424 = 2 (ABB' + ADD'). The sum of the south areas in column XI = 186.2012 = 2 (C'CBB' + D'DCC). But (C'CBB' + D'DCC) - (ABB' + ADD') = ABCD. Hence, 2 (C'CBB' + D'DCC) - 2 (ABB' + ADD') = 2 ABCD ; that is, 186.2012 - 56.2424 = 129.9588 = 2 ABCD. Hence, area ABCD = i of 129.9588 sq. ch. = 64.98 sq. ch. = 6.50 A. 60 SURVEYING Balancing the Work. In the survey, we pass entirely around the field ; hence, we move just as far north as south. There- fore, the sum of the northings should equal the sum of the southings. In like manner, the sum of the eastings should equal the sum of the westings. In this way the accuracy of the field work may be tested. In the example on page 59 the sum of the northings is equal to the sum of the southings, being 11.56 in each case ; and the sum of the eastings is equal to the sum of the westings, being 9.40 in each case. Hence, the work balances. In actual practice the work seldom balances. When it does not balance, corrections are generally applied to the latitudes and departures by the following rules : 1. The perimeter of a field is to any one side as the total error in latitude is to the correction required. 2. The perimeter of a field is to any one side as the total error in departure is to the correction require'd. Example. The perimeter of a field measured 306.62 chains and one side 72.47 chains, with a total error of 22 links in latitude and of 18 links in departure. Then 306.62 : 72.47 = 22 links : x = 18 links : y. Whence x = 5 links and y = 4 links. Hence the correction in latitude applied to the given side is 0.05 chains, and the correction in departure is 0.04 chains. If special difficulty was found in taking a particular bear- ing, or in measuring a particular line, the corrections should be applied to the corresponding latitudes and departures. The amount of error allowable varies in the practice of dif- ferent surveyors, and according to the nature of the ground. An error of 1 link in 8 chains would not be considered too great on smooth, level ground ; while on rough ground an error of 1 link in 3 chains might "be allowed. If the error is consider- able, the field measurements should be repeated. LAND SURVEYING 61 As another example let it be required to find the area of field ABCDEF from the following Field Notes 1 N. 73° 30' W. 5.00 2 S. 16° 30' W. 5.00 3 N. 28° 30' W. 7.07 4 N. 20° 00' E. 11.18 5 S. 43° 30' E. 5.00 6 S. 13°30'E. 10.00 Side Bearing DlST. N. S. E. W. M.D. D.M.D. N.A. S.A. AB BC CD DE EF FA N.20°00'E. S.43°30'E. S.13°30'E. N. 73°30"W. S.16°30"W. N. 28° 30'W. 11.18 5.00 10.00 5.00 5.00 7:07 10.51 1.42 6.21 3.63 9.72 4.79 3.82 3.44 2.33 4.79 4.80 1.42 3.37 BB 3.82 C'C 7.26 DD 9.59 E'E 4.79 F'F 3.37 0.00 BB 3.82 B'B+C'C 11.08 CC + D'D 16.85 DD + E'E 14.38 E'E + F'F 8.16 F'F 3.37 2 ABB' 40.1482 2 D'DEE' 20.4196 2AFF' 20.9277 2 C'CBB' 40.2204 ID'DCC 163.7820 2 F'FEE' 39.0864 43.25 18.14 18.14 9.59 9.58 9.59 81.4955 243.0888 43.25 : 5 = 0.01 : x. Area = 8.08 acres. The first station in the field notes is D, but we rearrange the numbers in the tablet so that A stands first. The northings and southings balance, but the eastings exceed the westings by 1 link. We apply the correction to the westing 4.79 (the distance DE being in doubt), making it 4.80, and write the correction. In practice, the corrected numbers are written in red ink, and often all the latitudes and departures are rewritten in four additional columns, headed, respectively, N', S', E', W. Supplying Omissions. If for any reason the bearing and the length of any side do not appear in the field notes, the lati- tude and departure of this side may be found in the following ' manner : 62 SURVEYING Find the latitudes and departures of the other sides as usual. The difference between the northings and southings gives the northing or southing of the unknown side, and the difference between the eastings and westings gives the easting or westing of the unknown side. If the length and the bearing of the unknown side are de- sired, they may be found by solving the right triangle, whose sides are the latitude and departure found by the method just explained, and whose hypotenuse is the length required. Obstructions. If the end of a line is not visible from its beginning, or if the line is inaccessible, its length and bearing may be found as follows : By means of a random line (p. 8). When it is impossible to run a random line, which is fre- quently the case on account of the extent of the obstruction, the following method may be used : Let AB (Fig. 40) represent an inaccessible line whose extremities A and B only are known, and B invisible from A. Set flagstaffs at convenient points, C and D. Find the bearings and lengths of AC, CD, and DB, and then proceed to find the latitude and departure of AB. Fig. 40 Example. lowing notes (see Fig. 40) : Suppose that we have the fol- Side Bearing DlST. N. s. E. w. AC CD BB S. 45° E. E. N. 30° E. 3.00 3.50 4.83 4.18 2.12 2.12 3.50 2.42 ,- 4.18 2.12 8.04 LAND SURVEYING 63 The northing of AB is AE = 2.06, and the easting, EB = 8.04. These numbers may be entered in the tablet ha the columns N. and E., opposite the side AB. If the bearing and length of AB are required, . „.„ BE 8.04 tan BAE = = AE 2.06 Hence, the angle BAE = 75° 38'. Also, 5.903. AB = ~^AE 2 + BE 2 = V8.04 2 + 2.06 2 = 8.30. Therefore, the bearing and length of AB are N. 75° 38' E. and 8.30. To make a Plot. A plot or map may be drawn to any desired scale. If a line 1 inch in length in the plot represents a line 1 chain in length, the plot is said to be drawn to a scale of 1 chain to an inch. In this case (Fig. 41) the plot is drawn to a scale of 8 chains to an inch. Draw the line NAS to represent the meridian, and lay off the first northing AB' = 8.14. Through B draw an indefinite line perpendicular "to NS and lay off B'B, the first easting, = 2.96. Draw AB ; then the line AB represents the first side of the field. Through B draw BC" perpendicular to BB', and make BC" = 1.71, the first southing. Through C" draw C"C perpendicular to BC", and equal to 4.70, the second easting. Draw BC. The line BC represents the second side of the field. Proceed in like manner until the field is completely represented. The extremity of the last line F'A, measured from F', should fall at A. test of the accuracy of the plot. Fig. 41 This is a 64 SURVEYING By drawing AC, AE, and EC, the hexagonal figure ABCDEFA is divided into triangles, the bases and altitudes of which may be measured and the area computed approxi- mately. Another method is as follows : Draw MN (Fig. 42) to represent a meridian. Let the' point A in this line be taken as the first station in the rearranged field notes of page 61. With the circular protractor mark off each of the bearings as b, c, d, e, f, and a. Draw AB to scale through b. With triangle and ruler (p. 48) or with parallel ruler draw to scale BC parallel to Ac ; and so on. After some * practice, still other methods will be suggested, but the methods given are among the best. Fig. 42 & & EXERCISE VI Find the areas of the following and make a plot of each. In 3 and 7, detours were made on account of obstructions (p. 62). The notes of the detours are written in braces. 12 3 St a. Bearings DlST. 1 S. 75° E. 6.00 2 S. 15° E. 4.00 3 S. 75° W. 6.93 4 N. 45° E. 5.00 5 N. 45° W. 5.19* Sta. Bearings DlST. 1. 2 3 4 N. 45° E. S. 75° E. S. 15° W. N. 45° W. 10.00 11.55 18.21 19.11 Sta. Bearings DlST. 1 S. 2°15'E. 9.68 2J N. 51°45'W. 2.39 S. 85°00'W. 6.47 1 S. 55°10'W. 1.62 3 N. 3°45'E. 6.39 4 S. 66°45'E. 1.70 5 N. 15°00'E. 4.98 6 S. 82°45'E. 6.03 LAND SURVEYING 65 STA. Bearings DlST. 1 N. 6°30'W. 6.08 2 S. 82°30'W. 6.51 3 S. 3°00'E. 5.33 4 E. 6.72 Sta. Bearings DlST. 1 2 3 4 N. 6°15'W. S. 81°50'W. S. 5°00'E. N. 88°30'E. 6.31 4.06 5.86 4.12 Sta. Bearings DlST. 1 N. 20°00'E. 4.621 2 N. 73WE. 4.16* 3 S. 45°15'E. 6.18* 4 S. 38°30'W. 8.00 5 Wanting Wanting Sta. Bearings DlST. '{ S. 81°20'W. 4.28 N. 76°30'W. 2.67 2 N. 5°00'E. 8.68 3 S. 87°30'E. 5.54 r S. 7°00'E. 1.79 4 S. 27°00'E. 1.94 S. 10°30'E. 5.35 i N. 76°45'W. 1.70 Sta. Bearings DlST. 1 K 89°45'E. 4.94 2 S. 7°00'W. 2.30 3 S. 28°00'E. 1.52 4 S. 0°45'E. 2.57 5 N. 84°45'W. 5.11 6 N. 2°30'W. 5.79 9. An Ohio farm is bounded and described as follows : Beginning at the southwest corner of lot No. 13, thence N. 1£° E. 132 rods and 23 links to a stake in the west boundary line of said lot ; thence S. 89° E. 32 rods, and 15 t 4 q links to a stake; thence N. li° E. 29 rods and 15 links to a stake in the north boundary line of said lot ; thence S. 89° E. 61 rods and 18 t 6 q links to a stake; thence S. 32^-° W. 54 rods to a stake ; thence S. 35^° E. 22 rods and 4 links to a stake ; thence S. 48° E. 33 rods and 2 links to a stake ; thence S. 7^° W. 76 rods and 20 links to a stake in the south boundary line of said lot ; thence N. 89° W. 96 rods and 10 links to the place of beginning. Containing 85.87 acres, more or less. Verify the area given and plot the farm. 66 SURVEYING Modification of the Latitude and Departure Method. The area of a field may be found by a modification of the latitude and departure method, if its sides and interior angles are known. Let A, B, C, D represent the interior angles of the field ABCD (Fig. 43). Let the side AB determine the direction of reference. The bearing of AB, with reference to AB, is 0°. The bearing of BC, with reference to. AB, is the angle b = 180° — B. The bearing of CD, with reference to AB, is the angle c = C — b. The bearing of DA, with reference to AB, is the angle d = A. The area may now be com- puted by the latitude and depar- ture method, regarding AB as the meridian. In practice, the exterior angles, when acut^e, are usually measured. As the interior, angles may be measured with considerable accu- racy by the transit, the latitudes and departures should be obtained by using a table of natural sines and cosines. EXERCISE VII 1. Find the area of the field ABCD, in which the angle A = 120°, B = 60°, C = 150°, and D = 30° ; and the side AB = 4 chains, BC = 4 chains, CD = 6.928 chains, and DA = 8 chains. Keep three decimal places, and use the Traverse Table. 2. Find the area of the farm ABCDE, in which the angle A = 106° 19', B = 99° 40', C = 120° 20', D = 86° 8', and E = 127° 33'; and the side ,45 = 79.86 rods, BC = 121.13 rods, CD = 90 rods, DE = 100.65 rods, and EA = 100 rods. Use the table of natural sines and cosines, keeping two decimal places in the results. LAND SURVEYING 67 General Remarks on determining Areas. Operations depend- ing upon the reading of the magnetic needle must lack accuracy. Hence, when great accuracy is required (which is seldom the case in land surveying) the method of pp. 58-61 cannot be employed. The best results are obtained by the methods explained on pp. 51-54 and 66, the horizontal angles being measured with the transit, and great care exercised in measuring the lines. SECTION XIV LOCATION SURVEYS Definition. In surveying proper we measure lines and angles as we find them, while in location surveys we mark them out on the ground where they are required to be in order to inclose a given area, or conform to a specified shape, or meet some other given condition. Laying out, parting off, and dividing up land are included in this class of surveys. The surveyor must, for the most part, depend on his general knowl- edge of Geometry and Trigonometry, and his own ingenuity, for the solutions of problems that arise in location surveys. Illustrative Problems. Problem 1. To divide a trian- gular field into two parts having a given A ratio, by a line through a given vertex. Let ABC (Fig. 44) be the triangle, and A the given vertex. f>j) Divide BC at D, so .that equals the given ratio , an d draw A B. A BB and ^4 D C are the parts O required ; for ABB-.ABC = BB:BC. Problem 2. To cut off from a triangular field a given area, by a line parallel to the base. SURVEYING Let ABC (Fig. 45) be the triangle, and let DE be the division line required. Then ABC : ABE = AB 2 : AD 2 . 'ABC : VADE = AB : AD. <4 AD = AB- APE >ABC' iQ Problem 3. To cut off from a Fig. 45 triangular field a given fraction of the field, by a line from a given point in a side. Let ABC (Fig. 46) be the triangle, and P the point from which the line PD is to be located so as to cut off, say, one-third the area of the triangle. AD = AB x AC -T- SAP. For ABC:APD = AB X AC : AP x AD = 8:1. Fig. 46 Problem 4. To divide any field into two parts having a given ratio, by a line through a given point in the perimeter. Let ABCDE (Fig. 47) represent the field, P the given point, and PQ the required division line. The areas of the whole field and of the required parts having been determined, run the line PD from P to a corner D, dividing the field, approximately, as required. „ Determine the area PBCD. The triangle PDQ represents* the part which must be added to PBCD to make the required division. LAND SURVEYING 69 Hence, Area PBQ BQ i x PB x BQ x sin PBQ. 2 x areaPPQ PD x sin PBQ Note. BQ = 2 x area PDQ This perpendicular from perpendicular from P on BE P on Di? may be run and measured directly. Problem 5. To divide a field into a given number of parts, so that access to a pond of water is given to each. Let ABCBE (Fig. 48) represent the field, and P the pond. Let it be required to divide the field into four parts. Find the area of the field and of each part. Let AP be one division line. Run PE, and find the area APE. Take the differ- ence between APE and the area of one of the required parts ; this gives the area of the triangle PQE, from which QE may be found, as in Problem 4. Draw PQ ; PAQ is one of the required parts. In like manner, PQR and PAS are determined; whence, PSR must be the fourth part required. EXERCISE VHI 1. Prom the square A BCD, containing 6 acres 1 rood 24 perches, part off 3 acres by a line EF parallel to AB. 2. Prom the rectangle ABCD, containing 8 acres 1 rood 24 perches, part off 2 acres 1 rood 32 perches by a line EF parallel to AD which is equal to 7 chains. Then, from the remainder of the rectangle, part off 2 acres 3 roods 25 perches, by a line GH parallel to EB. 3. Part off 6 acres 3 roods 12 perches from a rectangle ABCD, containing 15 acres, by a line EF parallel to AB ; AD being 10 chains. 70 SURVEYING 4. From a square ABCD, whose side is 9 chains, part off a triangle which shall contain 2 acres 1 rood 36 perches, by a line BE drawn from B to the side AD. 5. From ABCD, representing the rectangle, whose length is 12.65 chains, and breadth 7.58 chains, part off a trapezoid which shall contain 7 acres 3 roods 24 perches, by a line BE drawn from B to the side DC. 6. In the triangle ABC, AB = 12 chains, AC = 10 chains, and BC = 8 chains ; part off a trapezoid of 1 acre 2 roods 16 perches, by the line DE parallel to AB. 7. In the triangle ABC, AB = 26 chains, AC = 20 chains, and BC = 16 chains ; part off a trapezoid of 6 acres 1 rood 24 perches, by the line DE parallel to AB. 8. It is required to divide the triangular field ABC among three persons whose claims are as the -numbers 2, 3, and 5, so that they may all have the use of a watering place at C ; AB = 10 chains, AC = 6.85 chains, and CB = 6.10 chains. 9. Divide the five-sided field A B CHE' among three persons, X, Y, and Z, in proportion to their claims, X paying $500, Y paying $750, and Z paying $1000, so that each may have the use of an interior pond at P, the quality of the land being equal throughout. Given AB = 8.64 chains, BC = 8.27 chains, CH= 8.06 chains, HE = 6.82 chains, and EA = 9.90 chains. The perpendicular PD upon AB = 5.60 chains, PD' upon BC = 6.08 chains, PD" upon CH = 4.80 chains, PD'" upon HE = 5.44 chains, and PD"" upon EA = 5.40 chains. Assume PH as the divisional fence between the shares of X and Z, it is required to determine the position of the fences PM and PN between the shares of X and Y and between the shares of Y and Z. 10. Divide the triangular field ABC, whose sides AB, AC, and BC are 15, 12, and 10 chains, respectively, into three equal LAND SURVEYING 71 parts, by fences EG and DF parallel to BC, without finding the area of the field. 11. Divide the triangular field ABC, whose sides AB, BC, and AC are 22, 17, and 15 chains, respectively, among three persons, A, B, and C, by fences parallel to the base AB, so that A may have 3 acres above the line AB, B 4 acres above A's share, and C the remainder. SECTION XV LAYING OUT THE PUBLIC LANDS Reference Lines. The public lands north of the Ohio Biver and west of the Mississippi are generally laid out in accord- ance with what is known as the rectangular system of surveying. First, an initial point is selected with great care, and then astronomically established. Through this point a principal meridian, or true north and south line, is run by means of the solar compass, or the transit with observations on Polaris ; and also an east and west line, called a base line. Crossing the principal meridian at intervals of 24 miles, both north and south of the initial point, are run other east and west lines, called standard parallels, or correction lines. Northward from the base line and from each of the standard parallels, at intervals of 24 miles, both ways from the princi- pal meridian, are run true north and south lines, called guide meridians. Thus, the land is divided into blocks approxi- mately 24 miles square. Six principal meridians have been established, in addition to which and connected with which there are twenty or more independent meridians in the western states and territories. Division from Reference Lines; Townships. Within each block parallels to the base line, or to a standard parallel, are run at intervals of 6 miles. These are called township lines. 72 SURVEYING At the same intervals are also run north and south lines, called range lines. Thus, the tract would be divided into townships exactly 6 miles square if it were not for the con- vergence of the meridians on account of the curvature of the earth. An east and west series of townships is called a tier, and a north and south series is called a range. A township is designated by giving the number of the tier north or south of the base line and the number of the range east or west of N D \f' 1, i l\k I '[l 1 m\ j- t" \p" B t' \P' 1 t A ■ \p „ r i ■ i V r' r" | G' 1 1 G ■ D- — ' C ■ 1 L' E S Fig. 49 the principal meridian. Thus, T. 3 N., R. 2 W., read town- ship three north, range two west, means that the township is in the third tier north of the base line, and in the second tier west of the principal meridian. Let NS (Fig. 49) represent a principal meridian ; WE a base line; DL and D'L' standard parallels; GM and G'M' guide LAND SURVEYING 73 meridians ; rl, r'l', . . . , range lines ; tp, t'p', . . . , township lines. If Or is taken as 6 miles, then O'l will be less than 6 miles. O'k being equal to 6 miles and O'l being less, it will be observed that there will be offsets on the base line and on standard parallels at intervals of 6 miles. Township A would be designated thus : T. 2 1ST., E. 3 E. How would townships B and C be designated ? Subdivision of Townships. The townships are divided into sections approximately 1 mile square, and the sections are divided into quarter sections. The township, section, and quarter-section corners are permanently marked. The sections are numbered, beginning at the northeast corner, as in Fig. 50, which represents a township divided into sections. The quarter sections are designated, according to their position, as N.E., KW., S.E., and S.W. Section FlG . 50 lines are surveyed in such an order as to throw the errors on the northwest quarter sections, which are carefully measured and their areas calculated. Meander Lines. If in running a line a navigable stream or a lake more than 1 mile in length is encountered, it is meandered by marking the intersection of the line with the bank and running lines from this point along the bank to prominent points which are marked, and the lengths and bearings of the connecting lines recorded. Manual. For detail of methods, see the "Manual of Sur- veying Instructions," issued by the Commissioner of the General Land Office, at Washington, D.C., for the use of Surveyors-General. 6 7 18 19 30 31 5 8 17 20 29 32 4 9 16 21 28 33 3 10 15 22 27 34 2 11 14 23 26 35 1 12 13 24 25 36 CHAPTER IV TRIANGULATION SECTION XVI DEFINITIONS The third method of surveying explained on page 51 is an example of triangulation on a small scale. The simple principle there involved is elaborately worked out in hydro- graphic or topographic surveys, or in the measurement of terrestrial arcs, as in the " Transcontinental Triangulation and American Arc of the Parallel," recently completed by the United States Coast and Geodetic Survey. Let F (Fig. 51) represent a point whose position with reference to the base line AB is required. Connect AB with F by the series of triangles q ABC, ACD, ABE, and DEF, so that a signal at C is visible from A and B, a signal at D * visible from A and C, a signal at E visible from A and D, and a signal at F visible from D and E. In the tr ian gle A B C, the side AB is known, and the angles at A and B may be measured; hence, AC may be computed. In the triangle A CD, AC is known, and the angles at A and C may be measured ; hence, AD may be computed. In like manner, DE and EF or DF may be determined. DF, or some suitable line connected with DF, may be measured, and this result 74 TRIANGULATION 75 compared with the computed value to test the accuracy of the field measurement. This net or chain of triangles enables us to determine the relative position of all the points with respect to each other. If the point A is, furthermore, astronomically located, and the azimuth of line AB is known, then we have sufficient data also to determine the absolute geographical position of each of the points. Classification. Three orders of triangulation are recognized, viz. : primary, in which the sides are from 20 to 190 miles in length; secondary, in which the sides are from 5 to 40 miles in length, and which connect the primary with the tertiary ; tertiary, in which the sides are seldom over 5 miles in length, and which bring the survey down to such dimensions as to admit of the minor details being filled in by the compass and plane table. Measurement of Base Lines. Base lines should be measured with a degree of accuracy corresponding to their importance. Suitable ground must be selected and cleared of all obstruc- tions. Each extremity of the line may be marked by cross lines on the head of a copper tack driven into a stub which -is sunk to the surface of the ground. Poles are set up in line about half a mile apart, the alignment being controlled by a transit or theodolite placed over one end of the line. The preliminary measurement may be made with an iron wire about one-eighth of an inch in diameter and 60 meters in length, or with a steel chain of the same length. The final measurement is made with the tape line, or with bars 6 meters long, which are supported upon trestles when in use. These bars are placed end to end, and brought to a horizontal position, if this can be quickly accomplished; if not, the angle of inclination is taken by a sector, or a vertical offset is measxired with the aid of a transit, so that the exact horizontal distance can be computed. A thermometer is attached to each bar, so that the temperature of the bar may 76 SURVEYING be noted and a correction for temperature applied. Some- times the bars are laid in melting ice, in which case accuracy to at least one five-millionth part of the length measured is attainable. Measurement of Angles. Angles are measured by means of the transit with much greater accuracy than with the com- pass, since the reading of the plates of the transit is taken to minutes, and by means of microscopes to seconds, while the reading of the needle of the compass is to quarter or half- quarter degrees. In order to eliminate errors of observation and of adjust- ment, and errors arising from imperfect graduation of the circles, a large number of readings is made and their mean taken. Two methods are in use, viz., repetition and series. The method of repetition consists essentially in taking as many readings of an angle as is desired, the reading in each case after the first being from the index of the next preceding reading, and then taking the mean. The method of series is the one generally used when several angles about the same point are to be measured. It con- sists essentially in taking the readings successively on each station, then reversing the telescope and repeating the obser- vations in the reverse order, which completes a series. This process is repeated a number"of times, each series beginning with a different index. Then the mean of the different series is found. On account of the curvature of the earth, the sum of the three angles of a triangle upon its surface exceeds 180°. This spherical excess, as it is called, becomes appreciable only when the sides of the triangle are about 5 miles in length. To determine the angles of the rectilinear triangle having the same vertices, one-third of the spherical excess is generally deducted from each spherical angle. CHAPTER V LEVELING SECTION XVII DEFINITIONS A level surface is a surface parallel with the surface of still water, and is, therefore, slightly curved owing to the spheroidal shape of the earth. A level line is a line in a level surface. The line of apparent level of a place is a tangent to the level line at that place. Hence, the line of apparent level is perpendicular to the plumb line. Leveling is the process of finding the difference of level of two places, or the distance of one place above or below a level line through another place. Corrections for Curvature and Refraction. In ordinary leveling no distinction is made between true and apparent levels. In precise leveling the difference between the two is measured, i.e., correction is made for curvature of the earth. There is sometimes also a correction made for refraction of light. Let t (Fig. 52) represent the line of apparent level of the place P, a the level line, d the diameter of the earth ; then c represents the cor- rection for curvature. To compute the correction for curvature : t 2 = c(c + d). {Geometry, § 381.) t 2 a 2 Therefore, c = = — > approxi- c + d d ^ mately, since c is very small compared with • d, and t = a, very nearly. fm. 52 77 78 SURVEYING Since d is constant (=7920 miles, nearly), the correction for curvature varies as the square of the distance. Example. What is the correction for curvature for 1 mile ? By substituting in the formula deduced above, l 2 . miles = 8 inches, nearly. _ a _ C ~ ~d ~ 7920 Hence, the correction for curvature for any distance may be found in inches, approximately, by multiplying 8 by the square of the distance expressed in miles. If correction for refraction is also made, it is customary to diminish the above by about one-sixth of itself; or, c = f of 8 a 2 . SECTION XVIII DIFFERENTIAL LEVELING Single Setting of Instrument. To find the difference of level between two places when both are visible from some intermediate point, and the difference of level does not exceed 13 feet, only one setting of the level will usually be necessary. Let A and B (Fig. 53) represent the two places. Set the Y level at a station equally distant, or nearly so, from A and A' Fig. 53 B, but not necessarily on the line AB. After leveling the instrument, bring the telescope to bear upon the rod (p. 38), and by signal direct the rodman to move the target until its horizontal line is in the line of apparent level of the telescope. LEVELING 79 Let the rodman now record the height A A' of the target. In like manner find BB'. The difference between A A' and BB' is the difference of level required. If the instrument is equally distant from A and B, or nearly so, the curvature and the refraction on the two sides of the instrument balance, and no correction for curvature or refraction is necessary. Several Settings of Instrument. When both places are not visible from the same place, or when the difference of level between them is considerable, two or more settings of the level may be necessary. Let A and D (Fig. 54) represent the two places. Place the level midway between A and some intermediate station B. Fig. 54 Find A A' and BB', as in the preceding case, and record the former as a backsight and the latter as a foresight. Select another intermediate station C, and in like manner find the backsight BB" and the foresight CC ; and so continue until the place D is reached. The difference between the sum, of the foresights and the sum of the backsights ivill be the difference of level required. Since, BB' + CC + DD' - (AA' + BB" + CC") = BB' - BB" + CC - CC" + DD' - AA' = B'B" + CC" + D'D - A A' = A' A" - A A' = A A". 80 SURVEYING SECTION XIX PROFILE LEVELING Definitions. The intersection of a vertical plane with the surface of the earth is called a section, or profile. The term " profile," however, usually designates the plot, or representa- tion of the section on paper. Profile leveling is leveling to obtain the data necessary for making a profile or plot of any required section. A profile is made for the purpose of exhibiting in a single view the inequalities of the surface of the ground for great distances along the line of some proposed improvement, such as a railroad, canal, or ditch, thus facilitating the establishment of the proper grades. The data necessary for making a ru-ofile of any required section are the heights of its different points above some assumed horizontal plane, called the datum plane, together with their horizontal distances apart or their distances from the beginning of the section. The position of the datum plane is fixed with reference to some permanent object near the beginning of the section, called a bench mark, and in order to avoid negative heights is assumed at such a distance below this mark that all the points of the section shall be above it. The heights of the different points of the section above the datum plane are determined by means of the level and leveling rod ; and the horizontal length of the section is measured with an engineer's chain or tape, and divided into equal parts, usually 100 feet in length, called stations, marked by stakes numbered 0, 1, 2, 3, and so on. Where the ground is very irregular, it may be necessary, besides taking sights at the regular stakes, to take occasional sights at points between them. If, for instance, at a point LEVELING 81 40 feet in advance of stake 3 (Fig. 55) there is a sudden rise or fall in the surface, the height of this point would be determined and recorded as at stake 3.40. The readings of the rod are ordinarily taken to the nearest tenth of a foot, except on bench marks and points called turning points, where they are taken to thousandths of a foot. A turning point is a point on which the last sight is taken just before changing the position of the level, and the first sight from the new position of the instrument. A turning point may be coincident with one of the stakes, but must always be a hard point, so that the foot of the rod may stand at the same level for both readings. Fig. 55 Field Work. To explain the method of obtaining the field notes necessary for making a profile, let 0, 1, 2, 3, • • •, 11 (Fig. 55) represent a portion of a section to be leveled and plotted. Establish a bench mark at or near the beginning of the line, measure the horizontal length of the section, and set stakes 100 feet apart, numbering them 0, 1, 2, 3, and so on. Place the level at some point, as between 2 and 3, and take the reading of the rod on the beneh = 4.832. Let PP' repre- sent the datum plane, say 15 feet below the bench mark; then 15 + 4.832 = 19.832 is the height of the line of sight AB, called the height of the instrument, above the datum plane. 82 SURVEYING Now take the reading at = 5.2 = A, and subtract the same from 19.832, which leaves 14.6 = F, the height of the point above the datum plane. Next take sights at 1, 2, 3, 3.40, and 4, equal, respectively, to 3.7, 3.0, 5.1, 4.8, and 8.3, and subtract the same from 19.832 ; the remainders 16.1, 16.8, Fig. 56 14.7, 15.0, and 11.5 are respective heights of the points 1, 2, 3, 3.40, and 4. * Then, as it is necessary to change the "position of the instrument, select a point in the neighborhood of 4 suitable as a turning point (t.p. in the figure), and take a careful reading on it = 8.480 ; subtract this from 19.832, and the remainder, 11.352, is the height of the turning point. Now carry the instrument forward to a new position, as between 5 . and 6, shown in the figure, while the rodman remains at t.p.; take a second reading on t.p. = 4.102, and add it to 11.352, the height of t.p. above PP'; the sum 15.454 is the height of the instrument CD in its new position. Take sight upon 5, 6, and 7, equal, respectively, to 4.9, 2.8, and 0.904 ; subtract these sights from 15.454, and the results 10.6, 12.7, and 14.550 are. the heights of the points 5, 6, and 7, respectively. The point 7, being suitable, is made a turning point, and the instrument is moved forward to a point between 9 and 10. The sight at 7 = 6.870, added to the height of 7 gives 21.420 as the height of the instrument EF in its new position. The LEVELING 83 readings at 8, 9, 10, and 11, which are, respectively, 5.4, 3.6, 5.8, and 9.0, subtracted from 21.420 give the heights of these points, namely, 16.0, 17.8, 15.6, and 12.4. Proceed in like manner until the entire section is leveled, establishing bench marks at intervals along the line to serve as reference points for future operations. The bench marks should be described with sufficient minuteness to enable any one not connected with the survey to locate them easily and unmistakably. A record of the work is given in the following table : Station + s. H.I. -s. H.S. Eemabks B 4.832 15.0 Bench on rock 20 ft. 19.832 5.2 14.6 south of 1 3.7 16.1 2 3.0 16.8 3 5.1 14.7 3 to 3.40 turnpike road 3.40 4.8 15.0 4 8.3 11.5 t.p. 4.102 8.480 11.352 - 5 15.454 4.9 10.6 6 2.8 12.7 7 6.870 0.904 14.550 8 21.420 5.4 16.0 9 3.6 17.8 10 5.8 15.6 11 9.0 12.4 B Bench on oak stump 12 27 ft. N.E. of 12, etc. etc. The first column contains the numbers or names of all the points on which sights are taken. The second column con- tains the sight taken on the first bench mark, and the sight on each turning point taken immediately after the instrument 84 SURVEYING has been moved to a new position. These are called plus sights (+ S.) because they are added to the heights of the points on which they are taken to obtain the height of the instrument given in the third column (H.I.). The fourth column contains all the readings except those recorded in the second column. These are called minus sights (— S.) because they are subtracted from the numbers in the third column to obtain all the numbers in the fifth column except the first, which is the assumed depth of the datum plane below the bench. The fifth column (H.S., height of surface) contains the required heights of all the points of the section named in the first column together with the heights of all benches and turning points. Making the Profile. Draw a line PP' (Fig. 56), to repre- sent the datum plane, and beginning at some point as P, lay off the distances 100, 200, 300, 340, 400* feet, and so on, to the right, using some convenient scale, say 200 feet to the inch. At these points of division erect perpendiculars equal in length to the height of the points 0, 1, 2, 3.40, 4, • • •, given in the fifth column of the above field notes, using in this case a larger scale, say 20 feet to the inch. Through the extremities of these perpendiculars draw the irregular line 0, 1, 2, 3, • • •, 11> and the result, with some explanatory figures, is the required plot or profile. The making of a profile is much simplified by the use of profile paper, which may be had by the yard or roll. If a horizontal plot is required, the bearings of the differ- ent portions of the section must be taken. Such a plot should be made, if it will assist in properly understanding the field work, or if it is desirable for future reference in connection with the field notes. Sometimes both the profile and the plot are drawn side by side on the same sheet ; in this case, if the line leveled over is hot straight, the profile will be longer than the plot. LEVELING 85 SECTION XX TOPOGRAPHIC LEVELING The principal object of topographic surveying is to show the contour of the ground. This operation, called topographic leveling, is performed by representing on paper the curved lines in which parallel horizontal planes at uniform distances from each other would meet the surface. It is evident that all points in the intersection of a horizontal plane with the surface of the ground are at the same level. Hence, it is necessary only to find points at the same level and join these to determine a line of intersection. The method commonly employed will be understood by reference to Fig. 57. The ground ABCD is divided into equal squares, and a numbered stake driven at each intersection. By means of a level and leveling rod the heights of the other sta- tions above m and D, the lowest stations, are determined. A plot of the ground with the intersect- ing lines is then drawn, and the -P height of each station written as in the figure. Suppose that the horizontal planes are 2 feet apart ; if the first passes through m and D, the second will pass through p, which is 2 feet above m ; and since n is 3 feet above m, the second plane will cut the line mn in a point s determined by the proportion mn :ms = 3 : 2. In like manner, the points t, q, and r are determined. The irregular line tsp ■■• qr represents the intersection of the second horizontal plane with the surface of the ground. A 86 SURVEYING In like manner, the intersections of the planes, respectively, 4, 6, and 8 feet above m are traced. The more rapid the change in level the nearer these lines approach each other. SECTION XXI DRAINAGE SURVEYING Preliminaries. The locality to be drained should first be carefully reconnoitered, with the view of ascertaining the general feature of the land so as to enable the surveyor properly to locate the drains ; the beginning, route, and terminus of which should all be definitely planned. By the beginning of a drain is meant its highest point. Field Work. The field work is essentially the same for under drains and for open drains. The first thing is to establish the line of a drain. This includes' the setting of stakes at intervals of from 50 feet to 100 feet, and also wherever there is an angle in the line ; the bearings and lengths of the successive straight-line sections, beginning with the instrument set over the beginning of the drain ; and the designation by distances of the points of meeting of roads and land lines. Levels of the lines are then taken in accordance with the method described on pp. 81-83. If circumstances will permit, it is sometimes of advantage to have the leveling process go hand in hand with the estab- lishing of the line. Plot and Profile. If a considerable region is to be drained, a plot should be made of the entire tract, and on this plot should be drawn, in proper position, the lines of the drain and its branches. In a suitable place on the sheet should be noted the courses of the various sections of the drain and the number of linear feet* belonging to each owner of land within the tract drained. A profile should also be made, LEVELING 87 as shown on page 84. From this profile inspection will determine whether a single grade will suffice, or whether a succession of different grades will be better. EXERCISE IX 1. Find the difference of level of two places from the fol- lowing field notes: backsights, 5.2, 6.8, and 4.0; foresights, 8.1, 9.5, and 7.9. 2. Stake of the following notes stands at the lowest point of a pond to be drained into a creek ; stake 10 stands at the edge of the bank, and 10.25 at the bottom of the creek. Make a profile, draw the grade line through and 10.25, and fill out the columns H.G. and C, the former to show the height of grade line above the datum, and the latter, the depth of cut at the several stakes necessary to construct the drain. Station + s. H.I. -s. H.S. H.G. C. Remarks B 6.000 25 Bench on rock 10.2 20.8 0.0 30 ft. west of 1 5.3 5.3 stake 1 2 4.6 3 4.0 4 6.8 5 4.572 7.090 6 3.9 7 2.0 8 4.9 9 4.3 10 4.5 10.25 11.8 Horizontal scale, 2 ch. = 1 in. Vertical scale, 20 ft. = 1 in. 88 SURVEYING 3. Find the difference in altitude between the highest point and the lowest point of the campus or of a field. 4. Obtain the data necessary for a profile of a half mile of highway, and mate the profile. 5. Write the proper numbers in the third and fifth columns of the following table of field notes, and make a profile of the section. Station + S. H.I. -S-. H.S. Remarks B 6.944 20 Bench on post 22 ft. 7.4 north of 1 5.6 2 3.9 3 4.6 t.p. 3.855 5.513 K 4 4.9 - 5 3.5 6 1.2 CHAPTER VI RAILROAD SURVEYING SECTION XXII LAYING OUT THE ROUTE Preliminary Survey. After it has been decided which of several feasible lines is the best, a preliminary survey for final location should be made. This should include, among other things, data referring to elevations, depressions, streams to be crossed, highways, buildings obstructing, character of soil, and natural resources affording materials for construc- tion ; also data referring to proximity to towns, titles of land, rights of way, and so on. Establishing the Roadbed. When the general route of a railroad has been determined, a middle surface line is run With the transit. A profile of this line is determined, as on page 84. The leveling stations are commonly 1 chain (100 feet) apart. Places of different level are connected by a gradient line, which intersects the perpendiculars to the datum line at the leveling stations in points determined by simple proportion. Hence, the distance of each leveling station above or below the level or gradient line which represents the position of the roadbed is known. SECTION XXIII CROSS-SECTION WORK Excavations. If the roadbed lies below the surface, an excavation is made. Let ACBD (Pig. 58) represent a cross 89 90 SURVEYING section of an excavation, f a point in the middle surface line, /' the corresponding point in the roadbed, and CD the width of the excavation at the bottom. The slopes at the sides are commonly made so that A A ' = f A'C, and BB' = f DB'. When ff and CD are known, the points A, B, C, and D' are readily determined by a level and tape measure. If from the area of the trapezoid ABB' A' the areas of the triangles AA'C and BB'D are deducted, the remainder is the area of the cross section. In like manner the cross section at the next station may be • determined. These two cross sections, if similar, are the bases of a frustum of a quadrangular pyramid whose volume will be the amount of the excavation. In case the cross sections are not similar, the computations should be made by means of the Prismoidal Formula (Geometry, § 733). Embankments. If the roadbed lies above the surface, an embankment is made, the cross section of which is like that of the excavation, but inverted. Fig. 59 represents the.cross section of an embankment which is lettered so as to show its relation to the excavation of Fig. 58- RAILROAD SURVEYING 91 SECTION XXIV CURVES Piinciples. When it is necessary to change the direction of a railroad it is done gradually by a curve, usually the arc of a circle. Let AF and AG (Fig. 60) represent two lines to be thus connected. Take any convenient length AB = AE = t. The inter- section of the perpendicu- lars BC and EC determines the centre C, and the radius of curvature BC — r. The length of the radius de- pends on the angle A and the tangent AB. triangle ABC, BC For, in the right Hence, tan BA C = — — > or tan i- A AB 2 r — t tan-^1. The degree of a railroad curve is the angle subtended at the centre of the curve by a chord of 100 feet. If D is the degree of a curve and r its radius, 50 sin \ D = — } and r = 50 esc \ D. For example, a 6° curve has a radius of 955.37 feet. Sometimes the topography of the route is such as to neces- sitate a successive series of curves of different radii, in which case the whole series of curves is called a compound curve, the principles involved being the same for each component as for a simple curve. 92 SURVEYING Methods of laying out the Curve. 1. Let Bm (Fig. 61) represent a portion of the tangent. It is required to find mP, the perpendicu- lar to the tangent meeting the curve at P. Fig. 61 But mP = Bn = CB — Cn. CB = r, and Cn = ^~CP 2 - Pn 2 = Vr' 2 — t\ Hence, mP — v — Vr 2 — t' 2 . 2. It is required to find mP (Fig. 62) in the direction of the centre. mP = mC But mC PC. Fig. 62 VlBC' 2 + Bm 2 = V>- 2 + t\ Hence, mP = Vr 2 + t 2 — r. 3. Place transits at B and E (Fig. 63). Direct the tele- scope of the former to E, and of the latter to A . Turn each toward the curve the same number of degrees, and mark P, the point of intersection of the lines of sight. P is a point in the circle to which AB and AE are tangents at B and E, respectively. 4. If the degree B of the curve is given and the tangent BA at B (Fig. 64), place -the transit at B and direct the tele- scope toward A. Turn off successively the angles ABP, PBP', Fig. 63 RAILROAD SURVEYING 93 P'BP", • • -, each equal to \D, and take BP, PP', P'P", ■ ■ ■, each 100 feet, the length of the tape. Then, P, P', P", ■ ■ ■ lie on the required curve. If the angle A and the tangent distance BA = t are given, D can be found from the formulas 50 Fig. 64 sin £ D = — > and r = t tan \ A. 50 Whence, sin \ D = — cot \ A. EXERCISE X 1. The cross-section areas at five stations, 100 feet apart, of a railroad cut are, respectively, 576.8 square feet, 695.1 square feet, 809.5 square feet, 652.0 square feet, and 511.7 square feet. Compute the volume of material in this portion of the cut : (i) on the hypothesis that the cross sections are similar; (ii) on the hypothesis that they are dissimilar, the alternate cross sections being regarded as mid-sections. 2. Find the radius of a curve of 1°, of 2°, of 3°, of 4°, of 5°. 3. Two adjacent straight sections of a railroad form an angle of 148° 16'. They are joined by a curve touching each of them at the distance of 388 feet from the vertical point. Find the radius and the degree of the curve. 4. Lay out a curve by the first or second method, and check the work by means of one of the transit methods. CHAPTER VII CITY SURVEYING . SECTION XXV FIELD WORK Instruments. Since the principles in city surveying are essentially the same as those in land surveying, instruments of the same general character as the instruments already described may be used, except that in this class of work the ordinary compass and the chain are seaside. For the smaller cities, an instrument such as the surveyor's transit is suffi- cient in accuracy for the purposes of angle measurement and for leveling. However, when extreme accuracy is demanded, as in the case of large cities, specially made instruments should be used : a transit reading to 30 seconds, or even to 10 seconds ; a high-grade Y level of at least 20-inch length ^ and a standard tape, tested for sag and temperature. Streets. In most cases the city engineer must take the streets as he finds them. When a city has outgrown its original plan, if indeed it had any, sheer necessity may demand the location of additional streets or changes in existing streets. If a proposed town or city is to be laid out, the general contour of the ground and location of the site determine to a great extent the system of streets to be adopted. Experience has shown that wherever possible a rectangular system of street lines, with a few well-located diagonal streets, is the most satisfactory. Streets ordinarily vary in width from 50 to 100 feet, and each sidewalk from 7 94 CITY SURVEYING 95 Vincent Simpson .570 ' Athletic 9) s Field < ~1 C-O-l-1- 6-ff-e Sewer i^r^^^ s i t^t^ TQ"^^ ^: Fi<;. 65 to 15 feet. The principal improvements of streets are grad- ing, paving, setting curbs, laying sidewalks, constructing sewers, and laying water pipes. 96 SURVEYING The field work necessary for all these may be included under the heads of leveling, locating lines, and locating points, which have already been described. Blocks and Lots. There is no established rule for the size of either blocks or lots. Fig. 65 gives some idea of their dimensions. The location of a block is described by refer- ence to the streets which bound it. A lot is described by number and block, or by number alone, or by giving the location and length of its bounding lines. The co-ordinate system of location of points, described on page 53, has much in its favor for use in city surveying. Monuments at points of reference and at intersections of streets and corners of lots should be of permanent character, and set with extreme care. SECTION XXVI OFFICE WORK Plots. Among the more important plots that should be prepared by the city engineer are a complete city map, drawn to scale, showing the streets and alleys, blocks and lots, with dimensions, and the location of railroads, street-car lines, sew- age system, water-pipe lines, and so on ; a topographical map of the entire city, including as may be found desirable por- tions of the surrounding region ; a profile map of the streets. These are made from the field notes, which should be amply and carefully prepared.. Records. No work of importance, whether done in the field or in the office, should fail to be recorded in some perma- nent form. Field notes, computations, plots, and copies of work specially prepared should be properly indexed and filed away. ANSWERS 97 v SURVEYING Exercise II. Page 22 2. 540°. 4. N. 51° 30' E. Exercise III. Page 27 2. 360°. 3. 235 ft. 3.8 in. Exercise V. Page 55 1. 8 a. 64 p. 6. 13 a. 6^ i>. 11. 4 a. 35 p. 2. 16 a. 74|| p. 7. 2 a. 58| p. 12. 4 a. 110 p. 3. 4 a. 5^ r- »• 11 a. 157 p. 13. 6 a. 23|| p. 4. 115-.fr p. 9. 7.51925. 5. 3 a. 78 p. 10. 13.0735. Exercise VI. Page 64 1. 2 a. 26 p. 3. 8 a. 54 p. 5. 2 a. 78 p. 7. 5 a. 42 p. 2. 20 a. 12 p. 4. 3 a. 122 p. 6. 6 a. 2 p. 8. 2 a. 151 p. Exercise VII. Page 66 1. 2 a. 12| p. 2. 98 a. 92 p. Exercise VIII. Page 69 1. AE=S.lb ch. 4. AE = 5.50 ch. 2. AE = 3.50 ch. ; 5. CE = 4.456 ch. EG = 3.42 ch. 6 AI) _ 2 .275 ch. ; BE = 1.82 ch. 3. AE = 4.55 ch. 7. ylZ> = 4.51 ch.; BE = 3.61 ch. 8. The distances on ^4B are 2 ch., 3 ch., and 5 ch. 9. EM (on EA) = 2.5087 ch. ; AN (on AB) = 6.4390 ch. 98 SURVEYING 10. Let EG>BF; then AE = 12.247 ch., AG = 0.798 ch., AD = 8.660 ch., AF = 6.928 ch. 11. LelDG>EF; then CG = 14.862 ch., CD = 13.113 ch., CF= 11.404 ch., CE= 10.062 ch. Exercise IX. Page 87 1. 9.5. 2. Column H.G. 20.8, 20.4, 20.0, 19.6, 19.2, 18.8, 18.4, 18.0, 17.6, 17.2, 16.8, 16.7. Column C. 0.0, 5.3, 6.4, 7.4, 5.0, 5.1, 6.2, 8.5, 6.0, 7.0, 7.2, 0.0. 8 9 10 10.25 5. Third column : 26.944 opposite ; 25.286 opposite 4. Fifth column : 20, 19.5, 21.3, 23, 22.3, 21.431, 20.4, 21.8, 24.1. Exercise X. Page 93 1. 9986.5 cu. yd.; 9994.9 cu. yd. 2. 5730 ft.; 2865 ft.; 1910 ft.; 1433 ft.; 1146 ft. 3. 1365 ft.; 4° 11' 53". FIVE -PLACE Logarithmic and Trigonometric TABLES ARRANGED BY G. A. WENTWORTH, A.M. G. A. HILL, A.M. Boston, U.S.A., and London PUBLISHED BY GINN & COMPANY 1903 Entered according to Act of Congress, in the year 1882, by G. A. WENTWORTH and G. A. HILL in the office of the Librarian of Congress. a\ Washington Copyright, 1895, by G. A. Wentwoeth and G. A. Hill. INTRODUCTION. 1. If the natural numbers are regarded as powers of ten, the exponents of the powers are the Common or Briggs Logarithms of the numbers. If A and B denote natural numbers, a and b their logarithms, then 10 a = A, 10 6 = B ; or, written in logarithmic form, log A = a, log B = b. 2. The logarithm of a product is found by adding the logarithms of its factors. For, AX B = 10" X 10* = 10" + b . Therefore, log (A x B) = a + b = log A + log B. 3. The logarithm of a quotient is found by subtracting the logarithm of the divisor from that of the dividend. A 10 a For — = — =lo<* — i> A Therefore, log — = a — 6 = log A — log B. Jt> 4. The logarithm of a power of a number is found by multiply- ing the logarithm of the number by the exponent of the power. For, A n — (10 a )« = 10 are . Therefore, log A n — an = n log A . 5. The logarithm of the root of a number is found by dividing the logarithm of the number by the index of the root. For, y/A = \/To« = 10". Therefore, log yfI = - = ^^ • n n 6. The logarithms of 1, 10, 100, etc., and of 0.1, 0.01, 0.001, etc., are integral numbers. The logarithms of all other numbers are fractions. IV LOGARITHMS. For, 10° = 1, hence log 1 = 10 1 = 10, hence log 10 = 1 102 - ioo, hence log 100 = 2 10 3 = 1000, hence log 1000 = 3 10-i = 0.1, hence log 0. 1 = — 1 10-2= 0.01, hence log 0.01 = —2 10-s - o.OOl, hence log 0.001 = — 3 and so on. If the number is between 1 and 10, the logarithm is between and 1. If the number is between 10 and 100, the logarithm is between 1 and 2. If the number is between 100 and 1000, the logarithm is between 2 and 3. If the number is between land 0. 1 , the logarithm is between and — 1. If the number is between 0.1 and 0.01, the logarithm is between —1 and —2. If the number is between 0.01 and 0.001, the logarithm is between —2 and —3. And so on. 7. If the number is less than 1, the logarithm is negative (§ 6), but is written in such a form that the fractional part is always positive. Tor the number may be regarded as the product of two factors, one of which lies between 1 and 10, and the- other is a negative power of 10 ; the logarithm will then take the form of a difference whose minuend is a positive proper fraction, and whose subtrahend is a positive integral number. Thus, 0.48 = 4.8X0.1. Therefore (§ 2), log 0.48 = log 4.8 + log 0.1 = 0.68124 - 1. (Page 1.) Again, 0.0007 = 7x 0.0001. Therefore, log 0.0007 = log 7 + log 0.0001 = 0.84510 - 4. The logarithm 0.84510 — 4 is often written 4.84510. 8. Every logarithm, therefore, consists of two parts : a positive or negative integral number, which is called the Characteristic, and a positive proper fraction, which is called the Mantissa. Thus, in the logarithm 3.52179, the integral number 3 is the characteristic, and the fraction .52179 the mantissa. In the logarithm 0.78254 — 2, the inte- gral number — 2 is the characteristic, and the fraction 0.78254 is the mantissa. 9. If the logarithm is negative^ it is customary to change the form of the difference so that the subtrahend shall be 10 or a multiple of 10. This is done by adding to both minuend and subtrahend a number which will increase the subtrahend to 10 or a multiple of 10. Thus, the logarithm 0.78254 — 2 is changed to 8.78254 — 10 by adding 8 to both minuend and subtrahend. The logarithm 0.92737 — 13 is changed to 7.92737 — 20 by adding 7 to both minuend and subtrahend. 10. The following rules are derived from § 6 : — If the number is greater than 1, make the characteristic of the logarithm one unit less than the number of figures on the left of the decimal point. If the number is less than 1, make the characteristic of the loga- rithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number. INTRODUCTION". V If the characteristic of a given logarithm is positive, make the number of figures in the integral part of the corresponding number one more than the number of units in the characteristic. If the characteristic is negative, make the number of zeros between the decimal point and the first significant figure of the correspond- ing number one less than the number of units in the characteristic. Thus, the characteristic of log 7849.27 = 3 ; the characteristic of log 0.037 = — 2 = 8.00000 — 10. If the characteristic is 4, the corresponding number has five figures in its inte- gral part. If the characteristic is — 3, that is, 7.00000 — 10, the corresponding fraction has two zeros between the decimal point and the first significant figure. 11. The logarithms of numbers that can be derived one from another by multiplication or division by an integral power of 10 have the same mantissa. For, multiplying or dividing a number by an integral power of 10 will increase or diminish its logarithm by the exponent of that power of 10 ; and since this exponent is an integer, the mantissa of the logarithm will be unaffected. Thus, log 4.6021 =0.66296. (Page 9.) log 460.21 = log (4.6021 X 10 2 ) = log 4.6021 + log 10 2 = 0.66296 + 2 = 2.66296. log 460210 = log (4.6021 X 10 5 ) = log 4.6021 + log 10 5 = 0.66296 + 5 = 5.66296. log 0.046021 = log (4.6021 ■¥ 10 2 ) = log 4.6021 - log 10 2 = 0.66296 - 2 = 8.66296 - 10. TABLE I. 12. In this table (pp. 1-19) the vertical columns headed N con- tain the numbers, and the other columns the logarithms. On page 1 both the characteristic and the mantissa are printed. On pages 2-19 the mantissa only is printed. The fractional part of a logarithm can be expressed only approx- imately, aud in a five-place table all figures that follow the fifth are rejected. Whenever the sixth figure is 5, or more, the fifth figure is increased by 1. The figure 5 is written when the value of the figure in the place in which it stands, together with the succeeding figures, is more than 4^, but less than 5. Thus, if the mantissa of a logarithm written to seven places is 5328732, it is written in this table (a five-place table) 53287. If it is 5328751, it is written 53288. If it is 5328461 or 5328499, it is written in this table 53285. Again, if the mantissa is 5324981, it is written 5325.0 ; and if it is 4999967, it is written 50000. VI LOGARITHMS. This distinction between 5 and 5, in case it is desired to curtail still further the mantissas of logarithms, removes all doubt whether a 5 in the last given place, or in the last but one followed by a zero, should be simply rejected, or whether the rejection should lead us to increase the preceding figure by one unit. Thus, the mantissa 13925 when reduced to four places should be 1392 ; but 13925 should be 1393. To Find the Logarithm of a Given Number. 13. If the given number consists of one .or two significant figures, the logarithm is given on page 1. If zeros follow the significant figures, or if the number is a proper decimal fraction, the characteristic must be determined by § 10. 14. If the given number has three significant figures, it will be found in the column headed N (pp. 2-19), and the mantissa of its logarithm in the next column to the right, and on the same line. Thus, Page 2. log 145 = 2.16137, log 14500 = 4.16137. Page 14. log 716 = 2.85491, log.0?716 = 9.85491 - 10. 15. If the given number has four significant figures, the first three will be found in the column headed 1ST, and the fourth at the top of the page in the line containing the figures 1, 2, 3, etc. The mantissa will be found in the column headed by the fourth figure, and on the same line with the first three figures. Thus, Page 15. log 7682 = 3.88547„ log 76.85 = 1.88564. Page 18. log 93280 = 4.96979, log 0.9468 = 9.97626 — 10. 16. If the given number has five or more significant figures, a process called interpolation is required. Interpolation is based on the assumption that between two con- secutive mantissas of the table the change in the mantissa is directly proportional to the change in the number. Required the logarithm of 34237. The required mantissa is (§ 11), the same as the mantissa for 3423.7 ; there- fore it will be found by adding to the mantissa of 3423 seven-tenths of the difference between the mantissas for 3423 and 3424. The mantissa for 3423 is 53441. The difference between the mantissas for 3423 and 3424 is 12. Hence, the mantissa for 3423.7 is 53441 + (0.7 x 12) = 53449. Therefore, the required logarithm of 34237 is 4.53449. INTRODUCTION. Vll Required the logarithm of 0.0015764. The required mantissa is the same as the mantissa for 1576.4 ; therefore it will be found by adding to the mantissa for 1576 four-tenths of the difference between the mantissas for 1576 and 1577. The mantissa for 1576 is 19756. The difference between the mantissas for 1576 and 1577 is 27. Hence, the mantissa for 1576.4 is 19756 + (0.4 X 27) = 19767. Therefore, the required logarithm of 0.0015764 is 7.19767 — 10. Eequired the logarithm of 32.6708. The required mantissa is the same as the mantissa for 3267.08; therefore it will be found by adding to the mantissa for 3267 eight-hundredths of the difference between the mantissas for 3267 and 3268. The mantissa for 3267 is 51415. The difference between the mantissas for 3267 and 3268 is 13. Hence, the mantissa for 3267.08 is 51415 + (0.08 X 13) = 51416. Therefore, the required logarithm of 32.6708 is 1.51416. 17. When the fraction of a unit in the part to be added to the mantissa for four figures is less than 0.5 it is to be neglected ; when it is 0.5 or more than 0.5 it is to be taken as one unit. Thus, in the first example, the part to be added to the mantissa for 3423 is 8.4, and the .4 is rejected. In the second example, the part to be added to the mantissa for 1576 is 10.8, and 11 is added. To Find the Antilogarithm ; that is, the Number Corre- sponding to a Given Logarithm. ) 18. If the given mantissa can be found in the table, the first three figures of the required number will be found in the same line with the mantissa in the column headed 1ST, and the fourth figure at the top of the column containing the mantissa. The position of the decimal point is determined by the charac- teristic (§ 10). Find the number corresponding to the logarithm 0.92002. Page 16. The number for the mantissa 92002 is 8318. The characteristic is ; therefore, the required number is 8.318. Find the number corresponding to the logarithm 6.09167. Page 2. The number for the mantissa 09167 is 1235. The characteristic is 6 ; therefore, the required number is 1235000. Find the number corresponding to the logarithm 7.50325 — 10. Page 6. The number for the mantissa 50325 is 3186. The characteristic is — 3 ; therefore, the required number is 0.003186. Vlll LOGARITHMS. 19. If the given mantissa cannot be found in the table, find in the table the two adjacent mantissas between which the given mantissa lies, and the four figures corresponding to the smaller of these two mantissas will be the first four significant figures of the required number. If more than four figures are desired, they may be found by interpolation, as in the following examples : Find the number corresponding to the logarithm 1.48762. Here the two adjacent mantissas of the table, between which the given man- tissa 48762 lies, are found to be (page 6) 48756 and 48770. The corresponding numbers are 3078 and 3074. The smaller of these, 3073, contains the first four significant figures of the required number. The difference between the two adjacent mantissas is 14, and the difference between the corresponding numbers is 1. The difference between the smaller of the two adjacent mantissas, 48756, and the given mantissa, 48762, is 6. Therefore, the number to be annexed to 3073 is T 6 ¥ of 1 = 0.428, and the fifth significant figure of the required number is 4. Hence, the required number is 30.734. Find the number corresponding to the logarithm 7.82326 — 10. The two adjacent mantissas between which 82326 lies are (page 13) 82321 and 82328. The number corresponding to the mantissa 82321 is 6656. The difference between the two adjacent mantissas is 7, and the difference between the corresponding numbers is 1. The difference between the smaller mantissa, 82321, and the given mantissa, 82326, is 5. Therefore, the number to be annexed to 6656 is f of 1 = 0.7, and the fifth significant figure of the required number is 7. Hence, the required number is 0.0066567. In using a five-place table the numbers corresponding to man- tissas may be carried to five significant figures, and in the first part of the table to six figures.* 20. The logarithm of the reciprocal of a number is called the Cologarithm of the number. If A denotes any number, then colog A = log — = log 1 — log A (§ 3) = — log A. Hence, the cologarithm of a number is equal to the logarithm of the number with the minus sign prefixed, which sign affects the entire logarithm, both characteristic and mantissa. *In most tables of logarithms proportional parts are given as an aid to interpolation ; but, after a little practice, the operation can be performed nearly as rapidly without them. Their omission allows a page with larger-faced type and more open spacing, and consequently less trying to the eyes. INTRODUCTION. IX In order to avoid a negative mantissa in the cologarithm, it is customary to substitute for — log A its equivalent (10— log A)— 10. Hence, the cologarithm of a number is found by subtracting the logarithm of the number from 10, and then annexing — 10 to the remainder. The best way to perform the subtraction is to begin on the left and subtract each figure of log A from 9 until we reach the last significant figure, which must be subtracted from 10. If log A is greater in absolute value than 10 and less than 20, then in order to avoid a negative mantissa, it is necessary to write — log A in the form (20 - log A)— 20. So that, in this case, colog A is found by subtracting log A from 20, and then annexing — 20 to the remainder. Find the cologarithm of 4007. 10 -10 Page 8. log 4007 = 3.60282 colog 4007= 6.39718 — 10 Find the cologarithm of 103992000000. 20 -20 Page 2. log 103992000000 = 11.01700 colog 103992000000 = 8.98300 — 20 If the characteristic of log A is negative, then the subtrahend, — 10 or — 20, will vanish in finding the value of colog A. Find the cologarithm of 0.004007. 10 - 10 log 0.004007 = 7.60282 - 10 colog 0.004007 = 2.39718 With practice, the cologarithm of a number can be taken from the table as rapidly as the logarithm itself. By using cologarithms the inconvenience of subtracting the log- arithm of a divisor is avoided. For dividing by a number is equivalent to multiplying by its reciprocal. Hence, instead of subtracting the logarithm of a divisor its cologarithm may be added. LOGARITHMS. Exercises. Find the logarithms of : 1. 6170. 2. 0.617. 3. 2867. 4. 85.76. 5. 296.8. 6. 7004. 7. 0.8694. 8. 0.5908. 9. 73243. 10. 67.3208. 11. 18.5283. 12. 0.0042003. Find the cologarithms of 13. 72433. 14. 802.376. 15. 15.7643. 16. 869.278. 17. 154000. 18. 70.0426. 19. 0.002403. 20. 0.000777. 21. 0.051828. Find the antilogarithms of : 22. 2.47246. 23. 7.89081. 24. 2.91221. 25. 1.26784. 26. 3.79029. 27. 5.18752. 28. 9.79029-10. 29. 7.62328 — 10. 30. 6.15465-10. Computation by Logarithms. 21. (1) Find the value of x, if x = 72214 X 0.08203. Page 14. log 72214 = 4.85862 Page 16. log 0.08203 = 8.91397 — 10 By §2. logx =3.77259 Page 11. x = 5923.63 (2) Find the value of x, if x = 5250 -=- 23487. Page 10. Page 4. Page 4. log 5250 colog 23487 logx .-. X = 3.72016 = 5.62917 - 10 = 9.34933 - 10 = log 0.22353 = 0.22353 7.56 X 4667 X 567 '899.1X0.00337X23435 Page 15. log 7.56 = 0.87852 Page 9. log 4667 = 3.66904 Page 11. log 567 = 2.75358 Page 17. colog 899.1 = 7.04619 — 10 Page 6. colog 0.00337 = 2.47237 Page 4. colog 23435 = 5.63013 — 10 Page 5. log x = 2.44983 = log 281.73 .-. x = 281.73. INTRODUCTION. XI (4) Find the cube of 376. Page 7. log 376 = 2.57519 Multiply by 3 (§ 4), 3 Page 10. log 3763 = 7.72557 = log 53158600 .-. 37 6 3 = 53158600. (5) Find the square of 0.003278. Page 6. log 0.003278 = 7.51561 — 10 2 Page 2. log 0.003278 2 = 15.03122 — 20 = log 0.000010745 .-.0.0032782= 0.000010745. (6) Find the square root of 8322. Page 16. log 8322 = 3.92023 Divide by 2 (§ 5), 2 )3.92023 log V8322 = 1.96012 = log 91.226 .-. V8322 = 91.226. If the given number is a proper fraction, its logarithm will have as a subtrahend 10 or a multiple of 10. In this case, before divid- ing the logarithm by the index of the root, both the subtrahend and the number preceding the mantissa should be increased by such a number as will make the subtrahend, when divided by the index of the root, 10 or a multiple of 10. (7) Find the square root of 0.000043641. Page 8. log 0.000043641 = 5.63989— K 10 -10 Divide by 2 (§ 5), 2 )15.63989 — 20 Page 13. log V 0. 000043641 = 7.81995 — 10 = log 0.0066062 .-. V0.000043641 = 0.0066062. (8) Find the sixth root of 0.076553. Page 15. log 0.076553 = 8.88397-10 50 -50 Divide by 6 (§ 5), 6 )58.88397 — 60 Page 13. log V0. 076553 = 9.81400 - 10 = log 0.65163 .-. \/0.076553 = 0.65163. Exercises. Find by logarithms the value of : 45607 5.6123 2.567 ' 31045* ' 0.01987' ' 0.05786' Xll LOGARITHMS. 0.06547 ' 74.938 X 0.05938° r 4.657 X 0.03467 ' 3.908 X 0.07189' 0.0075389 X 0.0079 ' 0.00907 X 009784' 312 X 7.18 X 31.82 * 519 X 8.27 X 5.132* 0.007 x 57.83 X 28.13 ' 9.317 X 00.28 X 476.5* 5.55 X 0.0007632 X 0.87654 9. 2.79 X 0.0009524 X 1.46785 /(XOOj \o.oo; r . 003457 X 43.387 X 99.2 X 0.00025 '" 005824 X 15.724 X 1.38 X 0.00089 s/ 23.815 X 29.36 X 0.007 X 0.62487 X/ 0.00072 X 9.236 X 5.924 X 3.0007 ,^1416 X 0.031416 X 0.0031416 '■Vi 7285 X 0.017285 X 0.0017285 TABLE II. 22. This table (page 20) contains the value of the number nr its most useful combinations, and their logarithms. Find the length of an arc of 47° 32' 57' 1, in a unit circle. 47° 32' 57" = 171177" log 171177 "= 5.23344 log \ = 4.68557 - 10 ° a " • ■ log arc 47° 32' 57" = 9.91901 - 10 = log 0.82994 .-. length of arc = 0.82994. Find the angle if the length of its arc in a unit circle = 0.54936. log 0.54936 =9.73986-10 colog — = log a" = 5.31443 ° a log angle = 5.05429 = log 113316 .-. angle = 113316" = 31° 28' 36". INTRODUCTION. X1H 23. The relations between arcs and angles given in Table II. are readily deduced from the circular measure of an angle. In Circular Measure an angle is defined by the equation , arc angle = — -. — , ■ radius in which the word arc denotes the length of the arc corresponding to the angle, when both arc and radius are expressed in terms of the same linear unit. Since the arc and radius for a given angle in different circles vary in the same ratio, the value of the angle given by this equa- tion is independent of the value of the radius. The angle which is measured by a radius-arc is called a Radian, and is the angular unit in circular measure. C -J- C Since C = 2 ttB, it follows that — = 2 7r, and ■*=- = it. Therefore, Jx K If the arc = circumference, the angle = 2 nr. If the arc = semicircumference, the angle = it. If the arc = quadrant, the angle = ^ it. If the arc = radius, the angle = 1. Therefore, tt = 180°, \ it — 90°, £ it = 60°, ± it = 45°, £ it — 30", £ it = 22^°, and so on. Since 180° in common measure equals it units in circular measure, 1° in common measure = zr^ units in circular measure ; 180 -....., 180°. 1 unit in circular measure = m common measure. 7T By means of these two equations, the value of an angle expressed in one measure may be changed to its value in the other measure. Thus, the angle whose arc is equal to the radius is an angle of 180° 1 unit in circular measure, and is equal to , or 57° 17' 45", 7T very nearly. TABLE III. 24. This table (pp. 21-49) contains the logarithms of the trigo- nometric functions of angles. In order to avoid negative character- istics, the characteristic of every logarithm is printed 10 too large. Therefore, — 10 is to be annexed to each logarithm. On pages 28-49 the characteristic remains the same throughout each column, and is printed at the top and the bottom of the column. XIV LOGARITHMS. But on pp. 30, 49, the characteristic changes one unit in value at the places marked with bars. Above these bars the proper characteristic- is printed at the top, and below them at the bottom, of the column. 25. On pages 28-49 the log sin, log tan, log cot, and log cos, of 1° to 89°, are given to every minute. Conversely, this part of the table gives the value of the angle to the nearest minute when log sin, log tan, log cot, or log cos is known, provided log sin or log cos lies between 8.24186 and 9.99993, and log tan or log cot lies between 8.24192 and 11.75808. If the exact value of the given logarithm of a function is not found in the table, the value nearest to it is to be taken, unless interpolation is employed as explained in § 26. If the angle is less than 45° the number of degrees is printed at the top of the page, and the number of minutes in the column to the left of the columns containing the logarithm. If the angle is greater than 45°, the number of degrees is printed at the bottom of the page, and the number of minutes in the column to the right of the columns containing the logarithms. If the angle is less than 45°, the names of its functions are printed at the top of the page ; if greater than 45°, at the bottom of the page. Thus, Page 38. log sin 21° 37' = 9.56631-10. Page 45. log cot 36° 53' =10. 12473 -10 = 0. 12473. Page 37. log cos 69° 14' = 9.54969 — 10. Page 49. log tan 45° 59' = 10.01491 — 10 = 0.01491. Page 48. If log cos = 9.87468 — 10, angle = 41° 28'. Page 34. If log cot = 9.39353 — 10, angle = 76° 6'. If log sin = 9.47760 — 10, the nearest log sin in the table is 9.47774 — 10 (page 36), and the angle corresponding to this value is 17° 29'. If log tan = 0.76520 = 10.76520 — 10, the nearest log tan in the table is 10.76490 — 10 (page 32), and the angle corresponding to this value is 80° 15'. 26. If it is desired to obtain the logarithms of the functions of angles that contain seconds, or to obtain the value of the angle in degrees, minutes, and seconds, from the logarithms of its functions,, interpolation must be employed. Here it must be remembered that, The difference between two consecutive angles in the table is 60". Log sin and log tan increase as the angle increases ; log cos and log cot diminish as the angle increases. INTRODUCTION. XV Find log tan 70° 46' 8". Page 37. log tan 70° 46' = 0.45731. The difference between the mantissas of log tan 70° 46' and log tan 70° 47' is 41, and ^ of 41 — 5. As the function is increasing, the 5 must be added to the figure in the fifth place of the mantissa 45731 ; and Therefore log tan 70° 46' 8'' = 0.45736. Find log cos 47° 35' 4". Page 48. log cos 47° 35' = 9.82899 — 10. The difference between this mantissa and the mantissas of the next log cos is 14, and ^ of 14 = 1. As the function is decreasing, the 1 must be subtracted from the figure in the fifth place of the mantissa 82899 ; and Therefore log cos 47° 35' 4" = 9.82898 — 10. Find the angle for which log sin = 9.45359 — 10. Page 35. The mantissa of the nearest smaller log sin in the table is 45334. The angle corresponding to this value is 16° 30'. The difference between 45334 and the given mantissa, 45359, is 25. The difference between 45334 and the next following mantissa, 45377, is 43, and ff of 60" = 35". As the function is increasing, the 35" must be added to 16° 30'; and the required angle is 16° 30' 35". Find the angle for which log cot = 0.73478. Page 32. The mantissa of the nearest smaller log cot in the table is 73415. The angle corresponding to this value is 10° 27'. The difference between 73415 and the given mantissa is 63. The difference between 73415 and the next following mantissa is 71, and ff- of 60" = 53". As the function is decreasing, the 53" must be subtracted from 10° 27'; and the required angle is 10° 26' 7". Find Exercises. 1. log sin 30° 8' 9". 9. log tan 25° 27' 47". 2. log sin 54° 54' 40". 10. log cos 56° 11' 57". 3. log cos 43° 32' 31". 11. log cot 62° 0' 4". 4. log cos 69° 25' 11". 12. log cos 75° 26' 58". 5. log tan 32° 9' 17". 13. log tan 33° 27' 13". 6. log tan 50° 2' 2". 14. log cot 81° 55' 24". 7. log cot 44° 33' 17". 15. log tan 89° 46' 35". 8. log cot 55° 9' 32". 16. log tan 1° 25' 56". XVI LOGARITHMS. Find the angle A if 17. log sin A- 9.70075. 25. log cos A — 9.40008. 18. log sin A= 9.91289. 26. log cot A = 9.78815. 19. logcos^4= 9.86026. 27. log cos A - 9.34301. 20. log cos A= 9.54595. 28. log tan A = 10.52288. 21. logtan^= 9.79840. 29. log cot A = 9 65349. 22. log tan J. = 10.07671. 30. log sin A = 8.39316. 23. log cot A = 10.00675. 31. log sin A = 8.06678. 24. log cot A= 9.84266. 32. log tan A = 8.11148. 27. If log sec or log esc of an angle is desired, it may be found from the table by the formulas, sec A = 7 ; hence, log sec A = colog cos A. cos A ° esc A = — - ; hence, log esc A = colog sin A. sin A Page 31. log sec 8° 28' = colog cos 8° 28' = 0.00476. Page 42. log esc 59° 36' 44" = colog sin 59° 36' 44" = 0.06418. 28. If a given angle is between 0° and 1°, or between 89° and 90°; or, conversely, if a given log sin or log cos does not lie between the limits 8.24186 and 9.99993 in the table; or, if a given log tan or log cot does not lie between the limits 8.2 ; |192 and 11.75808 in the table ; then pages 21-24 of Table III. must be used. On page 21, log sin of angles between 0° and 0° 3', or log cos of the complementary angles between 89° 57' and 90°, are given to every second; for the angles between 0° and 0° 3', log tan = log sin, and log cos = 0.00000 ; for the angles between 89° 57' and 90°, log cot = log cos, and log sin = 0.00000. On pages 22-24, log sin, log'tan, and log cos of angles between 0° and 1°, or log cos, log cot, and log sin of the complementary angles between 89° and 90°, are given to every 10". Whenever log tan or log cot is not given, they may be found by the formulas, log tan = colog cot. • log cot = colog tan. Conversely, if a given log tan or log cot is not contained in the table, then the colog must be found ; this will be the log cot or log tan, as the case may be, and will be contained in the table. On pages 25-27 the logarithms of the functions of angles between 1° and 2°, or between 88° and 90°, are given in the manner employed on pages 22-24. These pages should be used if the angle lies between these limits, and if not only degrees and minutes, but degrees, minutes, and multiples of 10" are given or required. INTRODUCTION. XV11 When the angle is between 0° and 2°, or 88° and 90°, and a greater degree of accuracy is desired than that given by the table, interpolation may be employed ; but for these angles interpolation does not always give true results, and it is better to use Table IV. Find log tan 0° 2' 47", and log cos 89° 37' 20". Page 21. log tan 0° 2' 47" = log sin 0° 2" 47" = 6.90829 - 10. Page 23. log cos 89° 37' 20" = 7.81911 — 10. Find log cot 0° 2' 15". 10 -10 Page 21. log tan 0° 2' 15" = 6.81591-10 Therefore, log cot 0° 2' 15" = 3.18409 Find log tan 89° 38' 30". 10 -10 Page 23. log cot 89° 38' 30" = 7.79617 — 10 Therefore, log tan 89° 38' 30" = 2.20383 Find the angle for which log tan = 6.92090 — 10. Page 21. The nearest log tan is 6.92110 — 10. The corresponding angle for which is 0° 2' 52". Find the angle for which log cos = 7.70240 — 10. Page 22. The nearest log cos is 7.70261 — 10. Ihe corresponding angle for which is 89° 42' 40". Find the angle for which log cot = 2.37368. This log cot is not contained in the table. The colog cot = 7.62632 — 10 = log tan. The log tan in the table nearest to this is (page 22) 7.62510— 10, and the angle corresponding to this value of log tan is 0° 14' 30". 29. If an angle x is between 90° and 360°, it follows, from formulas established in Trigonometry, that, between 90° and 180°, between 180° and 270°, log sin x = \og sin (180° — x), log sin a; = log sin (x — 180°)„, log cos x = log cos (180° — x) n , log cos x = log cos (x — 180°)„, log tan x = log tan (180° — x) n , log tan x = log tan (x — 180°), log cot x = log cot (180° — x) n ; log cot x = log cot (x — 180°) ; between 270° and 360°, log sin £ = log sin (360° — x) n , log cos # = log cos (360° — x), log tan x = log tan (360° — x) n , log cot cc = log cot (360° — x) n . XV111 LOGARITHMS. The letter n is placed (according to custom) after the logarithms of those functions which are negative in value. The above formulas show, without further explanation, how to find by means of Table III. the logarithms of the functions of any angle between 90° and 360°. Thus, log sin 137° 45' 22" = log sin 42° 14' 38" = 9.82756 — 10. log cos 137° 45' 22" = log„ cos 42° 14' 38" = 9.86940 n — 10. log tan 137° 45' 22" = log„ tan 42° 14' 38" = 9.95815„ — 10. log cot 137° 45' 22" = log,, cot 42° 14' 38" = 0.04185„. log sin 209° 32' 50" = log, sin 29° 32' 50" = 9.69297 n — 10. log cos 330° 27' 10" = log cos 29° 32' 50" = 9.93949 — 10. Conversely, to a given logarithm of a trigonometric function there correspond between 0° and 360° four angles, one angle in each quadrant, and so related that if x denote the acute angle, the other three angles are 180° —x, 180° +x, and 360° — x. If besides the given logarithm it is known whether the function is positive or negative, the ambiguity is confined to two quadrants, therefore to two angles. Thus, if the log tan = 9.47451 — 10, the angles are 16° 36' 17" in Quadrant I. and 196° 36' 17" in Quadrant III. ; but if the log tan = 9.47451„— 10, the angles are 163° 23' 43" in Quadrant II. and 343° 23' 43" in Quadrant IV. To remove all ambiguity, further conditions . are required, or a knowledge of the special circumstances connected with the problem in question. TABLE IV. 30. This table (page 50) must be used when great accuracy is desired in working with angles between 0° and 2°, or between 88° and 90°. The values of S and T are such that when the angle a is expressed in seconds, S = log sin a — log a", T = log tan a — log a". Hence follow the formulas given on page 50. The values of S and T are printed with the characteristic 10 too large, and in using them — 10 must always be annexed. Find log sin 0° 58' 17". 0° 58' 17" = 3497" log 3497 = 3.54370 S = 4.68555 — 10 log sin 0° 58' 17" = 8.22925 - 10 Find log cos 88° 26' 41.2". 90° - 88° 26' 41.2" = 1° 33' 18.8" = 5598.8" log 5598.8 = 3.74809 S = 4.68552 - 10 log cos 88° 26' 41.2" = 8.43361 — 10 INTRODUCTION. Find log tan 0° 52' 47.5". 0° 52' 47.5" = 3167.5" log 3167.5 = 3.50072 T = 4.68561 — 10 , log tan 0° 52' 47.5" = 8.18633 - 10 Find log tan 89° 54' 37.362". 90° - 89° 54' 37.362" = 0° 5' 22.638" = 322.638" log 322.638 = 2.50871 T = 4.68558 — 10 log cot 89° 54' 37.362" = 7.19429 — *o log tan 89° 54' 37.362" = 2.80571 Find the angle, if log sin = 6. 72306 — 10. 6.72306-10 S= 4.68557 — 10 Subtract, 2.03749 109.015" = log 109.0K = 0° 1' 49.01 Find the angle for which log cot = 1.67604. colog cot - T Subtract, = 8.32396 - = 4.68564 - 3.63832 4348.3" 10 10 = log 4348.3 = 1° 12' 28.3 Find the angle for which log tan = 1.55407. colog tan = 8.44593 — 10 T = 4.68569 — 10 Subtract, 3.76024 = log 5757.6 5757.6" = 1° 35' 57.6", and 90° — 1° 35' 57.6" = 88° 24' 2.4". Therefore, the angle required is 88° 24' 2.4". TABLE V. 31. This table (p. 51), containing the circumferences and areas of circles, does not require explanation. TABLE VI. 32. Table VI. (pp. 52-69). contains the natural sines, cosines, tangents, and cotangents of angles from 0° to 90°, at inter- vals of 1'. If greater accuracy is desired it may be obtained by interpolation. Note. In preparing the preceding explanations, we have made free use of the Logarithmic Tables by F. G. Gauss. For Table VI. we are indebted to D. Carhart. TABLE VII. 33. This table (pp. 70-75) gives the latitude and departure to three places of decimals for distances from 1 to 10, corresponding to bearings from 0° to 90° at intervals of 15'. XX LOGARITHMS. If the bearing does not exceed 45° it is found in the left-hand column, and the designations of the columns under " Distance " are taken from the top of the page ; but if the bearing exceeds 45°, it is found in the right-h.a,n&. column, and the designations of the columns under " Distance " are taken from the bottom of the page. The method of using the table will be made plain by the follow- ing examples : — (1) Let it be required to find the latitude and departure of the course K 35° 15' E. 6 chains. On p. 75, left-hand column, look for 35° 15' ; opposite this hearing, in the vertical column headed "Distance 6," are found 4.900 and 3.463 under the headings ' ' Latitude ' ' and ' ' Departure ' ' respectively. Hence, latitude or northing = 4.900 chains, and departure or easting = 3.463 chains. (2) Let it be required to find the latitude and departure of the course S. 87° W. 2 chains. . As the bearing exceeds 45°, we look in the rigttt-hand column of p. 70, and opposite 87° in the column marked "Distance 2 " we find (taking the designa- tions of the columns from the bottom of the page) latitude = 0.105 chains, and departure = 1.997 chains. Hence, latitude or southing = 0.105 chains, and departure or westing = 1.997 chains. (3) Let it be required to find the latitude and departure of the course K 15° 45' W. 27.36 chains. In this case we find the required numbers for each figure of the distance separately, arranging the work as in the following table. In practice, only the last columns under ' ' Latitude ' ' and ' ' Departure ' ' are written. Distance. Latitude. Depaetuee. 20 = 2 X 10 7 0.3 =3 -M0 0.06 = 6 + 100 1.925 X 10 = 19.25 6.737 2.887 -M0 =0.289 5.776 -£.100 = 0.058 0.543 X 10 = 5.43 1.90 0.814 -M0 =0.081 1.628 -7- 100 = 0.016 27.36 26.334 7.427 Hence, latitude = 26.334 chains, and departure = 7.427 chains. TABLE I. THE COMMON OK BEIGGS LOGAEITHMS OF THE NATUEAL IUMBEES From 1 to 10000. 1-100 N log N log N log N log N log 1 0. 00 000 21 1.32 222 41 1.61278 61 1. 7S 533 81 1.90 849 2 0. 30 103 22 1.34 242 42 1. 62 325 62 1. 79 239 82 1. 91 3S1 3 0. 47 712 23 1.36173 43 1. 63 347 63 1. 79 934 83 1. 91 908 4 0. 60 206 24 1.3S021 44 1. 64 345 64 1.80 618 84 1.92 428 5 0.69 897 25 1. 39 794 45 1. 65 321 65 1. 81 291 85 1. 92 942 6 0. 77 815 26 1.41497 46 1.66 276 66 1. 81 954 86 1.93 450 7 0. 84 510 27 1. 43 136 47 1.67 210 67 1. 82 607 87 1. 93 952 8 0. 90 309 28 1. 44 716 48 1. 68 124 68 1. S3 251 88 1. 94 448 9 0. 95 424 29 1.46 240 49 1.69 020 69 1. S3 885 89 1. 94 939 10 1.00 000 30 1. 47 712 50 1. 69 897 70 1. 84 510 90 1. 95 424 11 1.04139 31 1. 49 136 51 1.70 757 71 1. 85 126 91 1.95 904 12 1.07 918 32 1.50 515 52 1. 71 600 72 1. 85 733 92 1.96 379 13 1. 11 394 33 1. 51851 53 1.72 428 73 1.86 332 93 1.96 848 14 1.14 613 34 1. 53 14S 54 1. 73 239 74 1.86 923 94 1.97 313 15 1.17 609 35 1. 54 407 55 1.74 036 75 1. 87 506 95 1. 97 772 16 1.20 412 36 1. 55 630 56 1.74 819 76 1.88 081 96 1. 98 227 17 1.23 045 37 1. 56 820 57 1. 75 587 77 1.8S649 97 1.98 677 18 1. 25 527 38 1.57 978 58 1.76 343 78 1. 89 209 98 1.99123 19 1.27 875 39 1. 59 106 59 1. 77 085 79 1. 89 763 99 1. 99 564 20 1. 30 103 40 1. 60 206 60 1. 77 815 80 1. 90 309 100 2. 00 000 N log N log N log N log N log 1-100 2 100-150 Sf O 1 2 3 4 5 6 7 8 9 100 00 000 00 043 00 087 00130 00173 00 217 00 260 00 303 00 346 00 389 101 00 432 00 475 00 518 00 561 00 604 00 647 00 689 00 732 00 775 00 817 102 00 860 00 903 00 945 00 988 01030 01072 0x115 01157 01199 01242 ,103 01284 01326 01368 01410 014S2 01494 01536 01578 01620 01662 104 01703 01745 01787 01828 01870 01912 01953 01995 02 036 02 078 105 02119 02160 02 202 02 243 02 284 02 325 02 366 02 407 02 449 02 490 106 02 531 02 572 02 612 02 653 02 694 02 735 02 776 02 816 02 857 02 898 107 02 938 02 979 03 019 03 060 03100 03 141 03181 03 222 03 262 03 302 108 03 342 03 383 03 423 03 463 03 503 03 543 03 583 03 623 03 663 03 703 109 03 743 03 782 03 822 03 862 03 902 03 941 03 981 04 021 04 060 04100 HO 04139 04179 04 218 04 258 04 297 04 336 04 376 04 415 04 454 04 493 111 04 532 04 571 04 610 04 650 04 689 04 727 04 766 04 805 04 844 04 883 112 04 922 04 961 04 999 05 038 05 077 05115 05 154 05 192 05 231 05 269 113 05 308 05 346 05 3S5 05 423 05 461 05 500 05.538 05 576 05 614 05 652 114 05 690 05 729 05 767 05 805 05 843 05 881 05 918 05 956 05 994 06 032 115 06 070 06108 06145 06183 06 221 06 258 06 296 06 333 06 371 06408 116 06 446 06 483 06 521 06 558 06 595 06 633 06 670 06 707 06 744 06 781 117 06 819 06 856 06 893 06 930 06 967 07 004 07 041 07 078 07115 07151 118 07188 07 225 07 262 07 298 07 335 07 372 07 408 07 445 07 482 07 518 119 07 555 07 591 07 628 07 664 07 700 07 737 07 773 07 809 07 846 07 882 120 07 918 07 954 07 990 08 027 08 063 08 099 08135 08171 08 207 08 243 121 08 279 08 314 08 350 08 386 08 422 08 458 08 493 08 529 08 565 08 600 122 08 636 08 672 08 707 08 743 08 778 08 814 08 849 08 884 08 920 08 955 123 08 991 09 026 09 061 09 096 09132 09167 09 202 09 237 09 272 09 307 124 09 342 09 377 09 412 09 447 09482 09 517 09 552 09 587 09 621 09 656 125 09 691 09 726 09 760 09 795 09 830 09 864 09 890 09 934 09 968 10 003 126 10 037 10 072 10106 10140 10175 10 209 10 243 10 278 10 312 10 346 127 10 380 10 415 10 449 10 483 10 517 10 551 10 585 10 619 10 653 10 687 128 10 721 10 755 10 789 10 823 10 857 10 890 10 924 10 958 10 992 11025 129 11059 11093 11126 11160 11193 11227 11261 11294 11327 11361 130 11394 11428 11461 11494 11528 11561 11594 11628 11661 11694 131 11727 11760 11793 11826 11860 11893 11926 11959 11992 12 024 132 12 057 12 090 12123 12156 12189 12 222 12 254 12 287 12 320 12 352 133 12 385 12 418 12 450 12 483 12 516 12 548 12 581 12 613 12 646 12 678 134 12 710 12 743 12 775 12 808 12 840 12 872 12 905 12 937 12 969 13 001 135 13 033 13 066 13 098 13130 13 162 13194 13 226 13 258 13 290 13 322 136 13 354 13 386 13 418 13 450 13 481 13 513 13 545 13 577 13 609 13 640 137 > 13 672 13 704 13 735 13 767 13 799 13 830 13 862 13 893 13 925 13 956 138 13 988 14 019 14 051 14 082 14114 14145 14176 14 208 14 239 14 270 139 14 301 14 333 14 364 14 395 14 426 14 457 14 489 14 520 14 551 14 582 140 14 613 14 644 14 675 14 706 14 737 14 768 14 799 14 829 14 860 14 891 141 14 922 14 953 14 983 15 014 15 045 15 076 15106 15 137 15 168 15 198 142 15 229 15 259 15 290 15 320 15 351 15 381 15 412 15 442 15 473 15 503 143 15 534 15 564 15 594 15 625 15 655 15 685 15 715 15 746 15 776 15 806 144 15 836 15 866 15 897 15 927 15 957 15 987 16 017 16 047 16 077 16107 145 16137 16167 16197 16 227 16 256 16 286 16 316 16 346 16 376 16 406 146 16 435 16 465 16 495 16 524 16 554 16 584 16 613 16 643 16 673 16 702 147 16 732 16 761 16 791 16 820 16 850 16 879 16 909 16 938 16 967 16 997 148 17 026 17 056 17 085 17114 17143 17173 17 202 17 231 17 260 17 2S9 149 17 319 17 348 17 377 17 406 17 435 17 464 17 493 17 522 17 551 17 580 150 17 609 17 638 17 667 17 696 17 725 17 754 17 782 17 811 17 840 17 869 N O 1 2 3 4 5 6 7 8 9 100-150 150-200 3 N 1 2 3 4 5 6 7 8 9 150 17 609 17 638 17 667 17 696 17 725 17 754 17 782 17 811 17 840 17 869 151 17 898 17 926 17 955 17 984 IS 013 18 041 IS 070 18 099 18127 18156 152 18184 18 213 18 241 18 270 18 298 18 327 IS 355 18 384 18 412 18 441 153 18 469 18 498 18 526 18 554 18 583 18 611 18 639 IS 667 18 696 18 724 154 18 752 18 780 18 SOS 18 837 18 865 18 893 18 921 18 949 IS 977 19 005 155 19 033 19 061 19 0S9 19117 19145 19173 19 201 19 229 19 257 19 2S5 156 19 312 19 340 19 368 19 396 19 424 19 451 19 479 19 507 19 535 19 562 157 19 590 19 618 19 645 19 673 19 700 19 728 19756 19 783 19 811 19 838 158 19 866 19 893 19 921 19 948 19 976 20 003 20 030 20 058 20 0S5 20112 159 20140 20167 20194 20 222 20 249 20 276 20 303 20 330 20 358 20 385 160 20 412 20 439 20 466 20 493 20 520 20 548 20 575 20 602 20 629 20 656 161 20 683 20 710 20 737 20 763 20 790 20 817 20 844 20 871 20 898 20 925 162 20 952 20 978 21005 21032 21059 21085 21112 21139 21165 21192 163 21219 21245 21272 21299 21325 21352 21378 21405 21431 21458 164 214S4 21511 21537 21564 21590 21617 21643 21669 21696 21722 165 21748 21775 21801 21827 21854 21880 21906 21932 21958 21985 166 '22 011 22 037 22 063 22 089 22115 22 141 22167 22194 22 220 22 246 167 22 272 22 29S 22 324 22 350 22 376 22 401 22 427 22 453 22 479 22 505 16S 22 531 22 557 22 583 22 608 22 634 22 660 22 686 22 712 22 737 22 763 169 22 789 22 814 22 840 22 866 22 891 22 917 22 943 22 968 22 994 23 019 170 23 045 23 070 23 096 23 121 23147 23172 23 19S 23 223 23 249 23 274 171 23 300 23 325 23 350 23 376 23 401 23 426 23 452 23 477 23 502 23 528 172 23 553 23 578 23 603 23 629 23 654 23 679 23 704 23 729 23 754 23 779 173 23 805 23 830 23 855 23 880 23 905 23 930 23 955 23 980 24 005 24 030 174 24 055 24 080 24105 24130 24155 24180 24 204 24 229 24 254 24 279 175 24 304 24 329 24 353 24 378 24 403 24 428 24 452 24 477 24 502 24 527 176 24 551 24 576 24 601 24 625 24 650 24 674 24 699 24 724 24 748 24 773 177 24 797 24 822 24 846 24 871 24 895 24 920 24 944 24 969 24 993 25 018 178 25 042 25 066 25 091 25 115 25 139 25 164 25 188 25 212 25 237 25 261 179 25 285 25 310 25 334 25 358 25 382 25 406 25 431 25 455 25 479 25 503 180 25 527 25 551 25 575 25 600 25 624 25 648 25 672 25 696 25 720 25 744 181 25 768 25 792 25 816 25 840 25 864 25 888 25 912 25 935 25 959 25 9S3 182 26 007 26 031 26 055 26 079 26102 26126 26150 26174 26198 26 221 183 26 245 26 269 26 293 26 316 26 340 26 364 26 387 26 411 26 435 26 458 184 26 482 26 505 26 529 26 553 26 576 26 600 26 623 26 647 26 670 26 694 185 26 717 26 741 26 764 26 788 26 811 26 834 26 858 26 881 26 905 26 928 186 26 951 26 975 26 99S 27 021 27 045 27 068 27 091 27114 2713S 27 161 187 27184 27 207 27 231 27 254 27 277 27 300 27 323 27 346 27 370 27 393 188 27 416 27439 27 462 27 485 27 508 27 531 27 554 27 577 27 600 27 623 189 27 646 27 669 27 692 27 715 27 738 27 761 27 784 27 807 27 830 27 852 190 27 875 27 898 27 921 27 944 27 967 27 989 28 012 28 035 2S058 28 081 191 28103 28126 28149 28171 2S194 28 217 28 240 28 262 28 285 28 307 192 28 330 28 353 28 375 28 398 28 421 28 443 28 466 28 488 28 511 28 533 193 28 556 28 578 28 601 28 623 28 646 28 668 2S691 28 713 28 735 28 758 194 28 780 28 803 28 825 28 847 28 870 28 892 28 914 28 937 28 959 28 981 195 29 003 29 026 29 048 29 070 29 092 29115 29137 29159 29181 29 203 196 29 226 29 248 29 270 29 292 29 314 29 336 29 358 29 380 29 403 29 425 197 29 447 29 469 29 491 29 513 29 535 29 557 29 579 29 601 29 623 29 645 198 29 667 29 68S 29 710 29 732 29 754 29 776 29 798 29 820 29 842 29 863 199 29 885 29 907 29 929 29 951 29 973 29 994 30 016 30 038 30 060 30 081 200 30103 30125 30146 30168 30190 4 30 211 30 233 30 255 30 276 30 298 N O 1 2 3 5 6 7 8 9 150 - 200 200 - 250 N O 1 2 3 4 5 6 7 8 9 200 30103 30125 30146 30168 30190 30 211 30 233 30 255 30 276 30 298 201 30 320 30 341 30 363 30 384 30 406 30428 30 449 30 471 30 492 30 514 202 30 535 30 557 30 578 30 600 30 621 30 643 30 664 30 685 30 707 30 728 203 30 750 30 771 30 792 30 814 30 835 30 856 30 878. 30 899 30 920 30 942 204 30 963 30 984 31006 31027 31048 31069 31091 31112 31133 31154 205 31175 31197 31218 31239 31260 31281 31302 31323 31345 31366 206 31387 31408 31429 31450 31471 31492 31513 31534 31555 31576 207 31597 31618 31639 31660 31681 31702 31723 31744 31765 31785 208 31806 31827 31 848 31869 31890 31911 31931- 31952 31973 31994 209 32 015 32 035 32 056 32 077 32 098 32118 32139 32160 32181 32 201 210 32 222 32 243 32 263 32 284 32 305 32 325 32 346 32 366 32 387 32 408 211 32 428 32 449 32 469 32 490 32 510 32 531 32 552 32 572 32 593 32 613 212 32 634 32 654 32 675 32 695 32 715 32 736 32 756 32 777 32 797 32 818 213 32 838 32 858 32 879 32 899 32 919 32 940 32 960 32 980 33 001 33 021 214 . 33 041 33 062 33 082 33102 33 122 33 143 33163 33183 33 203 33 224 215 33 244 33 264 33 284 33 304 33 325 33 345 33 365 33 385 33 405 33 425 216 33 445 33 465 33 486 33 506 33 526 33 546 33 566 33 586 33 606 33 626 217 33 646 33 666 33 686 33 706 33 726 33 746 33 766 33 786 33 806 33 826 218 33 846 33 866 33 885 33 905 33 925 33 945 33 965 33 985 34 005 34 025 219 34 044 34 064 34 084 34104 34 124 34143 34163 34183 34 203 34 223 220 34 242 34 262 34 282 34 301 34 321 34 341 34 361 34 380 34 400 34 420 221 34 439 34 459 34 479 34 498 34 518 34 537 34 557 34 577 34 596 34 616 222 34 635 34 655 34 674 34 694 34 713 34 733 34 753 34 772 34 792 34 811 223 34 830 34 850 34 869 34 889 34 908 34 928 34 947 34 967 34 986 35 005 224 35 025 35 044 35 064 35 083 35102 35 122 A. 35141 35160 35180 35199 225 35 218 35 238 35 257 35 276 35 295 35 315 35 334 35 353 35 372 35 392 226 35 411 35 430 35 449 35 468 35 488' 35 507 35 526 35 545 35 564 35 583 227 35 603 35 622 35 641 35 660 35 679 35 698 35 717 35 736 35 755 35 774 228 35 793 35 813 35 832 35 851 35 870 35 889 35 908 35 927 35 946 35 965 229 35 984 36 003 36 021 36 040 36059 36 078 36 097 36116 36135 36154 230 36173 36192 36 211 36 229 36 248 36 267 36 286 36 305 36 324 36 342 231 36 361 36 380 36 399 36 418 36 436 36 455 36 474 36 493 36 511 36530 232 36 549 36 568 36 586 36 605 36 624 36 642 36 661 36 680 36 698 36 717 233 36 736 36 754 36 773 36 791 36 810 36 829 36 847 36 866 36 884 36 903 234 36 922 36 940 36 959 36 977 36 996 37 014 37 033 37 051 37 070 37 088 235 37 107 37125 37144 37162 37181 37199 37 218 37 236 37 254 37 273 236 37 291 37 310 37 328 37 346 37 365 37 383 37 401 37 420 37 438 37 457 237 37 475 37 493 37 511 37 530 37 548 37 566 37 585 37 603 37 621 37 639 238 37 658 37 676 37 694 37 712 37 731 37 749 37 767 37 785 37 803 37 822 239 37 840 37 858 37 876 37 894 37 912 37 931 37 949 37 967 37 985 38 003 240 38 021 38 039 38 057 38 07,5 38 093 38112 38130 38148 38166 38184 241 38 202 38 220 38 238 38 256 38 274 38 292 38 310 38 328 38 346 38 364 242 38 382 38 399 38 417 38 435 38 453 38 471 38 489 38 507 38 525 38 543 243 38 561 38 578 38 596 38 614 38 632 38 650 38 668 38 686 38 703 38 721 244 38 739 38 757 38 775 38 792 38 810 38 828 38 846 38 863 38 881 38 899 245 38 917 38 934 38 952 38 970 38 987 39 005 39 023 39 041 39 058 39 076 246 39 094 39111 39129 39146 39164 39182 39199 39 217 39 235 39 252 247 39 270 39 287 39 305 39 322 39 340 39 358 39 375 39 393 39 410 39 428 248 39 445 39 463 39 480 39 498 39 515 39 533 39 550 39 568 39 585 39 602 249 39 620 39 637 39 655 39 672 39 690 39 707 39 724 39 742 39 759 39 777 250 39 794 39 811 39 829 39 846 39 863 39 881 39 898 39 915 39 933 39 950 N O 1 2 3 - 4 5 6 7 8 8 1 200-250 250-300 5 N 1 2 3 4 5 6 7 8 39 933 9 250 39 794 39S11 39 829 39S46 39 863 39 881 39 898 39 915 39 950 251 39 967 39 985 40 002 40 019 40 037 40 054 40 071 40 OSS 40106 40123 252 40140 40157 40175 40 192 40 209 40 226 40 243 40 261 40 278 40 295 253 40 312 40 329 40 346 40 364 40 381 40 398 40 415 40 432 40 449 40466 254 40 4S3 40 500 40 51S 40 535 40 552 40 569 40 586 40 603 40 620 40 637 255 40 654 40 671 40 688 40 705 40 722 40 739 40 756 40 773 40 790 40807 256 40 824 40S41 40 85 S 40S75 40 892 40 909 40 926 40 943 40 960 40976 257 40 993 41010 41027 41044 41061 4107S 41095 41111 41 128 41 145 258 41 162 41 179 41196 41212 41229 41246 41263 412S0 41296 41313 259 41330 41347 41363 41380 41397 41414 41430 41447 41464 414S1 260 41497 41514 41531 41547 41564 41581 41597 41614 41631 41647 261 41664 41681 41697 41714 41731 41747 41764 41780 41797 41814 262 41830 41847 41863 41 S80 41S96 41913 41929 41946 41963 41979 263 41996 42 012 42 029 42 045 42 062 42 078 42 095 42 111 42 127 42144 264 42 160 42 177 42 193 42 210 42 226 42 243 42 259 42 275 42 292 42 306 265 42 325 42 341 42 357 42 374 42 390 42 406 42 423 42 439 42 455 42 472 266 42 4SS 42 504 42 521 42 537 42 553 42 570 42 586 42 602 42 619 42 635 267 42 651 42 667 42 684 42 700 42 716 42 732 42 749 42 765 42 781 42 797 26S 42 813 42 830 42 846 42S62 42S7S 42 894 42 911 42 927 42 943 42 959 269 42 975 42 991 43 00S 43 024 43 040 43 056 43 072 43 OSS 43 104 43120 270 43 136 43 152 43169 43 1S5 43 201 43 217 43 233 43 249 43 265 43 281 271 43 297 43 313 43 329 43 345 43 361 43 377 43 393 43 409 43 425 43 441 272 43 457 43 473 43 489 43 505 43 521 43 537 43 553 43 569 43 584 43 600 273 43 616 43 632 43 64S 43 664 43 6S0 43 696 43 712 43 727 43 743 43 759 274 43 775 43 791 43 807 43S23 43 83S 43 854 43 870 43 886 43 902 43 917 275 43 933 43 949 43 965 43 981 43 996 44 012 44 02S 44 044 44 059 44 075 276 44 091 44107 44 122 44 13S 44154 44170 44 185 44 201 44 217 44 232 277 44 24S 44 264 44 279 44 295 44 311 44 326 44 342 44 358 44 373 44 389 27S 44 404 44 420 44 436 44 451 44 467 44 4S3 44 498 44 514 44 529 44 545 279 44 560 44 576 44 592 44 607 44 623 44 638 44 654 44 669 44 685 44 700 280 44 716 44 731 44 747 44 762 44 778 44 793 44 809 44 824 44 840 44 855 2S1 44 871 44 886 44 902 44 917 44 932 44 948 44 963 44 979 44 994 45 010 282 45 025 45 040 45 056 45 071 45 0S6 45 102 45 117 45 133 45 14S 45 163 283 45 179 45 194 45 209 45 225 45 240 45 255 45 271 45 286 45 301 45 317 2S4 45 332 45 347 45 362 45 378 45 393 45 408 45 423 45 439 45 454 45 469 285 45 484 45 500 45 515 45 530 45 545 45 561 45 576 45 591 45 606 45 621 286 45 637 45 652 45 667 45 682 45 697 45 712 45 728 45 743 45 758 45 773 287 45 78S 45 803 45 SIS 45 834 45 849 45S64 45 879 45 894 45 909 45 924 288 45 939 45 954 45 969 45 9S4 46 000 46 015 46 030 46 045 46 060 46 075 289 46 090 46105 46120 46135 46150 46165 46180 46195 46 210 46 225 290 46 240 46 255 46 270 46 285 46 300 46 315 46 330 46 345 46 359 46 374 291 46 389 46 404 46 419 46 434 46 449 46 464 46 479 46 494 46 509 46 523 292 46 538 46 553 46 56S 46 583 46 598 46 613 46 627 46 642 46 657 46 672 293 46 687 46 702 46 716 46 731 46 746 46 761 46 776 46 790 46 805 46 820 294 46 835 46 850 46 864 46 879 46 894 46 909 46 923 46 938 46 953 46 967 295 46 982 46 997 47 012 47 026 47 041 47 056 47 070 47 085 47 100 47114 296 47129 47 144 47159 47173 47 188 47 202 47 217 47 232 47 246 47 261 297 47 276 47 290 47 305 47 319 47 334 47 349 47 363 47 378 47 392 47 407 298 47 422 47 436 47 451 47 465 47 480 47 494 47 509 47 524 47 53S 47 553 299 47 567 47 582 47 596 47 611 47 625 47 640 47 654 47 669 47 6S3 47 69S 300 47 712 47 727 47 741 47 756 47 770 4 47 784 47 799 47 813 47 828 47 842 N 1 2 3 5 6 7 8 9 250-300 300-350 N O 1 2 3 4 5 6 7 8 9 300 47 712 47 727 47 741 47 756 47 770 47 784 47 799 47 813 47 828 47 842 301 47 857 47 871 47 885 47 900 47 914 47 929 47 943 47 958 47 972 47 986 302 48 001 48 015 48 029 48 044 48 058 48 073 48 087 48101 48116 4S130 303 48144 48159 4S173 48187 48 202 48 216 48 230 48 244 48 259 48 273 '304 48 287 48 302 48 316 48 330 48 344 48 359 48 373 48 387 48 401 48 416 305 48 430 48 444 48 458 48473 48 487 48 501 48 515 48 530 48 544 48 558 306 48 572 48 586 48 601 48 615 48 629 48 643 48 657 48 671 48 686 48 700 307 48 714 48 728 48 742 48 756 48 770 48 785 48 799 48 813 48 827 48 841 308 48 855 48 869 48 883 48 897 48 911 48 926 48 940 48 954 48 968 48 982 309 48 996 49 010 49 024 49 038 49 052 49 066 49 080 49 094 49 108 49122 310 49136 49150 49164 49178 49192 49 206 49 220 49 234 49 248 49 262 311 49 276 49 290 49 304 49 318 49 332 49 346 49 360 49 374 49 388 49 402 312 49 415 49 429 49 443 49457 49 471 49 485 49 499 49 513 49 527 49 541 313 49 554 49 56S 49 582 49 596 49 610 49 624 49.638 49 651 49 665 49 679 314 49 693 49 707 49 721 49 734 49 748 49 762 49 776 49 790 49 803 49 817 315 49 831 49 845 49 859 49 872 49 886 49 900 49 914 49 927 49 941 49 955 316 49 969 49 982 49 996 50 010 50 024 50 037 50 051 50 065 50 079 50 092 317 50106 50120 50133 50147 50161 50174 50188 50 202 50 215 50 229 318 50 243 50 256 50 270 50 284 50 297 50 311 50 325 50 338 50 352 50 365 319 50 379 50 393 50 406 50 420 50433 50 447 50 461 50 474 50 488 50 501 320 50 515 50 529 50 542 50 556 50 569 50 583 50 596 50 610 50 623 50 637 321 50 651 50 664 50 678 50 691 50 705 50 718 50 732 50 745 50 759 50 772 322 50 786 50 799 50 813 50 826 50 840 50S53 50 866 50 880 50 893 50 907 323 50 920 50 934 50 947 50 961 50 974 50 987 51001 51014 51028 51041 324 51055 51068 51081 51095 51108 51121 51135 51148 51162 51175 325 51188 51202 51215 51228 51242 51255 5126S 51282 51 295 51 308 326 51322 51335 51348 51362 51375 51388 51402 51415 51 428 51441 327 51455 51468 51481 51495 51508 51521 51534 51548 51561 51574 328 51587 51601 51614 51627 51640 51654 51667 51680 51693 51706 329 51720 51733 51746 51759 51772 51786 51799 51812 51825 51838 330 51851 51865 51878 51891 51904 51917 51930 51943 51957 51970 331 51983 51996 52 009 52 022 52 035 52 048 52 061 52 075 52 088 52101 332 52114 52 127 52 140 52153 52166 52179 52 192 52 205 52 218 52 231 333 52 244 52 257 52 270 52 284 52 297 52 310 52 323 52 336 52 349 52 362 334 52 375 52 388 52 401 52 414 52 427 52 440 52 453 52 466 52 479 52 492 335 52 504 52 517 52 530 52 543 52 556 52 569 52 582 52 595 52 60S 52 621 336 52 634 52 647 52 660 52 673 52 686 52 699 52 711 52 724 52 737 52 750 337 52 763 52 776 52 789 52 802 52 815 52 827 52 840 52 853 52 866 52 879 338 52 892 52 905 52 917 52 930 52 943 52 956 52 969 52 982 52 994 53 007 339 53 020 53 033 53 046 53 058 53 071 53 084 53 097 53110 53 122 53135 340 53148 53161 53173 53 186 53 199 53 212 53 224 53 237 53 250 53 263 341 53 275 53 288 53 301 53 314 53 326 53 339 53 352 53 364 53 377 53 390 342 53 403 53415 53 428 53 441 53 453 53 466 53 479 53 491 53 504 53 517 343 53 529 53 542 53 555 53 567 53 580 53 593 53 605 53 618 53 631 53 643 344 53 656 53 668 53 681 53 694 53 706 53 719 53 732 53 744 53 757 53 769 345 53 782 53 794 53 807 53 820*53 832 53 845 53 857 53 870 53 882 53 895 346 53 908 53 920 53 933 53 945 53 958 53 970 53 983 53 995 54 008 54 020 347 54 033 54 045 54 058 54 070 54 083 54 095 5410S 54120 54 133 54145 348 54158 54 170 54183 54195 54 208 54 220 54 233 54 245 54 258 54 270 349 54 283 54 295 54 307 54 320 54 332 54 345 54 357 54 370 54 382 54 394 350 54 407 54 419 54 432 54 444 54 456 54 469 54 481 54 494 54 506 54 518 N O 1 2 3 . 4 5 6 7 8 9 300-350 350-400 N 1 2 3 4 5 6 7 8 9 350 54 407 54 419 54 432 54 444 54 456 54 469 54 481 54 494 54 506 54 518 351 54 531 54 543 54 555 54 568 54 5S0 54 593 54 605 54 617 54 630 54 642 352 54 654 54 667 54 679 54 691 54 704 54 716 54 728 54 741 54 753 54 765 353 54 777 54 790 54S02 54 814 54 827 54 839 54 851 54 864 54 876 54 888 354 54 900 54 913 54 925 54 937 54 949 54 962 54 974 54 986 54 998 55 011 355 55 023 55 035 55 047 55 060 55 072 55 084 55 096 55 10S 55121 55133 356 55145 55 157 55 169 55 182 55 194 55 206 55 218 55 230 55 242 55 255 357 55 267 55 279 55 291 55 303 55 315 55 32S 55 340 55 352 55 364 55 376 358 55 3SS 55 400 55 413 55 425 55 437 55 449 55 461 55 473 55 485 55 497 359 55 509 55 522 55 534 55 546 55 558 55 570 55 582 55 594 55 606 55 618 360 55 630 55 642 55 654 55 666 55 678 55 691 55 703 55 715 55 727 55 739 361 55 751 55 763 55 775 55 787 55 799 55 811 55 823 55 835 55 847 55 859 362 55 871 55 883 55 895 55 907 55 919 55 931 55 943 55 955 55 967 55 979 363 55 991 56 003 56 015 56 027 56 038 56 050 56 062 56 074 56 086 56 09S 364 56110 56122 56134 56146 56158 56170 56182 56194 56 205 56 217 365 56 229 56 241 56 253 56 265 56 277 56 289 56 301 56 312 56 324 56 336 366 •56 348 56 360 56 372 56 384 56 396 56 407 56 419 56 431 56 443 56 455 367 56 467 56 47S 56 490 56 502 56 514 56 526 56 538 56 549 56 561 56 573 368 56 585 56 597 56 60S 56 620 56 632 56 644 56 656 56 667 56 679 56 691 369 56 703 56 714 56 726 56 738 56 750 56 761 56 773 56 7S5 56 797 56 SOS 370 56 820 56S32 56 844 56 855 56S67 56 879 56 891 56 902 56 914 56 926 371 56 937 56 949 56 961 56 972 56 984 56 996 57 008 57 019 57 031 57 043 372 57 054 57 066 57 078 57 089 57101 57113 57124 57136 57 148 57159 373 57171 57183 57194 57 206 57 217 57 229 57 241 57 252 57 264 57 276 374 57 287 57 299 57 310 57 322 57 334 57 345 57 357 57 36S 57 380 57 392 375 57403 57415 57 426 57 438 57449 57461 57 473 57484 57 496 57 507 376 57 519 57 530 57 542 57 553 57 565 57 576 57 58S 57 600 57 611 57 623 377 57 634 57 646 57 657 57 669 57 680 57 692 57 703 57 715 57 726 57 738 378 57 749 57 761 57 772 57 784 57 795 57 807 57 818 57S30 57 841 57 852 379 57 864 57S75 57 8S7 57S9S 57 910 57 921 57 933 57 944 57 955 57 967 380- 57 978 57 990 58 001 58 013 58 024 58 035 58 047 58 058 5S070 58 081 381 5S092 58104 58115 58127 58138 58149 58161 58172 58184 58195 3S2 58 206 58 218 5S229 58 240 58 252 58 263 58 274 58 286 58 297 58 309 383 58 320 58 331 58 343 5S354 58 365 58 377 58 388 58 399 58 410 58 422 " 384 58 433 58 444 58 456 58 467 58 478 58 490 58 501 58 512 5S524 58 535 385 58 546 58 557 58 569 58 580 58 591 58 602 58 614 5S625 58 636 58 647 386 58 659 58 670 58 681 58 692 58 704 58 715 58 726 58 737 58 749 58 760 387 58 771 58 782 58 794 5S805 58 816 58 827 5S83S 58 850 58 861 5SS72 388 5SSS3 58 894 5S906 58 917 58 928 58 939 58 950 58 961 58 973 58 984 389 58 995 59 006 59 017 59 028 59 040 59 051 59 062 59 073 59 084 59 095 390 59106 59118 59129 59 140 59151 59162 59173 59184 59195 59 207 391 59 218 59 229 59 240 59 251 59 262 59 273 59 284 59 295 59 306 59 318 392 59 329 59 340 59 351 59 362 59 373 59 3S4 59 395 59 406 59 417 59 428 393 59 439 59 450 59 461 59 472 59 483 59 494 59 506 59 517 59 52S 59 539 394 59 550 59 561 59 572 59 583 59 594 59 605 59 616 59 627 59 638 59 649 395 59 660 59 671 59 682 59 693 59 704 59 715 59 726 59 737 59 748 59 759 396 59 770 59 7S0 59 791 59 802 59 813 59 824 59 835 59 846 59 857 59 868 397 59 879 59 890 59 901 59 912 59 923 59 934 59 945 59 956 59 966 59 977 398 . 59 988 59 999 60 010 60 021 60 032 60 043 60 054 60 065 60 076 60 086 399 60 097 60108 60119 60130 60141 60152 60163 60173 60184 60195 400 60 206 60 217 60 22S 60 239 60 249 60 260 60 271 60 282 60 293 60 304 N O 1 2 3 4 5 6 7 8 9 350-400 400-450 N 1 2 3 4 5 6 7 8 9 400 60 206 60 217 60 22S 60 239 60 249 60 260 60 271 60 2S2 60 293 60 304 401 60 314 60 325 60 336 60 347 60 35S 60 369 60 379 60 390 60 401 60 412 402 60 423 60 433 60 444 60 455 60 466 60 477 60 4S7 60 49S 60 509 60 520 403 60 531 60 541 60 552 60 563 60 574 60 5S4 60 595 60 606 60 617 60 627 -404 60 63S 60 649 60 660 60 670 60 6S1 60 692 60 703 60 713 60 724 60 735 405 60 746 60 756 60 767 60 77S 60 7SS 60 799 60 S10 60S21 60S31 60 842 406 60 S53 60 863 60S74 60SS5 60 895 60 906 60 917 60 927 60 93S 60 949 407 60 959 60 970 60 9S1 60 991 61002 61013 61023 61034 61045 61 055 40S 61066 61077 610S7 6109S 61109 61119 61130 61140 61151 61162 409 61172 61 183 61 194 61204 61215 61225 61236 61247 61257 6126S 410 6127S 61289 61300 61310 61321 61331 61342 61352 61363 61374 411 613S4 61395 61 405 61416 61426 61437 6144S 61458 61469 61479 412 61490 61500 61511 61521 61532 61542 61553 61563 61574 615S4 413 61595 61606 61616 61627 61637 6164S 61658 61669 61679 61690 414 61700 61711 61721 61731 61742 61 752 61' 763 61773 61784 61794 415 61S05 61 815 61S26 61S36 61S47 61S57 61S6S 61S78 61SSS 61 899 416 61909 61920 61930 61941 61951 61962 61972 619S2 61993 62 003 417 62 014 62 024 62 034 62 045 62.055 62 066 62 076 62 0S6 62 097 62 107 41S 62 US 62 12S 62 13S 62 149 62159 62 170 62 ISO 62 190 62 201 62 211 419 62 221 62 232 62 242 62 252 62 263 62 273 62 2S4 62 294 62 304 62 315 420 62 325 62 335 62 346 62 356 62 366 62 377 62 3S7 62 397 62 40S 62 41S 421 62 42S 62 439 62 449 62 459 62 469 62 4S0 62 490 62 500 62 511 62 521 422 62 531 62 542 62 552 62 562 62 572 62 5S3 62 593 62 603 62 613 62 624 423 62 634 62 644 62 655 62 665 62 675 62 6S5 62 696 62 706 62 716 62 726 424 62 737 62 747 62 757 62 767 62 77S 62 7SS 62 798 62 SOS 62 SIS 62S29 425 62S39 62S49 62 859 62S70 62SS0 62S90 62 900 62 910 62 921 62 931 426 62 941 62 951 62 961 62 972 62 9S2 62 992 63 00"2 63 012 63 022 63 033 427 63 043 63 053 63 063 63 073 63 0S3 63 094 63 104 63 114 63 124 63134 42S 63 144 63 155 63 165 63 175 63 1S5 63 195 63 205 63 215 63 225 63 236 429 63 246 63 256 63 266 63 276 63 2S6 63 296 63 306 63 317 63 327 63 337 430 63 347 63 357 63 367 63 377 63 3S7 63 397 63 407 63 417 63 428 63 43S 431 63 44S 63 458 63 468 63 47S 63 4SS 63 49S 63 50S 63 518 63 52S 63 53S 432 63 54S 63 55S 63 56S 63 579 63 5S9 63 599 63 609 63 619 63 629 63 639 433 63 649 63 659 63 669 63 679 63 689 63 699 63 709 63 719 63 729 63 739 434 63 749 63 759 63 769 63 779 63 7S9 63 799 63S09 63S19 63 829 63S39 435 63S49 63S59 63S69 63S79 63SS9 63S99 63 909 63 919 63 929 63 939 436 63 949 63 959 63 969 63 979 63 9SS 63 99S 64 00S 64 01S 64 02S 64 03S 437 64 04S 64 058 64 06S 64 07S 64 OSS 64 09S 6410S 64 IIS 6412S 64137 438 . 64 147 64157 64 167 64 177 64 1S7 64197 64 207 64 217 64 227 64 237 439 64 246 64 256 64 266 64 276 64 2S6 64 296 64 306 64 316 64 326 64 335 440 64 345 64 355 64 365 64 375 64 3S5 64 395 64 404 64 414 64 424 64 434 441 64 444 64 454 64 464 64 473- 64 4S3 64 493 64 503 64 513 64 523 64 532 442 64 542 64 552 64 562 64 572 64 5S2 64 591 64 601 64 611 64 621 64 631 443 64 640 64650 64 660 64 670 64 6S0 64 6S9 64 699 64 709 64 719 64 729 444 64 73S 64 74S 64 75S 64 76S 64 777 64 787 64 797 64S07 64 816 64S26 445 64S36 64S46 64 856 64S65"64S75 64SS5 64S95 64 904 64 914 64 924 446 , 64 933 64 943 64 953 64 963 64 972 64 9S2 64 992 65 002 65 011 65 021 447 65 031 65 040 65 050 65 060 65 070 65 079 65 0S9 65 099 65 10S 65 IIS 44S 65 12S 65 137 65 147 65 157 65 167 65 176 65 1S6 65 196 65 205 65 215 449 65 225 65 234 65 244 65 254 65 263 65 273 65 2S3 65 292 65 302 65 312 450 65 321 65 331 65 341 65 350 65 360 65 369 65 379 65 3S9 65 39S 65 40S X O 1 2 3 4 5 6 7 8 9 1 400-450 450-500 9 N 1 2 3 4 5 6 7 8 9 450 65 321 65 331 65 341 65 350 65 360 65 369 65 379 65 389 65 398 65 408 451 65 418 65 427 65 437 65 447 65 456 65 466 65 475 65 485 65 495 65 504 452 65 514 65 523 65 533 65 543 65 552 65 562 65 571 65 581 65 591 65 600 453 65 610 65 619 65 629 65 639 65 648 65 658 65 667 65 677 65 686 65 696 454 65 706 65 715 65 725 65 734 65 744 65 753 65 763 65 772 65 782 65 792 455 65 801 65 811 65 820 65 830 65 839 65 849 65 858 65 868 65 877 65 887 456 65S96 65 906 65 916 65 925 65 935 65 944 65 954 65 963 65 973 65 982 457 65 992 66 001 66 011 66 020 66 030 66 039 66 049 66 058 66 068 66 077 458 66 087 66 096 66 106 66115 66124 66134 66143 66153 66162 66172 459 66181 66191 66 200 66 210 66 219 66 229 66 238 66 247 66 257 66 266 460 66 276 66 285 66 295 66 304 66314 66 323 66 332 66 342 66 351 66 361 461 66 370 66 380 66 389 66 398 66 408 66 417 66 427 66 436 66 445 66 455 462 66 464 66 474 66 483 66 492 66 502 66 511 66 521 66 530 66 539 66 549 463 66 558 66 567 66 577 66 586 66 596 66 605 66 614 66 624 66 633 66 642 464 66 652 66 661 66 671 66 680 66 689 66 699 66 708 66 717 66 727 66 736 465 66 745 66 755 66 764 66 773 66 783 66 792 66 801 66 811 66 820 66 829 466 66 839 66 84S 66 857 66 867 66 876 66 885 66 894 66 904 66 913 66 922 467 66 932 66 941 66 950 66 960 66 969 66 978 66 987 66 997 67 006 67 015 468 67 025 67 034 67 043 67 052 67 062 67 071 67 080 67 089 67 099 67 108 469 67117 67127 67136 67145 67154 67164 67173 67182 67191 67 201 470 67 210 67 219 67 228 67 237 67 247 67 256 67 265 67 274 67 284 67 293 471 67 302 67 311 67 321 67 330 67 339 67 348 67 357 67 367 67 376 67 385 472 67 394 67 403 67 413 67 422 67 431 67 440 67 449 67 459 67 468 67 477 473 67 486 67 495 67 504 67 514 67 523 67 532 67 541 67 550 67 560 67 569 474 67 578 67 587 67 596 67 605 67 614 67 624 67 633 67 642 67 651 67 660 475 67 669 67 679 67 688 67 697 67 706 67 715 67 724 67 733 67 742 67 752 476 67 761 67 770 67 779 67 78S 67 797 67 806 67 815 67 825 67 834 67 843 477 67 852 67 861 67 870 67 879 67 888 67 897 67 906 67 916 67 925 67 934 478 67 943 67 952 67 961 67 970 67 979 67 988 67 997 68 006 68 015 68 024 479 68 034 68 043 6S052 68 061 68 070 68 079 6S0S8 68 097 68106 68115 480 68124 68133 68142 68151 68160 68169 68178 68187 68196 68 205 481 68 215 68 224 68 233 68 242 68 251 68 260 68 269 68 27S 68 287 68 296 482 68 305 68 314 68 323 68 332 68 341 68 350 68 359 68 368 68 377 68 386 483 68 395 68 404 68 413 68 422 68 431 68 440 68 449 68 458 68 467 68 476 484 68 485 68 494 68 502 68 511 68 520 68 529 68 538 68 547 68 556 68 565 485 68 574 68 583 68 592 68 601 68 610 68 619 68 628 68 637 68 646 68 655 486 68 664 68 673 68 681 68 690 68 699 68 70S 68 717 68 726 68 735 68 744 487 6S753 6S762 68 771 68 780 68 789 68 797 68 806 68 815 68 824 68 833 488 6S842 6S851 6S860 6S869 6S878 68 886 68 895 68 904 68 913 68 922 489 68 931 68 940 68 949 68 958 68 966 68 975 68 984 68 993 69 002 69 011 490 69 020 69 028 69 037 69 046 69 055 69 064 69 073 69 082 69 090 69 099 491 69108 69117 69126 69135 69144 69152 69 161 69 170 69179 69188 492 69197 69 205 69 214 69 223 69 232 69 241 69 249 69 258 69 267 69 276 493 69 285 69 294 69 302 69 311 69 320 69 329 69 338 69 346 69 355 69 364 494 69 373 69 381 69 390 69 399 69 408 69 417 69 425 69 434 69 443 69 452 495 69 461 69 469 69 478 69 487 69 496 69 504 69 513 69 522 69 531 69 539 496 69 548 69 557 69 566 69 574 69 583 69 592 69 601 69 609 69 61S 69 627 497 69 636 69 644 69 653 69 662 69 671 69 679 69 688 69 697 69 705 69 714 498 69 723 69 732 69 740 69 749 69 75S 69 767 69 775 69 784 69 793 69 801 499 69 810 69 819 69 827 69 836 69S45 69 854 69 862 69 871 69 880 69 88S 500 69 897 69 906 69 914 69 923 69 932 69 940 69 949 69 958 69 966 69 975 S" 1 2 3 4 5 6 7 8 9 450 - 500 10 500-550 N O 1 2 3 4 5 6 7 8 9 500 69 897 69 906 69 914 69 923 69 932 69 940 69 949 69 958 69 966 69 975 501 69 984 69 992 70 001 70 010 70 018 70 027 70 036 70 044 70 053 70 062 502 70 070 70 079 70 OSS 70 096 70105 70114 70 122 70 131 70140 70148 .503 70157 70 165 70174 70183 70191 70 200 70 209 70 217 70 226 70 234 504 70 243 70 252 70 260 70 269 70 278 70 286 70 295 70 303 70 312 70 321 505 70 329 70 338 70 346 70 355 70 364 70 372 70 381 70 389 70 398 70 406 506 70 415 70 424 70 432 70 441 70 449 70 458 70 467 70 475 70 484 70 492 "507 70 501 70 509 70 518 70 526 70 535 70 544 70 552 70 561 70 569 70 578 508 70 586 70 595 70 603 70 612 70 621 70 629 70 638 70 646 70 655 70 663 509 70 672 70 680 70 689 70 697 70 706 70 714 70 723 70 731 70 740 70 749 510 70 757 70 766 70 774 70 783 70 791 70 800 70 SOS 70 817 70 825 70 834 511 70 842 70 851 70 859 70 868 70 876 70S85 70 893 70 902 70 910 70 919 512 70 927 70 935 70 944 70 952 70 961 70 969 70 97S 70 986 70 995 71003 513 71012 71020 71029 71037 71046 71054 71063 71071 71079 71 OSS 514 71096 71105 71 113 71 122 71 130 71139 71147 71 155 71 164 71172 515 71181 71189 71198 71206 71214 71223 71231 71240 7124S 71257 516 71265 71273 71282 71290 71299 71307 71315 71324 71332 71341 517 71349 71357 71366 71374 713S3 71391 71399 71408 71416 71425 518 71433 71441 71450 71458 71466 71475 71483 71492 71500 7150S 519 71517 71525 71533 71542 71550 71559 71567 71575 71584 71592 520 71600 71609 71617 71625 71634 71642 71650 71659 71667 71675 521 71684 71692 71700 71709 71717 71725 71734 71742 71750 71759 522 71767 71775 71784 71792 71800 71809 71817 71825 71834 71S42 523 71850 71858 71867 71875 71883 71892 71900 71908 71917 71925 524 71933 71941 71950 71958 71966 7197,5 71983 71991 71999 72 008 525 72 016 72 024 72 032 72 041 72 049 72 057 72 066 72 074. 72 082 72 090 526 72 099 72 107 72115 72 123 72 132 72 140 72 148 72156 72 165 72173 527 72 181 72 189 72 19S 72 206 72 214 72 222 72 230 72 239 72 247 72 255 528 72 263 72 272 72 2S0 72 28S 72 296 72 304 72 313 72 321 72 329 72 337 529 72 346 72 354 72 362 72 370 72 378 72 387 72 395 72 403 72 411 72 419 530 72 428 72 436 72 444 72 452 72 460 72 469 72 477 72 485 72 493 72 501 531 72 509 72 51S 72 526 72 534 72 542 72 550 72 558 72 567 72 575 72 583 532 72 591 72 599 72 607 72 616 72 624 72 632 72 640 72 648 72 656 72 665 533 72 673 72 681 72 689 72 697 72 7Q5 72 713 72 722 72 730 72 73S 72 746 534 72 754 72 762 72 770 72 779 72 787 72 795 72S03 72 811 72 819 72 827 535 72 835 72 843 72 852 72 860 72 868 72 876 72S84 72 892 72 900 72 908 536 72 916 72 925 72 933 72 941 72 949 72 957 72 965 72 973 72 981 72 989 537 72 997 73 006 73 014 73 022 73 030 73 038 73 046 73 054 73 062 73 070 538 73 078 73 086 73 094 73 102 73 111 73 119 73 127 73 135 73143 73151 539 73159 73 167 73 175 73 183 73 191 73199 73 207 73 215 73 223 73 231 540 73 239 73 247 73 255 73 263 73 272 73 2S0 73 28S 73 296 73 304 73 312 541 73 320 73 328 73 336 73 344 73 352 73 360 73 36S 73 376 73 384 73 392 542 73 400 73 408 73 416 73 424 73 432 73 440 73 44S 73 456 73 464 73 472 543 73 480 73 488 73 496 73 504 73 512 73 520 73 528 73 536 73 544 73 552 544 73 560 73 568 73 576 73 584 73 592 73 600 73 608 73 616 73 624 73 632 545 73 640 73 648 73 656 73 664 73 672 73 679 73 687 73 695 73 703 73 711 546 73 719 73 727 73 735 73 743 73 751 73 759 73 767 73 775 73 783 73 791 547 73 799 73 807 73 815 73S23 73 830 73 838 73 846 73S54 73 862 73 870 548 73S7S 73 886 73S94 73 902 73 910 73 918 73 926 73 933 73 941 73 949 549 73 957 73 965 73 973 73 981 73 9S9 73 997 74 005 74 013 74 020 74 028 550 74 036 74 044 74 052 74 060 74 06S 74 076 74 084 74 092 74 099 74107 N O 1 2 3 4 5 6 7 8 9 500-550 550-600 ii N 1 2 3 4 5 6 7 8 9 550 74 036 74 044 74 052 74 060 74 068 74 076 74 084 74 092 74 099 74 107 551 74115 74 123 74 131 74139 74147 74155 74162 74 170 74178 74 186 552 74194 74 202 74 210 74 218 74 225 74 233 74 241 74 249 74 257 74 265 553 74 273 74 280 74 2SS 74 296 74 304 74 312 74 320 74 327 74 335 74 343 554 74 351 74 359 74 367 74 374 74 382 74 390 74 398 74 406 74 414 74 421 555 74 429 74 437 74 445 74 453 74 461 74 468 74 476 74 484 74 492 74 500 556 74 507 74 515 74 523 74 531 74 539 74 547 74 554 74 562 74 570 74 578 557 74 5S6 74 593 74 601 74 609 74 617 74 624 74 632 74 640 74 648 74 656 558 74 663 74 671 74 679 74 687 74 695 74 702 74 710 74 71S 74 726 74 733 559 74 741 74 749 74 757 74 764 74 772 74 780 74 788 74 796 74S03 74 811 560 74 819 74 827 74 834 74S42 74 850 74 858 74 865 74 873 74 881 74 889 561 74 896 74 904 74 912 74 920 74 927 74 935 74 943 74 950 74 958 74 966 562 74 974 74 981 74 989 74 997 75 005 75 012 75 020 75 028 75 035 75 043 563 75 051 75 059 75 066 75 074 75 0S2 75 089 75 097 75 105 75 113 75 120 564 75 128 75 136 75143 75 151 75159 75 166 75 174 75 182 75 189 75 197 565 75 205 75 213 75 220 75 228 75 236 75 243 75 251 75 259 75 266 75 274 566 7-5 282 75 2S9 75 297 75 305 75 312 75 320 75 328 75 335 75 343 75 351 567 75 358 75 366 75 374 75 381 75 3S9 75 397 75 404 75 412 75 420 75 427 568 75 435 75 442 75 450 75 458 75 465 75 473 75 481 75 488 75 496 75 504 569 75 511 75 519 75 526 75 534 75 542 75 549 75 557 75 565 75 572 75 580 570 75 587 75 595 75 603 75 610 75 618 75 626 75 633 75 641 75 648 75 656 571 75 664 75 671 75 679 75 686 75 694 75 702 75 709 75 717 75 724 75 732 572 75 740 75 747 75 755 75 762 75 770 75 778 75 785 75 793 75 800 75 SOS 573 75 815 75 823 75 831 75 838 75 846 75 853 75S61 75 868 75 876 75 884 574 75 891 75 899 75 906 75 914 75 921 75 929 75 937 75 944 75 952 75 959 575" 75 967 75 974 75 982 75 989 75 997 76 005 76 012 76 020 76 027 76 035 576 76 042 76 050 76 057 76 065 76 072 76 080 76 087 76 095 76103 76110 577 76 US 76125 76133 76140 76148 76155 76163 76170 76178 76185 • 578 76193 76 200 76 20S 76 215 76 223 76 230 76 238 76 245 76 253 76 260 579 76 26S 76 275 76 283 76 290 76 298 76 305 76 313 76 320 76 328 76 335 580 - 76 343 76 350 76 358 76 365 76 373 76 380 76 388 76 395 76403 76 410 581 76 418 76 425 76 433 76 440 76 448 76 455 76 462 76 470 76 477 76 485 582 76 492 76 500 76 507 76 515 76 522 76 530 76 537 76 545 76 552 76 559 583 76 567 76 574 76 5S2 76 589 76 597 76 604 76 612 76 619 76 626 76 634 584 76 641 76 649 76 656 76 664 76 671 76 678 76 686 76 693 76 701 76 70S 585 76 716 76 723 76 730 76 738 76 745 76 753 76 760 76 768 76 775 76 782 586 76 790 76 797 76 805 76 812 76 819 76 827 76 834 76 842 76 849 76 856 587 76 864 76S71 76 879 76 8S6 76S93 76 901 76 908 76 916 76 923 76 930 588 76 938 76 945 76 953 76 960 76 967 76 975 76 9S2 76 989 76 997 77 004 589 77 012 77 019 77 026 77 034 77 041 77 048 77 056 77 063 77 070 77 078 590 77 085 77 093 77100 77107 77115 77122 77129 77137 77144 77151 591 77159 77166 77173 77181 77188 77195 77 203 77 210 77 217 77 225 592 77 232 77 240 77 247 77 254 77 262 77 269 77 276 77 283 77 291 77 298 593 77 305 77 313 77 320 77 327 77 335 77 342 77 349 77 357 77 364 77 371 594 77 379 77 386 77 393 77 401 77 408 77 415 77 422 77 430 77 437 77 444 595 77 452 77 459 77 466 77 474 77 481 77 488 77 495 77 503 77 510 77 517 596 77 525 77 532 77 539 77 546 77 554 77 561 77 568 77 576 77 583 77 590 597 77 597 77 605 77 612 77 619 77 627 77 634 77 641 77 64S 77 656 77 663 598 77 670 77 677 77 685 77 692 77 699 77 706 77 714 77 721 77 728 77 735 599 77 743 77 750 77 757 77 764 77 772 77 779 77 7S6 77 793 77 801 77 808 600 77 815 77 822 77 830 77 837 77 844 77 851 77 859 77 866 77 873 77 8SO N 1 2 3 4 5 6 7 8 9 550-600 12 600-650 N 1 2 3 4 5 77 851 6 7 8 9 600 77 815 77 822 77 830 77 837 77 844 77 859 77 866 77 873 77 880 601 77 887 77 895 77 902 77 909 77 916 77 924 77 931 77 938 77 945 77 952 602 77 960 77 967 77 974 77 981 77 988 77 996 78 003 78 010 78 017 78 025 603 78 032 78 039 78 046 78 053 78 061 78 068 78 075 78 082 78 0S9 78 097 '604 78104 78111 78118 78125 78132 78140 78147 78154 78161 78168 605 78176 78183 78190 78197 78 204 78 211 78 219 78 226 78 233 78 240 606 78 247 78 254 78 262 78 269 78 276 78 283 78 290 78 297 78 305 78 312 607 78 319 78 326 78 333 78 340 78 347 78 355 78 362 78 369 78 376 78 383 608 78 390 78 398 78 405 78 412 78 419 78 426 78 433 78 440 78 447 78 455 609 78 462 78 469 78 476 78 483 78 490 78 497 78 504 78 512 78 519 78 526 610 78 533 78 540 78 547 78 554 78 561 78 569 78 576 78 583 78 590 78 597 611 78 604 78 611 78 618 78 625 78 633 78 640 78 647 78 654 78 661 78 668 612 78 675 78 682 78 689 78 696 78 704 78 711 78 718 78 725 78 732 78 739 613 78 746 78 753 78 760 78 767 78 774 78 781 78 789 78 796 78 803 78 810 614 78 817 78 824 78 831 78 838 78 845 78 852 78 859 78 866 78 873 78 880 615 78 888 78 895 78 902 78 909 78 916 78 923 78 930 78 937 78 944 78 951 . 616 78 958 7S965 78 972 78 979 78 986 78 993 79 000 79 007 79 014 79 021 617 79 029 79 036 79 043 79 050 79 057 79 064 79 071 79 078 79 085 79 092 618 79 099 79 106 79113 79120 79127 79134 79141 79148 79155 79162 619 79169 79176 79183 79190 79197 79 204 79 211 79 218 79 225 79 232 620 79 239 79 246 79 253 79 260 79 267 79 274 79 281 79 288 79 295 79 302 621 79 309 79 316 79 323 79 330 79 337 79 344 79 351 79 358 79 365 79 372 622 79 379 79 386 79 393 79 400 79 407 79 414 79 421 79 428 79 435 79 442 623 79 449 79 456 79 463 79 470 79 477 79 484 79 491 79 498 79 505 79 511 624 79 518 79 525 79 532 79 539 79 546 79 553 79 560 79 567 79 574 79 581 625 79 588 79 595 79 602 79 609 79 616 79 623 79 63.0 79 637 79 644 79 650 626 79 657 79 664 79 671 79 678 79 685 79 692 79 699 79 706 79 713 79 720 627 79 727 79 734 79 741 79 748 79 754 79 761 79 768 79 775 79 782 79 789 628 79 796 79 803 79 810 79 817 79 824 79 831 79 837 79 844 79 851 79 858 629 79 865 79 872 79 879 79 8S6 79 893 79 900 79 906 79 913 79 920 79 927 630 79 934 79 941 79 948 79 955 79 962 79 969 79 975 79 982 79 9S9 79 996 631 80 003 80 010 80 017 SO 024 80 030 80 037 80 044 80 051 80 058 80 065 632 80 072 80 079 80 085 80 092 80 099 80106 80113 80120 80127 80 134 633 80140 80 147 80154 80161 80168 80175 80182 801SS SO 195 80 202 634 80 209 80 216 80 223 80 229 80 236 80 243 80 250 80 257 80 264 80 271 635 80 277 80 284 80 291 80 298 80 305 80 312 80 318 80 325 80 332 80 339 636 80 346 80 353 80 359 80 366 80 373 SO 380 80 387 80 393 80 400 80 407 637 80 414 80 421 80 428 80 434 80 441 80 448 80 455 80 462 80 468 80 475 638 80 482 80 489 80 496 80 502 80 509 80 516 80 523 80 530 80 536 80 543 639 80 550 80 557 80 564 80 570 80 577 80 584 SO 591 80 598 80 604 80 611 640 80 618 80 625 80 632 80 638 80 645 80 652 80 659 80 665 80 672 80 679 641 80 686 80 693 80 699 80 706 80 713 80 720 80 726 80 733 80 740 80 747 642 80 754 80 760 80 767 80 774 80 781 80 787 80 794 80 SOI SO 808 80 814 643 80 821 80 828 80 835 80 841 80 848 80 855 80 862 80 868 80 875 S0 8S2 644 80 889 80 895 80 902 80 909 80 916 80 922 80 929 80 936 80 943 80 949 645 80 956 80 963 80 969 80 976*80 983 80 990 80 996 81003 81010 SI 017 646 81023 81030 81037 81043 81050 81057 81064 81070 81077 81084 647 81090 81097 81104 81 111 81 117 81124 81131 81137 81144 81151 648 81158 81164 81171 81178 81184 81191 S119S 81204 81211 81218 649 81224 81231 81238 81245 81251 81258 81265 81271 81278 81285 650 81291 81298 1 81305 81311 SI 318 81325 81331 81338 81345 81351 X 2 3 . 4 5 6 7 8 9 600-650 650-700 13 N 1 2 3 4 5 6 7 8 9 650 SI 291 S129S 81305 SI 311 81318 81325 81331 81338 81345 81351 651 S135S SI 365 81 371 SI 378 SI 385 81391 81 398-81 405 81411 81418 652 81425 SI 431 SI 438 81445 SI 451 S145S SI 465 81471 81478 814S5 653 81491 8149S SI 505 81511 81518 81525 81531 SI 538 81544 81551 654 81558 SI 564 SI 571 S157S 81 5S4 81591 8159S SI 604 81611 81617 655 81624 SI 631 81637 81644 81 651 81657 81664 81671 81677 81684 656 81690 SI 697 81704 81710 81717 81723 81730 81737 81743 81750 657 81757 SI 763 81770 81776 817S3 81790 81796 81 803 81809 81816 • 658 81823 81829 81836 81842 81849 81856 81862 81869 81875 81882 659 SI 889 81895 81902 81908 81915 81921 81928 81935 81941 81948 660 81954 81961 81968 81974 81981 81987 SI 994 82 000 82 007 82 014 661 82 020 S2 027 82 033 82 040 82 046 82 053 82 060 82 066 82 073 82 079 662 82 086 82 092 82 099 82105 82112 82119 82125 82132 82138 82145 663 82 151 82 15S 82164 82 171 82 17S 82184 82 191 82197 82 204 82 210 664 82 217 82 223 82 230 82 236 82 243 82 249 82 256 82 263 82 269 82 276 665 82 282 82 289 82 295 82 302 82 308 82 315 82 321 82-328 82 334 82 341 666 -82 347 82 354 82 360 82 367 82 373 82 380 82 387 82 393 82 400 82 406 667 82 413 82 419 82 426 82 432 82 439 82 445 82 452 82 458 82 465 82 471 668 82 478 82 484 82 491 82 497 82 504 82 510 82 517 82 523 82 530 82 536 669 82 543 82 549 82 556 82 562 82 569 82 575 82 582 82 588 82 595 82 601 670 82 607 82 614 82 620 82 627 82 633 82 640 82 646 82 653 82 659 82 666 671 82 672 82 679 S2 6S5 82 692 82 698 82 705 82 711 82 718 82 724 82 730 672 82 737 82 743 82 750 82 756 82 763 82 769 82 776 82 782 82 789 82 795 673 82 802 82 SOS 82 814 82 821 82 827 82 834 82 840 82 847 82 853 82 860 ' 674 82 866 82 872 82 879 82 885 82 892 82 898 82 905 82 911 82 918 82 924 675 82 930 82 937 82 943 82 950 82 956 82 963 82 969 82 975 82 982 82 988 676 82 995 83 001 83 008 83 014 83 020 83 027 83 033 83 040 83 046 83 052 677 83 059 83 065 83 072 83 078 83 0S5 83 091 83 097 83 104 83110 83 117 678 83 123 83 129 83 136 83 142 83149 83 155 83 161 83 168 83174 83 181 679 83187 83 193 83 200 83 206 83 213 83 219 83 225 83 232 83 238 83 245 680 83 251 S3 257 83 264 83 270 83 276 83 283 83 2S9 83 296 83 302 83 308 681 83 315 83 321 83 327 83 334 83 340 83 347 83 353 83 359 83 366 83 372 682 83 378 S3 3S5 83 391 83 398 83 404 83 410 83 417 83 423 83 429 83 436 683 83 442 83 448 83 455 83 461 83 467 83 474 83 480 83 487 83 493 83 499 684 83 506 83 512 S3 51S 83 525 83 531 83 537 83 544 83 550 83 556 83 563 685 83 569 83 575 83 582 83 588 83 594 83 601 83 607 83 613 83 620 83 626 686 83 632 83 639 83 645 83 651 S3 658 83 664 83 670 83 677 83 683 83 689 687 83 696 S3 702 S3 708 83 715 83 721 83 727 83 734 83 740 83 746 83 753 688 83 759 83 765 83 771 83 778 83 784 83 790 83 797 83 803 83S09 83 816 689 83 822 83 828 83 835 83 841 83 847 83 853 83 860 83 866 83 872 83 879 690 83 885 83 891 83 897 83 904 83 910 83 916 83 923 83 929 83 935 83 942 691 83 948 83 954 83 960 83 967 83 973 83 979 S3 9S5 83 992 83 998 84 004 692 84 011 84 017 84 023 84 029 84 036 84 042 84 048 84 055 84 061 84 067 693 84 073 84 080 84 0S6 84 092 84 09S 84 105 84111 84 117 84123 84130 694 84 136 84142 84148 84155 84 161 84 167 84173 84 ISO S41S6 84192 695 84198 84 205 84 211 84 217 84 223 84 230 84 236 84 242 84 248 84 255 696 84 261 84 267 84 273 84 280 S4 2S6 84 292 84 298 84 305 84 311 84 317 697 84 323 84 330 84 336 84 342 84 34S 84 354 84 361 84 367 84 373 84 379 698 84 386 84 392 84 39S 84 404 84 410 84 417 84 423 84 429 S4 435 84 442 699 84 448 84 454 84 460 84 466 84 473 84 479 84 485 84491 84 497 84 504 700 S4 510 84 516 84 522 S4 528 84 535 84 541 84 547 84 553 84 559 84 566 N 1 2 3 4 5 6 7 8 9 650-700 14 700-750 N 1 2 3 4 5 84 541 6 7 8 9 700 84 510 84 516 84 522 84 528 84 535 84 547 84 553 84 559 84 566 701 84 572 84 578 84 584 84 590 84 597 84 603 84 609 84 615 84 621 84 628 702 84 634 84 640 84 646 84 652 84 658 84 665 84 671 S4 677 84 683 84 689 703 84 696 84 702 S4 708 84 714 84 720 84 726 84 733 84 739 84 745 84 751 704 84 757 84 763 84 770 84 776 84 782 84 788 84 794 84 800 84 807 84 813 705 84 819 84 825 84 831 84 837 84 844 84 850 84 856 84 862 84 868 84 874 706 84 880 84 887 84 893 84 899 84 905 84 911 84 917 84 924 84 930 84 936 707 84 942 84 948 84 954 84 960 84 967 84 973 84 979 84 985 84 991 84 997 708 85 003 85 009 85 016 85 022 85 028 85 034 85 040 85 046 85 052 85 058 709 85 065 85 071 85 077 85 083 85 089 85 095 85 101 85 107 85 114 85 120 710 85 126 85132 85 138 85 144 85 150 85156 85 163 85 169 85175 85181 711 85 187 85 193 85 199 85 205 85 211 85 217 85 224 85 230 85 236 85 242 712 85 248 85 254 85 260 85 266 85 272 85 278 85 285 85 291 85 297 85 303 713 85 309 85 315 85 321 85 327 85 333 85 339 85 345 85 352 85 358 85 364 714 . 85 370 85 376 S5 382 85 388 85 394 85 400 85 406 85 412 85 418 85 425 715 85 431 85 437 85 443 85 449 85 455 85 461 85 467 85 473 85 479 85 485 716 85 491 85 497 85 503 85 509 85 516 85 522 85 528 85 534 85 540 85 546 717 85 552 85 558 85 564 85 570 85 576 S5 582 85 588 85 594 85 600 85 606 718 85 612 85 618 85 625 85 631 85 637 85 643 85 649 85 655 85 661 85 667 719 85 673 85 679 85 685 85 691 85 697 85 703 85 709 85 715 85 721 85 727 720 85 733 85 739 85 745 85 751 85 757 85 763 85 769 85 775 85 781 85 788 721 85 794 85 800 85 806 85 812 85 818 85 824 85 830 85 836 85 842 85 848 722 85 854 85 860 85 866 85 872 85 878 85 884 85 890 85 896 85 902 85 908 723 85 914 85 920 85 926 85 932 85 938 85 944 85 950 85 956 85 962 85 968 724 85 974 85 980 85 986 85 992 85 998 86 004 86 010 86 016 86 022 86 028 725 86 034 86 040 86 046 86 052 S6 058 86 064 86 070 86 076 86 082 86 088 726 86 094 86100 86106 86112 86118 86124 86130 86136 86141 86147 727 86153 86159 86165 86171 86177 86183 86189 86195 86 201 S6 207 728 86 213 86 219 86 225 86 231 86 237 86 243 86 249 86 255 86 261 86 267 729 86 273 86 279 86 285 86 291 86 297 86 303 86 308 86 314 86 320 86 326 730 86 332 86 338 86 344 86 350 86 356 86 362 86 368 86 374 86 380 86 386 731 86 392 86 398 86 404 86 410 86 415 86 421 86 427 86 433 86 439 86 445 732 86 451 86 457 86 463 86 469 86 475 86 4S1 86 487 86 493 S6 499 86 504 733 86 510 86 516 86 522 86 528 86 534 86 540 86 546 86 552 86 558 86 564 734 86 570 86 576 86 581 86 587 86 593 86 599 86 605 86 611 86 617 86 623 735 86 629 86 635 86 641 86 646 86 652 86 658 86 664 86 670 86 676 86 682 736 86 688 86 694 86 700 86 705 86 711 86 717 86 723 86 729 86 735 86 741 737 86 747 86 753 86 759 86 764 86 770 86 776 86 782 86 788 86 794 86 800 738 86 806 86 812 86 817 86 823 86 829 86 835 86 841 86 847 86 853 86 859 739 86 864 86 870 86 876 86 882 86 888 86 894 86 900 86 906 86 911 86 917 740 86 923 86 929 86 935 86 941 86 947 86 953 86 958 86 964 86 970 86 976 741 86 982 86 98S S6 994 86 999 87 005 87 011 87 017 87 023 87 029 87 035 742 87 040 87 046 87 052 87 058 87 064 87 070 87 075 S7 0S1 87 087 87 093 743 87 099 87105 87111 87116 87122 87128 S7134 87 140 87146 87151 744 87157 87163 87169 87175 87181 871S6 87192 87198 87 204 87 210 745 87 216 87 221 87 227 87 233" 87 239 87 245 87 251 87 256 87 262 87 268 746 87 274 87 280 87 286 87 291 87 297 87 303 87 309 87 315 87 320 87 326 747 87 332 87 338 87 344 87 349 87 355 87 361 87 367 87 373 87 379 87 384 748 87 390 87 396 87 402 87 40S 87 413 87 419 87 425 87 431 87 437 87 442 749 87 448 87 454 87 460 87 466 S7 471 87 477 87 483 87 489 87 495 87 500 750 87 506 87 512 87 518 87 523 87 529 87 535 87 541 87 547 87 552 87 558 N O 1 2 3. 4 5 6 7 8 9 700 -7S0 750-800 15 X 1 2 3 4 5 6 7 8 9 750 87 506 87 512 87 5 IS 87 523 87 529 S7 535 S7 541 87 547 87 552 87 558 751 87 564 87 570 87 576 87 581 87 587 87 593 87 599 87 604 87 610 87 616 752 87 622 87 628 87 633 S7 639 87 645 S7 651 87 656 87 662 S7 668 87 674 753 87 679 S7 6S5 87 691 87 697 87 703 87 70S 87 714 87 720 87 726 87 731 754 87 737 87 743 87 749 87 754 87 760 87 766 87 772 87 777 87 783 87 789 755 87 795 87 800 87 806 87 812 87 SIS 87 823 87 829 87 835 87 841 87 846 756 87S52 S7S58 87 864 87 869 87S75 87 SSI 87 8S7 87 892 87 898 87 904 757 87 910 87 915 87 921 87 927 87 933 87 938 87 944 87 950 87 955 87 961 758 87 967 S7 973 87 978 87 9S4 87 990 87 996 8S001 88 007 8S013 88 018 759 88 024 88 030 88 036 88 041 8S047 88 053 88 058 88 064 88 070 88 076 760 88 081 88 087 88 093 SS09S 88104 88 110 88116 88121 88127 88133 761 88138 88144 88 150 8S156 88161 88167 88173 88178 88 184 8S190 762 88 195 SS201 88 207 88 213 88 218 88 224 88 230 88 235 88 241 88 247 763 88 252 88 258 88 264 88 270 88 275 88 281 88 287 88 292 88 298 88 304 764 88 309 88 315 88 321 88 326 88 332 88 338 88 343 88 349 88 355 88 360 765 88 366 88 372 88 377 S8 383 88 389 88 395 88 400 88 406 88 412 88 417 766 88 423 88 429 88 434 88 440 88 446 88 451 88 457 88 463 88 468 88 474 767 88 480 S8 485 88 491 88 497 88 502 88 508 88 513 88 519 88 525 88 530 76S 88 536 88 542 8S547 88 553 88 559 88 564 88 570 88 576 88 581 88 587 769 88 593 88 598 88 604 88 610 88 615 S8 621 88 627 88 632 88 638 8S643 770 88 649 88 655 88 660 88 666 88 672 88 677 88 683 8S6S9 88 694 88 700 771 88 705 88 711 88 717 88 722 88 728 88 734 88 739 88 745 88 750 88 756 772 88 762 88 767 88 773 88 779 88 784 88 790 88 795 88 801 88 807 88 812 773 88 818 88 824 8S829 88 835 88 840 88 846 88 852 88 857 88 863 88 868 774 88 874 S8 8S0 88 885 88 891 8SS97 88 902 88 908 88 913 88 919 88 925 775 88 930 88 936 88 941 88 947 8S953 88 958 88 964 88 969 88 975 88 981 776 88 986 88 992 88 997 89 003 89 009 89 014 89 020 89 025 89 031 89 037 777 89 042 89 048 89 053 89 059 89 064 89 070 89 076 89 081 89 087 89 092 773 89 098 89104 89 109 89 115 89120 89126 89 131 89 137 89143 89148 779 89154 89159 89165 89170 89176 89182 89187 89193 89198 89 204 780" 89 209 89 215 89 221 89 226 89 232 89 237 89 243 89 248 89 254 89 260 781 89 265 89 271 '89 276 89 282 89 287 89 293 89 298 89 304 89 310 89 315 782 89 321 89 326 89 332 89 337 89 343 89 348 89 354 89 360 89 365 89 371. - 783 89 376 89 382 89 387 89 393 89 398 89 404 89 409 89 415 89 421 89 426 784 89 432 89 437 89 443 89 448 89 454 89 459 89 465 89 470 89 476 89 481 785 89 487 89 492 89 498 89 504 89 509 89 515 89 520 89 526 89 531 89 537 786 89 542 89 548 89 553 89 559 89 564 89 570 89 575 89 581 89 586 89 592 787 89 597 89 603 89 609 89 614 89 620 89 62i 89 631 89 636 89 642 89 647 788 89 653 89 658 89 664 89 669 89 675 89 680 89 686 89 691 89 697 89 702 789 89 708 89 713 89 719 89 724 89 730 89 735 89 741 89 746 89 752 89 757 790 89 763 89 768 89 774 89 779 89 785 89 790 89 796 89 801 89 807 89 812 791 89 818 89 823 89 829 89 834 89S40 89 845 89 851 89 856 89 862 89 867 792 89S73 89 878 89 883 89 8S9 89 894 89 900 89 905 89 911 89 916 89 922 793 89 927 89 933 89 938 89 944 89 949 89 955 89 960 89 966 89 971 89 977 794 89 982 89 988 89 993 89 998 90 004 90 009 90 015 90 020 90 026 90 031 795 90 037 90 042 90 048 90 053 90 059 90 064 90 069 90 075 90 080 90 086 796 90 091 90 097 90 102 90 108 90113 90119 90124 90 129 90135 90140 797 90146 90151 90157 90162 9016S 90173 90179 90184 90189 90195 798 90 200 90 206 90 211 90 217 90 222 90 227 90 233 90 238 90 244 90 249 799 90 255 90 260 90 266 90 271 90 276 90 282 90 287 90 293 90 298 90 304 800 90 309 90 314 90 320 90 325 90 331 90 336 90 342 90 347 90 352 90 358 N O 1 2 3 4 5 6 7 8 9 750-800 16 800-850 N O 1 2 3 4 5 6 7 8 9 800 90 309 90 314 90 320 90 325 90 331 90 336 90 342 90 347 90 352 90 358 801 90 363 90 369 90 374 90 380 90 385 90 390 90 396 90 401 90 407 90 412 802 90 417 90 423 90 428 90 434 90 439 90 445 90 450 90 455 90 461 90 466 803 90 472 90 477 90 482 90 488 90 493 90 499 90 504 90 509 90 515 90 520 804 90 526 90 531 90 536 90 542 90 547 90 553 90 558 90 563 90 569 90 574 805 90 580 90 585 90 590 90 596 90 601 90 607 90 612 90 617 90 623 90 628 806 90 634 90 639 90 644 90 650 90 655 90 660 90 666 90 671 90 677 90 682 807 90 687 90 693 90 698 90 703 90 709 90 714 90 720 90 725 90 730 90 736 808 90 741 90 747 90 752 90 757 90 763 90 768 90 773 90 779 90 784 90 789 809 90 795 90 800 90 806 90 811 90 816 90 822 90 827 90 832 90 838 90 843 810 90 849 90 854 90 859 90 865 90 870 90 875 90 881 90 886 90 891 90 897 811 90 902 90 907 90913 90 918 90 924 90 929 90 934 90 940 90 945 90 950 812 90 956 90 961 90 966 90 972 90 977 90 982 90 988 90 993 90 998 91004 813 91009 91014 91020 91025 91030 91036 91041 91046 91052 91057 814 91 062 91068 91073 91078 91084 91089 91094 91100 91105 91110 815 91 116 91121 91126 91132 91137 91142 91148 91153 91158 91164 816 91169 91174 91180 91185 91190 91196 91201 91206 91212 91217 817 91222 91228 91233 91238 91243 91249 91254 91259 91265 91270 818 91275 912S1 91286 91291 91297 91302 91307 91312 91318 91323 819 91328 91334 91339 91344 91350 91355 91360 91365 91371 91376 820 91381 91387 91392 91397 91403 91408 91413 91418 91424 91429 821 91434 91440 91445 91450 91455 91461 91466 91471 91477 91482 822 91487 91492 91498 91503 91508 91514 91519 91524 91529 91535 823 91540 91545 91551 91556 91561 91566 91572 91577 91582 91587 824 91593 91598 91603 91609 91614 91 61^ 91 624 91630 91635 91640 825 91645 91651 91656 91661 91666 91 672 91677 91682 91687 91693 826 9169S 91703 91709 91714 91719 91724 91730 91735 91740 91745 827 91751 91756 91761 91766 91772 91777 91782 91787 91793 91798 828 91803 91808 91814 91819 91824 91829 91834 91840 91845 91850 829 91855 91861 91866 91871 91876 91882 91 887 91892 91897 91903 830 91908 91913 91918 91924 91929 91934 91939 91944 91950 91955 831 91960 91965 91971 91976 91981 91986 91991 91997 92 002 92 007 832 92 012 92 018 92 023 92 028 92 033 92 038 92 044 92 049 92 054 92 059 833 92 065 92 070 92 075 92 080 92 085. 92 091 92 096 92 101 92 106 92111 834 92 117 92 122 92 127 92132 92137 92 143 92 148 92 153 92158 92 163 835 92169 92174 92179 92184 92189 92195 92 200 92 205 92 210 92 215 836 92 221 92 226 92 231 92 236 92 241 92 247 92 252 92 257 92 262 92 267 837 92 273 92 278 92 283 92 288 92 293 92 298 92 304 92 309 92 314 92 319 838 92 324 92 330 92 335 92 340 92 345 92 350 92 355 92 361 92 366 92 371 839 92 376 92 381 92 387 92 .392 92 397 92 402 92 407 92 412 92 418 92 423 840 92 428 92 433 92 438 92 443 92 449 92 454 92 459 92 464 92 469 92 474 841 92 480 92 485 92 490 92 495 92 500 92 505 92 511 92 516 92 521 92 526 842 92 531 92 536 92 542 92 547 92 552 92 557 92 562 92 567 92 572 92 578 843 92 583 92 588 92 593 92 598 92 603 92 609 92 614 92 619 92 624 92 629 844 92 634 92 639 92 645 92 650 92 655 92 660 92 665 92 670 92 675 92 681 845 92 686 92 691 92 696 92 701 92 706 92 711 92 716 92 722 92 727 92 732 846 92 737 92 742 92 747 92 752 92 758 92 763 92 768 92 773 92 778 92 783 847 92 788 92 793 92 799 92 804 92 809 92S14 92 819 92 824 92 829 92 834 848 92 840 92 845 92 850 92 855 92S60 92 865 92 870 92 875 92 881 92 886 849 92 891 92 896 92 901 92 906 92 911 92 916 92 921 92 927 92 932 92 937 850 92 942 92 947 92 952 92 957 92 962 92 967 92 973 92 978 92 983 92 988 N O 1 2 3 - 4 5 6 7 8 9 800-850 850-900 17 N 1 2 3 4 5 6 7 8 9 850 92 942 92 947 92 952 92 957 92 962 92 967 92 973 92 978 92 983 92 988 851 92 993 92 998 93 003 93 008 93 013 93 018 93 024 93 029 93 034 93 039 852 93 044 93 049 93 054 93 059 93 064 93 069 93 075 93 080 93 085 93 090 853 93 095 93 100 93 105 93 110 93 115 93 120 93 125 93 131 93 136 93141 854 93 146 93 151 93 156 93161 93 166 93 171 93 176 93 181 93 186 93192 855 93197 93 202 93 207 93 212 93 217 93 222 93 227 93 232 93 237 93 242 .856 93 247 93 252 93 258 93 263 93 268 93 273 93 278 93 283 93 288 93 293 857 93 298 93 303 93 30S 93 313 93 318 93 323 93 328 93 334 93 339 93 344 858 93 349 93 354 93 359 93 364 93 369 93 374 93 379 93 384 93 389 93 394 859 93 399 93 404 93 409 93 414 93 420 93 425 93 430 93 435 93 440 93 445 860 93 450 93 455 93 460 93 465 93 470 93 475 93 480 93 485 93 490 93 495 861 93 500 93 505 93 510 93 515 93 520 93 526 93 531 93 536 93 541 93 546 862 93 551 93 556 93 561 93 566 93 571 93 576 93 581 93 586 93 591 93 596 863 93 601 93 606 93 611 93 616 93 621 93 626 93 631 93 636 93 641 93 646 864 93 651 93 656 93 661 93 666 93 671 93 676 93 682 93 687 93 692 93 697 865 93 702 93 707 93 712 93 717 93 722 93 727 93 732 93 737 93 742 93 747 866 - 93 752 93 757 93 762 93 767 93 772 93 777 93 782 93 787 93 792 93 797 867 93 802 93 807 93 812 93 817 93 822 93 827 93 832 93 837 93 842 93 847 868 93 852 93 857 93 862 93S67 93 872 93 877 93 882 93 887 93 892 93 897 869 93 902 93 907 93 912 93 917 93 922 93 927 93 932 93 937 93 942 93 947 870 93 952 93 957 93 962 93 967 93 972 93 977 93 982 93 987 93 992 93 997 871 94 002 94 007 94 012 94 017 94 022 94 027 94 032 94 037 94 042 94 047 872 94 052 94 057 94 062 94 067 94 072 94 077 94 082 94 086 94 091 94 096 873 94101 94 106 94111 94116 94121 94 126 94 131 94 136 94 141 94146 874 94151 94156 94161 94166 94 171 94176 94 181 94 186 94191 94196 875 94 201 94 206 94 211 94 216 94 221 94 226 94 231 94 236 94 240 94 245 876 94 250 94 255 94 260 94 265 94 270 94 275 94 280 94 285 94 290 94 295 877 94 300 94 305 94 310 94 315 94 320 94 325 94 330 94 335 94 340 94 345 878 94 349 94 354 94 359 94 364 94 369 94 374 94 379 94 384 94 389 94 394 879 94 399 94 404 94 409 94 414 94 419 94 424 94 429 94 433 94 438 94 443 880 94 448 94 453 94 458 94 463 94 468 94 473 94 478 94 483 94 488 94 493 881 94 498 94 503 94 507 94 512 94 517 94 522 94 527 94 532 94 537 94 542 882 94 547 94 552 94 557 94 562 94 567 94 571 94 576 94 581 94 586 94 591 883 94 596 94 601 94 606 94 611 94 616 94 621 94 626 94 630 94 635 94 640 884 94 645 94 650 94 655 94 660 94 665 94 670 94 675 94 680 94 685 94 689 885 94 694 94 699 94 704 94 709 94 714 94 719 94 724 94 729 94 734 94 73S 886 94 743 94 748 94 753 94 758 94 763 94 76S 94 773 94 778 94 783 94 787 887 94 792 94 797 94 802 94 807 94 812 94 817 94 822 94 827 94 832 94 836 888 94 841 94 846 94 851 94 856 94 861 94 866 94 871 94 876 94 880 94 885 889 94 890 94 895 94 900 94 905 94 910 94 915 94 919 94 924 94 929 94 934 890 94 939 94 944 94 949 94 954 94 959 94 963 94 968 94 973 94 978 94 983 891 94 988 94 993 94 998 95 002 95 007 95 012 95 017 95 022 95 027 95 032 •892 95 036 95 041 95 046 95 051 95 056 95 061 95 066 95 071 95 075 95 080 893 95 085 95 090 95 095 95 100 95 105 95 109 95 114 95 119 95 124 95 129 894 95 134 95 139 95143 95 148 95 153 95 158 95 163 95 16S 95 173 95177 895 95 182 95 187 95 192 95 197 95 202 95 207 95 211 95 216 95 221 95 226 896 95 231 95 236 95 240 95 245 95 250 95 255 95 260 95 265 95 270 95 274 897 95 279 95 284 95 289 95 294 95 299 95 303 95 308 95 313 95 31S 95 323 898 95 328 95 332 95 337 95 342 95 347 95 352 95 357 95 361 95 366 95 371 899 95 376 95 381 95 386 95 390 95 395 95 400 95 405 95 410 95 415 95 419 900 95 424 95 429 95 434 2 95 439 95 444 95 448 95 453 95 458 95 463 95 468 N O 1 3 4 5 6 7 8 9 850-900 18 900-950 N 1 95 429 2 3 4 5 6 7 8 9 900 95 424 95 434 95 439 95 444 95 448 95 453 95 458 95 463 95 468 901 95 472 95 477 95 482 95 487 95 492 95 497 95 501 95 506 95 511 95 516 902 95 521 95 525 95 530 95 535 95 540 95 545 95 550 95 554 95 559 95 564 903 95 569 95 574 95 578 95 583 95 588 95 593 95 598 95 602 95 607 95 612 904 95 617 95 622 95 626 95 631 95 636 95 641 95 646 95 650 95 655 95 660 905 95 665 95 670 95 674 95 679 95 684 95 689 95 694 95 698 95 703 95 708 906 95 713 95 718 95 722 95 727 95 732 95 737 95 742 95 746 95 751 95 756 907 95 761 95 766 95 770 95 775 95 780 95 785 95 789 95 794 95 799 95 804 908 95 809 95 813 95 818 95 823 95 828 95 832 95 837 95 842 95 847 95 852 909 95 856 95 861 95 866 95 871 95 875 95 880 95 885 95 890 95 895 95 899 910 95 904 95 909 95 914 95 918 95 923 95 928 95 933 95 938 95 942 95 947 911 95 952 95 957 95 961 95 966 95 971 95 976 95 980 95 985 95 990 95 995 912 95 999 96 004 96 009 96 014 96 019 96 023 96 028 96 033 96 038 96 042 913 96 047 96 052 96 057 96 061 96 066 96 071 96 076 96 080 96 085 96 090 914 96 095 96 099 96104 96109 96114 96118 96 123 96128 96133 96137 915 96142 96147 96152 96156 96 161 96166 96 171 96175 96180 96185 916 96190 96194 96199 96 204 96 209 96 213 96 218 96 223 96 227 96 232 917 96 237 96 242 96 246 96 251 96 256 96 261 96 265 96 270 96 275 96 280 918 96 284 96 289 96 294 96 298 96 303 96 308 96 313 96 317 96 322 96 327 919 96 332 96 336 96 341 96 346 96 350 96 355 96 360 96 365 96 369 96 374 920 96 379 96 384 96 388 96 393 96 398 96 402 96 407 96 412 96 417 96 421 921 96 426 96 431 96 435 96 440 96 445 96 450 96 454 96 459 96 464 96 468 922 96 473 96 478 96 483 96 487 96 492 96 497 96 501 96 506 96 511 96 515 923 96 520 96 525 96 530 96 534 96 539 96 544 96 548 96 553 96 558 96 562 924 96 567 96 572 96 577 96 581 96 586 96 591 *96 595 96 600 96 605 96 609 925 96 614 96 619 96 624 96 628 96 633 96 638 '96 642 •96 647 96 652 96 656 926 96 661 96 666 96 670 96 675 96 680 96 685 96 689 96 694 96 699 96 703 927 96 708 96 713 96 717 96 722 96 727 96 731 96 736 96 741 96 745 96 750 928 96 755 96 759 96 764 96 769 96 774 96 778 96 783 96 788 96 792 96 797 929 96 802 96 806 96 811 96 816 96 820 96 825 96 830 96 834 96 839 96 844 930 96 848 96 853 96 858 96 862 96 867 96 872 96 876 96 881 96 886 96 890 931 96 895 96 900 96 904 96 909 96 914 96 918 96 923 96 928 96 932 96 937 932 96 942 96 946 96 951 96 956 96 960 96 965 96 970 96 974 96 979 96 984 933 96 988 96 993 96 997 97 002 97 007 . 97 011 97 016 97 021 97 025 97 030 934 97 035 97 039 97 044 97 049 97 053 97 058 97 063 97 067 97 072 97 077 935 97 081 97 086 97 090 97 095 97100 97104 97109 97114 97118 97123 936 97128 97132 97137 97142 97 146 97151 97155 97160 97 165 97169 937 97174 97179 97183 97 188 97 192 97197 97 202 97 206 97 211 97 216 938 97 220 97 225 97 230 97 234 97 239 97 243 97 248 97 253 97 257 97 262 939 97 267 97 271 97 276 97 280. 97 2S5 . 97 290 97 294 97 299 97 304 97 308 940 97 313 97 317 97 322 97 327 97 331 97 336 97 340 97 345 97 350 97 354 941 97 359 97 364 97 368 97 373 97 377 97 382 97 387 97 391 97 396 97 400 942 97 405 97 410 97 414 97 419 97 424 97 428 97 433 97 437 97 442 97 447 943 97 451 97 456 97 460 97 465 97 470 97 474 97 479 97 483 97 488 97 493 944 97 497 97 502 97 506 97 511 97 516 97 520 97 525 97 529 97 534 97 539 945 97 543 97 548 97 552 97 557 97 562 97 566 97 571 97 575 97 580 97 585 946 97 589 97 594 97 598 97 603 97 607 97 612 97 617 97 621 97 626 97 630 947 97 635 97 640 97 644 97 649 97 653 97 658 97 663 97 667 97 672 97 676 948 97 681 97 685 97 690 97 695 97 699 97 704 97 70S 97 713 97 717 97 722 949 97 727 97 731 97 736 97 740 97 745 97 749 97 754 97 759 97 763 97 768 1 950 97 772 97 777 97 782 97 786 97 791 97 795 97 800 97 804 97 809 97 813 1 N O 1 2 3 4 5 6 7 8 9 900-950 950-1000 19 N 1 2 3 4 5 6 7 8 97 809 9 950 97 772 97 777 97 782 97 786 97 791 97 795 97 800 97 804 97 813 951 97 818 97 823 97 827 97 832 97 836 97 841 97 845 97 850 97 855 97S59 952 97 864 97 86S 97 873 97S77 97 882 97 886 97 891 97 896 97 900 97 905 953 97 909 97 914 97 918 97 923 97 928 97 932 97 937 97 941 97 946 97 950 954 97 955 97 959 97 964 97 96S 97 973 97 978 97 982 97 987 97 991 97 996 955 98 000 98 005 98 009 9S014 98 019 98 023 98 028 98 032 98 037 9S041 956 98 046 98 050 9S055 98 059 98 064 98 068 98 073 98 078 98 082 98 087 957 98 091 98 096 98100 98 105 9S109 98 114 98 118 98 123 98127 9S132 958 98137 98141 98146 98 150 98155 98159 98164 98168 98173 9S177 959 98182 98186 98 191 98195 98 200 98 204 98 209 98 214 98 218 98 223 960 98 227 98 232 98 236 98 241 98 245 98 250 98 254 98 259 98 263 98 268 961 98 272 98 277 98 281 98 286 98 290 98 295 98 299 98 304 98 308 98 313 962 98 318 98 322 98 327 9S331 98 336 98 340 98 345 98 349 98 354 98 358 963 98 363 98 367 9S372 98 376 98 381 98 385 98 390 98 394 98 399 98 403 964 98 408 98 412 98 417 98 421 98 426 98 430 98 435 98 439 98 444 98 448 965 98 453 98 457 9S462 98 466 98 471 98 475 98 480 98 484 98 489 98 493 966 98 498 98 502 9S507 9S511 98 516 98 520 98 525 98 529 98 534 98 538 967 98 543 98 547 9S552 98 556 98 561 98 565 9S570 98 574 98 579 98 583 968 98 588 98 592 98 597 98 601 98 605 98 610 98 614 98 619 98 623 98 628 969 98 632 98 637 98 641 9S646 98 650 98 655 98 659 98 664 98 668 98 673 970 98 677 98 682 9S686 98 691 98 695 98 700 98 704 98 709 98 713 98 717 971 98 722 98 726 98 731 98 735 98 740 98 744 98 749 98 753 98 758 98 762 972 98 767 98 771 98 776 98 780 98 784 98 789 98 793 98 798 98 802 98 807 ,973 98 811 98 816 98 820 98 825 98 829 98 834 98 838 9$843 98 847 98 851 974 98 856 9S860 9SS65 98 869 98 874 98 878 98 883 98 887 98 892 98 896 975 98 900 98 905 98 909 98 914 98 918 98 923 9S927 98 932 98 936 98 941 976 9S945 98 949 98 954 98 958 98 963 98 967 98 972 98 976 98 981 98 985 977 98 989 98 994 98 998 99 003 99 007 99 012 99 016 99 021 99 025 99 029 978 99 034 99 038 99 043 99 047 99 052 99 056 99 061 99 065 99 069 99 074 979 99 07S 99 083 99 0S7 99 092 99 096 99 100 99105 99109 99114 99118 980 " 99123 99127 99131 99136 99140 99145 99149 99154 99158 99162 981 99167 99171 99176 99 180 99 185 99189 99193 99198 99 202 99 207 982 99 211 99 216 99 220 99 224 99 229 99 233 99 238 99 242 99 247 99 251 983 99 255 99 260 99 264 99 269 99 273 99 277 99 282 99 286 99 291 99 295 984 99 300 99 304 99 308 99 313 99 317 99 322 99 326 99 330 99 335 99 339 985 99 344 99 348 99 352 99 357 99 361 99 366 99 370 99 374 99 379 99 383 986 99 388 99 392 99 396 99 401 99 405 99 410 99 414 99 419 99 423 99 427 987 99 432 99 436 99 441 99 445 99 449 99 454 99 458 99 463 99 467 99 471 . 988 99 476 99 480 99 484 99 489 99 493 99 498 99 502 99 506 99 511 99 515 989 99 520 99 524 99 528 99 533 99 537 99 542 99 546 99 550 99 555 99 559 990 99 564 99 568 99 572 99 577 99 581 99 585 99 590 99 594 99 599 99 603 991 99 607 99 612 99 616 99 621 99 625 99 629 99 634 99 638 99 642 99 647 992 99 651 99 656 99 660 99 664 99 669 99 673 99 677 99 682 99 686 99 691 993 99 695 99 699 99 704 99 708 99 712 99 717 99 721 99 726 99 730 99 734 994 99 739 99 743 99 747 99 752 99 756 99 760 99 765 99 769 99 774 99 778 995 99 782 99 787 99 791 99 795 99 800 99 804 99 808 99 813 99 817 99 822 996 99 826 99 830 99 835 99 839 99 843 99 848 99 852 99 856 99 861 99 865 997 99 870 99 874 99 878 99 883 99 887 99 891 99 896 99 900 99 904 99 909 998 99 913 99 917 99 922 99 926 99 930 99 935 99 939 99 944 99 948 99 952 999 99 957 99 961 99 965 99 970 99 974 99 978 99 983 99 987 99 991 99 996 1000 00 000 00 004 00 009 00 013 00 017 00 022 00 026 00 030 00 035 00 039 N O 1 2 3 4 5 6 7 8 9 950-1000 20 TABLE II. -LOGARITHMS OF CONSTANTS. Circumference of the Circle in degrees = 360 Circumference of the Circle in minutes = 21 600 Circumference of the Circle in seconds =1 296 000 If the radius r = 1, half the Circumference of the Circle is 7T = 3. 14 159 265 358 979 323 846 264 338 328 log 2. 55 630 250 4. 33 445 375 6. 11 260 500 0. 49 714 987 Also : 2tt= 6.28 318 531 4tt = 12.56 637 061 £ = 1.57 079 633 2 - = 1.04 719 755 — = 4.18 879 020 3 £= 0.78 539 816 4 - = 0.52 359 878 6 -= 0.31830 989 2*" 3 47T ■ = 0.15 915 494 = 0.95 492 966 = 1.27 323 954 = 0.23 873 241 log- 0. 79 817 987 1. 09 920 986 0. 19 611 988 0. 02 002 862 0. 62 208 861 9. 89 508 988 - 10 9. 71 899 862 - 10 9. 50 285 013 - 10 9. 20 182 013 - 10 9. 97 997 138 - 10 0. 10 491 012 9. 37 791 139 - 10 1 4- 3/„ — y/ir — 1 _ 3)_3_ = 9. 86 960 440 = 0. 10 132 118 = 1. 77 245 385 = 0.56 418 958 = 0. 97 720 502 1.12 837 917 1. 46 459 1S9 0.68 278 406 2. 14 502 940 0. 62 035 049 0. SO 599 598 log 0. 99 429 975 9. 00 570 025 - 10 0.24 857494 9. 75 142 506 - 10 9. 98 998 569 - 10 0. 05 245 506 0. 16 571 662 9. 83 428 338 - 10 0. 33 143 325 9. 79 263 713 - 10 9. 90 633 287 - 10 Arc a, whose length is equal to the radius r, is : 180 in degrees a in minutes a' in seconds a" 10 800 648 000 = 57.29 577 951°. = 3 437. 74 677' . . = 206 264. 806" . . Arc 2 a, whose length is equal to twice the radius, 2 r, is 360 in degrees 2 a° . . . . = . . . 7T 21600 in minutes 2 a' : in seconds 2 a" .... = 1 296 000 If the radius r = 1, the length of the arc is-; 180 " for 1 degree .... for 1 minute .... for 1 second for J degree for I- minute. . . . for \ second or _1 a'"' J_ a"'" 1 2tt°' 1 2 a'" 1 2 a"' 10 800 IT 648 000 ' IT 360"" 21600 = 114. 59 155 903° = 6 875.49 354'.. = 412 529. 612" . . = 0. 01 745 329. . . = 0. 00 029 089. . . = 0.00 000 485... . = 0. 00 872 665. . . . = 0. 00 014 544. . . = 0.00 000 242... 1 296 000 Sin 1" in the unit circle = 0. 00 000 485. , log 1. 75 812 263 3. 53 627 388 5.31442 513 2. 05 915 263 3. 83 730 388 5. 61 545 513 8. 24 187 737 - 10 6.46372 612-10 4.68 557487-10 7. 94 0S4 737 - 10 6. 16 269 612 - 10 4. 38 454 487 - 10 4. 68 557 487 - 10 21 TABLE III. THE LOGARITHMS OF THE TRIGONOMETRIC FUNCTIONS : From 0° to 0° 3', or 89° 57' to 90°, for every second ; From 0° to 2°, or 88° to 90°, for every ten seconds ; Prom 1° t( Note. T log sin ) 89°, for every minute is to be appended. log tan = log sin log cos = 10, 00 000 o all the logarithms — ] 0° tt 0' 1' 2' tt tt 0' 1' 2' tt 30 . 6. 46 373 6. 76 476 60 30 6. 16 270 6. 63 982 6. 86 167 1 4. 68 557 6. 47 090 6. 76 836 59 31 6. 17 694 6. 64 462 6. 86 455 29 2 4. 9S 660 6. 47 797 6. 77 193 5S 32 6. 19 072 6. 64 936 6. 86 742 28 3 5. 16 270 6. 48 492 6. 77 548 57 33 6. 20 409 6. 65 406 6. 87 027 27 ■4 5. 2S 763 6.49175 6. 77 900 56 34 6. 21 705 6. 65 870 6.87 310 26 5 5. 38 454 6. 49 849 6. 78 24S 55 35 6. 22 964 6.66 330 6. 87 591 25 6 5. 46 373 6.50 512 6. 78 595 54 36 6. 24 188 6. 66 785 6. 87 870 24 7 5. 53 067 6. 51 165 6. 78 938 53 37 6. 25 378 6. 67 235 6. 88 147 23 8 5. 58 866 6. 51 808 6. 79 278 52 38 6. 26 536 6. 67 680 6. 88 423 22 9 5. 63 982 6. 52 442 6. 79 616 51 39 6. 27 664 6. 68 121 6. 88 697 21 10 5. 6S557 6. 53 067 6. 79 952 50 40 6. 28 763 6. 68 557 6. SS 969 20 11 5.72 697 6. 53 683 6. 80 285 49 41 6. 29 836 6. 68 990 6. 89 240 19 12 5. 76 476 6. 54 291 6. 80 615 4S 42 6. 30 882 6. 69 418 6. 89 509 18 13 5.79 952 6. 54 890 6. 80 943 47 43 6. 31 904 6. 69 841 6. 89 776 17 14 5. S3 170 6. 55 481 6. 81 26S 46 44 6. 32 903 6. 70 261 6. 90 042 16 15 5. 86 167 6. 56 064 6. 81 591 45 45 6. 33 879 6. 70 676 6. 90 306 15 16 5.88 969 6. 56 639 6.81911 44 46 6. 34 833 6. 71 088 6. 90 568 14 17 5. 91 602 6. 57 207 6. 82 230 43 47 6. 35 767 6. 71 496 6. 90 829 13 18 5. 94 085 6. 57 767 6. 82 545 42 48 6. 36 682 6. 71 900 6. 91 088 12 19 5.96 433 6. 58 320 6. 82 859 41 49 6.37 577 6. 72 300 6. 91 346 11 20 5. 98 660 6. 58 866 6. 83 170 40 50 6. 38 454 6. 72 697 6. 91 602 10 21 6. 00 779 6. 59 406 6. 83 479 39 51 6.39 315 6. 73 090 6. 91 857 9 22 . 6. 02 800 6. 59 939 6. S3 786 38 52 6. 40 158 6. 73 479 6. 92 110 8 23 6. 04 730 6. 60 465 6. 84 091 37 53 6. 40 985 6. 73 865 6. 92 362 7 24 6. 06 579 6. 60 985 6. 84 394 36 54 6. 41 797 6. 74 248 6. 92 612 6 25 6. OS 351 6.61499 6. 84 694 35 55 6. 42 594 6. 74 627 6. 92 S61 5 26 6.10 055 6. 62 007 6. 84 993 34 56 6. 43 376 6. 75 003 6. 93 109 4 27 6. 11 694 6. 62 509 6. 85 289 33 57 6. 44 145 6. 75 376 6. 93 355 3 2S 6. 13 273 6. 63 006 6. 85 5S4 32 58 6. 44 900 6. 75 746 6. 93 599 2 29 6. 14 797 6. 63 496 6. S5 876 31 59 6. 45 643 6. 76 112 6. 93 843 1 30 ft 6. 16 270 6. 63 982 6. S6 167 30 60 6. 46 373 6.76 476 6. 94 085 59' 58' 57' tt tt 59' 58' 57' ft log cot = log cos log sin = 10. 00 000 89 c log cos 22 0° t tt log sin log tan log COS ft I t tt log sin log tan log COS tt t 10 00000 60 10 7. 46 373 7. 46 373 10.00000 50 10 5.68 557 5. 68 557 30.00000 50 10 7. 47 090 7. 47 091 10.00000 50 20 5.98 660 5.98 660 10 00000 40 20 7.47 797 7.47 797 10.00000 40 30 6. 16 270 6. 16 270 10.00000 30 30 7. 48 491 7. 48 492 10 00000 30 ' 40 6. 28 763 6. 28 763 10.00000 20 40 7. 49 175 7. 49 176 10.00000 20 50 6. 38 454 6. 38 454 10.00000 10 50 7. 49 849 7. 49 849 10.00000 10 1 6.46 373 6. 46 373 10 00000 59 110 7.50 512 7.50 512 10.00000 49 10 6. 53 067 6. 53 067 10.00000 50 10 7. 51 165 7. 51 165 10.00000 50 20 6. 58 866 6. 58 866 1000000 40 20 7.51808 7.51809 10.00000 40 30 6. 63 9S2 6. 63 982 1000000 30 30 7. 52 442 7. 52 443 10.00000 30 40 6. 68 557 6. 68 557 10.00000 20 40 7. 53 067 7. 53 067 10 00000 20 SO 6. 72 697 6. 72 697 1000000 10 50 7. 53 683 7. 53 683 10.00000 10 2 6.76 476 6.76 476 10 00000 58 12 7. 54 291 7. 54 291 10 00000 48 10 6. 79 952 6. 79 952 10.00000 50 10 7. 54 890 7. 54 890 10 00000 50 20 6 83 170 6. 83 170 10.00000 40 20 7. 55 481 7. 55 481 10 00000 40 30 6. 86 167 6. 86 167 10 00000 30 30 7.56 064 7.56 064 10.00000 30 40 6. 8S 969 6. 88 969 10 00000 20 40 7. 56 639 7. 56 639 10.00000 20 50 6. 91 602 6. 91 602 10.00000 10 50 7. 57 206 7. 57 207 10.00000 10 3 6. 94 085 6. 94 0S5 10 00000 057 13 7. 57 767 7. 57 767 10.00000 047 10 6 96 433 6. 96 433 10 00000 50 10 7.58 320 7.58 320 10.00000 50 20 6. 98 660 6. 98 661 10 00000 40 20 7.58 866 7.58 867 10 00000 40 30 7. 00 779 7. 00 779 10 00000 30 30 7. 59 406 7. 59 406 10.00000 30 40 7. 02 800 7. 02 800 10 00000 20 40 7. 59 939 7. 59 939 10.00000 20 50 7. 04 730 7. 04 730 10.00000 10 50 7. 60 465 7. 60 466 10.00000 10 4 7. 06 579 7.06 579 10.00000 56 14 7. 60 985 7. 60 986 10.00000 46 10 7. OS 351 7. 08 352 10.00000 50 10 7. 61 499 7. 61 500 10.00000 50 20 7.10 055 7. 10 055 1000000 40 20 7. 62 007 7. 62 008 10.00000 40 30 7.11694 7. 11 694 10.00000 30 30 7. 62 509 7. 62 510 10.00000 30 40 7. 13 273 7. 13 273 1000000 20 40 7. 63 006 7. 63 006 10.00000 20 50 7. 14 797 7. 14 797 10.00000 10 50 7. 63 496 7. 63 497 10.00000 10 5 7. 16 270 7. 16 270 10 00000 55 15 7.63 982 .7.63 982 10.00000 45 10 7. 17 694 7. 17 694 10.00000 50 10 7. 64 461 7. 64 462 10.00000 50 20 7. 19 072 7. 19 073 10.00000 40 20 7.64 936. 7.64 937 10.00000 40 30 7. 20 409 7. 20 409 10.00000 30 30 7. 65 406 7. 65 406 10.00000 30 40 7. 21 705 7. 21 705 10 00000 20 40 7.65 870 7.65 871 10.00000 20 50 7. 22 964 7. 22 964 10.00000 10 50 7. 66 330 7. 66 330 10.00000 10 6 7. 24 188 7. 24 188 10.00000 54 16 7.66 784 7.66 785 10.00000 44 10 7. 25 378 7. 25 378 10.00000 50 10 7. 67 235 7. 67 235 10.00000 50 20 7. 26 536 7.26536 10.00000 40 20 7. 67 6S0 7. 67 680 10.00000 40 30 7. 27 664 7. 27 664 10.00000 30 30 7.68121 7. 68 121 10.00000 30 40 7. 28 763 7. 28 764 10.00000 20 • 40 7.68 557 7.68 558 9.99999 20 50 7. 29 836 7. 29 836 10.00000 10 50 7. 68 989 7. 68 990 9.99999 10 7 7. 30 882 7. 30 882 10.00000 53 170 7. 69 417 7. 69 418 9. 99 999 43 10 7. 31 904 7. 31 904 10.00000 50 10 7. 69 841 7. 69 842 9. 99 999 50 20 7. 32 903 7. 32 903 10.00000 40 20 7. 70 261 7. 70 261 9. 99 999 40 30 7. 33 879 7. 33 879 10.00000 30 30 7. 70 676 7. 70 677 9. 99 999 30 40 7. 34 833 7. 34 833 10.00000 20 40 7.71088 7.71088 9. 99 999 20 50 7. 35 767 7. 35 767 10.00000 10 50 7. 71 496 7. 71 496 9. 99 999 10 8 7. 36 682 7. 36 682 10.00000 52 18 7. 71 900 7. 71 900 9. 99 999 42 10 7.37 577 7.37 577 10.00000 50 10 7. 72 300 7. 72 301 9. 99 999 50 20 7. 38 454 7. 38 455 10.00000 40 20 7. 72 697 7. 72 697 9. 99 999 40 30 7.39 314 7.39 315 10.00000 30 30 7. 73 090 7. 73 090 9. 99 999 30 40 7. 40 158 7. 40 158 10.00000 20 40 7. 73 479 7. 73 480 9. 99 999 20 50 7. 40 985 7. 40 985 10.00000 10 50 7. 73 865 7. 73 866 9. 99 999 10 9 7. 41 797 7. 41 797 10.00000 051 190 7. 74 248 7. 74 248 9. 99 999 041 10 7. 42 594 7. 42 594 10.00000 50 10 7. 74 627 7. 74 628 9. 99 999 50 20 7. 43 376 7. 43 376 10 00000 40 20 7. 75 003 7. 75 004 9. 99 999 40 30 7. 44 145 7. 44 145 10.00000 30 30 7.75 376 7.75 377 9. 99 999 30 40 7. 44 900 7. 44 900 10.00000 20 40 7. 75 745 7. 75 746 9. 99 999 20 50 7. 45 643 7. 45 643 10.00000 10 50 7. 76 112 7. 76 113 9. 99 999 10 100 7. 46 373 7.46373 10.00000 50 20 7.76 475 7.76476 9. 99 999 4O t tt log cos log cot log sin . tt t t tt log cos log cot log sin tt t 89 c 0° 23 t " log sin log tan log cos ft t t tr log sin log tan log COS rt t 20 7. 76 475 7. 76 476 9. 99 999 40 30 7. 94 084 7. 94 086 9. 99 998 30 10 7. 76 836 7. 76 837 9. 99 999 50 10 7. 94 325 7. 94 326 9. 99 998 50 20 7. 77 193 7. 77 194 9. 99 999 40 20 7. 94 564 7. 94 566 9. 99 998 40 30 7. 77 548 7. 77 549 9. 99 999 30 30 7. 94 802 7. 94 804 9. 99 99S 30 40 7. 77 899 7. 77 900 9. 99 999 20 40 7. 95 039 7. 95 040 9. 99 998 20 50 .7. 78 248 7. 78 249 9. 99 999 10 50 7. 95 274 7. 95 276 9. 99 998 10 210 7. 78 594 7. 78 595 9. 99 999 39 31 7. 95 508 7.95 510 9. 99 998 29 10 7. 78 938 7. 78 938 9. 99 999 50 10 7. 95 741 7. 95 743 9. 99 998 50 20 7. 79 278 7. 79 279 9. 99 999 40 20 7. 95 973 7. 95 974 9. 99 998 40 30 7. 79 616 7.79 617 9. 99 999 30 30 7. 96 203 7. 96 205 9. 99 998 30 40 7. 79 952 7. 79 952 9. 99 999 20 40 7. 96 432 7. 96 434 9. 99 998 20 50 7. 80 284 7. SO 285 9. 99 999 10 50 7. 96 660 7. 96 662 9. 99 998 10 220 7. 80 615 7. SO 615 9. 99 999 38 32 7. 96 887 7. 96 889 9. 99 998 28 10 7. 80 942 7. SO 943 9. 99 999 50 10 7. 97 113 7. 97 114 9. 99 998 50 20 7. 81 26S 7. 81 269 9. 99 999 40 20 7. 97 337 7. 97 339 9. 99 998 40 30 7. SI 591 7. 81 591 9. 99 999 30 30 7. 97 560 7. 97 562 9. 99 998 30 40 7. SI 911 7.81912 9. 99 999 20 40 7. 97 7S2 7. 97 784 9. 99 998 20 50 7. 82 229 7. 82 230 9. 99 999 10 50 7. 98 003 7. 98 005 9. 99 998 10 230 7. 82 545 7. 82 546 9. 99 999 37 33 7. 98 223 7. 98 225 9. 99 998 27 10 7.S2S59 7. 82 860 9. 99 999 50 10 7. 98 442 7. 98 444 9. 99 998 50 20 7.83 170 7. 83 171 9. 99 999 40 20 7. 98 660 7. 98 662 9. 99 998 40 30 7. 83 479 7. S3 480 9. 99 999 30 30 7. 9S 876 7. 98 878 9. 99 998 30 40 7. 83 786 7. S3 787 9. 99 999 20 40 7. 99 092 7. 99 094 9. 99 998 20 50 7. 84 091 7. S4 092 9. 99 999 10 50 7.99 306 7. 99 308 9. 99 998 10 240 7. 84 393 7. 84 394 9. 99 999 36 34 7. 99 520 7. 99 522 9. 99 998 26 10 7. 84 694 7. 84 695 9. 99 999 50 10 7. 99 732 7. 99 734 9. 99 998 50 20 7. 84 992 7. 84 994 9. 99 999 40 20 7. 99 943 7. 99 946 9. 99 998 40 30 7. 85 289 7. S5 290 9. 99 999 30 30 8. 00 154 8.00156 9. 99 998 30 40 7. 85 583 7. 85 584 9. 99 999 20 40 8. 00 363 8. 00 365 9. 99 998 20 50 7. 85 876 7. 85 877 9. 99 999 10 50 8.00 571 8.00 574 9. 99 998 10 250 7. 86 166 7. 86 167 9. 99 999 35 35 8. 00 779 8. 00 781 9. 99 998 25 10 7. 86 455 7. 86 456 9. 99 999 50 10 8. 00 985 8. 00 987 9. 99 998 50 20 7. 86 741 7. 86 743 9. 99 999 40 20 8. 01 190 8. 01 193 9. 99 998 40 30 7. 87 026 7. 87 027 9. 99 999 30 30 8. 01 395 8. 01 397 9. 99 998 30 40 7. 87 309 7.87 310 9. 99 999 20 40 8. 01 598 8. 01 600 9. 99 998 20 50 7. 87 590 7. 87 591 9. 99 999 10 50 8. 01 801 8. 01 803 9. 99 998 10 260 7:87 870 7. 87 871 9. 99 999 34 36 S. 02 002 8. 02 004 9. 99 998 24 10 7. SS 147 7. 88 148 9. 99 999 50 10 8. 02 203 8. 02 205 9. 99 998 50 20 7. SS 423 7. SS 424 9. 99 999 40 20 S. 02 402 8. 02 405 9. 99 998 40 30 7. 88 697 7. S8 698 9. 99 999 30 30 8. 02 601 8. 02 604 9. 99 998 30 40 7. SS 969 7. 88 970 9. 99 999 20 40 8. 02 799 8. 02 801 9. 99 998 20 50 7. 89 240 7. 89 241 9. 99 999 10 50 8. 02 996 8. 02 998 9. 99 998 10 270 7. S9 509 7.89 510 9. 99 999 33 37 8. 03 192 8. 03 194 9. 99 997 23 10 7. S9 776 7. 89 777 9. 99 999 50 10 8. 03 387 8. 03 390 9. 99 997 50 20 7. 90 041 7. 90 043 9. 99 999 40 20 8 03 581 8. 03 5S4 9. 99 997 40 30 7. 90 305 7. 90 307 9. 99 999 30 30 8. 03 775 8. 03 777 9. 99 997 30 40 7. 90 568 7. 90 569 9. 99 999 20 40 8. 03 967 8. 03 970 9. 99 997 20 50 7. 90 829 7. 90 S30 9. 99 999 10 50 8. 04 159 8. 04 162 9. 99 997 10 280 7. 91 088 7. 91 0S9 9. 99 999 32 38 8. 04 350 8. 04 353 9. 99 997 22 10 7. 91 346 7. 91 347 9. 99 999 50 10 S. 04 540 8. 04 543 9. 99 997 50 20 7. 91 602 7. 91 603 9. 99 999 40 20 8. 04 729 8. 04 732 9. 99 997 40 30 7.91857 7. 91 858 9. 99 999 30 30 S. 04 918 8. 04 921 9. 99 997 30 40 7.92 110 7.92111 9. 99 998 20 40 8. 05 105 8. 05 10S 9. 99 997 20 50 7. 92 362 7. 92 363 9. 99 998 10 50 8. 05 292 8. 05 295 9. 99 997 10 290 7. 92 612 7. 92 613 9. 99 998 031 39 8. 05 478 8. 05 481 9. 99 997 021 10 7. 92 S61 7. 92 862 9. 99 998 50 10 8. 05 663 S. 05 666 9. 99 997 50 20 7. 93 10S 7.93 110 9. 99 998 40 20 8. 05 848 8.05 851 9. 99 997 40 30 7. 93 354 7. 93 356 9. 99 998 30 30 8.06 031 8. 06 034 9. 99 997 30 40 7. 93 599 7. 93 601 9. 99 99S 20 40 8. 06 214 S. 06 217 9. 99 997 20 50 7. 93 842 7. 93 844 9. 99 998 10 50 8. 06 396 S. 06 399 9. 99 997 10 30 7. 94 084 log cos 7. 94 086 9. 99 99S 30 40 8.06 578 8. 06 581 9. 99 997 20 t tt log cot log sin tt t r ft log cos log cot log sin tt t 89 c 24 ° f " log sin log tan log COS tt J t tt log sin log tan log cos it t 40 8. 06 578 8. 06 581 9. 99 997 20 50 8. 16 268 8. 16 273 9. 99 995 01O 10 8. 06 758 8. 06 761 9. 99 997 50 10 8. 16 413 8.16 417 9. 99 995 50 20 8. 06 938 8. 06 941 9. 99 997 40 20 8.16 557 8.16 561 9. 99 995 40 30 S. 07 117 8. 07 120 9. 99 997 30 30 8. 16 700 8. 16 705 9. 99 995 30 40 8. 07 295 8. 07 299 9. 99 997 20 40 8. 16 843 8. 16 848 9. 99 995 20 50 8. 07 473 8. 07 476 9. 99 997 10 50 8. 16 986 8. 16 991 9. 99 995 10 410 8. 07 650 8. 07 653 9. 99 997 19 510 8. 17 128 8. 17 133 9. 99 995 9 10 S. 07 826 8. 07 829 9. 99 997 50 10 8.17 270 8. 17 275 9. 99 995 50 20 8. 08 002 8. 08 005 9. 99 997 40 20 8.17 411 8.17 416 9. 99 995 40 30 S. 08 176 8. 08 ISO 9. 99 997 30 30 8. 17 552 8.17 557 9. 99 995 30 40 8. OS 350 8. 08 354 9. 99 997 20 40 8. 17 692 8. 17 697 9. 99 995 20 50 8. 08 524 8. 08 527 9. 99 997 10 50 8. 17 832 8. 17 837 9. 99 995 10 420 8. OS 696 8. 08 700 9. 99 997 018 52 8. 17 971 8. 17 976 9. 99 995 8 10 8. OS 868 8. 08 872 9. 99 997 50 10 8.18110 8. 18 115 9. 99 995 50 20 8. 09 040 8. 09 043 9. 99 997 40 20 8. 18 249 8. 18 254 9. 99 995 40 30 8. 09 210 8. 09 214 9. 99 997 30 30 8. 18 387 8. 18 392 9. 99 995 30 40 S. 09 380 S. 09 384 9. 99 997 20 40 8. 18 524 8. 18 530 9. 99 995 20 50 8.09 550 8. 09 553 9. 99 997 10 50 8. 18 662 8. IS 667 9. 99 995 10 430 8. 09 718 8. 09 722 9. 99 997 017 53 8. 18 798 8. 18 804 9. 99 995 7 10 8. 09 886 S. 09 890 9. 99 997 50 10 8. 18 935 8. 18 940 9. 99 995 50 20 8.10 054 8.10 057 9. 99 997 40 20 8.19 071 8. 19 076 9. 99 995 40 30 8. 10 220 8. 10 224 9. 99 997 30 30 S. 19 206 8.19 212 9. 99 995 30 40 8. 10 3S6 8. 10 390 9. 99 997 20 40 8. 19 341 8. 19 347 9. 99 995 20 50 8. 10 552 8. 10 555 9. 99 996 10 50 8. 19 476 8. 19 481 9. 99 995 10 440 8.10 717 8. 10 720 9. 99 996 016 54 8.19 610 8. 19 616 9. 99 995 6 10 S. 10 881 8. 10 884 9. 99 996 50 10 8. 19 744 8. 19 749 9. 99 995 50 20 8. 11 044 8. 11 048 9. 99 996 40 20 8. 19 877 8. 19 8S3 9. 99 995 40 30 8. 11 207 8.11211 9. 99 996 30 30 8. 20 010 8. 20 016 9. 99 995 30 40 8. 11 370 8. 11 373 9. 99 996 20 40 8. 20 143 8. 20 149 9. 99 995 20 50 8.11531 8. 11 535 9. 99 996 10 50 8.*20 275 8. 20 281 9. 99 994 10 450 8. 11 693 8. 11 696 9. 99 996 015 55 8:20 407 8. 20 413 9. 99 994 5 10 8. 11 853 8. 11 857 9. 99 996 50 10 8. 20 538 8. 20 544 9. 99 994 50 20 8.12 013 8.12 017 9. 99 996 40 20 8. 20 669 8. 20 675 9. 99 994 40 30 8. 12 172 8. 12 176 9. 99 996 30 30 8. 20 800 8. 20 806 9. 99 994 30 40 8.12 331 8. 12 335 9. 99 996 20 40 8. 20 930 8. 20 936 9. 99 994 20 50 8. 12 489 8. 12 493 9. 99 996 10 50 8. 21 060 8. 21 066 9. 99 994 10 460 8. 12 647 8. 12 651 9. 99 996 014 56 8. 21 189 8. 21 195 9. 99 994 4 10 8. 12 804 8. 12 SOS 9. 99 996 50 10 8. 21 319 8. 21 324 9. 99 994 50 20 S. 12 961 8. 12 965 9. 99 996 40 20 8. 21 447 8. 21 453 9. 99 994 40 30 8. 13 117 8. 13 121 9. 99 996 30 30 8. 21 576 8. 21 581 9. 99 994 30 40 8. 13 272 8. 13 276 9. 99 996 20 40 8. 21 703 8. 21 709 9. 99 994 20 50 8. 13 427 8. 13 431 9. 99 996 10 50 8. 21 831 8. 21 837 9. 99 994 10 47 8. 13 581 8. 13 585 9. 99 996 013 57 8. 21 958 8. 21 964 9. 99 994 3 10 8. 13 735 8. 13 739 9. 99 996 50 10 8. 22 085 8. 22 091 9. 99 994 50 20 S. 13 8SS S. 13 892 9. 99 996 40 20 8.22 211 8.22 217 9. 99 994 40 30 8. 14 041 8. 14 045 9. 99 996 30 30 8. 22 337 8. 22 343 9. 99 994 30 40 8. 14 193 8. 14 197 9. 99 996 20 40 8. 22 463 8. 22 469 9. 99 994 20 50 8. 14 344 S. 14 348 9.99996 10 50 8. 22 588 8. 22 595 9. 99 994 10 480 8. 14 495 8. 14 500 9. 99 996 012 58 8. 22 713 8. 22 720 9. 99 994 2 10 8. 14 646 8. 14 650 9. 99 996 50 10 8. 22 83S 8. 22 S44 9. 99 994 50 20 8. 14 796 8. 14 800 9. 99 996 40 20 8. 22 962 8. 22 968 9. 99 994 40 30 8. 14 945 8. 14 950 9. 99 996 30 30 8. 23 086 S. 23 092 9. 99 994 30 40 8. 15 094 8. 15 099 9. 99 996 20 40 8. 23 210 8. 23 216 9. 99 994 20 50 8. 15 243 8. 15 247 9. 99 996 .10 50 8. 23 333 8. 23 339 9.99 994 10 490 8. 15 391 8. 15 395 9. 99 996 011 59 8. 23 456 8. 23 462 9. 99 994 1 10 8. 15 538 8. 15 543 9. 99 996 50 10 8. 23 578 8. 23 585 9. 99 994 50 20 8. 15 6S5 8. 15 690 9. 99 996 40 20 S. 23 700 8. 23 707 9. 99 994 40 30 8. 15 832 8. 15 836 9. 99 996 30 30 8. 23 822 8. 23 S29 9. 99 993 30 40 8. 15 97S S. 15 982 9. 99 995 20 40 S. 23 944 8. 23 950 9. 99 993 20 50 8. 16 123 8. 16 128 9. 99 995 10 50 8. 24 065 8. 24 071 9. 99 993 10 50 S. 16 268 8. 16 273 9. 99 995 01O 60 S. 24 1S6 S. 24 192 9. 99 993 t it log cos log cot log sin. tt t t tt log cos log cot log sin ft t 89 c 1 O 25 / " log sin log tan log COS tt t i ft log sin log tan log cos tt t 8. 24 186 S. 24 192 9. 99 993 60 10 8. 30 S79 8. 30 888 9. 99 991 50 10 8.24 306 S. 24 313 9. 99 993 50 10 8. 30 983 S. 30 992 9. 99 991 50 20 ' 8. 24 426 S. 24 433 9. 99 993 40 20 8. 31 0S6 8. 31 095 9. 99 991 40 30 ; 8. 24 546 S. 24 553 9. 99 993 30 30 8.31188 8. 31 198 9. 99 991 30 40 8. 24 665 S. 24 672 9. 99 993 20 40 8. 31 291 8. 31 300 9.99 991- 20 50 | 8. 24 785 8. 24 791 9. 99 993 10 50 8. 31 393 8. 31 403 9. 99 991 10 1 8.24 903 8. 24 910 9. 99 993 59 110 8. 31 495 8. 31 505 9. 99 991 49 10 : 8. 25 022 8. 25 029 9. 99 993 50 10 8. 31 597 8. 31 606 9. 99 991 50 20 S. 25 140 8. 25 147 9. 99 993 40 20 8. 31 699 8. 31 708 9. 99 991 40 30 8. 25 25S 8. 25 265 9. 99 993 30 30 8. 31 800 8. 31 809 9. 99 991 30 40 8. 25 375 S. 25 382 9. 99 993 20 40 8. 31 901 8.31911 9. 99 991 20 50 8. 25 493 S. 25 500 9. 99 993 10 50 8. 32 002 8. 32 012 9. 99 991 10 2 8. 25 609 S. 25 616 9. 99 993 58 12 8. 32 103 8.32112 9. 99 990 48 10 8. 25 726 8. 25 733 9. 99 993 50 10 8. 32 203 8.32 213 9. 99 990 50 20 1 8. 25 842 8. 25 849 9. 99 993 40 20 8 32 303 8.32 313 9. 99 990 40 30 8. 25 958 8. 25 965 9. 99 993 30 30 8. 32 403 8.32 413 9. 99 990 30 40 i 8. 26 074 8. 26 0S1 9. 99 993 20 40 8. 32 503 8.32 513 9. 99 990 20 50 8. 261S9 8. 26 196 9. 99 993 10 50 8. 32 602 8. 32 612 9. 99 990 10 3 8. 26 304 8.26 312 9. 99 993 057 13 8. 32 702 8.32 711 9. 99 990 47 10 8.26 419 8. 26 426 9. 99 993 50 10 S. 32 801 8.32 811 9. 99 990 50 20 8. 26 533 S. 26 541 9. 99 993 40 20 8. 32 899 8. 32 909 9. 99 990 40 30 ! 8. 26 648 8. 26 655 9. 99 993 30 30 8. 32 998 8. 33 008 9. 99 990 30 40 ] 8. 26 761 8. 26 769 9. 99 993 20 40 S. 33 096 8. 33 106 9. 99 990 20 50 8. 26 875 8. 26 882 9. 99 993 10 50 8. 33 195 8. 33 205 9. 99 990 10 4 8.26 9SS 8. 26 996 9. 99 992 56 14 8. 33 292 8. 33 302 9. 99 990 46 10 S. 27 101 8. 27 109 9. 99 992 50 10 8. 33 390 8. 33 400 9. 99 990 50 20 S. 27 214 8. 27 221 9. 99 992 40 20 8. 33 488 8. 33 498 9. 99 990 40 30 S. 27 326 8. 27 334 9. 99 992 30 30 8. 33 585 8. 33 595 9. 99 990 30 40 S. 27 438 8. 27 446 9. 99 992 20 40 8. 33 682 8. 33 692 9. 99 990 20 50 S. 27 550 8. 27 558 9. 99 992 10 50 8. 33 779 8. 33 789 9. 99 990 10 5 8. 27 661 8. 27 669 9. 99 992 55 15 8. 33 875 8. 33 886 9. 99 990 45 10 8. 27 773 8. 27 780 9. 99 992 50 10 8. 33 972 8. 33 9S2 9. 99 990 50 20 8. 27 SS3 8. 27 891 9. 99 992 40 20 S. 34 06S 8. 34 078 9. 99 990 40 30 8. 27 994 8. 2S 002 9. 99 992 30 30 S. 34 164 8. 34 174 9. 99 990 30 40 1 8. 2S 104 8.28112 9. 99 992 20 40 S. 34 260 8. 34 270 9. 99 989 20 50 8.28 215 8. 28 223 9. 99 992 10 50 S. 34 355 8.34 366 9. 99 9S9 10 6 8. 28 324 8. 28 332 9. 99 992 54 16 8. 34 450 8. 34 461 9. 99 989 44 10 8. 28 434 8. 28 442 9. 99 992 50 10 8. 34 546 8. 34 556 9. 99 989 50 20 8. 28 543 8. 28 551 9. 99 992 40 20 8. 34 640 8.34 651 9. 99 989 40 , 30 8. 28 652 8. 28 660 9. 99 992 30 30 8. 34 735 8. 34 746 9. 99 989 30 40 8. 28 761 8. 28 769 9. 99 992 20 40 8. 34 830 8. 34 840 9. 99 989 20 50 8. 28 869 8. 2S S77 9. 99 992 10 50 8. 34 924 8. 34 935 9. 99 9S9 10 7 8. 28 977 8. 28 9S6 9. 99 992 53 170 8. 35 018 8. 35 029 9. 99 989 43 10 8. 29 0S5 8. 29 094 9. 99 992 50 10 8.35 112 8. 35 123 9. 99 989 50 20 8. 29 193 8. 29 201 9. 99 992 40 20 8. 35 206 8. 35 217 9. 99 989 40 30 8. 29 300 8. 29 309 9. 99 992 30 30 S. 35 299 8. 35 310 9. 99 989 30 40 8. 29 407 8. 29 416 9. 99 992 20 40 8. 35 392 8. 35 403 9. 99 989 20 50 8.29 514 8. 29 523 9. 99 992 10 50 8. 35 485 8. 35 497 9. 99 989 10 8 8. 29 621 8. 29 629 9. 99 992 52 18 8. 35 578 8. 35 590 9. 99 989 42 10 8. 29 727 8. 29 736 9. 99 991 50 10 S. 35 671 8. 35 682 9. 99 989 50 20 8. 29 833 8. 29 842 9. 99 991 40 20 8. 35 764 8. 35 775 9. 99 989 40 30 8. 29 939 8. 29 947 9. 99 991 30 30 8. 35 856 8. 35 867 9. 99 989 30 40 8.30 044 8. 30 053 9. 99 991 20 40 8. 35 948 8. 35 959 9. 99 989 20 50 8. 30 150 8. 30 158 9. 99 991 10 50 8. 36 040 8.36 051 9. 99 989 10 9 8. 30 255 8. 30 263 9. 99 991 51 19 8.36131 8. 36 143 9. 99 989 41 10 8.30 359 8. 30 368 9. 99 991 50 10 S. 36 223 8. 36 235 9. 99 988 50 20 8. 30 464 8. 30 473 9. 99 991 40 20 S. 36 314 8. 36 326 9. 99 988 40 30 8. 30 56S 8.30 577 9. 99 991 30 30 8. 36 405 8.36 417 9. 99 988 30 40 8. 30 672 8. 30 681 9. 99 991 20 40 8. 36 496 8. 36 508 9. 99 988 20 50 8. 30 776 8. 30 785 9. 99 991 10 50 8. 36 587 8. 36 599 9. 99 988 10 1O0 8. 30 879 8. 30 888 9. 99 991 50 20 8. 36 678 8. 36 689 9. 99 988 40 t tt log cos log cot log sin it t t tt log COS log cot log sin tt t 88 c 26 ] t tt log sin log tan log COS tt t t tt log sin log tan log cos ft t 200 8. 36 673 8. 36 689 9. 99 988 40 30 8. 41 792 8. 41 807 9. 99 985 30 10 8. 36 768 S. 36 780 9. 99 988 50 10 8. 41 872 8. 41 8S7 9. 99 985 50 20 8. 36 S58 S. 36 870 9. 99 988 40 20 8. 41 952 S. 41 967 9. 99 9S5 40 30 8. 36 94S 8. 36 960 9. 99 988 30 30 8. 42 032 8. 42 048 9. 99 985 30 ' 40 8. 37 038 8. 37 050 9. 99 988 20 40 S. 42 112 8.42 127 9. 99 985 20 50 8.37128 8. 37 140 9. 99 988 10 50 8. 42 192 8. 42 207 9. 99 985 10 210 8.37 217 8. 37 229 9. 99 988 39 310 8. 42 272 8. 42 287 9. 99 985 29 10 8.37 306 8.37 318 9. 99 988 50 10 8. 42 351 8. 42 366 9. 99 985 50 20 8. 37 395 8. 37 408 9. 99 9S8 40 20 8. 42 430 8. 42 446 9. 99 985 40 30 8. 37 484 8.37 497 9. 99 988 30 30 8.42 510 8.42 525 9. 99 985 30 40 8.37 573 8. 37 585 9. 99 988 20 40 8. 42 589 8. 42 604 9. 99 985 20 SO 8. 37 662 8. 37 674 9. 99 988 10 50 8. 42 667 8. 42 683 9. 99 985 10 220 8. 37 750 8. 37 762 9. 99 988 38 32 8. 42 746 8. 42 762 9. 99 984 28 10 S. 37 838 8. 37 850 9. 99 98S 50 10 8.42 825 8.42 840 9. 99 984 50 20 8. 37 926 8. 37 938 9. 99 988 40 20 8. 42 903 8. 42 919 9. 99 984 40 30 8.38 014 8. 38 026 9. 99 987 30 30 8. 42 982 8. 42 997 9. 99 984 30 40 8.3S101 8.38114 9. 99 987 20 40 8.43 060 8.43 075 9. 99 984 20 SO 8. 38 189 8. 38 202 9. 99 987 10 50 8. 43 138 8. 43 154 9. 99 984 10 230 S. 38 276 8. 38 289 9. 99 987 037 33 8. 43 216 8. 43 232 9. 99 984 027 10 8. 38 363 8. 38 376 9. 99 987 50 10 8. 43 293 • 8. 43 309 9. 99 984 50 20 8.38 450 8. 38 463 9. 99 987 40 20 8. 43 371 8. 43 387 9. 99 984 40 30 8. 38 537 S. 38 550 9. 99 987 30 30 8. 43 44S 8. 43 464 9. 99 984 30 40 8. 38 624 8 38 636 9. 99 987 20 40 8. 43 526 8. 43 542 9. 99 984 20 50 8. 38 710 8. 38 723 9. 99 987 10 50 8. 43 603 8. 43 619 9. 99 984 10 240 8. 38 796 8. 38 809 9. 99 987 36 34 8. 43 680 8. 43 696 9. 99 984 26 10 8. 38 882 8. 38 895 9. 99 987 50 10 8. 43 757 8. 43 773 9. 99 984 50 20 8. 38 968 8. 38 981 9. 99 987 40 20 8. 43 834 8. 43 850 9. 99 984 40 30 8. 39 054 8. 39 067 9. 99 987 30 30 8.43 910' 8.43 927 9. 99 984 30 40 8.39.139 8. 39 153 9. 99 987 20 40 8. 43 987 8. 44 003 9. 99 984 20 50 8. 39 225 8. 39 238 9. 99 987 10 50 8.44 063 8.44 080 9. 99 983 10 250 8. 39 310 8. 39 323 9. 99 987 35 35 8.44139 .8.44156 9. 99 983 25 10 8. 39 395 8. 39 408 9. 99 987 50 10 8.44 216 8.44 232 9. 99 983 50 20 8. 39 480 8. 39 493 9. 99 9S7 40 20 8. 44 292 8. 44 308 9. 99 983 40 30 8. 39 565 8. 39 578 9. 99 987 30 30 8. 44 367 8. 44 384 9. 99 983 30 40 8. 39 649 8. 39 663 9. 99 987 20 40 8. 44 443 8. 44 460 9. 99 983 20 50 8. 39 734 8. 39 747 9. 99 986 10 50 8.44 519 8.44 536 9. 99 983 10 260 8. 39 818 8. 39 832 9. 99 986 34 36 8.44 594 8.44 611 9. 99 983 24 10 8. 39 902 S. 39 916 9. 99 986 50 10 8.44 669 8.44 686 9. 99 983 50 20 8. 39 986 8. 40 000 9. 99 986 40 20 8.44 745 8.44 762 9. 99 983 40 30 8. 40 070 8. 40 083 9. 99 986 30 30 8. 44 820 8. 44 837 9. 99 983 30 40 8. 40 153 8. 40 167 9. 99 986 20 40 8. 44 895 8. 44 912 9. 99 983 20 50 8. 40 237 8.40 251 9. 99 9S6 10 50 8.44 969 8.44 987 9. 99 983 10 270 8. 40 320 8. 40 334 9. 99 986 33 37 8. 45 044 8. 45 061 9. 99 983 23 10 8. 40 403 8.40 417 9. 99 986 50 10 8.45 119 8.45 136 9. 99 983 50 20 8. 40 486 8. 40 500 9. 99 986 40 20 8. 45 193 8. 45 210 9. 99 983 40 30 8. 40 569 8. 40 583 9. 99 986 30 30 8. 45 267 8. 45 285 9. 99 983 30 40 8.40 651 8. 40 665 9. 99 986 20 40 8. 45 341 8. 45 359 9. 99 982 20 50 8. 40 734 8. 40 748 9. 99-986 10 50 8. 45 415 8. 45 433 9. 99 982 10 280 8. 40 816 8. 40 830 9. 99 9S6 32 38 8. 45 489 8. 45 507 9. 99 982 22 10 8. 40 898 8. 40 913 9. 99 986 50 10 8. 45 563 8. 45 581 9. 99 982 50 20 8. 40 980 8. 40 995 9. 99 986 40 20 8. 45 637 8. 45 655 9. 99 982 40 30 8. 41 062 8. 41 077 9. 99 986 30 30 8. 45 710 8. 45 728 9. 99 982 30 40 8. 41 144 8. 41 158 9. 99 986 20 40 8. 45 784 8. 45 S02 9. 99 982 20 50 8. 41 225 8. 41 240 9. 99 986 .10 50 8.45 857 8.45 875 9. 99 982 10 290 8. 41 307 8.41321 9. 99 985 031 39 8.45 930 8.45 948 9. 99 982 21 10 8. 41 388 8. 41 403 9. 99 985 50 10 8. 46 003 8. 46 021 9. 99 982 50 20 8. 41 469 8. 41 484 9. 99 985 40 ' 20 8. 46 076 8. 46 094 9. 99 982 40 30 8. 41 550 8. 41 565 9. 99 9S5 30 30 8. 46 149 8. 46 167 9. 99 982 30 40 8.41631 8. 41 646 9. 99 985 20 40 8. 46 222 8. 46 240 9. 99 982 20 50 8. 41 711 8. 41 726 9. 99 985 10 50 8.46 294 8.46 312 9. 99 982 10 300 8. 41 792 8. 41 807 9. 99 985 30 40 8.46 366 8.46 385 9. 99 982 20 t tt log cos log cot log sin . it t t tt log cos log cot log sin tt t 88° ] o 27 f tt log sin log tan log COS ft f t ft log sin log tan log COS tt t 40 8. 46 366 8. 46 385 9. 99 982 20 50 S. 50 504 8.50 527 9. 99 97S 1O 10 8. 46 439 8.46 457 9. 99 982 50 10 8. 50 570 8. 50 593 9. 99 978 50 20 8.46 511 8. 46 529 9. 99 982 40 20 8. 50 636 8. 50 658 9. 99 97S 40 30 8. 46 583 8. 46 602 9. 99 981 30 30 8. 50 701 8. 50 724 9. 99 978 30 40 8.46 655 8. 46 674 9. 99 981 20 40 8. 50 767 8. 50 789 9. 99 977 20 50 8. 46 727 8. 46 745 9. 99 981 10 50 8. 50 832 S. 50 855 9. 99 977 10 410 8. 46 799 8.46S17 9. 99 981 19 510 8. 50 897 8. 50 920 9. 99 977 9 10 8. 46 870 8. 46 889 9. 99 9S1 50 10 8. 50 963 8. 50 985 9. 99 977 50 20 8. 46 942 8. 46 960 9. 99 981 40 20 8. 51 028 8.51050 9. 99 977 40 30 8. 47 013 8. 47 032 9. 99 981 30 30 8.51092 8.51115 9. 99 977 30 40 8. 47 084 8. 47 103 9. 99 9S1 20 40 8. 51 157 8. 51 180 9. 99 977 20 50 8.47155 8. 47 174 9. 99 981 10 50 8. 51 222 8. 51 245 9. 99 977 10 42 8. 47 226 8. 47 245 9. 99 981 18 52 8. 51 287 8.51310 9. 99 977 8 10 8. 47 297 8.47 316 9. 99 981 50 10 8.51351 8. 51 374 9. 99 977 50 20 S. 47 368 8. 47 387 9. 99 981 40 20 8.51416 8. 51 439 9. 99 977 40 30 8. 47 439 8. 47 458 9. 99 981 30 30 8. 51 480 8. 51 503 9. 99 977 30 40 8. 47 509 8. 47 528 9. 99 981 20 40 8. 51 544 8. 51 568 9. 99 977 20 50 8. 47 580 8. 47 599 9. 99 981 10 50 8. 51 609 8. 51 632 9. 99 977 10 430 8. 47 650 8. 47 669 9. 99 981 017 53 8. 51 673 8. 51 696 9. 99 977 7 10 8.47720 8. 47 740 9. 99 980 50 10 8. 51 737 8. 51 760 9. 99 976 50 20 8. 47 790 8. 47 810 9. 99 980 40 20 S. 51 801 8. 51 824 9. 99 976 40 30 8. 47 860 8. 47 880 9. 99 980 30 30 8. 51 864 8. 51 888 9. 99 976 30 40 8. 47 930 8 47 950 9. 99 980 20 40 8. 51 928 8. 51 952 9. 99 976 20 50 8. 48 000 8. 48 020 9. 99 980 10 50 8. 51 992 8.52 015 9. 99 976 10 44 S. 48 069 8. 48 090 9. 99 980 016 54 8. 52 055 8. 52 079 9. 99 976 6 10 8. 48 139 8. 48 159 9. 99 980 50 10 8.52 119 8. 52 143 9. 99 976 50 20 S. 48 208 8. 48 228 9. 99 980 40 20 S. 52 182 8. 52 206 9. 99 976 40 30 8. 48 278 8. 48 298 9. 99 980 30 30 8. 52 245 8. 52 269 9. 99 976 30 40 8. 48 347 8. 48 367 9. 99 980 20 40 8. 52 308 8. 52 332 9. 99 976 20 50 8.48 416 8. 48 436 9. 99 980 10 50 8.52 371 8. 52 396 9. 99 976 10 450 8. 48 485 8. 48 505 9. 99 980 15 55 8. 52 434 8. 52 459 9. 99 976 5 10 8.48 554 8. 48 574 9. 99 980 50 10 8. 52 497 8. 52 522 9. 99 976 50 20 8. 48 622 8. 48 643 9. 99 980 40 20 8. 52 560 8. 52 584 9. 99 976 40 30 8. 48 691 8.4S711 9. 99 980 30 30 8. 52 623 8. 52 647 9. 99 975 30 40 8. 48 760 8. 48 780 9. 99 979 20 40 8. 52 685 8. 52 710 9. 99 975 20 50 8. 48 828 8. 48 849 9. 99 979 10 50 8. 52 748 8. 52 772 9. 99 975 10 460 8". 48 896 8. 48 917 9. 99 979 14 56 8. 52 810 8. 52 835 9. 99 975 4 10 8. 48 965 8. 48 985 9. 99 979 50 10 8.52 872 8. 52 897 9. 99 975 50 20 8. 49 033 8. 49 053 9. 99 979 40 20 8. 52 935 8. 52 960 9. 99 975 40 30 8. 49 101 8. 49 121 9. 99 979 30 30 8. 52 997 8. 53 022 9. 99 975 30 40 8. 49 169 8. 49 189 9. 99 979 20 40 8. 53 059 8. 53 084 9. 99 975 20 50 8. 49 236 8. 49 257 9. 99 979 10 50 8.53 121 8. 53 146 9.99 975 10 470 8. 49 304 8. 49 325 9. 99 979 13 57 8. 53 183 8. 53 208 9. 99 975 3 10 S. 49 372 8. 49 393 9. 99 979 50 10 8. 53 245 8. 53 270 9. 99 975 50 20 8. 49 439 8. 49 460 9. 99 979 40 20 8. 53 306 8. 53 332 9. 99 975 40 30 8. 49 506 8. 49 528 9. 99 979 30 30 8. 53 368 8. 53 393 9. 99 975 30 40 8.49 574 8. 49 595 9. 99 979 20 40 8. 53 429 8. 53 455 9. 99 975 20 50 8. 49 641 8. 49 662 9. 99 979 10 50 8. 53 491 8. 53 516 9. 99 974 10 480 8. 49 708 8. 49 729 9. 99 979 12 58 8. 53 552 8.53 578 9. 99 974 2 10 8. 49 775 8. 49 796 9. 99 979 50 10 8. 53 614 8. 53 639 9. 99 974 50 20 8. 49 842 8. 49 863 9. 99 97S 40 20 8. 53 675 8. 53 700 9. 99 974 40 30 8. 49 908 8. 49 930 9. 99 978 30 30 8. 53 736 8. 53 762 9. 99 974 30 40 8.49 975 8. 49 997 9. 99 978 20 40 8. 53 797 8. 53 823 9. 99 974 20 50 8. 50 042 8. 50 063 9. 99 978 10 50 8. 53 858 8. 53 884 9. 99 974 10 49 8. 50 108 8. 50 130 9. 99 97S 011 59 8. 53 919 8. 53 945 9. 99 974 1 10 8. 50 174 8. 50 196 9. 99 97S 50 10 8. 53 979 8. 54 005 9. 99 974 50 20 8. 50 241 8. 50 263 9. 99 978 40 20 8. 54 040 8. 54 066 9. 99 974 40 30 8.50 307 8. 50 329 9. 99 978 30 30 8. 54 101 8. 54 127 9. 99 974 30 40 8.50 373 8. 50 395 9. 99 978 20 40 8. 54 161 8. 54 187 9. 99 974 20 50 8. 50 439 8. 50 461 9. 99 978 10 50 8. 54 222 8. 54 248 9. 99 974 10 50 8. 50 504 8. 50 527 9. 99 978 01O 60 8. 54 282 8. 54 308 9. 99 974 O t tt log cos log cot log sin tt t / /' log cos log cot log sin tt t m 28 1° f log sin log tan log cot log cos t 8 8 11 9 241S6 24 192 75 SOS 99 993 60 1 24 903 24 910 75 090 99 993 59 2 25 609 25 616 74 3S4 99 993 5S 3 26 304 26 312 73 6SS 99 993 57 ' 4 26 9SS 26 996 73 004 99 992 56 5 27 661 27 669 72 331 99 992 55 6 2S324 28 332 7166S 99 992 54 7- 2S977 2S9S6 71014 99 992 53 S 29 621 29 629 70 371 99 992 52 9 30 255 30 263 69 737 99 991 51 10 30S79 30SSS 69112 99 991 50 11 31495 31 505 6S495 99 991 49 12 32103 32112 67SSS 99 990 4S 13 32 702 32 711 67 2S9 99 990 47 14 33 292 33 302 66 69S 99 990 46 15 33 S75 33 SS6 66114 99 990 45 16 34 450 34 461 65 539 99 9S9 44 17 35 018 35 029 64 971 99 9S9 43 IS 35 57S 35 590 64 410 99 9S9 42 19 36131 36 143 63S57 99 9S9 41 20 36 67S 36 6S9 63 311 99 9SS 40 21 37 217 37 229 62 771 99 9SS 39 22 37 750 37 762 62 23S 99 9S8 3S 23 3S276 3S2S9 61711 99 9S7 37 24 3S796 3SS09 61191 99 9S7 36 25 39 310 39 323 60 677 99 9S7 35 26 39 81S 39S32 6016S 99 9S6 34 27 40 320 40 334 59 666 99 9S6 33 2S 40S16 40S30 59170 99 9S6 32 29 41307 41321 5S679 99 9S5 31 30 41792 41S07 58 193 99 9S5 30 31 42 272 42 2S7 57 713 99 985 29 32 42 746 42 762 57 23S 99 9S4 2S 33 43 216 43 232 56 76S 99 9S4 27 34 43 6S0 43 696 56 304 99 9S4 26 35 44139 44 156 55S44 99 983 25 36 44 594 44 611 55 3S9 99 9S3 24 37 45 044 45 061 54 939 99 9S3 23 3S 45 4S9 45 507 54493 99 9S2 22 39 45 930 45 94S 54 052 99 9S2 21 40 46 366 46 3S5 53 615 99 9S2 20 41 46 799 46817 53 1S3 99 9S1 19 42 47 226 47 245 52 755 99 9S1 IS 43 47 650 47 669 52 331 99 9S1 17 44 4S069 4S0S9 51911 99 9S0 16 45 4S 4S5 4S505 51495 99 9S0 15 46 4SS96 4S917 510S3 99 979 14 47 49 304 49 325 50 675 99979 13 4S 49 70S 49 729 50 271 99 979 12 49 50 10S 50130 49S70 99 97S 11 50 50 504 50 527 49 473 99 97S 10 51 50 S97 50 920 49 0S0 99 977 9 52 51 2S7 51310 4S690 99 977 S 53 51 673 51696 4S304 99 977 - 7 54 52 055 52 079 47 921 99 976 6 55 52 434 52 459 47 541 99 976 5 56 52 S10 52S35 47165 99 975 4 57 53 1S3 53 20S 46 792 99 975 3 58 53 552 53 57S 46 422 99 974 2 59 53 919 53 945 46 055 99 974 1 60 54 2S2 54 30S 45 692 99 974 8 log cos 8 log cot 11 log tan 9 log sin" t t 2 o t log sin log tan log cot log cos / 8 54 2S2 8 54 30S 11 45 692 9 99 974 60 1 54 642 54 669 45 331 99 973 59 2 54 999 55 027 44 973 99 973 58 3 55 354 55 3S2 44 61S 99 972 57 4 55 705 55 734 44 266 99 972 56 5 56 054 56 0S3 43 917 99 971 55 6 56 400 56 429 43 571 99 971 54 7 56 743 56 773 43 227 99 970 53 S 57 0S4 57 114 42SS6 99 970 52 9 57 421 57 452 42 54S 99 969 51 10 57 757 57 7SS 42 212 99 969 50 11 5S 0S9 58 121 41 879 99 96S 49 12 58 419 58 451 41 549 99 96S 4S 13 58 747 5S779 41221 99 967 47 14 59 072 59 105 40S95 99 967 46 15 59 395 59 428 40 572 99 967 45 16 59 715 ' 59 749 40 251 99 966 44 17 60 033 60 068 39 932 99 966 43 IS 60 349 60 3S4 39 616 99 965 42 19 60 662 60 69S 39 302 99 964 41 20 60 973 61009 3S991 99 964 40 21 612S2 61319 3S6S1 99 963 39 22 61 589 61626 3S 374 99 963 3S 23 61S94 61931 3S069 99 962 37 24 62196 62 234 37 766 99 962 36 25 62 497 62 535 37 465 99 961 35 26 62 795 62S34 37166 99 961 34 27 63 091 63 131 36S69 99 960 33 2S 63 3S5 63 426 36 574 99 960 32 29 6S67S 63 71S 36 2S2 99 959 31 30 63 96S 64 009 35 991 99 959 30 31 64 256 64 29S 35 702 99 95 S 29 32 64 543 64 5S5 35 415 99 95S 2S 33 64 827 64 870 35 130 99 957 27 34 65 110 65 154 34S46 99 956 26 35 65 391 65 435 34 565 99 956 25 36 65 670 65 715 34 2S5 99 955 24 37 65 947 65 993 34 007 99 955 23 3S 66 223 66 269 33 731 99 954 22 39 66 497 66 543 33 457 99 954 21 40 66 769 66S16 331S4 99 953 20 41 67 039 67 0S7 32 913 99 952 19 42 67 30S 67 356 32 644 99 952 IS 43 67 575 67 624 32 376 99 951 17 44 67S41 67S90 32110 99 951 16 45 6S104 6S 154 31S46 99 950 15 46 6S367 6S417 31 5S3 99 949 14 47 6S627 6S67S 31322 99 949 13 4S 6SSS6 6S93S 31062 99 94S 12 49 69144 69196 30S04 99 94S 11 50 69 400 69 453 30 547 99 947 10 51 69 654 69 70S 30 292 99 946 9 52 69 907 69 962 30 03S 99 946 S 53 70 159 70 214 29 7S6 99 945 7 54 70 409 70 465 29 535 99 944 6 55 70 65S 70 714 29 2S6 99 944 5 56 70 905 70 962 29 03S 99 943 4 57 71151 7120S 2S792 99 942 3 58 71395 71453 2S547 99 942 2 59 7163S 71697 2S303 99 941 1 60 71SS0 71940 2S060 99 940 8 8 11 9 t log cos log cot log tan log sin r 88 87 ; S o f log sin log tan log cot log cos r 8 71SS0 8 71940 11 28 060 9 99 940 60 1 72 120 72 1S1 27 819 99 940 59 2 72 359 72 420 27 580 99 939 5S 3 72 597 72 659 27 341 99 938 57 4 72S34 72 896 27 104 99 938 56 5 73 069 73 132 26S6S 99 937 55 6 73 303 73 366 26 634 99 936 54 7- 73 535 73 600 26 400 99 936 53 8 73 767 73 832 26168 99 935 52 9 73 997 74 063 25 937 99 934 51 10 74 226 74 292 25 708 99 934 50 11 74 454 74 521 25 479 99 933 49 12 74 680 74 748 25 252 99 932 4S 13 74 906 74 974 25 026 99 932 47 1+ 75 130 75199 24 SOI 99 931 46 15 75 353 75 423 24 577 99 930 45 16 75 575 75 645 24 355 99 929 44 17 75 795 75 867 24133 99 929 43 18 76 015 76 087 23 913 99 928 42 19 76 234 76 306 23 694 99 927 41 20 76 451 76 525 23 475 99 926 40 21 76 667 76 742 23 258 99 926 39 22 76 883 76 95S 23 042 99 925 38 23 77 097 77 173 22 827 99 924 37 24 77 310 77 387 22 613 99 923 36 25 77 522 77 600 22 400 99 923 35 26 77 733 77 811 22 189 99 922 34 27 77 943 7S022 21978 99 921 33 2S 7S152 78 232 2176S 99 920 32 29 78 360 78 441 21559 99 920 31 30 78 568 78 649 21351 99 919 30 31 78 774 78S55 21145 99 91S 29 32 78 979 79 061 20 939 99 917 28 33 79183 79 266 20 734 99 917 27 34 79 386 79 470 20 530 99 916 26 35 79 5SS 79 673 20 327 99 915 25 36 79 789 79 875 20125 99 914 24 37 79 990 SO 076 19 924 99 913 23 38 SO 189 80 277 19 723 99 913 22 39 80 38S 80 476 19 524 99 912 21 40 80 585 80 674 19 326 99 911 20 41 80 782 80S72 19128 99 910 19 42 80 978 81068 18 932 99 909 18 43 SI 173 81264 IS 736 99 909 17 44 81367 81459 18 541 99 90S 16 45 81560 81653 18 347 99 907 15 46 81752 SI 846 18 154 99 906 14 47 SI 944 82 038 17 962 99 905 13 48 82134 82 230 17 770 99 904 12 49 S2 324 82 420 17 580 99 904 11 50 S2 513 82 610 17 390 99 903 10 51 S2 701 82 799 17 201 99 902 9 52 82 8SS 82 987 17 013 99 901 8 53 83 075 S3 175 16 825 99 900 7 54 83 261 83 361 16 639 99 899 6 55 83 446 83 547 16 453 99 898 5 56 83 630 S3 732 16 26S 99 898 4 57 83 813 83 916 16 084 99 897 3 58 83 996 84 100 15 900 99S96 2 59 84177 84 282 15 718 99 895 1 60 84 358 84 464 15 536 99 894 O 8 log cos 8 log cot 11 log tan 9 log sin t t 4° 29 r log sin log tan log cot log cos t 8 S4 35S 8 84 464 11 15 536 9 99 894 60 1 84 539 S4 646 15 354 99 893 59 2 84 718 S4S26 15 174 99 892 58 3 84 897 S5 006 14 994 99 S91 57 4 85 075 S5 1S5 14 815 99 S91 56 5 85 252 S5 363 14 637 99 890 55 6 85 429 85 540 14 460 99 889 54 7 85 605 85 717 14 283 99 888 53 8 85 780 85 893 14 107 99 887 52 9 S5 955 86 069 13 931 99 886 51 10 86128 86 243 13 757 99 885 50 11 86 301 86 417 13 583 99 884 49 12 S6 474 86 591 13 409 99 883 48 13 86 645 86 763 13 237 99 882 47 14 86 816 86 935 13 065 99S81 46 15 86 987 87106 12 894 99,880 45 16 87 156 87 277 12 723 99 879 44 17 87 325 87 447 12 553 99S79 43 18 87 494 S7 616 12 384 99 878 42 19 87 661 87 785 12 215 99S77 41 20 S7S29 87 953 12 047 99 876 40 21 87 995 88 120 11 880 99 875 39 22 88 161 88 2S7 11713 99 874 38 23 88 326 88 453 11547 99 873 37 24 S8 490 SS618 11382 99 872 36 25 8S654 88 783 11217 99 871 35 26 88 817 88 948 11052 99 870 34 27 88 980 89111 10SS9 99S69 33 28 89142 S9 274 10 726 99 868 32 29 89 304 89 437 10 563 99 867 31 30 89 464 89 598 10 402 99S66 30 31 89 625 89 760 10 240 99 865 29 32 89 784 S9 920 10 080 99 864 28 33 S9 943 90 080 09 920 99 863 27 34 90 102 90 240 09 760 99 862 26 35 90 260 90 399 09 601 99 861 25 36 90 417 90 557 09 443 99 860 24 37 90 574 90 715 09 285 99 859 23 3S 90 730 90 872 09128 99 85S 22 39 90 885 91029 08 971 99 857 21 40 91040 91185 08 815 99 856 20 41 91195 91340 08 660 99S55 19 42 91349 91495 08 505 99 854 18 43 91502 91 650 08 350 99 853 17 44 91655 91803 08197 99 852 16 45 91807 91957 08 043 99 851 15 46 91959 92 110 07 S90 99 850 14 47 92 110 92 262 07 738 99S4S 13 48 92 261 92 414 07 586 99 847 12 49 92 411 92 565 07 435 99 846 11 50 92 561 92 716 07 284 99 845 10 51 92 710 92 866 07 134 99 844 9 52 92 859 93 016 06 984 99 843 8 53 93 007 93 165 06 835 99 842 7 54 93154 93 313 06 687 99 841 6 55 93 301 93 462 06 538 99 840 5 56 93 448 93 609 06 391 99 839 4 57 93 594 93 756 06 244 99 838 3 58 93 740 93 903 06 097 99 837 2 59 93SS5 94 049 05 951 99 836 1 60 94 030 94195 05 80i 99 834 8 log cos 8 log cot 11 log tan 9 log sin f t 86 c 85 30 5 O r log sin log tan log cot log cos t 8 8 11 9 O 94 030 94 195 05 805 99 834 60 1 94174 94 340 05 660 99 833 59 2 94 317 94 485 05 515 99 832 5S 3 94 461 94 630 05 370 99 831 57 -4 94 603 94 773 05 227 99 830 56 5 94 746 94 917 05 083 99 829 55 6 94 887 95 060 04 940 99 828 54 7 95 029 95 202 04 798 99 827 53 8 95 170 95 344 04 656 99 825 52 9 95 310 95 486 04 514 99 824 51 10 95 450 95 627 04 373 99 823 50 11 95 589 95 767 04 233 99 822 49 12 95 728 95 908 04 092 99 821 48 13 95 867 96 047 03 953 99 820 47 14 96 005 96187 03 813 99 819 46 15 96143 96 325 03 675 99 817 45 16 96 280 96 464 03 536 99 816 44 17 96 417 96 602 03 398 99 815 43 18 96 553 96 739 03 261 99 814 42 19 96 689 96 877 03 123 99 813 41 20 96 825 97 013 02 987 99 812 40 21 96 960 97150 02 850 99 810 39 22 97 095 97 285 02 715 99 809 38 23 97 229 97 421 02 579 99 808 37 24 97 363 97 556 02 444 99 807 36 25 97 496 97 691 02 309 99 806 35 26 97 629 97 825 02 175 99 804 34 27 97 762 97 959 02 041 99 803 33 28 97 894 98 092 01908 99 802 32 29 98 026 98 225 01775 99 801 31 30 98157 98 358 01642 99 800 30 31 98 288 98 490 01510 99 798 29 32 98 419 98 622 01378 99 797 28 33 98 549 98 753 01247 99 796 27 34 98 679 98 884 01116 99 795 26 35 98 808 99 015 00 985 99 793 25 36 98 937 99145 00 855 99 792 24 37 99 066 99 275 00 725 99 791 23 38 99194 99 405 00 595 99 790 22 39 99 322 99 534 00 466 99 788 21 40 99 450 99 662 00 338 99 787 20 41 99 577 99 791 00 209 99 786 19 42 99 704 99 919 00 081 99 785 18 43 99 830 00 046 99 9^4 99 783 17 44 99 956 00174 99 826 99 782 16 45 00 082 00 301 99 699 99 781 15 46 00 207 00 427 99 573 99 780 14 47 00 332 00 553 99 447 99 778 13 48 00 456 00 679 99 321 99 777 12 49 00 5S1 00 805 99195 99 776 11 50 00 704 00 930 99 070 99 775 10 51 00 828 01055 98 945 99 773 9 52 00 951 01179 98 821 99 772 8 53 01074 01303 98 697 99 771 •7 54 01196 01427 98 573 99 769 6 55 01318 01550 98 450 99 768 5 56 01440 01673 98 327 99 767 4 57 01561 01796 98 204 99 765 3 58 01682 01918 98 082 99 764 2 59 01803 02 040 97 960 99 763 1 60 01923 02 162 97 838 99 761 9 9 10 9 t log COS log cot log tan log sin - t 6° t log sin log tan log cot log cos / 9 01923 9 • 02 162 io 97 83S 9 99 761 o 60 1 02 043 02 283 97 717 99 760 59 2 02 163 02 404 97 596 99 759 58 3 02 283 02 525 97 475 99 757 57 4 02 402 02 645 97 355 99 756 56 5 02 520 02 766 97 234 99 755 55 6 02 639 02 885 97115 99 753 54 7 02 757 03 005 96 995 99 752 53 8 02 874 03 124 96 876 99 751 52 9 02 992 03 242 96 758 99 749 51 10 03 109 03 361 96 639 99 748 50 11 03 226 03 479 96 521 99 747 49 12 03 342 03 597 96 403 99 745 48 13 03 458 03 714 96 286 99 744 47 14 03 574 03 832 96168 99 742 46 15 03 690 03 948 96 052 99 741 45 16 03 805 04 065 95 935 99 740 44 17 03 920 04 181 95 819 99 738 43 18 04 034 04 297 95 703 99 737 42 19 04 149 04 413 95 587 99 736 41 20 04 262 04 528 95 472 99 734 40 21 04 376 04 643 95 357 99 733 39 22 04 490 04 75S 95 242 99 731 38 23 04 603 04 873 95 127 99 730 37 24 04 715 04 987 95 013 99 728 36 25 04 82S 05 101 94 899 99 727 35 26 04 940 05 214 94 786 99 726 34 27 05 052 05 328 94 672 99 724 33 28 05 164 05 441 94 559 99 723 32 29 05^75 05 553 94 447 99 721 31 30 05'386 05 666 94 334 99 720 30 31 05 497 05 778 94 222 99 718 29 32 05 607 05 890 94 110 99 717 28 33 05 717 06 002 93 998 99 716 27 34 05 827 06113 93 887 99 714 26 35 05 937 06 224 93 776 99 713 25 36 06 046 06 335 93 665 99 711 24 37 06155 06 445 93 555 99 710 23 38 06 264 06 556 93 444 99 708 22 39 06 372 06 666 93 334 99 707 21 40 06 481 06 775 93 225 99 705 20 41 06 589 06 885 93 115 99 704 19 42 06 696 06 994 93 006 99 702 18 43 06 804 07 103 92 897 99 701 17 44 06 911 07 211 92 789 99 699 16 45 07 018 07 320 92 680 99 698 15 46 07 124. 07 428 92 572 99 696 14 47 07 231 07 536 92 464 99 695 13 48 07 337 07 643 92 357 99 693 12 49 07 442 07 751 92 249 99 692 11 50 07 548 07 858 92142 99 690 10 51 07 653 07 964 92 036 99 689 9 52 07 758 08 071 91929 99 687 8 53 07 863 08 177 91823 99 686 7 54 07 968 08 283 91717 99 684 6 55 08 072 08 389 91611 99 683 5 56 08 176 08 495 91 505 99 681 4 57 08 280 08 600 91400 99 680 3 58 08 383 08 705 91 295 99 678 2 59 0S4S6 0SS10 91190 99 677 1 60 08 589 08 914 91086 99 675 O 9 log cos 9 log cot 10 log tan 9 log sin t t 84 c 83 c 7 o r log sin log tan log cot log cos t 9 OS 589 9 08 914 10 91086 9 99 675 60 1 08 692 09 019 90 981 99 674 59 2 OS 795 09123 90 877 99 672 5S 3 OS 897 09 227 90 773 99 670 57 4 OS 999 09 330 90 670 99 669 56 5 09101 09 434 90 566 99 667 55 6 09 202 09 537 90 463 99 666 54 7 09 304 09 640 90 360 99 664 53 8 09 405 09 742 90 258 99 663 52 9 09 506 09 845 90155 99 661 51 io 09 606 09 947 90 053 99 659 50 11 09 707 10 019 89 951 99 65S 49 12 09 807 10150 89 850 99 656 48 13 09 907 10 252 89 748 99 655 47 14 10 006 10 353 89 647 99 653 46 15 10106 10 454 89 546 99 651 45 16 10 205 10 555 89 445 99 650 44 17 10 304 10 656 89 344 99 64S 43 18 10 402 10 756 89 244 99 647 42 19 10 501 10 856 89144 99 645 41 20 10 599 10 956 89 044 99 643 40 21 10 697 11056 88 944 99 642 39 22 10 795 11 155 88 845 99 640 38 23 10S93 11254 88 746 99 638 37 24 10 990 11353 88 647 99 637 36 25 11087 11452 8S548 99 635 35 26 11184 11551 88 449 99 633 34 27 11281 11649 SS351 99 632 33 ' 28 11377 11747 88 253 99 630 32 29 11474 11845 88155 99 629 31 30 11570 11943 88 057 99 627 30 31 11666 12 0+0 87 960 99 625 29 32 11761 12 138 87 862 99 624 28 33 11857 12 235 87 765 99 622 27 34 11952 12 332 87 668 99 620 26 35 12 047 12 428 87 572 99 618 25 36 "12 142 12 525 87 475 99 617 24 37 12 236 12 621 S7 379 99 615 23 3S 12 331 12 717 87 283 99 613 22 39 12 425 12 813 87 187 99 612 21 40 12 519 12 909 87 091 99 610 20 41 12 612 13 004 86 996 99 60S 19 42 12 706 13 099 86 901 99 607 18 43 12 799 13 194 86 806 99 605 17 44 12 892 13 289 86 711 99 603 16 45 12 985 13 384 86 616 99 601 15 46 13 078 13 478 86 522 99 600 14 47 13 171 13 573 86 427 99 598 13 48 13 263 13 667 86 333 99 596 12 49 13 355 13 761 86 239 99 595 11 50 13 447 13 854 86146 99 593 IO 51 13 539 13 948 86 052 99 591 9 52 13 630 14 0+1 85 959 99 589 8 53 13 722 14 134 85 866 99 588 7 54 13 813 14 227 85 773 99 586 6 55 13 904 14 320 85 6S0 99 584 5 56 13 994 14 412 85 58S 99 582 4 57 14 085 14 50+ 85 496 99 581 3 58 14 175 14 597 85 403 99 579 2 59 14 266 14 688 85 312 99 577 1 60 14 356 14 780 85 220 99 575 O 9 log cos 9 log cot IO log tan 9 log sin t f 8 o 31 t log sin log tan log cot log cos r 9 9 10 9 o 14 356 14 780 85 220 99 575 60 1 14 445 14 872 85 128 99 574 59 2 14 535 14 963 85 037 99 572 5S 3 14 62+ 15 054 84 946 99 570 57 4 14 714 15 145 84 855 99 568 56 5 14 803 15 236 84 764 99 566 55 6 14 891 15 327 84 673 99 565 54 7 14 980 15 417 84 583 99 563 53 S 15 069 15 508 84 492 99 561 52 9 15 157 15 598 84 402 99 559 51 10 15 245 15 688 84 312 99 557 50 11 15 333 15 777 84 223 99 556 49 12 15 421 15 867 84133 99 554 48 13 15 50S 15 956 84 044 99 552 47 14 15 596 16 046 83 954 99 550 46 15 15 683 16135 83 865 99 548 45 16 15 770 16 224 83 776 99 546 44 17 15S57 16 312 83 688 99 545 43 18 15 944 16 401 83 599 99 543 42 19 16 030 16 489 83 511 99 541 41 20 16116 16 577 83 423 99 539 40 21 16 203 16 665 83 335 99 537 39 22 16 289 16 753 83 247 99 535 38 23 16 374 16 841 83 159 99 533 37 24 16 460 16 928 83 072 99 532 36 25 16 545 17 016 82 984 99 530 35 26 16 631 17 103 82 897 99 528 34 27 16 716 17 190 82 810 99 526 33 2S 16 801 17 277 82 723 99 524 32 29 16 886 17 363 82 637 99 522 31 30 16 970 17 450 82 550 99 520 30 31 17 055 17 536 82 464 99 518 29 32 17 139 17 622 82 378 99 517 28 33 17 223 17 708 82 292 99 515 27 34 17 307 17 794 82 206 99 513 26 35 17 391 17 880 82 120 99 511 25 36 17 474 17 965 82 035 99 509 24 37 17 558 18 051 81949 99 507 23 38 17 641 18 136 81864 99 505 22 39 17 724 18 221 81779 99 503 21 40 17 807 18 306 81694 99 501 20 41 17 890 18 391 81609 99 499 19 42 17 973 18 475 81525 99 497 18 43 18 055 18 560 81440 99 495 17 44 18137 18 644 81356 99 494 16 45 18 220 18 728 81272 99 492 15 46 18 302 18 812 811SS 99 490 14 47 1S3S3 18 896 81 104 99 488 13 48 18 465 18 979 81021 99 486 12 49 18 547 19 063 80 937 99 484 11 50 18 628 19146 80 854 99 4S2 10 51 18 709 19 229 80 771 99 480 9 52 18 790 19 312 80 688 99 478 8 53 18S71 19 395 80 605 99 476 7 54 18 952 19 478 80 522 99 474 6 55 19 033 19 561 80 439 99 472 5 56 19113 19 643 80 357 99 470 4 57 19193 19 725 80 275 99 468 3 58 19 273 19 807 80193 99 466 2 59 19 353 19 889 80 111 99 464 1 60 19 433 19 971 80 029 99 462 9 log cos 9 log cot IO log tan 9 log sin r r 82 8r 32 9 t log sin log tan log cot log cos / 9 9 10 9 o 19 433 19 971 80 029 99 462 60 1 19 513 20 053 79 947 99 460 59 2 19 592 20134 79 866 99 458 58 3 19 672 20 216 79 784 99 456 57 4' 19 751 20 297 79 703 99 454 56 5 19 830 20 378 79 622 99 452 55 6 19 909 20 459 79 541 99 450 54 7 19 9S8 20 540 79 460 99 448 53 8 20 067 20 621 79 379 99 446 52 9 20145 20 701 79 299 99 444 51 10 20 223 20 782 79 218 99 442 50 11 20 302 20 862 79138 99 440 49 12 20 380 20 942 79 058 99 438 48 13 20 458 21022 78 978 99 436 47 14 20 535 21102 78 898 99 434 46 15 20 613 21182 78 818 99 432 45 16 20 691 21261 78 739 99 429 44 17 20 768 21341 78 659 99 427 43 18 20 845 21420 78 580 99 425 42 19 20 922 21499 78 501 99 423 41 20 20 999 21578 78 422 99 421 40 21 21076 21657 78 343 99 419 39 22 21153 21736 78 264 99 417 3S 23 21229 21814 78 186 99 415 37 24 21306 21893 78107 99 413 36 25 21382 21971 78 029 99 411 35 26 21458 22 049 77 951 99 409 34 27 21534 22 127 77 873 99 407 33 28 21610 22 205 77 795 99 404 32 29 21685 22 2S3 77 717 99 402 31 30 21761 22 361 77 639 99 400 30 31 21836 22 438 77 562 99 398 29 32 21912 22 516 77 484 99 396 28 33 21987 22 593 77 407 99 394 27 34 22 062 22 670 77 330 99 392 26 35 22137 22 747 77 253 99 390 25 36 22 211 22 824 77176 99 388 24 37 22 286 22 901 77 099 99 385 23 38 22 361 22 977 77 023 99 383 22 39 22 435 23 054 76 946 99 381 21 40 22 509 23 130 76 870 99 379 20 41 22 583 23 206 76 794 99 377 19 42 22 657 23 283 76 717 99 375 18 43 22 731 23 359 76 641 99 372 17 44 22 805 23 435 76 565 99 370 16 45 22 878 23 510 76 490 99 368 15 46 22 952 23 5S6 76 414 99 366 14 47 23 025 23 661 76 339 99 364 13 48 23 098 23 737 76 263 99 362 12 49 23171 23 812 76188 99 359 11 50 23 244 23 887 76113 99 357 IO 51 23 317 23 962 76 038 99 355 9 52 23 390 24 037 75 963 99 353 8 53 23 462 24112 75 888 99 351 7- 54 23 535 24186 75 814 99 348 6 55 23 607 24 261 75 739 99 346 5 56 23 679 24 335 75 665 99 344 4 57 23 752 24 410 75 590 99 342 3 58 23 823 24 484 75 516 99 340 2 59 23 895 24 558 75 442 99 337 1 60 23 967 24 632 75 368 99 335 9 log cos 9 log cot io log tan 9 log sin t ■f 10 c t log sin log tan log cot log cos / 9 23 967 9 24 632 10 75 368 9 99 335 o 60 1 24 039 24 706 75 294 99 333 59 2 24110 24 779 75 221 99 331 58 3 24 181 24 853 75 147 99 328 57 4 24 253 24 926 75 074 99 326 56 5 24 324 25 000 75 000 99 324 55 6 24 395 25 073 74 927 99 322 54 7 24 466 25 146 74 854 99 319 53 8 24 536 25 219 74 781 99 317 52 9 24 607 25 292 74 708 99 315 51 IO 24 677 25 365 74 635 99 313 50 11 24 748 25 437 74 563 99 310 49 12 24 818 25 510 74 490 99 308 48 13 24 888 25 582 74 418 99 306 47 14 24 958 25 655 74 345 99 304 46 15 25 028 25 727 74 273 99 301 45 16 25 098 25 799 74 201 99 299 44 17 25 168 25 871 74129 99 297 43 18 25 237 25 943 74 057 99 294 42 19 25 307 26 015 73 985 99 292 41 20 25 376 26 086 73 914 99 290 40 21 25 445 26158 73 842 99 288 39 22 25 514 26 229 73 771 99 285 38 23 25 583 26 301 73 699 99 283 37 24 25 652 26 372 73 628 99 281 36 25 25 721 26 443 73 557 99 278 35 26 25 790 26 514 73 486 99 276 34 27 25 858 26 585 73 415 99 274 33 28 25 927 26 655 73 345 99 271 32 29 25 995 26 726 73 274 99 269 31 30 26 06'3 26 797 73 203 99 267 30 31 26131 26 867 73 133 99 264 29 32 26199 26 937 73 063 99 262 28 33 26 267 27 008 72 992 99 260 27 34 26 335 27 078 72 922 99 257 26 35 26 403 27148 72 852 99 255 25 36 26 470 27 218 72 782 99 252 24 37 26 538 27 28S 72 712 99 250 23 38 26 605 27 357 72 643 99 248 22 39 26 672 27 427 72 573 99 245 21 40 26 739 27 496 72 504 99 243 20 41 26 806 27 566 72 434 99 241 19 42 26 873 27 635 72 365 99 238 18 43 26 940 27 704 72 296 99 236 17 44 27 007 27 773 72 227 99 233 16 45 27 073 27 842 72 158 99 231 15 46 27 140 27 911 72 089 99 229 14 47 27 206 27 980 72 020 99 226 13 4S 27 273 28 049 71951 99 224 12 49 27 339 28117 71883 99 221 11 50 27 405 28186 71814 99 219 IO 51 27 471 28 254 71746 99 217 9 52 27 537 28 323 71677 99 214 8 53 27 602 28 391 71609 99 212 7 54 27 668 28 459 71541 99 209 6 55 27 734 28 527 71473 99 207 5 56 27 799 28 595 71405 99 204 4 57 27 864 28 662 71338 99 202 3 5S 27 930 28 730 71270 99 200 2 59 27 995 28 79S 71202 99197 1 60 28 060 28 865 71135 99 195 O 9 log cos 9 log cot IO log tan 9 log sin t f 80 c W ir t log sin log tan log cot log cos t 9 28 060 9 28 865 10 71135 9 99 195 60 1 28 125 2S933 71067 99 192 59 2 28 190 29 000 71000 99 190 58 3 28 254 29 067 70 933 99 187 57 4 28 319 29134 70 866 99 185 56 5 2S3S4 29 201 70 799 99 1S2 55 6 28 448 29 268 70 732 99 180 54 7 2S512 29 335 70 665 99177 53 8 28 577 29 402 70 598 99 175 52 9 28 641 29 46S 70 532 99 172 51 io 2S705 29 535 70 465 99170 50 11 2S769 29 601 70 399 99 167 49 12 28 S33 29 66S 70 332 99165 4S 13 2SS96 29 734 70 266 99 162 47 14 2S960 29 800 70 200 99160 46 15 29 024 29 866 70134 99 157 45 16 29 0S7 29 932 70 068 99 155 44 17 29150 29 99S 70 002 99 152 43 IS 29 214 30 064 69 936 99150 42 19 29-277 30130 69 870 99 147 41 20 29 340 30195 69 805 99 145 40 21 29 403 30 261 69 739 99 142 39 22 29 466 30 326 69 674 99 140 38 23 29 529 30 391 69 609 99 137 37 24 29 591 30 457 69 543 99135 36 25 29 654 30 522 69 478 99 132 35 26 29 716 30 587 69 413 99130 34 27 29 779 30 652 69 348 99 127 33 2S 29 841 30 717 69 283 99124 32 29 29 903 30 782 69 218 99122 31 30 29 966 30 846 69154 99119 30 31 30 028 30 911 69 089 99 117 29 32 30 090 30 975 69 025 99114 28 33 30 151 31040 6S960 99112 27 34 30 213 31104 6SS96 99109 26 35 30 275 31168 68 832 99 106 25 36 "30 336 31233 68 767 99104 24 37 30 39S 31297 68 703 99 101 23 38 30 459 31361 68 639 99 099 22 39 30 521 31425 6S575 99 096 21 40 30 5S2 31489 6S511 99 093 20 41 30 643 31552 6S448 99 091 19 42 30 704 31616 6S3S4 99 OSS 18 43 30 765 31679 68 321 99 0S6 17 44 30 826 31743 6S257 99 083 16 45 30 887 31S06 6S194 99 0S0 15 46 30 947 31870 6S130 99 078 14 47 31008 31933 68 067 99 075 13 4S 31068 31996 6S004 99 072 12 49 31129 32 059 67 941 99 070 11 50 31189 32122 67 87S 99 067 10 51 31250 32 185 67 815 99 064 9 52 31310 32 24S 67 752 99 062 8 53 31370 32311 67 689 99 059 7 54 31430 32 373 67 627 99 056 6 55 31490 32 436 67 564 99 054 5 56 31549 32 49S 67 502 99 051 4 57 31609 32 561 67 439 99 04S 3 5S 31669 32 623 67 377 99 046 2 59 3172S 32 685 67 315 99 043 1 60 31788 32 747 67 253 99 040 9 log COS 9 log cot 10 log tan 9 log sin f f 12 c t log sin log tan log cot log cos t 9 31 7SS 9 32 747 10 67 253 9 99 040 60 1 31847 32 810 67 190 99 03S 59 2 31 907 32 872 67 128 99 035 58 3 31966 32 933 67 067 99 032 57 4 32 025 32 995 67 005 99 030 56 5 32 0S4 33 057 66 943 99 027 55 6 32 143 33 119 66 881 99 024 54 7 32 202 33 ISO 66 820 99 022 53 S 32 261 33 242 66 758 99 019 52 9 32 319 33 303 66 697 99 016 51 10 32 37S 33 365 66 635 99 013 50 11 32 437 33 426 66 574 99 011 49 12 32 495 33 4S7 66 513 99 008 48 13 32 553 33 548 66 452 99 005 47 14 32 612 33 609 66 391 99 002 46 15 32 670 33 670 66 330 99 000 45 16 32 728 33 731 66 269 9S997 44 17 32 786 33 792 66 208 9S994 43 IS 32 844 33 S53 66 147 98 991 42 19 32 902 33 913 66 087 9S9S9 41 20 32 960 33 974 66 026 98 986 40 21 33 01S 34 034 65 966 9S9S3 39 22 33 075 34 095 65 905 98 980 38 23 33 133 34155 65 845 98 978 37 24 33 190 34 215 65 785 98 975 36 25 33 248 34 276 65 724 98 972 35 26 33 305 34 336 65 664 98 969 34 27 33 362 34 396 65 604 98 967 33 28 33 420 34 456 65 544 98 964 32 29 33 477 34 516 65 484 9S961 31 30 33 534 34 576 65 424 98 95S 30 31 33 591 34 635 65 365 98 955 29 32 33 647 34 695 65 305 9S953 28 33 33 704 34 755 65 245 98 950 27 34 33 761 34 814 65 186 98 947 26 35 33 SIS 34 874 65 126 98 944 25 36 33 874 34 933 65 067 98 941 24 37 33 931 34 992 65 008 98 93S 23 38 33 987 35 051 64 949 98 936 22 39 34 043 35 111 64 8S9 98 933 21 40 34 100 35 170 64 830 9S930 20 41 34 156 35 229 64 771 98 927 19 42 34 212 35 288 64 712 98 924 18 43 34 26S 35 347 64 653 9S921 17 44 34 324 35 405 64 595 9S919 16 45 34 380 35 464 64 536 98 916 15 46 34 436 35 523 64 477 98 913 14 47 34 491 35 581 64 419 98 910 13 48 34 547 35 640 64 360 98 907 12 49 34 602 35 698 64 302 98 904 11 50 34 65S 35 757 64 243 98 901 10 51 34 713 35 815 64 185 98 898 9 52 34 769 35 873 64 127 98 896 8 53 34S24 35 931 64 069 9SS93 7 54 34 879 35 989 64 011 9SS90 6 55 34 934 36 047 63 953 98 887 5 56 34 989 36105 63 895 98 884 4 57 35 044 36163 63 837 9SSS1 3 5S 35 099 36 221 63 779 9SS78 2 59 35 154 36 279 63 721 98 875 1 60 35 209 36 336 63 664 9S872 O 9 9 IO 9 t log cos log cot log tan log sin i 78 r 7?t 34 13° r log sin log tan log cot log cos t 9 9 io 9 O 35 209 36 336 63 664 9SS72 60 1 35 263 36 394 63 606 98S69 59 2 35 318 36 452 63 548 98S67 58 3 35 373 36 509 63 491 98 864 57 4 35 427 36 566 63 434 98 861 56 5 35 481 36 624 63 376 9S858 55 6 35 536 36 681 63 319 98 855 54 7 35 590 36 738 63 262 98 852 53 8 35 644 36 795 63 205 98 849 52 9 35 69S 36 852 63 148 98 846 51 10 35 752 36 909 63 091 98 843 50 11 35 806 36 966 63 034 9SS40 49 12 35 860 37 023 62 977 98 837 4S 13 35 914 37 080 62 920 98 834 47 14 35 968 37137 62 863 98 831 46 15 36 022 37193 62 807 98 828 45 16 36 075 37 250 62 750 98 825 44 17 36129 37 306 62 694 98 822 43 IS 36182 37 363 62 637 98 819 42 19 36 236 37 419 62 581 98 816 41 20 36 289 37 476 62 524 9S813 40 21 36 342 37 532 62 468 98 810 39 22 36 395 37 588 62 412 98 807 38 23 36 449 37 644 62 356 98 804 37 24 36 502 37 700 62 300 98 801 36 25 36 555 37 756 62 244 98 798 35 26 36 608 37 812 62188 98 795 34 27 36 660 37 868 62132 98 792 33 2S 36 713 37 924 62 076 98 789 32 29 36 766 37 980 62 020 98 786 31 30 36 819 38 035 61965 9S7S3 30 31 36 871 38 091 61909 98 780 29 32 36 924 38 147 61853 98 777 28 33 36 976 38 202 61798 98 774 27 34 37 028 38 257 61743 98 771 26 35 37 081 38 313 61687 9S 768 25 36 37133 38 368 61632 98 765 24 37 37 1S5 38 423 61 577 98 762 23 38 37 237 38 479 61521 9S759 22 39 37 2S9 38 534 61466 98 756 21 40 37 341 3S589 61411 98 753 20 41 37 393 38 644 61356 98 750 19 42 37 445 38 699 61301 9S 746 18 43 37 497 3S754 61246 98 743 17 44 37 549 38 808 61192 98 740 16 45 37 600 3S863 61137 98 737 15 46 37 652 38 918 610S2 98 734 14 47 37 703 38 972 61028 9S731 B 48 37 755 39 027 60 973 98 728 12 49 37 806 39 0S2 60 918 98 725 11 50 37 858 39 136 60 864 98 722 10 51 37 909 39 190 60 810 98 719 9 52 37 960 39 245 60 755 98 715 8 53 38 011 39 299 60 701 98 712 7 54 3S062 39 353 60 647 98 709 6 55 38113 39 407 60 593 98 706 5 56 38 164 39 461 60 539 98 703 4 57 38 215 39 515 60 485 98 700 3 58 38 266 39 569 60 431 98 697 2 59 38 317 39 623 60 377 9S694 1 60 38 368 39 677 60 323 98 690 O 9 log cos 9 log cot 10 log tan 9 log sin t t 14 c t log sin log tan log cot log cos / 9 38 368 9 39 677 10 60 323 9 98 690 60 1 38 418 39 731 60 269 98 687 59 2 38 469 39 785 60 215 98 684 58 3 38 519 39 838 60162 98 681 57 4 38 570 39 892 60108 98 678 56 5 38 620 39 945 60 055 98 675 55 6 38 670 39 999 60 001 98 671 54 7 38 721 40 052 59 948 98 668 53 8 38 771 40106 59 894 98 665 52 9 38 821 40159 59 841 98 662 51 10 38 871 40 212 59 788 98 659 50 11 3S921 40 266 59 734 98 656 49 12 38 971 40 319 59 681 98 652 48 13 39 021 40 372 59 628 98 649 47 14 39 071 40 425 59 575 98 646 46 15 39121 40 478 59 522 98 643 45 16 39170 40 '531 59 469 98 640 44 17 39 220 40 584 59 416 98 636 43 IS 39 270 40 636 59 364 98 633 42 19 39 319 40 689 59 311 98 630 41 20 39 369 40 742 59 258 9S627 40 21 39 418 40 795 59 205 98 623 39 22 39 467 40 847 59153 98 620 3S 23 39 517 40 900 59100 98 617 37 24 39 566 40 952 59 048 98 614 36 25 39 615 41005 58 995 98 610 35 26 39 664 41057 58 943 98 607 34 27 39 713 41109 58 891 98 604 33 28 39 762 41161 58 839 98 601 32 29 39 811, 41214 58 786 98 597 31 30 39 860 41266 58 734 98 594 30 31 39 909 41318 58 682 9S591 29 32 39 958 41370 58 630 98 588 28 33 40 006 41422 58 578 98 584 27 34 40 055 41474 58 526 98 581 26 35 40103 41526 58 474 98 578 25 36 40152 41578 58 422 98 574 24 37 40 200 41629 58 371 98 571 23 38 40 249 41681 58 319 98 568 22 39 40 297 41733 58 267 98 565 21 40 40 346 41784 58 216 98 561 20 41 40 394 41836 58164 98 558 19 42 40 442 41887 58113 98 555 IS 43 40 490 41939 58 061 98 551 17 44 40 538 41990 58 010 98 548 16 45 40 586 42 041 57 959 98 545 15 46 40 634 42 093 57 907 98 541 14 47 40 682 42144 57 856 98 538 13 48 40 730 42195 57 805 98 535 12 49 40 77S 42 246 57 754 98 531 11 50 40 825 42 297 57 703 98 528 10 51 40 873 42 348 57 652 98 525 9 52 40 921 42 399 57 601 98 521 8 53 40 968 42 450 57 550 98 518 7 54 41016 42 501 57 499 98 515 6 55 41063 42 552 57 448 98 511 5 56 41111 42 603 57 397 98 508 4 57 41158 42 653 57 347 98 505 3 58 41205 42 704 57 296 98 501 2 59 41252 42 755 57 245 98 49S 1 60 41300 42 805 57195 98 494 9 log cos 9 log cot IO log tan 9 log sin t t 76 ( 75 c 15° r log sin log tan log cot log cos r 9 41300 9 42 805 io 57195 9 9S494 60 1 41347 42 856 57 144 9S491 59 2 41394 42 906 57 094 98 488 5S 3 41441 42 957 57 043 98 484 57 4 41488 43 007 56 993 98 481 56 5 41535 43 057 56 943 98 477 55 6 41 582 43 108 56S92 9S474 54 7 41628 43158 56S42 9S471 53 8~ 41675 43 208 56 792 98 467 52 9 41722 43 258 56 742 9S464 51 10 41768 43 30S 56 692 9S460 50 11 41815 43 358 56 642 9S457 49 12 41861 43 40S 56 592 98 453 48 13 41908 43 458 56 542 98 450 47 14 41954 43 508 56 492 98 447 46 15 42 001 43 558 56 442 98 443 45 16 42 047 43 607 56 393 9S440 44 17 42 093 43 657 56 343 9S436 43 18 42 140 43 707 56 293 98 433 42 19 42 186 43 756 56 244 98 429 41 20 42 232 43 806 56194 98 426 40 21 42 278 43 855 56145 98 422 39 22 42 324 43 905 56 095 98 419 38 23 42 370 43 954 56 046 98 415 37 24 42 416 44 004 55 996 98 412 36 25 42 461 44 053 55 947 9S409 35 26 42 507 44102 55 898 9S405 34 27 42 553 44151 55 849 98 402 33 ■28 42 599 44 201 55 799 98 398 31 29 42 644 44 250 55 750 98 395 31 30 42 690 44 299 55 701 98 391 30 31 42 735 44 348 55 652 9S388 29 32 42 781 44 397 55 603 9S3S4 28 33 42S26 44 446 55 554 9S381 27 34 42 872 44 495 55 505 9S377 26 35 42 917 44 544 55 456 9S373 25 36 42 962 44 592 55 40S 9S370 24 37 43 00S 44 641 55 359 98 366 23 38 43 053 44 690 55 310 98 363 22 39 43 09S 44 73S 55 262 98 359 21 40 43 143 44 787 55 213 98 356 20 41 43 188 44 836 55 164 98 352 19 42 43 233 44 884 55 116 9S349 18 43 43 27S 44 933 55 067 9S345 17 44 43 323 44 981 55 019 98 342 16 45 43 367 45 029 54 971 98 338 15 46 43 412 45 078 54 922 98 334 14 47 43 457 45 126 54 874 98 331 13 4S 43 502 45 174 54 826 98 327 12 49 43 546 45 222 54 778 98 324 11 50 43 591 45 271 54 729 98 320 10 51 43 635 45 319 54 681 98 317 9 52 43 680 45 367 54 633 9S313 8 53 43 724 45 415 54 585 98 309 7 54 43 769 45 463 54 537 9S306 6 55 43 813 45 511 54 489 98 302 5 56 43 857 45 559 54 441 98 299 4 57 43 901 45 606 54 394 9S295 3 58 43 946 45 654 54 346 98 291 2 59 43 990 45 702 54 298 98 28S 1 60 44 034 45 750 54 250 9S284 9 log cos 9 log cot IO log tan 9 log sin t r 16° 35 r log sin log tan log cot log cos t 9 44 034 9 45 750 IO 54 250 9 98 284 60 1 44 078 45 797 54 203 98 281 59 2 44 122 45 845 54155 98 277 58 3 44166 45 892 54 108 98 273 57 4 44 210 45 940 54 060 98 270 56 5 44 253 45 987 54 013 98 266 55 6 44 297 46 035 53 965 98 262 54 7 44 341 46 082 53 918 98 259 53 S 44 385 46130 53 870 98 255 52 9 44 428 46177 53 823 98 251 51 10 44 472 46 224 53 776 98 248 50 11 44 516 46 271 53 729 98 244 49 12 44 559 46 319 53 681 98 240 48 13 44 602 46 366 53 634 98 237 47 14 44 646 46 413 53 587 98 233 46 15 44 689 46 460 53 540 98 229 45 16 44 733 46 507 53 493 98 226 44 17 44 776 46 554 53 446 98 222 43 18 44 819 46 601 53 399 98 218 42 19 44 862 46 648 53 352 98 215 41 20 44 905 46 694 53 306 98 211 40 21 44 948 46 741 53 259 98 207 39 22 44 992 46 788 53 212 98 204 38 23 45 035 46 835 53 165 98 200 37 24 45 077 46 881 53 119 98196 36 25 45 120 46 928 53 072 98192 35 26 45 163 46 975 53 025 98189 34 27 45 206 47 021 52 979 98185 33 2S 45 249 47 068 52 932 98 181 32 29 45 292 47114 52 886 98177 31 30 45 334 47160 52 840 9S174 30 31 45 377 47 207 52 793 98 170 29 32 45 419 47 253 52 747 98166 28 33 45 462 47 299 52 701 9S162 27 34 45 504 47 346 52 654 98159 26 35 45 547 47 392 52 608 98155 25 36 45 589 47 438 52 562 98151 24 37 45 632 47 484 52 516 98 147 23 38 45 674 47 530 52 470 98144 22 39 45 716 47 576 52 424 98140 21 . 40 45 758 47 622 52 378 98136 20 41 45 801 47 668 52 332 98132 19 42 45 843 47 714 52 286 9S129 18 43 45 885 47 760 52 240 98125 17 44 45 927 47 806 52194 98121 16 45 45 969 47 852 52 148 98117 15 46 46 011 47 897 52 103 98113 14 47 46 053 47 943 52 057 98 110 13 48 46 095 47 989 52 011 98106 12 49 46136 48 035 51965 98102 11 50 46178 48 080 51920 98 098 IO 51 46 220 48126 51874 98 094 9 52 46 262 48 171 51829 98 090 8 53 46 303 48 217 51783 98 087 7 54 46 345 48 262 51738 9S0S3 6 55 46 386 48 307 51693 98 079 5 56 46 428 48 353 51647 98 075 4 57 46 469 48 398 51602 98 071 3 58 46 511 48 443 51 557 98 067 2 59 46 552 48 489 51511 98 063 1 60 46 594 48 534 51466 98 060 O 9 9 10 9 t log cos log cot log tan log sin t 74 c 73 c 36 17° t log sin log tan log cot log cos f 9 9 io 9 o 46 594 48 534 51466 98 060 00 1 46 635 48 579 51421 98 056 59 2 46 676 48 624 51376 98 052 58 3 46 717 48 669 51331 98 048 57 4 46 758 48 714 51286 98 044 56 5 46 800 48 759 51241 98 040 55 6 46 841 48 804 51196 98 036 54 7 46 882 48 849 51151 98 032 53 8 46 923 48 894 51 106 98 029 52 9 46 964 48 939 51061 98 025 51 10 47 005 48 984 51016 98 021 50 11 47 045 49 029 50 971 98 017 49 12 47 086 49 073 50 927 98 013 48 13 47127 49118 50 882 98 009 47 14 47168 49163 50 837 98 005 46 15 47 209 49 207 50 793 98 001 45 16 47 249 49 252 50 748 97 997 44 17 47 290 49 296 50 704 97 993 43 18 47 330 49 341 50 659 97 989 42 19 47 371 49 385 50 615 97 986 41 20 47 411 49 430 50 570 97 982 40 21 47 452 49 474 50 526 97 978 39 22 47 492 49 519 50 481 97 974 38 23 47 533 49 563 50 437 97 970 37 24 47 573 49 607 50 393 97 966 36 25 47 613 49 652 50 348 97 962 35 26 47 654 49 696 50 304 97 958 34 27 47 694 49 740 50 260 97 954 33 28 47 734 49 784 50 216 97 950 32 29 47 774 49 828 50172 97 946 31 30 47 814 49 872 50128 97 942 30 31 47 854 49 916 50 084 97 938 29 32 47 894 49 960 50 040 97 934 28 33 47 934 50 004 49 996 97 930 27 34 47 974 50 048 49 952 97 926 26 35 48 014 50 092 49 908 97 922 25 36 48 054 50136 49 864 97 918 24 37 48 094 50180 49 820 97 914 23 38 48133 50 223 49 777 97 910 22 39 48173 50 267 49 733 97 906 21 40 48 213 50311 49 689 97 902 20 41 48 252 50 355 49 645 97 898 19 42 48 292 50 398 49 602 97 894 18 43 48 332 50 442 49 558 97 890 17 44 48 371 50 485 49 515 97 886 16 45 48 411 50 529 49 471 97 882 15 46 48 450 50 572 49 428 97 878 14 47 48 490 50 616 49 384 97 874 • 13 48 48 529 50 659 49 341 97 870 12 49 48 568 50 703 49 297 97 866 11 50 48 607 50 746 49 254 97S61 10 51 48 647 50 789 49 211 97 857 9 52 48 686 50 833 49167 97 853 8 53 48 725 50 876 49 124 97 849 7 54 48 764 50 919 49 081 97 845 6 55 48 803 50 962 49 038 97 841 5 56 48 842 51005 48 995 97S37 4 57 48 881 51048 48 952 97 833 3 58 48 920 51092 48 908 97 829 2 59 48 959 51135 4S865 97S25 1 60 48 998 51178 4S822 97 821 9 9 IO 9 t log COS log cot log tan log sin t 18 c r log sin log tan log cot log cos / 9 9 IO 9 O 48 998 51 178 48 822 97 821 60 1 49 037 51 221 48 779 97 817 59 2 49 076 51264 48 736 97S12 58 3 49115 51306 48 694 97 808 57 4 49153 51349 48 651 97 804 56 5 49 192 51 392 48 60S 97 800 55 6 49 231 51435 4S565 97 796 54 7 49 269 51478 48 522 97 792 53 8 49 308 51 520 48 480 97 78S 52 9 49 347 51563 48 437 97 784 51 IO 49 385 51606 48 394 97 779 50 11 49 424 51648 48 352 97 775 49 12 49 462 51 691 48 309 97 771 48 13 49 500 51734 48 266 97 767 47 14 49 539 51776 48 224 97 763 46 15 49 577 51819 48181 97 759 45 16 49 615 '51861 48139 97 754 44 17 49 654 51903 48 097 97 750 43 18 49 692 51 946 48 054 97 746 42 19 49 730 51988 48 012 97 742 41 20 49 768 52 031 47 969 97 738 40 21 49 806 52 073 47 927 97 734 39 22 49 844 52 115 47 885 97 729 38 23 49 882 52 157 47 843 97 725 37 24 49 920 52 200 47 800 97 721 36 25 49 958 52 242 47 758 97 717 35 26 49 996 52 284 47 716 97 713 34 27 50 034 52 326 47 674 97 708 33 28 50 072 52 368 47 632 97 704 32 29 50410 52 410 47 590 97 700 31 30 50148 52.452 47 548 97 696 30 31 50 185 52 494 47 506 97 691 29 32 50 223 52 536 47 464 97 687 28 33 50 261 52 578 47 422 97 683 27 34 50 298 52 620 47 380 97 679 26 35 50 336 52 661 47 339 97 674 25 36 50 374 52 703 47 297 97 670 24 37 50 411 52 745 47 255 97 666 23 38 50 449 52 787 47 213 97 662 22 39 50 486 52 829 47171 97 657 21 40 50 523 52 870 47 130 97 653 20 41 50 561 52 912 47 088 97 649 19 42 50 598 52 953 47 047 97 645 18 43 50 635 52 995 47 005 97 640 17 44 50 673 53 037 46 963 97 636 16 45 50 710 53 078 46 922 97 632 15 46 50 747 53 120 46 880 97 628 14 47 50 784 53 161 46S39 97 623 13 48 50 821 53 202 46 798 97 619 12 49 50 858 53 244 46 756 97 615 11 50 50 896 53 285 46 715 97 610 10 51 50 933 53 327 46 673 97 606 9 52 50 970 53 368 46 632 97 602 8 53 51007 53 409 46 591 97 597 7 54 51043 53 450 46 550 97 593 6 55 51 0S0 53 492 46 508 97 589 5 56 51117 53 533 46 467 97 584 4 57 51154 53 574 46 426 97 580 3 58 51 191 53 615 46 385 97 576 2 59 51227 53 656 46 344 97 571 1 60 51264 53 697 46 303 97 567 9 9 IO 9 t log cos log cot log tan log sin r 72 c n 19° t log sin log tan log cot log cos t 9 51264 9 53 697 IO 46 303 9 97 567 o 60 1 51301 53 73S 46 262 97 563 59 2 5133S 53 779 46 221 97 558 58 3 51374 53 820 46 180 97 554 57 4 51411 53 861 46139 97 550 56 5 51447 53 902 46 098 97 545 55 6 514S4 53 943 46 057 97 541 54 7 51520 53 984 46 016 97 536 53 8' 51 557 54 025 45 975 97 532 52 9 51593 54 065 45 935 97 528 51 io 51629 54106 45 894 97 523 50 11 51666 54147 45 853 97 519 49 12 51702 541S7 45 813 97 515 48 13 51738 S4 22S 45 772 97 510 47 14 51774 54 269 45 731 97 506 46 15 51811 54 309 45 691 97 501 45 16 51847 54 350 45 650 97 497 44 17 518S3 54 390 45 610 97 492 43 18 51919 54 431 45 569 97 488 42 19 51955 54 471 45 529 97 484 41 20 51991 54 512 45 488 97 479 40 21 52 027 54 552 45 448 97 475 39 22 52 063 54 593 45 407 97 470 38 23 52 099 54 633 45 367 97*466 37 24 52 135 54 673 45 327 97 461 36 25 52171 54 714 45 286 97 457 35 26 52 207 54 754 45 246 97 453 34 27 52 242 54 794 45 206 97 448 33 28 52 27S 54 835 45 165 97 444 32 29 52 314 54 875 45 125 97 439 31 30 52 350 54 915 45 0S5 97 435 30 31 52 385 54 955 45 045 97 430 29 32 52 421 54 995 45 005 97 426 28 33 52 456 55 035 44 965 97 421 27 34 52 492 55 075 44 925 97 417 26 35 52 527 55115 44 885 97 412 25 36 52 563 55 155 44 845 97 408 24 37 52 598 55 195 44 805 97 403 23 3S 52 634 55 235 44 765 97 399 22 39 52 669 55 275 44 725 97 394 21 40 52 705 55 315 44 685 97 390 20 41 52 740 55 355 44 645 97 385 19 42 52 775 55 395 44 605 97 3S1 18 43 52 811 55 434 44 566 97 376 17 44 52 846 55 474 44 526 97 372 16 45 52 881 55 514 44 486 97 367 15 46 52 916 55 554 44 446 97 363 14 47 52 951 55 593 44 407 97 358 13 48 52 986 55 633 44 367 97 353 12 49 53 021 55 673 44 327 97 349 11 SO 53 056 55 712 44 2SS 97 344 IO 51 53 092 55 752 44 248 97 340 9 52 53 126 55 791 44 209 97 335 8 53 53 161 55 831 44 169 97 331 7 54 53 196 55 870 44130 97 326 6 55 53 231 55 910 44 090 97 322 5 56 53 266 55 949 44 051 97 317 4 57 53 301 55 989 44 011 97 312 3 58 53 336 56 028 43 972 97 308 2 59 53 370 56 067 43 933 97 303 1 60 53 405 56 107 43 893 97 299 O 9 log cos 9 log cot 10 log tan 9 log sin f t 20° 37 t log sin log tan log cot log cos t 9 9 IO 9 53 405 56107 43 893 97 299 60 1 53 440 56146 43 854 97 294 59 2 53 475 561S5 43 815 97 289 58 3 53 509 56 224 43 776 97 285 57 4 53 544 56 264 43 736 97 280 56 5 53 578 56 303 43 697 97 276 55 6 53 613 56 342 43 65S 97 271 54 7 53 647 56 381 43 619 97 266 53 8 53 682 56 420 43 580 97 262 52 9 53 716 56 459 43 541 97 257 51 10 53 751 56 498 43 502 97 252 50 11 53 785 56 537 43 463 97 248 49 12 53 819 56 576 43 424 97 243 48 13 53 854 56 615 43 385 97 238 47 14 53 88S 56 654 43 346 97 234 46 15 53 922 56 693 43 307 97 229 45 16 53 957 56 732 43 268 97 224 44 17 53 991 56 771 43 229 97 220 43 18 54 025 56 810 43 190 97 215 42 19 54 059 56 849 43 151 97 210 41 20 54 093 56 887 43 113 97 206 40 21 54 127 56 926 43 074 97 201 39 22 54161 56 965 43 035 97 196 38 23 54195 57 004 42 996 97 192 37 24 54 229 57 042 42 958 97187 36 25 54 263 57 081 42 919 97 182 35 26 54 297 57120 42 880 97 178 34 27 54 331 57158 42 842 97 173 33 28 54 365 57 197 42 S03 97 168 32 29 54 399 57 235 42 765 97163 31 30 54 433 57 274 42 726 97159 30 31 54 466 57 312 42 688 97 154 29 32 54 500 57 351 42 649 97 149 28 33 54 534 57 389 42 611 97 145 27 34 54 567 57 428 42 572 97 140 26 35 54 601 57 466 42 534 97135 25 36 54 635 57 504 42 496 97 130 24 37 54 668 57 543 42 457 97 126 23 38 54 702 57 581 42 419 97 121 22 39 54 735 57 619 42 381 97116 21 40 54 769 57 658 42 342 97 111 20 41 54 802 57 696 42 304 97 107 19 42 54 836 57 734 42 266 97 102 IS 43 54 869 57 772 42 228 97 097 17 44 54 903 57 810 42 190 97 092 16 45 54 936 57 849 42 151 97 087 15 46 54 969 57 887 42 113 97 083 14 47 55 003 57 925 42 075 97 078 13 48 55 036 57 963 42 037 97 073 12 49 55 069 58 001 41999 97 068 11 50 55 102 58 039 41961 97 063 10 51 55 136 58 077 41923 97 059 9 52 55 169 58 115 41 885 97 054 8 53 55 202 58153 41847 97 049 7 54 55 235 58 191 41809 97 044 6 55 55 268 58 229 41771 97 039 5 56 55 301 58 267 41733 97 035 4 57 55 334 58 304 41 696 97 030 3 58 55 367 5S 342 41 658 97 025 2 59 55 400 58 380 41620 97 020 1 60 55 433 58 418 41582 97 015 O 9 log cos 9 log cot IO log tan 9 log sin t t w 69 c 38 21° t log sin log tan log cot log cos t 9 55 433 9 58 418 IO 41582 9 97 015 o 60 1 55 466 58 455 41545 97 010 59 2 55 499 58 493 41507 97 005 58 3 55 532 58 531 41469 97 001 57 4. 55 564 58 569 41431 96 996 56 5 55 597 58 606 41394 96 991 55 6 55 630 58 644 41356 96 986 54 7 55 663 58 681 41319 96 981 53 8 55 695 58 719 41281 96 976 52 9 55 72S 58 757 41243 96 971 51 io 55 761 58 794 41206 96 966 50 11 55 793 58 832 41168 96 962 49 12 55 826 58 869 41131 96 957 48 13 55 858 58 907 41093 96 952 47 14 55 891 58 944 41056 96 947 46 15 55 923 58 981 41019 96 942 45 16 55 956 59 019 40 981 96 937 44 17 55 988 59 056 40 944 96 932 43 18 56 021 59 094 40 906 96 927 42 19 56 053 59131 40 869 96 922 41 20 56 085 59168 40 832 96 917 40 21 56118 59 205 40 795 96 912 39 22 56150 59 243 40 757 96 907 38 23 56182 59 280 40 720 96 903 37 24 56 215 59 317 40 683 96 898 36 25 56 247 59 354 40 646 96 893 35 26 56 279 59 391 40 609 96 888 34 27 56 311 59 429 40 571 96 883 33 28 56 343 59 466 40 534 96 878 32 29 56 375 59 503 40 497 96 873 31 30 56 408 59 540 40 460 96 868 30 31 56 440 59 577 40 423 96 863 29 32 56 472 59 614 40 386 96 858 28 33 56 504 59 651 40 349 96 853 27 34 56 536 59 688 40 312 96 848 26 35 56 568 59 725 40 275 96 843 25 36 56 599 59 762 40 238 96 838 24 37 56 631 59 799 40 201 96 833 23 38 56 663 59 835 40165 96 828 22 39 56 695 59 872 40128 96 823 21 40 56 727 59 909 40 091 96 818 20 41 56 759 59 946 40 054 96 813 19 42 56 790 59 983 40 017 96 808 18 43 56 822 60 019 39 981 96 803 17 44 56 854 60 056 39 944 96 798 16 45 56 886 60 093 39 907 96 793 15 46 56 917 60130 39 870 96 788 14 47 56 949 60166 39S34 96 783 13 48 56 980 60 203 39 797 96 778 12 49 57 012 60 240 39 760 96 772 11 50 57 044 60 276 39 724 96 767 IO 51 57 075 60 313 39 687 96 762 9 52 57107 60 349 39 651 96 757 8 53 57 138 60 386 39 614 96 752 7 54 57169 60 422 39 578 96 747 6": 55 57 201 60 459 39 541 96 742 5 56 57 232 60 495 39 505 96 737 4 57 57 264 60 532 39 468 96 732 3 58 57 295 60 568 39 432 96 727 2 59 57 326 60 605 39 395 96 722 1 60 57 358 60 641 39 359 96 717 9 log COS 9 log cot IO log tan 9 log sin t f 22 c t log sin log tan log cot log cos / 9 9 10 9 o 57 358 60 641 39 359 96 717 60 1 57 389 60 677 39 323 96 711 59 2 57 420 60 714 39 286 96 706 58 3 57 451 60 750 39 250 96 701 57 4 57 482 60 786 39 214 96 696 56 5 57 514 60 823 39177 96 691 55 6 57 545 60 859 39141 96 686 54 7 57 576 60 895 39105 96 681 53 8 57 607 60 931 39 069 96 676 52 9 57 638 60 967 39 033 96 670 51 10 SI 669 61004 38 996 96 665 50 11 57 700 61040 38 960 96 660 49 12 57 731 61076 38 924 96 655 48 13 57 762 61112 38 888 96 650 47 14 57 793 61148 38 852 96 645 46 15 57 824 61184 38 816 96 640 45 16 57 855 61220 38 780 96 634 44 17 57 885 61256 38 744 96 629 43 18 57 916 61292 38 708 96 624 42 19 57 947 61328 38 672 96 619 41 20 57 978 61364 38 636 96 614 40 21 58 008 61400 38 600 96 608 39 22 58 039 61436 38 564 96 603 38 23 58 070 61472 38 528 96 598 37 24 58101 61508 38 492 96 593 36 25 58131 61544 38 456 96 588 35 26 58 162 61579 38 421 96 582 34 27 58192 61615 38 385 96 577 33 28 58 223 61651 38 349 96 572 32 29 58 25^3 61687 38 313 96 567 31 30 58 284 61722 38 278 96 562 30 31 58 314 61758 38 242 96 556 29 32 58 345 61794 38 206 96 551 28 33 58 375 61830 38170 96 546 27 34 58 406 61865 38135 96 541 26 35 58 436 61901 38 099 96 535 25 36 58 467 61936 38 064 96 530 24 37 58 497 61972 38 028 96 525 23 38 58 527 62 008 37 992 96 520 22 39 58 557 62 043 37 957 96 514 21 40 58 588 62 079 37 921 96 509 20 41 58 618 62 114 37 886 96 504 19 42 58 648 62150 37 850 96 498 18 43 58 678 62 185 37 815 96 493 17 44 58 709 62 221 37 779 96 488 16 45 58 739 62 256 37 744 96 483 15 46 58 769 62 292 37 708 96 477 14 47 58 799 62 327 37 673 96 472 13 48 58 829 62 362 37 638 96 467 12 49 58 859 62 398 37 602 96 461 11 50 58 889 62 433 37 567 96 456 IO 51 58 919 62 468 37 532 96 451 9 52 58 949 62 504 37 496 96 445 8 53 58 979 62 539 37 461 96 440 7 54 59 009 62 574 37 426 96 435 6 55 59 039 62 609 37 391 96 429 5 56 59 069 62 645 37 355 96 424 4 57 59 098 62 680 37 320 96 419 3 58 59128 62 715 37 285 96 413 2 59 59158 62 750 37 250 96 408 1 60 5918S 62 785 37 215 96 403 9 9 IO 9 r log cos log cot log tan log sin t 68' 67 c 23 ( t log sin log tan log cot log cos r 9 9 10 9 o 5918S 62 785 37 215 96 403 60 1 59 218 62 820 37 180 96 397 59 2 59 247 62 855 37 145 96 392 58 3 59 277 62 890 37110 96 387 57 4 59 307 62 926 37 074 96 381 56 5 59 336 62 961 37 039 96 376 55 6 59 366 62 996 37 004 96 370 54 7 59 396 63 031 36 969 96 365 53 8 '59 425 63 066 36 934 96 360 52 9 59 455 63 101 36 899 96 354 51 10 59 484 63 135 36 865 96 349 50 11 59 514 63 170 36 830 96 343 49 12 59 543 63 205 36 795 96 338 48 13 59 573 63 240 36 760 96 333 47 14 59 602 63 275 36 725 96 327 46 15 59 632 63 310 36 690 96 322 45 16 59 661 63 345 36 655 96 316 44 17 59 690 63 379 36 621 96 311 43 18 59 720 63 414 36 586 96 305 42 19 59 749 _ 63 449 36 551 96 300 41 20 59 778 63 484 36 516 96 294 40 21 59 808 63 519 36 481 96 289 39 22 59 837 63 553 36 447 96 284 38 23 59 866 63 58S 36 412 96 278 37 24 59 895 63 623 36 377 96 273 36 25 59 924 63 657 36 343 96 267 35 26 59 954 63 692 36 308 96 262 34 27 59 983 63 726 36 274 96 256 33 28 60 012 63 761 36 239 96 251 32 29 60 041 63 796 36 204 96 245 31 30 60 070 63 830 36 170 96 240 30 31 60 099 63 865 36 135 96 234 29 32 60128 63 899 36101 96 229 2S 33 60157 63 934 36 066 96 223 27 34 60186 63 968 36 032 96 218 26 35 60 215 64 003 35 997 96 212 25 36 60 244 64 037 35 963 96 207 24 37 60 273 64 072 35 928 96 201 23 38 60 302 64106 35 894 96196 22 39 60 331 64140 35 860 96190 21 40 60 359 64175 35 825 96 185 20 41 60 388 64 209 35 791 96179 19 42 60 417 64 243 35 757 96174 18 43 60 446 64 278 35 722 96168 17 44 60 474 64 312 35 688 96162 16 45 60 503 64 346 35 654 96157 15 46 60 532 64 381 35 619 96151 14 47 60 561 64 415 35 585 96146 13 48 60 589 64 449 35 551 96140 12 49 60 618 64 483 35 517 96135 11 50 •60 646 64 517 35 483 96129 io 51 60 675 64 552 35 448 96123 9 52 60 704 64 586 35 414 96118 8 53 60 732 64 620 35 380 96112 7 54 60 761 64 654 35 346 96107 6 55 60 789 64 688 35 312 96101 5 56 60 818 64 722 35 278 96 095 4 57 60 846 64 756 35 244 96 090 3 58 60 875 64 790 35 210 96 084 2 59 60 903 64 824 35 176 96 079 1 60 60 931 64 858 35 142 96 073 O 9 9 log cos log cot 10 log tan 9 log sin t t 24° 39 t log sin log tan log cot log cos t 60 931 9 64 858 IO 35 142 9 96 073 60 1 60 960 64 892 35 108 96 067 59 2 60 988 64 926 35 074 96 062 58 3 61016 64 960 35 040 96 056 57 4 61045 64 994 35 006 96 050 56 5 61073 65 028 34 972 96 045 55 6 61 101 65 062 34 938 96 039 54 7 61129 65 096 34 904 96 034 53 8 61158 65 130 34 870 96 028 52 9 61186 65 164 34 836 96 022 51 10 61214 65 197 34 803 96 017 50 11 61242 65 231 34 769 96 011 49 12 61270 65 265 34 735 96 005 48 13 61298 65 299 34 701 96 000 47 14 61326 65 333 34 667 95 994 46 15 61354 65 366 34 634 95 988 45 16 61382 65 400 34 600 95 982 44 17 61411 65 434 34 566 95 977 43 18 61438 65 467 34 533 95 971 42 19 61466 65 501 34 499 95 965 41 20 61494 65 535 34 465 95 960 40 21 61522 65 568 34 432 95 954 39 22 61550 65 602 34 398 95 948 38 23 61578 65 636 34 364 95 942 37 24 61606 65 669 34 331 95 937 36 25 61634 65 703 34 297 95 931 35 26 61662 65 736 34 264 95 925 34 27 61689 65 770 34 230 95 920 33 28 61717 65 803 34197 95 914 32 29 61745 65 837 34163 95 908 31 30 61773 65 870 34130 95 902 30 31 61800 65 904 34 096 95 897 29 32 61828 65 937 34 063 95 891 28 33 61856 65 971 34 029 95 885 27 34 61883 66 004 33 996 95 879 26 35 61911 66 038 33 962 95 873 25 36 61939 66 071 33 929 95 868 24 37 61966 66104 33 896 95 862 23 38 61994 66138 33 862 95 856 22 39 62 021 66171 33 829 95 850 21 40 62 049 66 204 33 796 95 844 20 41 62 076 66 238 33 762 95 839 19 42 62 104 66 271 33 729 95 833 18 43 62 131 66 304 33 696 95 827 17 44 62 159 66 337 33 663 95 821 16 45 62 186 66 371 33 629 95 815 15 46 62 214 66 404 33 596 95 810 14 47 62 241 66 437 33 563 95 804 13 48 62 268 66 470 33 530 95 798 12 49 62 296 66 503 33 497 95 792 11 50 62 323 66 537 33 463 95 786 10 51 62 350 66 570 33 430 95 780 9 52 62 377 66 603 33 397 95 775 8 53 62 405 66 636 33 364 95 769 7 54 62 432 66 669 33 331 95 763 6 55 62 459 66 702 33 298 95 757 5 56 62 486 66 735 33 265 95 751 4 57 62 513 66 768 33 232 95 745 3 58 62 541 66 801 33 199 95 739 2 59 62 56S 66 834 33 166 95 733 1 60 62 595 66 867 33 133 95 728 9 log cos 9 log cot 10 log tan 9 log sin r t 66 c 65 ( 40 25° t log sin log tan log cot log cos t 9 9 io 9 62 595 66 867 33 133 95 728 60 1 62 622 66 900 33 100 95 722 59 2 62 649 66 933 33 067 95 716 58 3 62 676 66 966 33 034 95 710 57 4 62 703 66 999 33 001 95 704 56 5 62 730 67 032 32 968 95 698 55 6 62 757 67 065 32 935 95 692 54 7 62 784 67 098 32902 95 686 53 8 62 811 67 131 32 869 95 680 52 9 62 838 67163 32 837 95 674 51 10 62 865 67196 32 804 95 668 50 11 62 892 67 229 32 771 95 663 49 12 62 918 67 262 32 738 95 657 48 13 62 945 67 295 32 705 95 651 47 14 62 972 67 327 32 673 95 645 46 15 62 999 67 360 32 640 95 639 45 16 63 026 67 393 32 607 95 633 44 17 63 052 67 426 32 574 95 627 43 18 63 079 67 458 32 542 95 621 42 19 63 106 67 491 32 509 95 615 41 20 63133 67 524 32 476 95 609 40 21 63 159 67 556 32 444 95 603 39 22 63 186 67 589 32 411 95 597 38 23 63 213 67 622 32 378 95 591 37 24 63 239 67 654 32 346 95 585 36 25 63 266 67 687 32 313 95 579 35 26 63 292 67 719 32 281 95 573 34 27 63 319 67 752 32 248 95 567 33 28 63 345 67 785 32 215 95 561 32 29 63 372 67 817 32 183 95 555 31 30 63 398 67 850 32150 95 549 30 31 63 425 67 882 32 118 95 543 29 32 63 451 67 915 32 085 95 537 28 33 63 478 67 947 32 053 95 531 27 34 63 504 67 980 32 020 95 525 26 35 63 531 68 012 319S8 95 519 25 36 63 557 68 044 31956 95 513 24 37 63 583 6S077 31923 95 507 23 38 63 610 68109 31891 95 500 22 39 63 636 68] 42 31858 95 494 21 40 63 662 68174 31826 95 488 20 41 63 689 68 206 31794 95 482 19 42 63 715 68 239 31761 95 476 18 43 63 741 68 271 31729 95 470 17 44 63 767 68 303 31697 95 464 16 45 63 794 68 336 31664 95 458 15 46 63 820 68 36S 31632 95 452 14 47 63 846 68 400 31600 95 446 13 48 63 872 68 432 31 568 95 440 12 49 63 898 68 465 31535 95 434 11 50 63 924 68 497 31503 95 427 10 51 63 950 68 529 31471 95 421 9 52 63 976 68 561 31439 95 415 8 53 64 002 68 593 31407 95 409 - 7 54 64 028 68 626 31374 95 403 6 55 64 054 68 658 31342 95 397 5 56 64 080 68 690 31310 95 391 4 57 64 106 68 722 31278 95 384 3 5S 64132 68 754 31246 95 378 2 59 64 158 68 786 31214 95 372 1 60 64184 68 818 31182 95 366 9 9 IO 9 t log cos log cot log tan log sin " t 26 c t log sin log tan log cot log cos f 9 9 10 9 o 64184 68 818 31182 95 366 60 1 64 210 68 850 31150 95 360 59 2 64 236 68 882 31118 95 354 58 3 64 262 68 914 31086 95 348 57 4 64 288 68 946 31054 95 341 56 5 64 313 68 978 31022 95 335 55 6 64 339 69 010 30 990 95 329 54 7 64 365 69 042 30 958 95 323 53 8 64 391 69 074 30 926 95 317 52 9 64 417 69106 30 894 95 310 51 IO 64 442 69138 30 862 95 304 50 11 64 46S 69170 30 830 95 298 49 12 64 494 69 202 30 798 95 292 48 13 64 519 69 234 30 766 95 286 47 14 64 545 69 266 30 734 95 279 46 15 64 571. 69 298 30 702 95 273 45 16 64 596 69 329 30 671 95 267 44 17 64 622 69 361 30 639 95 261 43 18 64 647 69 393 30 607 95 254 42 19 64 673 69 425 30 575 95 248 41 20 64 698 69 457 30 543 95 242 40 21 64 724 69 488 30 512 95 236 39 22 64 749 69 520 30 480 95 229 38 23 64 775 69 552 30 448 95 223 37 24 64 800 69 584 30 416 95 217 36 25 64 826 69 615 30 385 95 211 35 26 64 851 69 647 30 353 95 204 34 27 64 877 69 679 30 321 95 198 33 28 64902 69 710 30 290 95 192 32 29 .64 927 69 742 30 258 95 185 31 30 64 953 69 774 30 226 95 179 30 31 64 978 69 805 30195 95 173 29 32 65 003 69 837 30163 95 167 28 33 65 029 69 868 30132 95 160 27 34 65 054 69 900 30100 95 154 26 35 65 079 69 932 30 068 95 148 25 36 65 104 69 963 30 037 95 141 24 37 65 130 69 995 30 005 95 135 23 38 65 155 70 026 29 974 95 129 22 39 65 180 70 058 29 942 95 122 21 40 65 205 70 089 29 911 95 116 20 41 65 230 70 121 29 879 95 110 19 42 65 255 70152 29 848 95 103 18 43 65 281 70184 29 816 95 097 17 44 65 306 70 215 29 785 95 090 16 45 65 331 70 247 29 753 95 084 15 46 65 356 70 278 29 722 95 078 14 47 65 381 70 309 29 691 95 071 13 48 65 406 70 341 29 659 95 065 12 49 65 431 70 372 29 628 95 059 11 50 65 456 70 404 29 596 95 052 10 51 65 481 70 435 29 565 95 046 9 52 65 506 70 466 29 534 95 039 8 53 65 531 70 498 29 502 95 033 7 54 65 556 70 529 29 471 95 027 6 55 65 580 70 560 29 440 95 020 5 56 65 605 70 592 29 408 95 014 4 57 65 630 70 623 29 377 95 007 3 58 65 655 70 654 29 346 95 001 2 59 65 680 70 6S5 29 315 94 995 1 60 65 705 70 717 29 283 94 988 9 9 10 9 r log cos log cot log tan log sin t 64 c 63 c 27' t log sin log tan log cot log cos t 9 65 705 9 70 717 10 29 283 9 94 988 o 60 1 65 729 70 748 29 252 94 982 59 2 65 754 70 779 29 221 94 975 58 3 65 779 70 810 29190 94 969 57 4 65 804 70 841 29159 94 962 56 5 65 828 70 873 29127 94 956 55 6 65 853 70 904 29 096 94 949 54 7 65 878 70 935 29 065 94 943 53 S 65 902 70 966 29 034 94 936 52 9 65 927 70 997 29 003 94 930 51 10 65 952 71028 28 972 94 923 50 11 65 976 71059 28 941 94 917 49 12 66 001 71090 28 910 94 911 48 13 66 025 71121 28 879 94 904 47 14 66 050 71153 28 847 94 898 46 15 66 075 71184 28 816 94 891 45 16 66 099 71215 28 785 94 885 44 17 66124 71246 28 754 94 878 43 18 66148 71277 28 723 94 871 42 19 66173 71308 28 692 94 865 41 20 66197 71339 28 661 94S58 40 21 66 221 71370 28 630 94 852 39 22 66 246 71401 28 599 94 845 38 23 66 270 71431 2S569 94 839 37 24 66 295 71462 28 538 94 832 36 25 66 319 71493 28 507 94 826 35 26 66 343 71524 28 476 94 819 34 27 66 368 71555 28 445 94S13 33 28 66 392 71586 28 414 94 806 32 29 66 416 71617 28 383 94 799 31 30 66 441 71648 28 352 94 793 30 31 66465 71679 28 321 94 786 29 32 66 489 71709 28 291 94 780 28 33 66 513 71740 28 260 94 773 27 34 66 537 71771 28 229 94 767 26 35 66 562 71802 28 19S 94 760 25 36 66586 71833 28 167 94 753 24 37 66 610 71863 28137 94 747 23 38 66 634 71894 28106 94 740 22 39 66 658 71925 28 075 94 734 21 40 66 6S2 71955 28 045 94 727 20 41 66 706 71986 28 014 94 720 19 42 66 731 72 017 27 983 94 714 18 43 66 755 72 048 27 952 94 707 17 44 66 779 72 078 27 922 94 700 16 45 66 803 72 109 27 891 94 694 15 46 66 827 72 140 27 860 94 6S7 14 47 66 851 72 170 27 830 94 680 13 48 66 875 72 201 27 799 94 674 12 49 66 899 72 231 27 769 94 667 11 50 66 922 72 262 27 73S 94 660 10 51 66 946 72 293 27 707 94 654 9 52 66 970 72 323 27 677 94 647 8 53 66 994 72 354 27 646 94 640 7 54 67 018 72 384 27 616 94 634 6 55 67 042 72 415 27 585 94 627 5 56 67 066 72 445 27 555 94 620 4 57 67 090 72 476 27 524 94 614 3 58 67 113 72 506 27 494 94 607 2 59 67137 72 537 27 463 94 600 1 60 67161 72 567 27 433 94 593 O 9 9 10 9 t log cos log cot log tan log sin r 28° 41 r log sin log tan log cot log cos r 9 67 161 9 72 567 10 27 433 9 94 593 60 1 67185 72 598 27 402 94 587 59 2 67 208 72 628 27 372 94 580 58 3 67 232 72 659 27 341 94 573 57 4 67 256 72 689 27 311 94 567 56 5 67 280 72 720 27 280 94 560 55 6 67 303 72 750 27 250 94 553 54 7 67 327 72 780 27 220 94 546 53 8 67 350 72 811 27 189 94 540 52 9 67 374 72 841 27159 94 533 51 io 67 398 72 872 27128 94 526 50 11 67 421 72 902 27 098 94 519 49 12 67 445 72 932 27 068 94 513 48 13 67 468 72 963 27 037 94 506 47 14 67 492 72 993 27 007 94 499 46 15 67 515 73 023 26 977 94 492 45 16 67 539 73 054 26 946 94 485 44 17 67 562 73 084 26 916 94 479 43 18 67 586 73 114 26 886 94 472 42 19 67 609 73 144 26 856 94 465 41 20 67 633 73 175 26 825 94 458 40 21 67 656 73 205 26 795 94 451 39 22 67 680 73 235 26 765 94 445 3S 23 67 703 73 265 26 735 94 438 37 24 67 726 73 295 26 705 94 431 36 25 67 750 73 326 26 674 94 424 35 26 67 773 73 356 26 644 94 417 34 27 67 796 73 386 26 614 94 410 33 28 67 820 73 416 26 584 94 404 32 29 67 843 73 446 26 554 94 397 31 30 67 866 73 476 26 524 94 390 30 31 67 890 73 507 26 493 94 383 29 32 67 913 73 537 26 463 94 376 28 33 67 936 73 567 26 433 94 369 27 34 67 959 73 597 26 403 94 362 26 35 67 982 73 627 26 373 94 355 25 36 68 006 73 657 26 343 94 349 24 37 68 029 73 687 26 313 94 342 23 38 68 052 73 717 26 283 94 335 22 39 68 075 73 747 26 253 94 328 21 40 68 098 73 777 26 223 94 321 20 41 68 121 73 807 26193 94 314 19 42 68 144 73 837 26163 94 307 18 43 68167 73 867 26133 94 300 17 44 68190 73 897 26103 94 293 16 45 68 213 73 927 26 073 94 286 15 46 68 237 73 957 26 043 94 279 14 47 68 260 73 987 26 013 94 273 13 48 68 2S3 74 017 25 983 94 266 12 49 68 305 74 047 25 953 94 259 11 50 68 328 74 077 25 923 94 252 10 51 68 351 74 107 25 893 94 245 9 52 68 374 74137 25 863 94 238 8 53 68 397 74 166 25 834 94 231 7 54 68 420 74196 25 804 94 224 6 55 68 443 74 226 25 774 94 217 5 56 68 466 74 256 25 744 94 210 4 57 68 489 74 286 25 714 94 203 3 58 68 512 74 316 25 684 94196 2 59 68 534 74 345 25 655 94 189 1 60 68 557 74 375 25 625 94 182 9 9 10 9 t log cos log cot log tan log sin t 62° 6r 42 29° t log sin log tan log cot log cos f 9 68 557 9 74 375 io 25 625 9 94 182 o 60 1 68 580 74 405 25 595 94 175 59 2 68 603 74 435 25 565 94168 5S 3 68 625 74 465 25 535 94 161 57 4 68 648 74 494 25 506 94154 56 5 68 671 74 524 25 476 94147 55 6 68 694 74 554 25 446 94 140 54 7 68 716 74 583 25 417 94 133 53 8 68 739 74 613 25 387 94 126 52 9 68 762 74 643 25 357 94 119 51 10 68 784 74 673 25 327 94112 50 11 6SS07 74 702 25 298 94 105 49 12 68 829 74 732 25 268 94 098 48 13 68 852 74 762 25 238 94 090 47 14 68 875 74 791 25 209 94 083 46 15 68 897 74 821 25 179 94 076 45 16 68 920 74 851 25 149 94 069 44 17 68 942 74 880 25 120 94 062 43 18 68 965 74 910 25 090 94 055 42 19 6S9S7 74 939 25 061 94 048 41 20 69 010 74 969 25 031 94 041 40 21 69 032 74 99S 25 002 94 034 39 22 69 055 75 028 24 972 94 027 38 23 69 077 75 05S 24 942 94 020 37 24 69 100 75 087 24 913 94 012 36 25 69 122 75 117 24 883 94 005 35 26 69 144 75 146 24 854 93 998 34 27 69 167 75 176 24 824 93 991 33 28 69 1S9 75 205 24 795 93 984 32 29 69 212 75 235 24765 93 977 31 30 69 234 75 264 24 736 93 970 30 31 69 256 75 294 24 706 93 963 29 32 69 279 75 323 24 677 93 955 28 33 69 301 75 353 24 647 93 948 27 34 69 323 75 3S2 24 618 93 941 26 35 69 345 75 411 24 589 93 934 25 36 69 368 75 441 24 559 93 927 24 37 69 390 75 470 24 530 93 920 23 38 69 412 75 500 24 500 93 912 22 39 69 434 75 529 24 471 93 905 21 40 69 456 75 558 24 442 93S9S 20 41 69 479 75 588 24 412 93 891 19 42 69 501 75 617 24 383 93 884 18 43 69 523 75 647 24 353 93 S76 17 44 69 545 75 676 24 324 93 869 16 45 69 567 75 705 24 295 93 862 15 46 69 5S9 75 735 24 265 93 855 14 47 69 611 75 764 24 236 93 847 13 ' 4S 69 633 75 793 24 207 93 840 12 49 69 655 75S22 24 178 93 833 11 50 69 677 75 852 24 148 93 826 10 51 69 699 75S81 24 119 93 819 9 52 69 721 75 910 24 090 93 811 8 53 69 743 75 939 24 061 93 804 • 7 54 69 765 75 969 24 031 93 797 6 55 69 7S7 75 998 24 002 93 7S9 5 56 69 809 76 027 23 973 93 782 4 57 69 831 76 056 23 944 93 775 3 58 69S53 76 086 23 914 93 768 2 59 69S75 76115 23SS5 93 760 1 60 69 897 76144 23 856 93 753 9 9 IO 9 t log cos log cot log tan log sin- t 30° t log sin log tan log cot log cos / 9 9 IO 9 o 69 897 76 144 23 856 93 753 60 1 69 919 76173 23 827 93 746 59 2 69 941 76 202 23 798 93 738 58 3 69 963 76 231 23 769 93 731 57 4 69 984 76 261 23 739 93 724 56 5 70 006 76 290 23 710 93 717 55 6 70 02S 76 319 23 681 93 709 54 7 70 050 76 348 23 652 93 702 53 8 70 072 76 377 23 623 93 695 52 9 70 093 76 406 23 594 93 687 51 10 70115 76 435 23 565 93 680 50 11 70137 76 464 23 536 93 673 49 12 70159 76 493 23 507 93 665 48 13 70180 76 522 23 478 93 658 47 14 70 202 76 551 23 449 93 650 46 15 70 224 76 580 23 420 93 643 45 16 70 245 76 609 23 391 93 636 44 17 70 267 76 639 23 361 93 628 43 18 70 288 76 668 23 332 93 621 42 19 70 310 76 697 23 303 93 614 41 20 70 332 76 725 23 275 93 606 40 21 70 353 76 754 23 246 93 599 39 22 70 375 76 783 23 217 93 591 38 23 70 396 76 812 23 188 93 584 37 24 70 418 76 841 23 159 93 577 36 25 70 439 76 870 23 130 93 569 35 26 70 461 76 899 23 101 93 562 34 27 70 482 76 928 23 072 93 554 33 28 70 504 76 957 23 043 93 547 32 29 . W 525 76 986 23 014 93 539 31 30 70 547 77 015 22 985 93 532 30 31 70 568 77 044 22 956 93 525 29 32 70 590 77 073 22 927 93 517 28 33 70 611 77101 22 899 93 510 27 34 70 633 77130 22 870 93 502 26 35 70 654 77159 22 841 93 495 25 36 70 675 771S8 22 812 93 487 24 37 70 697 77 217 22 783 93 480 23 38 70 718 77 246 22 754 93 472 22 39 70 739 77 274 22 726 93 465 21 40 70 761 77 303 22 697 93 457 20 41 70 7S2 77 332 22 668 93 450 19 42 70 803 77 361 2 1 639 93 442 IS 43 70 824 77 390 22 610 93 435 17 44 70 846 77 418 22 582 93 427 16 45 70 867 77 447 22 553 93 420 15 46 70G88 77 476 22 524 93 412 14 47 70 909 77 505 22 495 93 405 13 4S 70 931 77 533 22 467 93 397 12 49 70 952 77 562 22 438 93 390 11 50 70 973 77 591 22 409 93 382 10 51 70 994 77 619 22 381 93 375 9 52 71 015 77 648 22 352 93 367 8 53 71 036 77 677 22 323 93 360 7 54 71 058 77 706 22 294 93 352 6 55 71079 77 734 22 266 93 344 5 56 71100 77 763 22 237 93 337 4 57 71121 77 791 22 209 93 329 3 58 71142 77 820 22 180 93 322 2 59 71163 77S49 22 151 93 314 1 60 71184 77 877 22 123 93 307 9 log cos 9 log cot IO log tan 9 log sin t r 60 c 59 c 3r f log sin log tan log cot log cos t 9 71184 9 77 877 10 22123 9 93 307 60 1 71205 77 906 22 094 93 299 59 2 71226 77 935 22 065 93 291 58 3 71247 77 963 22 037 93 284 57 4 71268 77 992 22 008 93 276 56 5 71289 78 020 219S0 93 269 55 6 71310 78 049 21951 93 261 54 7 71331 78 077 21923 93 253 53 S 71352 78 106 21894 93 246 52 9 7"1 373 78135 21865 93 238 51 10 71393 78163 21837 93 230 50 11 71414 78192 21808 93 223 49 12 71435 78 220 21780 93 215 48 13 71456 78 249 21751 93 207 47 14 71477 78 277 21723 93 200 46 15 71498 78 306 21694 93 192 45 16 71519 78 334 21666 93 184 44 17 71539 78 363 21637 93 177 43 18 71560 78 391 21609 93 169 42 19 71581 78 419 21581 93 161 41 20 71602 78 448 21552 93 154 40 21 71622 78 476 21524 93 146 39 22 71643 78 505 21495 93 138 38 23 71664 78 533 21467 93 131 37 24 71685 78 562 21438 93 123 36 25 71705 78 590 21410 93 115 35 26 71726 78 618 21382 93 108 34 27 71747 78 647 21353 93 100 33 28 71767 78 675 21325 93 092 32 29 71788 78 704 21296 93 084 31 30 71809 78 732 21268 93 077 30 31 71829 78 760 21240 93 069 29 32 71S50 78 789 21211 93 061 28 33 71870 78 817 21183 93 053 27 34 71891 78 845 21155 93 046 26 35 71911 78 874 21126 93 038 25 36 71932 78 902 21098 93 030 24 37 71952 78 930 21070 93 022 23 38 71973 78 959 21041 93 014 22 39 71994 78 9S7 21013 93 007 21 40 72 014 79 015 20 985 92 999 20 41 72 034 79 043 20 957 92 991 19 42 72 055 79 072 20 928 92 983 18 43 72 075 79100 20 900 92 976 17 44 72 096 7912S 20 872 92 968 16 45 72 116 79156 20 844 92 960 15 46 72137 79185 20 815 92 952 14 47 72157 79 213 20 787 92 944 13 48 72177 79 241 20 759 92 936 12 49 72198 79 269 20 731 92 929 11 50 72 218 79 297 20 703 92 921 IO 51 72 238 79 326 20 674 92 913 9 52 72 259 79 354 20 646 92 905 8 53 72 279 79 382 20 618 92 897 7 54 72 299 79 410 20 590 92 889 6 55 72 320 79 43S 20 562 92 881 5 56 72 340 79 466 20 534 92 874 4 57 72 360 79 495 20 505 92 866 3 58 72 381 79 523 20 477 92 858 2 59 72 401 79 551 20 449 92 850 1 60 72 421 79 579 20 421 92 842 9 log cos 9 log cot io log tan 9 log sin f t 32° 43 f log sin log tan log cot log cos r 9 72 421 9 79 579 10 20 421 9 92 842 60 1 72 441 79 607 20 393 92 834 59 2 72 461 79 635 20 365 92 826 58 3 72 482 79 663 20 337 92 818 57 4 72 502 79 691 20 309 92 810 56 5 72 522 79 719 20 281 92S03 55 6 72 542 79 747 20 253 92 795 54 7 72 562 79 776 20 224 92 787 53 S 72 582 79 804 20196 92 779 52 9 72 602 79 832 20168 92 771 51 IO 72 622 79 860 20140 92 763 50 11 72 643 79 888 20112 92 755 49 12 72 663 79 916 20 084 92 747 48 13 72 683 79 944 20 056 92 739 47 14 72 703 79 972 20 028 92 731 46 15 72 723 80 000 20 000 92 723 45 16 72 743 80 028 19 972 92 715 44 17 72 763 80 056 19 944 92 707 43 18 72 783 80 084 19 916 92 699 42 19 72 803 80112 19 888 92 691 41 20 72 823 80140 19 860 92 683 40 21 72 843 80168 19 832 92 675 39 22 72 863 80195 19 805 92 667 38 23 72 883 80 223 19 777 92 659 37 24 72 902 80 251 19 749 92 651 36 25 72 922 80 279 19 721 92 643 35 26 72 942 80 307 19 693 92 635 34 27 72 962 80 335 19 665 92 627 33 28 72 982 80 363 19 637 92 619 31 29 73 002 80 391 19 609 92 611 31 30 73 022 80 419 19 581 92 603 30 31 73 041 80 447 19 553 92 595 29 32 73 061 80 474 19 526 92 587 28 33 73 081 80 502 19 498 92 579 27 34 73101 80 530 19 470 92 571 26 35 73 121 80 558 19 442 92 563 25 36 73 140 80 586 19 414 92 555 24 37 73 160 80 614 19 386 92 546 23 38 73180 80 642 19 358 92 538 22 39 73 200 80 669 19 331 92 530 21 40 73 219 80 697 19 303 92 522 20 41 73 239 80 725 19 275 92 514 19 42 73 259 80 753 19 247 92 506 18 43 73 278 80 781 19 219 92 498 17 44 73 29S 80 808 19192 92 490 16 45 73 318 80 836 19164 92 482 15 46 73 337 80 864 19136 92 473 14 47 73 357 80 892 19108 92 465 13 48 73 377 80 919 19 081 92 457 12 49 73 396 80 947 19 053 92 449 11 50 73 416 8Q975 19 025 92 441 10 51 73 435 81003 18 997 92 433 9 52 73 455 81030 18 970 92 425 8 53 73 474 8105S 18 942 92 416 7 54 73 494 81086 18 914 92 408 6 55 73 513 81113 18 887 92 400 5 56 73 533 81141 18 859 92 392 4 57 73 552 81169 18 831 92 384 3 58 73 572 81196 18 804 92 376 2 59 73 591 81224 18 776 92 367 1 60 73 611 81252 18 74S 92 359 O 9 log cos 9 log cot IO log tan 9 log sin t t 58 c 57 c 44 33° t log sin log tan log cot log cos / 9 73 611 9 81252 10 18 748 9 92 359 o 60 1 73 630 81279 18 721 92 351 59 2 73 650 81307 18 693 92 343 58 3 73 669 81335 18 665 92 335 57 4 73 689 81362 18 638 92 326 56 5 73 708 81390 18 610 92 318 55 6 73 727 81418 18 582 92 310 54 7 73 747 81445 18 555 92 302 53 8 73 766 81473 18 527 92 293 52 9 73 785 81500 18 500 92 285 51 10 73 805 81528 18 472 92 277 50 11 73 824 81556 18 444 92 269 49 12 73 843 81583 18 417 92 260 48 13 73 863 81611 18 389 92 252 47 14 73 882 81638 18 362 92 244 46 15 73 901 81666 18 334 92 235 45 16 73 921 81693 18 307 92 227 44 17 73 940 81721 18 279 92 219 43 18 73 959 81748 18 252 92 211 42 19 73 978 81776 18 224 92 202 41 20 73 997 81803 18 197 92 194 40 21 74 017 81831 18169 92186 39 22 74 036 81858 18142 92 177 38 23 74 055 81886 18 114 92 169 37 24 74 074 81913 18 087 92 161 36 25 74 093 81941 18 059 92 152 35 26 74113 81968 18 032 92144 34 27 74132 81996 18 004 92 136 33 28 74151 82 023 17 977 92 127 32 29 74170 82 051 17 949 92119 31 30 74189 82 078 17 922 92111 30 31 74 208 82106 17 894 92 102 29 32 74 227 82 133 17 867 92 094 28 33 74 246 82 161 17 839 92 086 27 34 74 265 82 188 17 812 92 077 26 35 74 284 82 215 17 785 92 069 25 36 74 303 82 243 17 757 92 060 24 37 74 322 82 270 17 730 92 052 23 38 74 341 82 298 17 702 92 044 22 39 74 360 82 325 17 675 92 035 21 40 74 379 82 352 17 648 92 027 20 41 74 398 82 380 17 620 92 018 19 42 74 417 82 407 17 593 92 010 18 43 74 436 82 435 17 565 92 002 17 44 74 455 82 462 17 538 91993 16 45 74 474 82 489 17 511 91985 15 46 74 493 82 517 17 483 91976 14 47 74 512 82 544 17 456 91968 13 48 74 531 82 571 17 429 91959 12 49 74 549 82 599 17 401 91951 11 50 74 568 82 626 • 17 374 91942 10 51 74 587 82 653 17 347 91934 9 52 74 606 82 681 17 319 91925 8 53 74 625 82 708 17 292 91917 7. 54 74 644 82 735 17 265 91908 6 55 74 662 82 762 17 238 91900 5 56 74 681 82 790 17 210 91891 4 57 74 700 82 817 17183 91883 3 58 74 719 82 844 17156 91874 2 59 74 737 82 871 17129 91866 1 60 74 756 82 899 17101 91857 9 9 10 9 t log cos log cot log tan log sin j 34 c r log sin log tan log cot log cos / 9 74 756 9 10 82 899 17101 9 91857 60 1 74 775 82 926 17 074 91849 59 2 74 794 82 953 17 047 91840 58 3 74 812 82 980 17 020 91832 57 4 74 831 83 008 16 992 91823 56 5 74 850 83 035 16 965 91815 55 6 74 868 83 062 16 938 91806 54 7 74 887 83 089 16 911 91798 53 8 74 906 83 117 16 883 91789 52 9 74 924 83 144 16 856 91781 51 10 74 943 83 171 16 829 91772 50 11 74 961 83 198 16 802 91763 49 12 74 980 83 225 16 775 91755 48 13 74 999 83 252 16 748 91746 47 14 75 017 83 280 16 720 91738 46 15 75 036 83 307 16 693 91729 45 16 75 054 83 334 16 666 91720 44 17 75 073 83 361 16 639 91712 43 18 75 091 83 388 16 612 91703 42 19 75 110 83 415 16 585 91695 41 20 75 128 83 442 16 558 91686 40 21 75 147 83 470 16 530 91677 39 22 75 165 83 497 16 503 91669 38 23 75 184 83 524 16 476 91660 37 24 75 202 83 551 16 449 91651 36 25 75 221 83 578 16 422 91643 35 26 75 239 83 605 16 395 91634 34 27 75 258 83 632 16 368 91625 33 28 75 276 83 659 16 341 91617 32 29 75 294 83 686 16 314 91608 31 30 31 75 313 83 713 16 287 91599 30 75 331 83 740 16 260 91 591 29 32 75 350 83 768 16 232 91582 28 33 75 368 83 795 16 205 91 573 27 34 75 386 83 822 16178 91565 26 35 75 405 83 849 16 151 91556 25 36 75 423 83 876 16124 91547 24 37 75 441 83 903 16 097 91538 23 38 75 459 83 930 16 070 91530 22 39 75 478 83 957 16 043 91521 21 40 75 496 83 984 16 016 91512 20 41 75 514 84 011 15 989 91504 19 42 75 533 84 038 15 962 91495 18 43 75 551 84 065 15 935 91486 17 44 75 569 84 092 15 908 91477 16 45 75 587 84119 15 881 91469 15 46 75 605 84146 15 854 91460 14 47 75 624 84173 15 827 91451 13 48 75 642 84 200 15 800 91442 12 49 75 660 84 227 15 773 91433 11 50 75 678 84 254 15 746 91425 10 51 75 696 84 280 15 720 91416 9 52 75 714 84 307 15 693 91407 8 53 75 733 84 334 15 666 91398 7 54 75 751 84 361 15 639 91389 6 55 75 769 84 388 15 612 91 381 5 56 75 787 84 415 15 585 91372 4 57 75 805 84 442 15 558 91363 3 58 75 823 84 469 15 531 91354 2 59 75 841 84 496 15 504 91345 1 60 75 859 84 523 15 477 91336 9 log oos 9 10 log cot log tan 9 log sin t r I 56 c 55 c 35 c f log sin log tan log cot log cos t 9 75 859 9 84 523 10 15 477 9 91336 60 1 75 877 84 550 15 450 91328 59 2 75 895 84 576 15 424 91319 58 3 75 913 84 603 15 397 91310 57 4 75 931 84 630 15 370 91301 56 5 75 949 84 657 15 343 91292 55 6 75 967 84 684 15 316 91283 54 7 75 985 84 711 15 289 91274 53 8 76 003 84 738 15 262 91 266 52 9 76 021 84 764 15 236 91257 51 10 76 039 84 791 15 209 91248 50 11 76 057 84 818 15 182 91239 49 12 76 075 84 845 15 155 91230 48 13 76 093 84 872 15 128 91 221 47 14 76111 84 899 15 101 91212 46 15 76129 84 925 15 075 91203 45 16 76146 84 952 15 048 91194 44 17 76164 84 979 15 021 91 185 43 18 76 182 85 006 14 994 91176 42 19 76 200 85 033 14 967 91167 41 20 76 218 85 059 14 941 91158 40 21 76 236 85 086 14 914 91149 39 22 76 253 85 113 14 887 91141 38 23 76 271 85 140 14 860 91132 37 24 76 289 85 166 14 834 91123 36 25 76 307 85 193 14 807 91114 35 26 76 324 85 220 14 780 91105 34 27 76 342 85 247 14 753 91096 33 28 76 360 85 273 14 727 91087 32 29 76 378 85 300 14 700 91078 31 30 76 395 85 327 14 673 91069 30 31 76 413 85 354 14 646 91060 29 32 76 431 85 380 14 620 91051 28 33 76 448 85 407 14 593 91042 27 34 76 466 85 434 14 566 91033 26 35 76484 85 460 14 540 91023 25 36 76 501 85 487 14 513 91014 24 37 76 519 85 514 14 486 91005 23 38 76 537 85 540 14 460 90 996 22 39 76 554 85 567 14 433 90 987 21 40 76 572 85 594 14 406 90 978 20 41 76 590 85 620 14 380 90 969 19 42 76 607 85 647 14 353 90 960 18 43 76 625 85 674 14 326 90 951 17 44 76 642 S5 700 14 300 90 942 16 45 76 660 85 727 14 273 90 933 15 46 76 677 85 754 14 246 90 924 14 47 76 695 85 780 14 220 90 915 13 48 76 712 85 807 14193 90 906 12 49 76 730 85 834 14 166 90 896 11 50 76 747 85 860 14140 90 887 10 51 76 765 85 887 14 113 90 878 9 52 76 782 85 91'3 14 087 90 869 8 53 76 800 85 940 14 060 90 860 7 54 76 817 85 967 14 033 90 851 6 55 76 835 85 993 14 007 90 842 5 56 76 852 86 020 13 980 90 832 4 57 76 870 86 046 13 954 90 823 3 58 76 887 86 073 13 927 90 814 2 59 76 904 86 100 13 900 90 805 1 60 76 922 86126 13 874 90 796 9 log COS 9 log cot 10 log tan 9 log sin r t 36° 45 r log sin log tan log cot log cos t 9 76 922 9 86126 10 13 874 9 90 796 60 1 76 939 86 153 13 847 90 787 59 2 76 957 86 179 13 821 90 777 58 3 76 974 86 206 13 794 90 768 57 4 76 991 86 232 13 768 90 759 56 5 77 009 86 259 13 741 90 750 55 6 77 026 86 285 13 715 90 741 54 7 77 043 86 312 13 688 90 731 53 8 77 061 86 338 13 662 90 722 52 9 77 078 86 365 13 635 90 713 51 10 77 095 86 392 13 608 90 704 50 11 77 112 86 418 13 582 90 694 49 12 77130 86 445 13 555 90 685 48 13 77147 86 471 13 529 90 676 47 14 77 164 86 498 13 502 90 667 46 15 77181 86 524 13 476 90 657 45 16 77199 86 551 13 449 90 648 44 17 77 216 86 577 13 423 90 639 43 18 77 233 86 603 13 397 90 630 42 19 77 250 86 630 13 370 90 620 41 20 77 268 86 656 13 344 90 611 40 21 77 285 86 683 13 317 90 602 39 22 77 302 86 709 13 291 90 592 38 23 77 319 86 736 13 264 90 583 37 24 77 336 86 762 13 238 90 574 36 25 77 353 86 789 13 211 90 565 35 26 77 370 86 815 13 185 90 555 34 27 77 387 86 842 13 158 90 546 33 28 77 405 86 868 13 132 90 537 32 29 77 422 86 894 13 106 90 527 31 30 77 439 86 921 13 079 90 518 30 31 77 456 86 947 13 053 90 509 29 32 77 473 86 974 13 026 90 499 28 33 77 490 87 000 13 000 90 490 27 34 77 507 87 027 12 973 90 480 26 35 77 524 87 053 12 947 90 471 25 36 77 541 87 079 12 921 90 462 24 37 77 558 87106 12 894 90 452 23 38 77 575 87132 12 868 90 443 22 39 77 592 87158 12 842 90 434 21 40 77 609 87185 12 815 90 424 20 41 77 626 87 211 12 789 90 415 19 42 77 643 87 238 12 762 90 405 18 43 77 660 87 264 12 736 90 396 17 44 77 677 87 290 12 710 90 386 16 45 77 694 87 317 12 683 90 377 15 46 77 711 87 343 12 657 90 368 14 47 77 728 87 369 12 631 90 358 13 48 77 744 87 396 12 604 90 349 12 49 77 761 87 422 12 578 90 339 11 50 77 778 87 448 12 552 90 330 10 51 77 795 87 475 12 525 90 320 9 52 77 812 87 501 12 499 90 311 8 53 77 829 87 527 12 473 90 301 7 54 77 846 87 554 12 446 90 292 6 55 77 862 87 580 12 420 90 282 5 56 77 879 87 606 12 394 90 273 4 57 77 896 87 633 12 367 90 263 3 58 77 913 87 659 12 341 90 254 2 59 77 930 87 685 12 315 90 244 1 60 77 946 87 711 12 289 90 235 9 9 io 9 r log cos log cot log tan log sin t 54 c 53 c 46 37° t log sin log tan log cot log cos t 9 77 946 9 87 711 10 12 289 9 90 235 o 60 1 77 963 87 738 12 262 90 225 59 2 77 980 87 764 12 236 90 216 58 3 77 997 87 790 12 210 90 206 57 '4 78 013 87 817 12183 90197 56 5 78 030 87 843 12157 90187 55 6 78 047 87 869 12 131 90178 54 7 78 063 87 895 12 105 90168 53 8 78 080 87 922 12 078 90 159 52 9 78 097 87 948 12 052 90149 51 10 78113 87 974 12 026 90139 50 11 78130 88 000 12 000 90130 49 12 78 147 88 027 11973 90120 48 13 78 163 88 053 11947 90111 47 14 78 180 88 079 11921 90 101 46 15 78 197 88 105 11895 90 091 45 16 78 213 88 131 11869 90 082 44 17 78 230 88158 11842 90 072 43 18 78 246 88 184 11816 90 063 42 19 78 263 S8 210 11790 90 053 41 20 78 280 88 236 11764 90 043 40 21 78 296 88 262 11738 90 034 39 22 78 313 88 289 11711 90 024 38 23 78 329 88 315 11685 90 014 37 24 7S346 88 341 11659 90 005 36 25 78 362 88 367 11633 89 995 35 26 78 379 88 393 11607 89 985 34 27 78 395 88 420 11580 89 976 33 28 78 412 88 446 11554 89 966 32 29 78 428 88 472 11528 89 956 31 30 78 445 88 498 11502 89 947 30 31 78 461 8S524 11476 89 937 29 32 78 478 88 550 11450 89 927 28 33 78 494 88 577 11423 89 918 27 34 78 510 88 603 11397 89 908 26 35 78 527 88 629 11371 89 898 25 36 78 543 88 655 11345 89 888 24 37 78 560 88 681 11319 89 879 23 38 78 576 88 707 11293 89 869 22 39 78 592 88 733 11267 89 859 21 40 78 609 88 759 11241 89 849 20 41 78 625 88 786 11214 89 840 19 42 78 642 88S12 11188 89 830 18 43 78 658 88 838 11162 89 820 17 44 78 674 88 864 11136 89 810 16 45 78 691 88 890 11110 89 801 15 46 78 707 88 916 11084 89 791 14 47 78 723 88 942 11058 89 781' 13 48 78 739 8S96S 11 032 89 771 12 49 78 756 88 994 11006 89 761 11 50 78 772 89 020 10 980 89 752 10 51 78 788 89 046 10 954 89 742 9 52 78 805 89 073 10 927 89 732 8 53 78 821 89 099 10 901 89 722 -7 54 78 837 89125 10 875 89 712 6 55 78 853 89 151 10 849 89 702 5 56 78 869 89 177 10 823 89 693 4 57 78 886 89 203 10 797 89 683 3 58 78 902 89 229 10 771 89 673 2 59 78 918 89 255 10 745 89 663 1 60 78 934 S9 2S1 10 719 89 653 O 9 log cos 9 log cot io log tan 9 log sin t - t 38 c t log sin log tan log cot log cos / 9 78 934 9 89 281 10 10 719 9 89 653 o 60 1 78 950 89 307 10 693 89 643 59 2 78 967 89 333 10 667 89 633 58 3 78 983 89 359 10 641 89 624 « 57 4 78 999 S9 3S5 10 615 89 614 56 5 79 015 89 411 10 5S9 89 604 55 6 79 031 89 437 10 563 89 594 54 7 79 047 S9 463 10 537 89 584 53 8 79 063 89 489 10 511 89 574 52 9 79 079 89 515 10 485 89 564 51 10 79 095 89 541 10 459 89 554 50 11 79 111 89 567 10 433 89 544 49 12 79 128 89 593 10 407 89 534 48 13 79144 89 619 10 381 89 524 47 14 79160 89 645 10 355 89 514 46 15 79 176 . 89 671 10 329 89 504 45 16 79192 89 697 10 303 89 495 44 17 79 208 89 723 10 277 89 485 43 18 79 224 89 749 10 251 89 475 42 19 79 240 89 775 10 225 89 465 41 20 79 256 89 801 10 199 89 455 40 21 79 272 89 827 10173 89 445 39 22 79 288 89 853 10147 89 435 38 23 79 304 89 879 10 121 89 425 37 24 79 319 89 905 10 095 89 415 36 25 79 335 89 931 10 069 89 405 35 26 79 351 89 957 10 043 89 395 34 27 79 367 89 983 10 017 89 385 33 28 79 383 90 009 09 991 89 375 32 29 79*399 90 035 09 965 89 364 31 30 79'415 90 061 09 939 89 354 30 31 79 431 90 086 09 914 89 344 29 32 79 447 90 112 09 888 89 334 28 33 79 463 90138 09 862 89 324 27 34 79 478 90164 09 836 89 314 26 35 79 494 90190 09 810 89 304 25 36 79 510 90 216 09 784 89 294 24 37 79 526 90 242 09 758 89 284 23 38 79 542 90 26S 09 732 89 274 22 39 79 558 90 294 09 706 S9 264 21 40 79 573 90 320 09 680 89 254 20 41 79 589 90 346 09 654 89 244 19 42 79 605 90 371 09 629 89 233 IS 43 79 621 90 397 09 603 89 223 17 44 79 636 90 423 09 577 89 213 16 45 79 652 90 449 09 551 89 203 15 46 79 668 90 475 09 525 89193 14 47 79 684 90 501 09 499 89 183 13 48 79 699 90 527 09 473 89173 12 49 79 715 90 553 09 447 89162 11 50 79 731 90 578 09 422 89152 10 51 79 746 90 604 09 396 89142 9 52 79 762 90 630 09 370 S9 132 8 53 79 77S 90 656 09 344 89122 7 54 79 793 90 6S2 09 318 89112 6 55 79 809 90 708 09 292 89 101 5 56 79 825 90 734 09 266 89 091 4 57 79 840 90 759 09 241 89 081 3 58 79 856 90 785 09 215 89 071 2 59 79 872 90 811 09 189 89 060 1 60 79 887 90 837 09 163 89 050 O 9 9 10 9 r log COS log cot log tan log sin t 52 c 51 c 39° t log sin log tan leg cot log cos t 9 79 8S7 9 90S37 10 9 09163 S9 050 60 1 79 903 90 863 09137 S9 040 59 2 79 91S 90SS9 09 111 89 030 5S 3 79 934 90 914 09 086 S9 020 57 4 79 950 90 940 09 060 89 009 56 5 79 965 90 966 09 034 SS999 55 6 79 981 90 992 09 00S 88 989 54 7 79 996 91018 08 9S2 SS97S 53 S 80 012 91043 OS 957 88 968 52 9 80 027 91069 OS 931 SS958 51 10 SO 043 91095 08 905 88 948 50 11 80 058 91121 0SS79 88 937 49 12 SO 074 91147 08 853 88 927 4S 13 80 0S9 91172 08 82S 88 917 47 14 SO 105 91198 0SS02 8S906 46 15 SO 120 91224 08 776 88 896 45 16 SO 136 91250 OS 750 88 886 44 17 80151 91276 08 724 88 875 43 IS SO 166 91301 08 699 SSS65 42 19 80 182 91327 08 673 8S85i 41 20 80 197 91 353 OS 647 88 844 40 21 80 213 91379 OS 621 88 834 39 22 SO 228 91404 08 596 8S824 38 23 80 244 91430 OS 570 88 813 37 24 80 259 91456 OS 544 88S03 36 25 80 274 91482 0S51S SS793 35 26 SO 290 91507 08 493 88 782 34 27 SO 305 91533 08 467 88 772 33 2S ' 80 320 91559 08 441 88 761 32 29 80 336 91585 08 415 88 751 31 30 80 351 91610 08 390 88 741 30 31 80 366 91636 OS 364 88 730 29 32 80 382 91662 OS 338 88 720 28 33 SO 397 916SS OS 312 8S709 27 34 80 412 91713 08 287 88 699 26 35 80428 91739 08 261 S8 6S8 25 36 80 443 91765 OS 235 SS678 24 37 S0 45S 91791 OS 209 8S66S 23 38 SO 473 91816 OS 184 8S657 22 39 S0 4S9 91842 0S15S SS647 21 40 80 504 91868 08132 88 636 20 41 80 519 91893 08 107 88 626 19 42 80 534 91919 08 081 88 615 18 43 80 550 91945 OS 055 S8 605 17 44 80 565 91971 08 029 88 594 16 45 80 5S0 91996 08 004 88 584 15 46 80 595 92 022 07 978 8S573 14 47 80 610 92 04S 07 952 88 563 13 48 SO 625 92 073 07 927 88 552 12 49 SO 641 92 099 07 901 88 542 11 50 80 656 92125 07 875 SS531 10 51 80 671 92 150 07 850 88 521 9 52 S0 6S6 92 176 07 824 88 510 S 53 80 701 92 202 07 798 88 499 7 54 80 716 92 227 07 773 8S4S9 6 55 SO 731 92 253 07 747 88 478 5 56 80 746 92 279 07 721 • SS 468 4 57 80 762 92 304 07 696 88 457 3 58 SO 777 92 330 07 670 8S447 2 59 80 792 92 356 07 644 88 436 1 60 80 807 92 3S1 07 619 88 425 9 log cos 9 log cot 10 9 log tan log sin t r 40° 47 f log sin log tan log cot log cos t 9 80S07 9 92 3S1 10 07 619 9 SS425 60 1 S0S22 92 407 07 593 88 415 59 2 SO 837 92 433 07 567 SS404 58 3 SO S52 92 45S 07 542 88 394 57 4 SO 867 92 484 07 516 88 383 56 5 S0 8S2 92 510 07 490 8S372 55 6 SO 897 92 535 07 465 SS362 54 7 80 912 92 561 07 439 88 351 53 8 80 927 92 587 07 413 SS340 52 9 80 942 92 612 07 388 88 330 51 10 80 957 92 638 07 362 88 319 50 11 80 972 92 663 07 337 8S30S 49 12 80 987 92 689 07 311 88 298 48 13 81002 92 715 07 285 88 287 47 14 81017 92 740 07 260 88 276 46 15 81032 92 766 07 234 88 266 45 16 81047 92 792 07 208 88 255 44 17 81061 92 817 07 183 88 244 43 18 81076 92 843 07 157 88 234 42 19 81091 92 868 07132 88 223 41 20 81106 92S94 07106 88 212 40 21 81121 92 920 07 080 88 201 39 22 81136 92 945 07 055 88191 38 23 81151 92 971 07 029 88 180 37 24 81166 92 996 07 004 8S169 36 25 81180 93 022 06 978 8S158 35 26 81195 93 048 06 952 S8 14S 34 27 81210 93 073 06 927 SS137 33 28 81225 93 099 06 901 88 126 32 29 81240 93 124 06 876 88115 31 30 81254 93 150 06 850 88 105 30 31 81269 93 175 06S25 88 094 29 32 81284 93 201 06 799 88 083 2S 33 81299 93 227 06 773 88 072 27 34 81314 93 252 06 748 88 061 26 35 81328 93 278 06 722 88 051 25 36 81343 93 303 06 697 88 040 24 37 81358 93 329 06 671 8S029 23 38 SI 372 93 354 06 646 88 018 22 39 81387 93 380 06 620 88 007 21 40 81402 93 406 06 594 87 996 20 41 81417 93 431 06 569 87 985 19 42 SI 431 93 457 06 543 87 975 18 43 81446 93 482 06 518 87 964 17 44 81461 93 508 06 492 87 953 16 45 81475 93 533 06 467 87 942 15 46 81490 93 559 06 441 87 931 14 47 81505 93 584 06 416 87 920 13 48 81519 93 610 06 390 87 909 12 49 81534 93 636 06 364 S7S98 11 50 81549 93 661 06 339 87 887 10 51 SI 563 93 687 06 313 87 877 9 52 81578 93 712 06 28S 87S66 8 53 81592 93 738 06 262 S7 855 7 54 81607 93 763 06 237 S7 844 6 55 81622 93 7S9 06 211 87 833 5 56 81636 93S14 06186 87 822 4 57 81651 93 840 06160 87 811 3 58 81665 93 865 06135 S7S00 2 59 81680 93 891 06109 87 7S9 1 60 81694 93 916 06 0S4 87 778 9 log cos 9 log cot 10 log tan 9 log sin t t 50 c 49' 48 41° t log sin log tan log cot log cos t 9 9 io 9 o 81694 93 916 06 084 87 778 60 1 81709 93 942 06 05S S7 767 59 2 81723 93 967 06 033 87 756 58 3 S173S 93 993 06 007 87 745 57 4 81752 94 01S 05 982 S7 734 56 5 81767 94 044 05 956 87 723 55 6 81781 94 069 05 931 S7 712 54 7 SI 796 94 095 05 905 87 701 53 8 81810 94 120 05 8SO 87 690 52 9 SI 825 94146 05 854 87 679 51 10 81S39 94171 05 829 87 668 50 11 81854 94197 05 803 87 657 49 12 S1S6S 94 222 05 778 87 646 48 13 81882 94 248 05 752 87 635 47 14 81S97 94 273 05 727 87 624 46 15 81911 94 299 05 701 S7 613 45 16 81 926 94 324 05 676 87 601 44 17 SI 940 94 350 05 650 87 590 43 IS 81955 94 375 05 625 87 579 42 19 81969 94 401 05 599 87 568 41 20 81983 94 426 05 574 87 557 40 21 81998 94 452 05 548 87 546 39 22 82 012 94 477 05 523 S7 535 38 23 S2 026 94 503 05 497 S7 524 37 24 82 041 94 528 05 472 87 513 36 25 S2 055 94 554 05 446 87 501 35 26 82 069 94 579 05 421 87 490 34 27 S2 0S4 94 604 05 396 87 479 33 28 82 098 94 630 05 370 S7 46S 32 29 82 112 94 655 05 345 87 457 31 30 82 126 94 681 05 319 87 446 30 31 82 141 94 706 05 294 87 434 29 32 S2 155 94 732 05 26S 87 423 28 33 82 169 94 757 05 243 87 412 27 34 82 184 94 783 05 217 87 401 26 35 82198 94 808 05 192 87 390 25 36 82 212 94 834 05 166 87 378 24 37 S2 226 94 859 05 141 87 367 23 38 S2 240 94 884 05 116 87 356 22 39 82 255 94 910 05 090 87 345 21 40 82 269 94 935 05 065 87 334 20 41 82 283 94 961 05 039 87 322 19 42 82 297 94 986 05 014 87 311 IS 43 82 311 95 012 04 988 87 300 17 44 82 326 95 037 04 963 87 2SS 16 45 82 340 95 062 04 938 87 277 15 46 S2 354 95 OSS 04 912 87 266 14 47 82 368 95 113 04 887 87 255 13 48 82 382 95 139 04 861 87 243 12 49 82 396 95 164 04S36 87 232 11 50 82 410 95 190 04 810 87 221 10 51 82 424 95 215 04 785 87 209 9 52 82 439 95 240 04 760 S719S S 53 82 453 95 266 04 734 87 1S7 7 54 82 467 95 291 04 709 87175 6 55 82 481 95 317 04 683 S7 164 5 56 82 495 95 342 04 65S 87 153 4 57 82 509 95 368 04 632 87 141 3 58 82 523 95 393 04 607 87 130 2 59 82 537 95 41S 04 5S2 87119 1 60 82 551 95 444 04 556 87107 9 log COS 9 log cot IO log tan 9 log sin t - t 42 c t log sin log tan log cot log cos / 9 9 10 9 82 551 95 444 04 556 87107 60 1 82 565 95 469 04 531 87 096 59 2 82 579 95 495 04 505 87 085 58 3 82 593 95 520 04 480 87 073 57 4 S2 607 95 545 04 455 87 062 56 5 82 621 95 571 04 429 87 050 55 6 82 635 95 596 04 404 87 039 54 7 82 649 95 622 04 378 87 02S 53 8 82 663 95 647 04 353 87 016 52 9 82 677 95 672 04 328 87 005 51 10 82 691 95 69S 04 302 S6 993 50 11 82 705 95 723 04 277 S6 9S2 49 12 82 719 95 748 04 252 86 970 48 13 82 733 95 774 04 226 86 959 47 14 82 747 95 799 04 201 S6 947 46 15 82 761 95 825 04175 S6 936 45 16 82 775 95 850 04 150 86 924 44 17 82 7S8 95 875 04 125 S6 913 43 18 82 802 95 901 04 099 86 902 42 19 82 816 95 926 04 074 S6S90 41 20 82 830 95 952 04 048 86 879 40 21 S2 844 95 977 04 023 S6S67 39 22 82 858 96 002 03 998 86 855 3S 23 82 872 96 02S 03 972 86 844 37 24 82 885 96 053 03 947 86 832 36 25 82 899 96 07S 03 922 86 821 35 26 82 913 96 104 03 896 86 809 34 27 82 927 96129 03 871 86 798 33 2S 82 941 96155 03 845 S6 7S6 32 29 82^55 96180 03S20 86 775 31 30 82 968 96'205 03 795 86 763 30 31 82 982 96 231 03 769 S6 752 29 32 82 996 96 256 03 744 S6 740 28 33 83 010 96 281 03 719 S6 72S 27 34 83 023 96 307 03 693 86 717 26 35 83 037 96 332 03 668 S6 705 25 36 83 051 96 357 03 643 86 694 24 37 83 065 96 383 03 617 S6 682 23 3S 83 078 96 40S 03 592 86 670 22 39 83 092 96 433 03-567 86 659 21 40 83 106 96 459 03 541 86 647 20 41 83 120 96 484 03 516 S6 635 19 42 83 133 96 510 03 490 86 624 18 43 83 147 96 535 03 465 S6 612 17 44 83 161 96 560 03 440 86 600 16 45 83 174 96 586 03 414 86 589 15 46 83 188 96 611 03 389 S6 577 14 47 83 202 96 636 03 364 86 565 13 48 83 215 96 662 03 338 86 554 12 49 S3 229 96 687 03 313 86 542 11 50 83 242 96 712 03 2SS S6 530 10 51 S3 256 96 738 03 262 86 518 9 52 83 270 96 763 03 237 S6 507 8 53 83 283 96 78S 03 212 86 495 7 54 83 297 96S14 03 186 S6 4S3 6 55 S3 310 96 839 03 161 S6 472 5 56 S3 324 • 96 864 03 136 86 460 4 57 S3 33S 96 890 03 110 S6 448 3 5S S3 351 96 915 03 085 86 436 2 59 S3 365 96 940 03 060 86 425 1 60 83 37S 96 966 03 034 86 413 9 9 10 9 t log cos log cot log tan log sin t 48 c 47 c 43 c t log sin log tan log cot log cos t 9 83 378 9 96 966 10 03 034 9 86 413 60 1 83 392 96 991 03 009 S6 401 59 2 83 405 97 016 02 9S4 86 3S9 58 3 83 419 97 042 02 958 86 377 57 4 83 432 97 067 02 933 86 366 56 5 83 446 97 092 02 90S 86 354 55 6 83 459 97 US 02 882 86 342 54 7 83 473 97 143 02 857 S6 330 53 S S3 4S6 97 16S 02 832 86 31S 52 9 83 500 97193 02 807 86 306 51 10 S3 513 97 219 02 781 S6 295 50 11 83 527 97 244 02 756 S6 2S3 49 12 S3 540 97 269 02 731 86 271 48 13 S3 554 97 295 02 705 86 259 47 14 83 567 97 320 02 680 S6 247 46 15 83 581 97 345 02 655 86 235 45 16 83 594 97 371 02 629 86 223 44 17 83 608 97 396 02 604 86 211 43 18 83 621 97 421 02 579 86 200 42 19 83 634 97 447 02 553 861SS 41 20 S3 648 97 472 02 52S 86176 40 21 83 661 97 497 02 503 86 164 39 22 83 674 97 523 02 477 86 152 38 23 S3 6SS 97 54S 02 452 86140 37 24 83 701 97 573 02 427 86128 36 25 S3 715 97 598 02 402 86 116 35 26 83 728 97 624 02 376 86104 34 27 83 741 97 649 02 351 S6 092 33 28 83 755 97 674 02 326 S6 0S0 32 29 83 768 97 700 02 300 86 068 31 30 83 781 97 725 02 275 86 056 30 31 S3 795 97 750 02 250 86 044 29 32 83 SOS 97 776 02 224 86 032 28 33 83 821 97 801 02 199 86 020 27 34 83 834 97 826 02 174 S6 00S 26 35 83S4S 97 851 02149 85 996 25 36 S3S61 97 877 02 123 S5 984 24 37 83 874 97 902 02 098 85 972 23 38 83 8S7 97 927 02 073 85 960 22 39 83 901 97 953 02 047 S5 94S 21 40 83 914 97 978 02 022 85 936 20 41 83 927 98 003 01997 85 924 19 42 83 940 98 029 01971 S5 912 IS 43 83 954 9S054 01946 85 900 17 44 83 967 98 079 01921 S5 888 16 45 83 9S0 98 104 01896 85 876 15 46 83 993 98 130 01S70 85 864 14 47 84 006 98155 01S45 S5 851 13 48 84 020 98 180 01820 S5S39 12 49 84 033 98 206 01794 S5S27 11 50 84 046 98 231 01769 85S15 10 51 S4 059 98 256 01744 85 803 9 52 84 072 9S-2S1 01719 85 791 8 53 S4 0S5 98 307 01693 85 779 7 54 84 098 9S332 0166S 85 766 6 55 84 112 98 357 01643 85 754 5 56 S4 125 98 3S3 01617 85 742 4 57 84 138 9S40S 01592 85 730 3 5S 84 151 98 433 01567 S5 718 2 59 S4 164 98 458 01542 85 706 1 60 84 177 98 484 01516 85 693 9 9 10 9 -H t log cos log cot log tan log sin ' 44° 49 t log sin log tan log cot log cos t 9 84 177 9 98 484 10 01516 9 85 693 60 1 84 190 98 509 01491 85 681 59 2 84 203 98 534 01466 85 669 58 3 84 216 98 560 01440 85 657 57 4 84 229 9S5S5 01415 85 645 56 5 84 242 98 610 01390 85 632 55 6 84 255 98 635 01365 85 620 54 7 84 269 9S661 01339 85 608 53 S S4 2S2 98 6S6 01314 85 596 52 9 84 295 98 711 01289 85 583 51 10 84 30S 98 737 01263 85 571 50 11 84 321 98 762 01238 85 559 49 12 84 334 9S7S7 01213 85 547 48 13 84 347 9S812 01188 85 534 47 14 84 360 98 838 01162 85 522 46 15 84 373 98 863 01137 85 510 45 16 84 385 98SS8 01112 85 497 44 17 84 398 98 913 01087 85 485 43 18 S4 411 98 939 01061 85 473 42 19 84 424 98 964 01036 85 460 41 20 84 437 98 989 01011 S5 44S 40 21 84 450 99 015 00 985 85 436 39 22 S4 463 99 040 00 960 85 423 38 23 84 476 99 065 00 935 85 411 37 24 84 489 99 090 00 910 85 399 36 25 84 502 99116 00 884 85 386 35 26 84 515 99141 00 859 85 374 34 27 84 528 99 166 00 834 85 361 33 28 84 540 99191 00 809 85 349 32 29 84 553 99 217 00 783 85 337 31 30 84 566 99 242 00 758 85 324 30 31 84 579 99 267 00 733 85 312 29 32 84 592 99 293 00 707 85 299 28 33 84 605 99 318 00 6S2 85 2S7 27 34 84 618 99 343 00 657 85 274 26 35 84 630 99 368 00 632 85 262 25 36 S4 643 99 394 00 606 85 250 24 37 84 656 99 419 00 581 85 237 23 3S 84 669 99 444 00 556 85 225 22 39 84 6S2 99 469 00 531 85 212 21 40 84 694 99 495 00 505 85 200 20 41 S4 707 99 520 00 480 85 187 19 42 84 720 99 545 00 455 85 175 18 43 84 733 99 570 00 430 85 162 17 44 84 745 99 596 00 404 85 150 16 45 84 758 99 621 00 379 85 137 15 46 84 771 99 646 00 354 85 125 14 47 84 784 99 672 00 328 85 112 13 48 84 796 99 697 00 303 85 100 12 49 84 809 99 722 00 278 85 087 11 50 84 822 99 747 00 253 85 074 10 51 84 835 99 773 00 227 85 062 9 52 84 847 99 798 00 202 85 049 8 53 84S60 99 823 00 177 85 037 7 54 84S73 99 848 00152 85 024 6 55 84 885 99 874 00 126 85 012 5 56 84S9S 99 899 00101 84 999 4 57 84 911 99 924 00 076 84 986 3 58 84 923 99 949 00 051 S4 974 2 59 S4 936 99 975 00 025 84 961 1 60 84 949 00 000 00 000 84 949 O 9 10 10 9 t log cos log cot log tan log sin t 46 : 45 50 TABLE IV. HAN CAN BE DONE BY For Determining wite [ Greater Accuracy i means of Table III. : 1. log sin, log tan, and log cot, when the angle is between 0° and 2° ; 2. log cos, log tan, and log cot, when the angle is between 88° and 90° ; 3. The value of the angle when the logarithm of the function does not lie between the limits 8. 54 684 and 11. 45 316. FORMULAS FOR THE USE OF THE 1STUMBERS S AND T. I. When the angle a is between 0° and 2° : log sin a = log a" + S. log a" = log sin a — S, log tan a = log a" + T. = log tan a — T, log cot a = colog tan a. = colog cot a — T. II. When the angle a is between 88° and 90° : log cos a = log (90° - a)" + S. log (90° - a)" = log cos a - -s, log cot a = log (90° - a)" + T. = log cot a - - T, log tan a = colog cot a. = colog tan a — T, . * and a = 90° - (90 >-«). »«VKo« Values of S ato T, . a" S log sin a a" T log tan a a T log tan a — — 5146 8. 39 713 4. 68 557 4. 68 557 4. 68 567 2 409 8. 06 740 200 6. 98 660 5 424 8. 41 999 4. 68 556 4. 68 558 4. 68 568 3 417 8. 21 920 1 726 7. 92 263 5 689 8. 44 072 4. 68 555 4. 68 559 4. 68 569 3 823 8. 26 795 2 432 8. 07 156 5 941 8. 45 955 4. 68 555 4. 68 560 4. 68 570 4 190 8. 30 776 2 976 8. 15 924 6184 8. 47 697 4. 68 554 • 4.68 561 4. 68 571 4 840 8. 37 038 3 434 8. 22 142 6 417 8. 49 305 4. 68 553 4. 68 562 4. 68 572 5 414 8. 4.1 904 3 838 . 8. 26 973 6 642 S. 50 802 4. 68 552 4. 68 563 4. 68 573 5 932 8.45 872 4 204 8. 30 930 6 859 8. 52 200 4. 68 551 4. 68 564 4. 68 574 6 408 8. 49 223 4 540 8.34 270 7 070 8.53 516 4. 6S 550 4. 68 565 4. 68 575 6 633 8. 50 721 4 699 8. 35 766 7173 S. 54 145 4. 68 550 4. 68 565 4. 68 575 6 851 8.52 125 4 853 8. 37 167 7 274 S. 54 753 4. 68 549 4. 68 566 7 267 8. 54 684 5 146 8. 39 713 a" S log sin a a" . T log tan a a T log tan a 1 TABLE V.— Circumferences and Areas of Circles. 61 If .ZV"= the radius of the circle, the circumference = 2 ?r n: If JST = the radius of the circle, the < irea = TriV 2 . If iV = the circumference of the circle, the radius = — 2tt N. If iV" = the circumference of the circle, the area = — 4tt 2V 2 . N 2TT2? Wjf2 2ir if 0.00 N 27TJV irJT* ±jst 2ir 47T 0.00 0.0 0.000 50 314. 16 7 854 7.96 198. 94 1 6.28 3.1 0.159 0.08 51 320. 44 8171 8.12 206. 98 2 12.57 12.6 0.318 0.32 52 326. 73 8 495 8.2S 215. 18 3 18.85 28.3 0.477 0.72 53 333. 01 8 825 8.44 223. 53 4 25. 13 50.3 0.637 1.27 54 339. 29 9161 8.59 232. 05 5 31.42 78.5 0.796 1.99 55 345. 58 9 503 8.75 240. 72 6 37.70 113.1 0.955 2.86 56 351.86 9 852 8.91 249. 55 7 43.98 153.9 1.114 3.90 57 358. 14 10 207 9.07 258. 55 8 50.27 201.1 1.273 5.09 58 364. 42 10 568 9.23 267. 70 9 56.55 254.5 1.432 6.45 59 370. 71 10 936 9.39 277. 01 10 62.83 .314.2 1.592 7.96 60 376. 99 11310 9.55 286. 48 11 69.12 380.1 1.751 9.63 61 383. 27 11690 9.71 296. 11 12 75.40 452.4 1.910 11.46 62 389. 56 12 076 9.87 305. 90 13 81. 6S 530.9 2.069 13.45 63 395. 84 12 469 10.03 315. 84 14 87.96 615.8 2.228 15.60 64 402. 12 12 868 10.19 325. 95 15 94.25 706.9 2.387 17.90 65 408. 41 13 273 10.35 336. 21 16 100. 53 80+. 2 2.5+6 20.37 66 414. 69 13 685 10.50 346. 64 17 106. 81 907.9 2.706 23.00 67 420. 97 14103 10.66 357. 22 IS 113. 10 1017.9 2.865 25.78 68 427. 26 14 527 10.82 367. 97 19 119. 38 1 134. 1 3.02+ 28. 73 69 433. 54 14 957 10.98 378. 87 20 125. 66 1 256. 6 3.183 31.83 70 439. S2 15 394 11.14 389. 93 21 131.95 1 385. 4 3.3+2 35. 09 71 446. 11 15 837 11.30 401. 15 22 138. 23 1 520. 5 3.501 38.52 72 452. 39 16 286 11.46 412. 53 23 144. 51 1661.9 3.661 42.10 73 458. 67 16 742 11.62 424. 07 24 150. 80 1 S09. 6 3.820 45.8+ 74 464. 96 17 203 11.78 435. 77 25 157. OS 1 963. 5 3.979 49.74 75 471. 24 17 671 11.94 447. 62 26 163. 36 2 123. 7 +. 13S 53.79 76 477. 52 18146 12.10 459. 64 27 169. 65 2 290. 2 4.297 58.01 77 483. 81 18 627 12.25 471. 81 28 175.93 2 463. 4.456 62.39 78 490. 09 19113 12.41 484. 15 29 182. 21 2 6+2. 1 4.615 66.92 79 496. 37 19 607 12.57 496. 64 . 30 18S. 50 2 827. 4 4.775 71.62 80 502. 65 20106 12.73 509. 30 31 19+. 78 3 019. 1 4.934 76.47 81 508. 94 20 612 12.89 522. 11 32 201. 06 3 217.0 5.093 81.49 82 515. 22 21124 13.05 535. 08 33 207. 35 3 421. 2 5.252 86.66 83 521. 50 21642 13.21 548. 21 34 213. 63 3 631. 7 5.411 91.99 84 527. 79 22167 13.37 561. 50 35 219. 91 3 84S. 5 5.570 97.48 85 534. 07 22 698 13.53 574. 95 36 226. 19 4 071.5 5.730 103. 13 86 540. 35 23 235 13.69 588. 55 37 232. 48 4 300. 8 5.8S9 108. 94 87 546. 64 23 779 13.85 602. 32 3S 23S. 76 4 536. 5 6.048 114.91 88 552.92 24 328 14.01 616. 25 39 245. 04 4 778.4 6.207 121. 04 89 559. 20 24 885 14.16 630. 33 40 251.33 5 026. 5 6.366 127. 32 90 565. 49 25 447 14.32 644. 58 41 257. 61 5 281.0 6.525 133. 77 91 571.77 26 016 14.48 658. 98 42 263. 89 5-541.8 6. 6S5 1+0. 37 92 578. 05 26 590 14.64 673. 54 43 270. 18 5 SOS. 8 6.8++ 147. 14 93 584. 34 27 172 14.80 688. 27 44 276. 46 6 0S2. 1 7.003 154. 06 9+ 590. 62 27 759 14.96 703. 15 45 2S2. 74 6 361.7 7.162 161. 14 95 596. 90 28 353 15.12 718. 19 46 289 03 6 647. 6 7.321 168. 39 96 603. 19 28 953 15.28 733. 39 47 295.31 6 939. 8 7. 4S0 175. 79 97 609. 47 29 559 15.44 748. 74 4S 301. 59 7 238. 2 7.639 183.35 98 615. 75 30 172 15.60 764. 26 49 307. SS 7 543. 7.799 191. 07 99 622. 04 30 791 15.76 779. 94 50 314. 16 7 854. 7.958 198. 94 100 628. 32 31416 15.92 795. 77 N 2 7TiV irN 2 l-N JL^a N 2ir_iV ±-V ±-N* <2,ir 4ir lit 47T 52 TABLE VI. -NATUBAL FUNCTIONS • / o° 1° -2° 3° 4° f sin cos sin cos sin cos sin cos sin cos o 0000 1.000 0175 9998 0349 9994 0523 9986 0698 9976 60 i 0003 1.000 0177 9998 0352 9994 0526 9986 0700 9975 59 2 0006 1.000 0180 9998 0355 9994 0529 9986 0703 9975 58 3 0009 1.000 0183 9998 0358 9994 0532 9986 0706 9975 57 ' 4 0012 1.000 0186 9998 0361 9993 0535 9986 0709 9975 56 5 0015 1.000 0189 9998 0364 9993 0538 9986 0712 9975 55 6 0017 1.000 0192 9998 0366 9993 0541 9985 0715 9974 54 7 0020 1.000 0195 9998 0369 9993 0544 9985 0718 9974 53 8 0023 1.000 0198 9998 0372 9993 0547 9985 0721 9974 52 9 0026 1.000 0201 9998 0375 9993 0550 9985 0724 9974 51 10 0029 1.000 0204 9998 0378 9993 0552 9985 0727 9974 50 11 0032 1.000 0207 9998 0381 9993 0555 9985 0729 9973 49 12 0035 1.000 0209 9998 0384 9993 0558 9984 0732 9973 48 13 0038 1.000 0212 9998 0387 9993 0561 9984 0735 9973 47 14 0041 1.000 0215 9998 0390 9992 0564 9984 0738 9973 46 15 0044 1.000 0218 9998 0393 9992 0567 9984 0741 9973 45 16 0047 1.000 0221 9998 0396 9992 0570 9984 0744 9972 44 17 0049 1.000 0224 9997 0398 9992 0573 9984 0747 9972 43 IS 0052 1.000 0227 9997 0401 9992 0576 9983 0750 9972 42 19 0055 1.000 0230 9997 0404 9992 0579 9983 0753 9972 41 20 0058 1.000 0233 9997 0407 9992 0581 9983 0756 9971 40 21 0061 1.000 0236 9997 0410 9992 0584 9983 0758 9971 39 22 0064 1.000 0239 9997 0413 9991 0587 9983 0761 9971 38 23 0067 1.000 0241 9997 0416 9991 0590 9983 0764 9971 37 24 0070 1.000 0244 9997 0419 9991 0593 9982 0767 9971 36 25 0073 1.000 0247 9997 0422 9991 0596 9982 0770 9970 35 26 0076 1.000 0250 9997 0425 9991 0599 9982 0773 9970 34 27 0079 1.000 0253 9997 0427 9991 0602 9982 0776 9970 33 2S 0081 1.000 0256 9997 0430 9991 0605 9982 0779 9970 32 29 0084 1.000 0259 9997 0433 9991 .0608 9982 0782 9969 31 30 0087 1.000 0262 9997 0436 9990 0610 9981 0785 9969 30 31 0090 1.000 0265 9996 0439 9990 0613 9981 0787 9969 29 32 0093 1.000 0268 9996 0442 9990 0616 9981 0790 9969 28 33 0096 1000 0270 9996 0445 9990 0619 9981 0793 9968 27 34 0099 1.000 0273 9996 0448 9990 0622 9981 0796 9968 26 35 0102 9999 0276 9996 0451 9990 0625 9980 0799 9968 25 36 0105 9999 0279 9996 0454 9990 0628 9980 0802 9968 24 37 0108 9999 0282 9996 0457 9990 0631 9980 0805 9968 23 38 0111 9999 0285 9996 0459 9989 0634 9980 0808 9967 22 39 0113 9999 02SS 9996 0462 9989 0637 9980 0811 9967 21 40 0116 9999 0291 9996 0465 9989 0640 9980 0814 9967 20 41 0119 9999 0294 9996 0468 9989 0642 9979 0816 9967 19 42 0122 9999 0297 9996 0471 9989 0645 9979 0819 9966 IS 43 0125 9999 0300 9996 0474 9989 0648 9979 0822 9966 17 44 0128 9999 0302 9995 0477 9989 0651 9979 0825 9966 16 45 0131 9999 0305 9995 0480 9988 0654 9979 082S 9966 15 46 0134 9999 0308 9995 0483 9988 0657 9978 0831 9965 14 47 0137 9999 0311 9995 ■ 0486 9988 0660 9978 0834 9965 13 48 0140 9999 0314 9995 0488 9988 0663 9978 0837 9965 12 49 0143 9999 0317 9995 0491 9988 0666 9978 0840 9965 11 50 0145 9999 0320 9995 0494 9988 0669 9978 0843 9964 10 51 0148 9999 0323 9995 0497 9988 0671 9977 0845 9964 9 52 0151 9999 0326 9995 0500 9987 0674 9977 0848 9964 8 53 0154 9999 0329 9995 0503 9987 0677 9977 0851 9964 7 54 0157 9999 0332 9995 0506 9987 06S0 9977 0854 9963 6 55 0160 9999 0334 9994 0509 9987 0683 9977 0857 9963 5 56 0163 9999 0337 9994 0512 9987 06S6 9976 0860 9963 4 57 0166 9999 0340 9994 0515 9987 0689 9976 0863 9963 3 58 0169 9999 0343 9994 0518 99S7 0692 9976 0866 9962 2 59 0172 9999 0346 9994 0520 9986 0695 9976 0S69 9962 1 60 0175 9999 0349 9994 0523 9986 069S 9976 0872 9962 O cos sin cos sin cos sin cos sin cos sin r 89° 88° 87° 80° 85° t NATUKAL SINES AND COSINES. 53 / 5° 6° 7° 8° 9° t sin cos sin cos sin cos sin cos sin cos o 0872 9962 1045 9945 1219 9925 1392 9903 1564 9877 60 1 0874 9962 1048 9945 1222 9925 1395 9902 1567 9876 59 2 0877 9961 1051 9945 1224 9925 1397 9902 1570 9876 58 3 0S80 9961 1054 9944 1227 9924 1400 9901 1573 9876 57 4 0SS3 9961 1057 9944 1230 9924 1403 9901 1576 9875 56 5 0SS6 9961 1060 9944 1233 9924 1406 9901 1579 9875 55 6 0889 9960 1063 9943 1236 9923 1409 9900 1582 9874 54 7 0892 9960 1066 9943 1239 9923 1412 9900 1584 9874 53 8 0S95 9960 1068 9943 1241 9923 1415 9899 1587 9873 52 9 089S 9960 1071 9942 1245 9922 1418 9899 1590 9873 51 10 0901 9959 1074 9942 1248 9922 1421 9899 1593 9872 50 11 0903 9959 1077 9942 1250 9922 1423 9898 1596 9872 49 12 0906 9959 1080 9942 1253 9921 1426 9898 1599 9871 48 13 0909 9959 1083 9941 1256 9921 1429 9897 1602 9871 47 14 0912 9958 1086 9941 1259 9920 1432 9897 1605 9870 46 15 0915 9958 1089 9941 1262 9920 1435 9897 1607 9870 45 16 0918 9958 1092 9940 1265 9920 1438 9896 1610 9869 44 17 0921 9958 1094 9940 1268 9919 1441 9896 1613 9869 43 18 0924 9957 1097 9940 1271 9919 1444 9895 1616 9869 42 19 0927 9957 1100 9939 1274 9919 1446 9895 1619 9868 41 20 0929 9957 1103 9939 1276 9918 1449 9894 1622 9868 40 21 0932 9956 1106 9939 1279 9918 1452 9894 1625 9867 39 22 0935 9956 1109 9938 12S2 9917 1455 9894 1628 9S67 38 23 0938 9956 1112 9938 1285 9917 1458 9893 1630 9866 37 24 0941 9956 1115 9938 1288 9917 1461 9893 1633 9866 36 25 0944 9955 1118 9937 1291 9916 1464 9892 1636 9865 35 26 0947 9955 1120 9937 1294 9916 1467 9892 1639 9865 34 27 0950 9955 1123 9937 1297 9916 1469 9891 1642 9864 33 28 0953 9955 1126 9936 1299 9915 1472 9891 1645 9864 32 29 0956 9954 1129 9936 1302 9915 1475 9891 1648 9863 31 30 0958 9954 1132 9936 1305 9914 1478 9890 1650 9863 30 31 0961 9954 1135 9935 1308 9914 1481 9890 1653 9862 29 32 0964 9953 1138 9935 1311 9914 1484 9889 1656 9862 28 33 0967 9953 1141 9935 1314 9913 1487 9889 1659 9861 27 34 0970 9953 1144 9934 1317 9913 1490 9888 1662 9861 26 35 ■ 0973 9953 1146 9934 1320 9913 1492 9888 1665 9860 25 36 0976 9952 1149 9934 1323 9912 1495 9888 1668 9860 24 37 0979 9952 1152 9933 1325 9912 1498 9887 1671 9859 23 38 0982 9952 1155 9933 1328 9911 1501 98S7 1673 9S59 22 39 0985 9951 1158 9933 1331 9911 1504 9886 1676 9859 21 40 09S7 9951 1161 9932 1334 9911 1507 9886 1679 9858 20 41 0990 9951 1164 9932 1337 9910 1510 9885 1682 9858 19 42 0993 9951 1167 9932 1340 9910 1513 9885 1685 9S57 IS 43 0996 9950 1170 9931 1343 9909 1515 9884 16S8 9857 17 44 0999 9950 1172 9931 1346 9909 1518 9884 1691 9856 16 45 1002 9950 1175 9931 1349 9909 1521 9884 1693 9856 15 46 1005 9949 1178 9930 1351 9908 1524 9883 1696 9855 14 47 1008 9949 1181 9930 1354 990S 1527 9883 1699 9S55 13 4S 1011 9949 1184 9930 1357 9907 1530 9882 1702 9854 12 49 1013 9949 1187 9929 1360 9907 1533 9882 1705 9854 11 50 1016 9948 1190 9929 1363 9907 1536 9881 1708 9853 10 51 1019 9948 1193 9929 1366 9906 1538 9881 1711 9853 9 52 1022 9948 1196 9928 1369 9906 1541 9880 1714 9852 8 53 1025 9947 1198 992S 1372 9905 1544 9880 1716 9S52 7 54 1028 9947 1201 9928 1374 9905 1547 9880 1719 9851 6 55 1031 9947 1204 9927 1377 9905 1550 9879 1722 9851 5 56 1034 9946 1207 9927 13S0 9904 1553 9879 1725 9850 4 57 1037 9946 1210 9927 1383 9904 1556 9878 1728 9850 3 58 1039 9946 1213 9926 13S6 9903 1559 9878 1731 9849 2 59 1042 9946 1216 9926 1389 9903 1561 9877 1734 9849 1 60 1045 9945 1219 9925 1392 9903 1564 9877 1736 9848 cos sin cos sin cos sin cos sin cos sin t 84° 83° 82° 81° 80° t 54 NATITKAL SINES AND COSINES. / 10° 11° 12° 13° 14° t sin cos sin cos sin cos sin cos sin cos 1736 9848 1908 9816 2079 9781 2250 9744 2419 9703 60 1 1739 9848 1911 9816 2082 97S1 2252 9743 2422 9702 59 2 1742 9847 1914 9815 2085 9780 2255 9742 2425 9702 58 3 1745 9847 1917 9815 2088 9780 2258 9742 2428 9701 57 ' 4 1748 9846 1920 9814 2090 9779 2261 9741 2431 9700 56 5 1751 9846 1922 9813 2093 9778 2264 9740 2433 9699 55 6 1754 9845 1925 9813 2096 9778 2267 9740 2436 9699 54 7 1757 9845 1928 9S12 2099 9777 2269 9739 2439 9698 53 8 1759 9844 1931 9812 2102 9777 2272 9738 2442 9697 52 9 1762 9843 1934 9811 2105 9776 2275 9738 2445 9697 51 10 1765 9843 1937 9811 2108 9775 2278 9737 2447 9696 50 11 1768 9842 1939 9810 2110 9775 2281 9736 2450 9695 49 12 1771 9842 1942 9810 2113 9774 2284 9736 2453 9694 48 13 1774 9841 1945 9809 2116 9774 2286 9735 2456 9694 47 14 1777 9841 1948 9808 2119 9773 2289 9734 2459 9693 46 15 1779 9840 1951 9808 2122 9772 2292 9734 2462 9692 45 16 . 1782 9840 1954 9807 2125 9772 2295 9733 2464 9692 44 17 1785 9839 1957 9807 2127 9771 2298 9732 2467 9691 43 18 1788 9839 1959 9806 2130 9770 2300 9732 2470 9690 42 19 1791 983S 1962 9806 2133 9770 2303 9731 2473 9689 41 20 1794 9838 1965 9805 2136 9769 2306 9730 2476 9689 40 21 1797 9837 1968 9804 2139 9769 2309 9730 2478 96SS 39 22 1799 9S37 1971 9804 2142 9768 2312 9729 2481 9687 38 23 1802 9836 1974 9803 2145 9767 2315 9728 2484 9687 37 24 1805 9836 1977 9S03 2147 9767 2317 9728 2487 9686 36 25 1808 9835 1979 9802 2150 9766 2320 9727 2490 9685 35 26 1811 9835 1982 9802 2153 9765 2323 9726 2493 9684 34 27 1814 9834 1985 9801 2156 9765 2326 9726 2495 9684 33 28 1817 9834 1988 9800 2159 9764 2329 9725 2498 9683 32 29 1819 9833 1991 9800 2162 9764 2232 9724 2501 9682 31 30 1822 9833 1994 9799 2164 9763 2334 9724 2504 9681 30 31 1825 9S32 1997 9799 2167 9762 2337 9723 2507 9681 29 32 182S 9831 1999 9798 2170 9762 2340 9722 ■2509 9680 28 33 1831 9831 2002 9798 2173 9761 2343 9722 2512 9679 27 34 1834 9830 2005 9797 2176 9760 2346 9721 2515 9679 26 35 1837 9830 200S 9796 2179 9760 2349 9720 2518 9678 25 36 1840 9829 2011 9796 2181 9759 2351 9720 2521 9677 24 37 1842 9829 2014 9795 2184 9759 2354 9719 2524 9676 - 23 38 1845 9828 2016 9795 2187 9758 2357 9718 2526 9676 22 39 1848 9828 2019 9794 2190 9757 2360 9718 2529 9675 21 40 1851 9827 2022 9793 2193 9"757 2363 9717 2532 9674 20 41 1854 9827 2025 9793 2196 9756 2366 9716 2535 9673 19 42 1857 9826 2028 9792 2198 9755 2368 9715 2538 9673 IS 43 1860 9826' 2031 9792 2201 9755 2371 9715 2540 9672 17 44 1862 9825 2034 9791 2204 9754 2374 9714 2543 9671 16 45 1865 9825 2036 9790 2207 9753 2377 9713 2546 9670 15 46 1S68 9824 2039 9790 2210 9753 2380 9713 2549 9670 14 47 1871 9823 2042 9789 • 2213 9752 2383 9712 2552 9669 13 48 1874 9823 2045 9789 2215 9751 2385 9711 2554 966S 12 49 1877 9822 2048 9788 2218 9751 2388 9711 2557 9667 11 50 1880 9822 2051 9787 2221 9750 2391 9710 2560 9667 10 51 1882 9821 2054 9787 2224 9750 2394 9709 2563 9666 9 52 1885 9821 2056 9786 2227 9749 2397 9709 2566 9665 8 53 1888 9820 2059 9786 2230 9748 2399 9708 2569 9665 7 54 1891 9820 2062 9785 2233 9748 2402 9707 2571 9664 6 55 1894 9819 2065 9784 2235 9747 2405 9706 2574 9663 5 56 1897 9S18 206S 9784 2238 9746 2408 9706 2577 9662 4 57 1900 9818 2071 9783 2241 9746 2411 9705 2580 9662 3 5S 1902 9S17 2073 9783 2244 9745 2414 9704 2583 9661 2 59 1905 9S17 2076 9782 2247 9744 2416 9704 25S5 9660 1 60 1908 9816 2079 9781 2250 9744 2419 9703 2588 9659 cos sin cos sin cos sin cos sin cos sin t 79° 78° 77° 76° 75° ' | NATURAL SINES AND COSINES. 55 / 15° 16° 17° 18° 19° t sin cos sin cos sin cos sin cos sin cos 25S8 9659 2756 9613 2924 9563 3090 9511 3256 9455 60 1 2591 9659 2759 9612 2926 9562 3093 9510 3258 9454 59 2 2594 965S 2762 9611 2929 9561 3096 9509 3261 9453 58 3 2597 9657 2165 9610 2932 9560 3098 9508 3264 9452 57 4 2599 9656 276S 9609 2935 9560 3101 9507 3267 9451 56 5 2602 9655 2770 9609 2938 9S59 3104 9506 3269 9450 55 6 2605 9655 2773 9608 2940 9558 3107 9505 3272 9449 54 7 260S 9654 2776 9607 2943 9557 3110 9504 3275 9449 53 8 2611 9653 2779 9606 2946 9556 3112 9503 3278 9448 52 9 ' 2613 9652 2782 9605 2949 9555 3115 9502 3280 9447 51 10 2616 9652 2784 9605 2952 9555 3118 9502 3283 9446 50 11 2619 9651 27S7 9604 2954 9554 3121 9501 3286 9445 49 12 2622 9650 2790 9603 2957 9553 3123 9500 3289 9444 48 13 2625 9649 2793 9602 2960 9552 3126 9499 3291 9443 47 14 262S 9649 2795 9601 2963 9551 3129 9498 3294 9442 46 15 2630 964S 2798 9600 2965 9550 3132 9497 3297 9441 45 16 2633 9647 2801 9600 296S 9549 3134 9496 3300 9440 44 17 2636 9646 2S04 9599 2971 9548 3137 9495 3302 9439 43 IS 2639 9646 2807 9598 2974 9548 3140 9494 3305 9438 42 19 2642 9645 2S09 9597 2977 9547 3143 9493 3308 9437 41 20 2644 9644 2812 9596 2979 9546 3145 9492 3311 9436 40 21 2647 9643 2815 9596 2982 9545 3148 9492 3313 9435 39 22 2650 9642 2818 9595 29S5 9544 3151 9491 3316 9434 38 23 2653 9642 2821 9594 2988 9543 3154 9490 3319 9433 37 24 2656 9641 2823 9593 2990 9542 3156 9489 3322 9432 36 25 265S 9640 2826 9592 2993 9542 3159 9488 3324 9431 35 26 2661 9639 2829 9591 2996 9541 3162 9487 3327 9430 34 27 2664 9639 2832 9591 2999 9540 3165 9486 3330 9429 33 2S 2667 9638 2835 9590 3002 9539 3168 9485 3333 9428 32 29 2670 9637 2837 9589 3004 9538 3170 9484 3335 9427 31 30 2672 9636 2840 9588 3007 9537 3173 9483 3338 9.426 30 31 2675 9636 2843 9587 3010 9536 3176 9482 3341 9425 29 32 2678 9635 2846 9587 3013 9535 3179 9481 3344 9424 28 33 26S1 9634 2849 9586 3015 9535 3181 9480 3346 9423 27 34 2684 9633 2851 9585 3018 9534 3184 9480 3349 9423 26 35 2686 9632 2854 9584 3021 9533 3187 9479 3352 9422 25 36 2689 9632 2S57 9583 3024 9532 3190 9478 3355 9421 24 37 2692 9631 2S60 95S2 3026 9531 3192 9477 3357 9420 23 38 2695 9630 2862 9582 3029 9530 3195 9476 3360 9419 22 39 269S 9629 2865 9581 3032 9529 3198 9475 3363 9418 21 40 2700 9628 2868 9580 3035 9528 3201 9474 3365 9417 20 41 2703 962S 2871 9579 3038 9527 3203 9473 336S 9416 19 42 2706 9627 2874 9578 3040 9527 3206 9472 3371 9415 IS 43 2709 9626 2876 9577 3043 9526 3209 9471 3374 9414 17 44 2712 9625 2879 9577 3046 9525 3212 9470 3376 9413 16 45 2714 9625 2882 9576 3049 9524 3214 9469 3379 9412 15 46 2717 9624 2885 9575 3051 9523 3217 9468 3382 9411 14 47 2720 9623 2888 9574 3054 9522 3220 9467 3385 9410 13 4S 2723 9622 2890 9573 3057 9521 3223 9466 3387 9409 12 49 2726 9621 2893 9572 3060 9520 3225 9466 3390 9408 11 50 2728 9621 2896 9572 3062 9520 3228 9465 3393 9407 io 51 2731 9620 2899 9571 3065 9519 3231 9464 3396 9406 9 52 2734 9619 2901 9570 306S 9518 3234 9463 339S 9405 8 53 2737 9618 2904 9569 3071 9517 3236 9462 3401 9404 7 54 2740 9617 2907 9568 3074 9516 3239 9461 3404 9403 6 55 2742 9617 2910 9567 3076 9515 3242 9460 3407 9402 5 56 2745 9616 2913 9566 3079 9514 3245 9459 3409 9401 4 57 2748 9615 2915 9566 30S2 9513 3247 9458 3412 9400 3 58 2751 9614 2918 9565 3085 9512 3250 9457 3415 9399 2 59 2754 9613 2921 9564 3087 9511 3253 9456 3417 9398 1 60 2756 9613 2924 9563 3090 9511 3256 9455 3420 9397 cos sin cos sin cos sin cos sin cos sin t 74° 73° 72° 71° 70° t 56 NATURAL SINES AND COSINES. / 20° 21° 22° 23° 24° r sin cos sin cos sin cos sin cos sin cos o 3420 9397 3584 9336 3746 9272 3907 9205 4067 9135 60 1 3423 9396 3586 9335 3749 9271 3910 9204 4070 9134 59 2 3426 9395 3589 9334 3751 9270 3913 9203 4073 9133 58 3 3428 9394 3592 9333 3754 9269 3915 9202 4075 9132 57 - 4 3431 9393 3595 9332 3757 9267 3918 9200 4078 9131 56 5 3434 9392 3597 9331 3760 9266 3921 9199 4081 9130 55 6 3437 9391 3600 9330 3762 9265 3923 9198 4083 9128 54 7 3439 9390 3603 9328 3765 9264 3926 9197 4086 9127 53 8 3442 9389 3605 9327 3768 9263 3929 9196 4089 9126 52 9 3445 9388 3608 9326 3770 9262 3931 9195 4091 9125 51 10 3448 9387 3611 9325 3773 9261 3934 9194 4094 9124 50 11 3450 9386 3614 9324 3776 9260 3937 9192 4097 9122 49 12 3453 9385 3616 9323 3778 9259 3939 9191 4099 9121 48 13 3456 9384 3619 9322 3781 9258 3942 9190 4102 9120 47 14 3458 9383 3622 9321 3784 9257 3945 9189 4105 9119 46 15 3461 9382 3624 9320 3786 9255 3947 9188 4107 9118 45 16 3464 9381 3627 9319 3789 9254 3950 '9187 4110 9116 44 17 ' 3467 9380 3630 9318 3792 9253 3953 9186 4112 9115 43 18 3469 9379 3633 9317 3795 9252 3955 9184 4115 9114 42 19 3472 9378 3635 9316 3797 9251 3958 9183 4118 9113 41 20 3475 9377 3638 9315 3800 9250 3961 9182 4120 9112 40 21 3478 9376 3641 9314 3803 9249 3963 9181 4123 9110 39 22 3480 9375 3643 9313 3805 9248 3966 9180 4126 9109 38 23 3483 9374 3646 9312 3808 9247 3969 9179 4128 9108 37 24 3486 9373 3649 9311 3811 9245 3971 9178 4131 9107 36 25 3488 9372 3651 9309 3813 9244 3974 9176 4134 9106 35 26 3491 9371 3654 9308 3816 9243 3977 9175 4136 9104 34 27 3494 9370 3657 9307 3819 9242 3979 9174 4139 9103 33 28 3497 9369 3660 9306 3821 9241 3982 9173 4142 9102 32 29 3499 9368 3662 9305 3824 9240 5985 9172 4144 9101 31 30 3502 9367 3665 9304 3827 9239 ' 3987 9171 4147 9100 30 31 3505 9366 3668 9303 3830 9238 3990 9169 4150 9098 29 32 3508 9365 3670 9302 3832 9237 3993 9168 4152 9097 28 33 3510 9364 3673 9301 3835 9235 3995 9167 4155 9096 27 34 3513 9363 3676 9300 3838 9234 3998 9166 4158 9095 26 35 3516 9362 3679 9299 3840 9233 4001 9165. 4160 9094 25 36 3518 9361 3681 9298 3843 9232 4003 9164 4163 9092 24 37 3521 9360 3684 9297 3846 9231 4006 9162 4165 9091 23 38 3524 9359 3687 9296 3848 9230 4009 9161 4168 9090 ■ 22 39 3527 9358 3689 9295 3851 9229 4011 9160 4171 9088 21 40 3529 9356 3692 9293 3854-9228 4014 9159 4173 9088 20 41 3532 9355 3695 9292 3856 9227 4017 9158 4176 9086 19 42 3535 9354 3697 9291 3859 9225 4019 9157 4179 9085 18 43 3537 9353 3700 9290 3862 9224 4022 9155 4181 9084 17 44 3540 9352 3703 9289 3864 9223 4025 9154 4184 9083 16 45 3543 9351 3706 9288 3867 9222 4027 9153 4187 9081 15 46 3546 9350 3708 9287 3870 9221 4030 9152 4189 9080 14 47 3548 9349 3711 9286. 3872 9220 4033 9151 4192 9079 13 48 3551 9348 3714 9285 3875 9219 4035 9150 4195 9078 12 49 3554 9347 3716 9284 - 3878 9218 4038 9148 4197 9077 11 50 3557 9346 3719 9283 3881 9216 4041 9147 4200 9075 10 51 3559 9345 3722 9282 ■ 3883 9215 4043 9146 4202 9074 9 52 3562 9344 3724 9281 3886 9214 4046 9145 4205 9073 8 53 3565 9343 3727 9279 3889 9213 4049 9144 4208 9072 7 54 3567 9342 3730 9278 "3891 9212 4051 9143 4210 9070 6 55 3570 9341 3733 9277 3894 9211 4054 9141 4213 9069 5 56 3573 9340 3735 9276 3S97 9210 4057 9140 4216 9068 4 57 3576 9339 3738 9275 3S99 9208 4059 9139 4218 9067 3 58 3578 9338 3741 9274 3902 9207 4062 9138 4221 9066 2 59 3581 9337 3743 9273 3905 9206 4065 9137 4224 9064 1 60 3584 9336 3746 9272 3907 9205 4067 9135 4226 9063 cos sin cos sin cos sin cos sin cos sin t 69° 68° 67° 66° 65° ; NATURAL SINES AND COSINES. 57 t 25° 26° sin cos 2 1° 28° 29° t sin cos sin cos sin cos sin cos 4226 9063 4384 S98S 4540 8910 4695 8S29 4848 8746 60 1 4229 9062 4386 S987 4542 8909 4697 8828 4851 8745 59 2 4231 9061 4389 S9S5 4545 8907 4700 8827 4853 8743 58 3 4234 9059 4392 89S4 4548 8906 4702 8825 4856 8742 57 4 4237 9058 4394 8983 4550 8905 4705 8824 4858 8741 56 5 4239 9057 4397 S9S2 4553 8903 470S 8823 4861 8739 55 6 4242 9056 4399 8980 4555 8902 4710 8821 4863 873S 54 7 4245 9054 4402 8979 4558 8901 4713 8820 4866 8736 53 8 4247 9053 4405 897S 4561 8899 4715 8819 486S 8735 52 9 -4250 9052 4407 8976 4563 8S98 4718 8817 4871 8733 51 10 4253 9051 4410 8975 4566 8897 4720 8816 4874 8732 50 11 4255 9050 4412 8974 4568 8895 4723 8814 4876 8731 49 12 425S 9048 4415 8973 4571 8894 4726 8813 4879 8729 48 13 4260 9047 4418 8971 4574 SS93 4728 8812 4881 8728 47 14 4263 9046 4420 8970 4576 8892 4731 8810 4884 8726 46 15 4266 9045 4423 8969 4579 8890 4733 8809 4886 8725 45 16 4268 9043 4425 S967 45S1 8889 4736 8808 4889 8724 44 17 4271 9042 4428 8966 4584 888S 4738 8806 4891 8722 43 18 4274 9041 4431 8965 4586 8SS6 4741 8805 4894 8721 42 19 4276 9040 4433 8964 4589 8885 4743 8803 4896 8719 41 20 4279 9038 4436 8962 4592 8884 4746 8802 4899 8718 40 21 42S1 9037 4439 8961 4594 S882 4749 8801 4901 8716 39 22 4284 9036 4441 8960 4597 8881 4751 8799 4904 8715 38 23 4287 9035 4444 8958 4599 8879 4754 8798 4907 8714 37 24 4289 9033 4446 8957 4602 8878 4756 8796 4909 8712 36 25 4292 9032 4449 8956 4605 8877 4759 8795 4912 8711 35 26 4295 9031 4452 8955 4607 8875 4761 8794 4914 8709 34 27 4297 9030 4454 8953 4610 8874 4764 8792 4917 8708 33 • 28 - 4300 9028 4457 8952 4612 8873 4766 8791 4919 8706 32 29 4302 9027 4459 8951 4615 8871 4769 8790 4922 8705 31 30 4305 9026 4462 8949 4617 8870 4772 8788 4924 8704 30 31 430S 9025 4465 8948 4620 8869 4774 8787 4927 8702 29 32 4310 9023 4467 8947 4623 8867 4777 8785 4929 8701 28 33 4313 9022 4470 8945 4625 8866 4779 8784 4932 8699 27 34 4316 9021 4472 8944 4628 8865 4782 8783 4934 8698 26 35 4318 9020 4475 8943 4630 8863 4784 8781 4937 8696 25 36 '4321 9018 4478 8942 4633 8862 4787 8780 4939 8695 24 37 4323 9017 4480 8940 4636 8861 4789 8778 4942 8694 23 38 4326 9016 4483 8939 4638 8859 4792 8777 4944 8692 22 39 4329 9015 4485 8938 4641 8858 4795 8776 4947 8691 21 40 4331 9013 4488 8936 4643 SS57 4797 8774 4950 8689 20 41 4334 9012 4491 8935 4646 8855 4800 8773 4952 8688 19 42 4337 9011 4493 8934 4648 8854 4802 8771 4955 8686 IS 43 4339 9010 4496 8932 4651 8853 4805 8770 4957 8685 17 44 4342 9008 4498 8931 4654 8851 4807 8769 4960 8683 16 45 4344 9007 4501 8930 4656 8850 4810 8767 4962 8682 15 46 4347 9006 4504 8928 4659 8849 4812 8766 4965 8681 14 47 4350 9004 4506 8927 4661 8847 4815 S764 4967 8679 13 48 4352 9003 4509 8926 4664 8846 4818 8763 4970 8678 12 49 4355 9002 4511 8925 4666 8844 4820 8762 4972 8676 11 50 4358 9001 4514 8923 4669 8843 4823 S760 4975 8675 10 51 4360 8999 4517 8922 4672 8S42 4825 8759 4977 8673 9 52 4363 8998 4519 8921 4674 8840 482S 8757 4980 8672 8 53 4365 8997 4522 8919 4677 8839 4830 8756 4982 8670 7 54 4368 8996 4524 8918 4679 8838 4833 8755 4985 8669 6 55 4371 8994 4527 8917 4682 8836 4835 8753 4987 8668 5 56 4373 8993 4530 8915 4684 SS35 4838 8752 4990 8666 4 57 4376 8992 4532 8914 46S7 8834 4840 8750 4992 8665 3 5S 4378 8990 4535 8913 4690 8832 4843 8749 4995 8663 2 59 4381 8989 4537 8911 4692 S831 4846 8748 4997 8662 1 60 4384 S9S8 4540 8910 4695 8829 4848 8746 5000 8660 O cos sin cos sin cos sin cos sin cos sin r 64° 63° 6: 2° 61° 60° t 58 NATURAL SINES AND COSINES. / 30° 31° 32° 33° sin cos 34° t sin cos sin cos sin cos sin cos 5000 8660 5150 8572 5299 8480 5446 8387 5592 8290 60 1 5003 8659 5153 8570 5302 8479 5449 8385 5594 8289 59 2 5005 8657 5155 8569 5304 8477 5451 8384 5597 8287 58 3 5008 8656 5158 8567 5307 8476 5454 8382 5599 8285 57 ■ 4 5010 8654 5160 8566 5309 S474 5456 83S0 5602 8284 56 5 5013 8653 5163 8564 5312 8473 5459 8379 5604 82S2 55 6 5015 8652 5165 S563 5314 8471 5461 8377 5606 8281 54 7 5018 8650 5168 S561 5316 8470 5463 8376 5609 8279 53 8 5020 8649 5170 8560 5319 8468 5466 8374 5611 8277 52 9 5023 8647 5173 8558 5321 8467 5468 8372 5614 8276 51 10 5025 8646 5175 8557 5324 8465 5471 8371 5616 8274 50 11 5028 8644 5178 8555 5326 8463 5473 8369 5618 8272 49 12 5030 8643 5180 8554 5329 8462 5476 8368 5621 8271 48 13 5033 8641 5183 8552 5331 8460 5478 8366 5623 8269 47 14 5035 8640 5185 8551 5334 8459 5480 8364 5626 8268 46 15 5038 8638 5188 8549 5336 8457 5483 8363 5628 8266 45 16 5040 8637 5190 8548 5339 8456 5485 '8361 5630 8264 44 17 5043 8635 5193 8546 5341 8454 5488 8360 5633 8263 43 18 5045 8634 5195 8545 5344 8453 5490 8358 5635 8261 42 19 5048 8632 5198 8543 5346 8451 5493 8356 5638 8259 41 20 5050 8631 5200 8542 5348 8450 5495 8355 5640 8258 40 21 5053 8630 5203 8540 5351 8448 5498 8353 5642 8256 39 22 5055 8628 5205 8539 5353 8446 5500 8352 5645 8254 38 23 5058 8627 5208 8537 5356 8445 5502 8350 5647 8253 37 24 5060 8625 5210 8536 5358 8443 5505 8348 5650 8251 36 25 5063 8624 5213 8534 5361 8442 5507 8347 5652 8249 35 26 5065 8622 5215 8532 5363 8440 5510 8345 5654 8248 34 27 5068 8621 5218 8531 5366 8439 5512 8344 5657 8246 33 28 5070 8619 5220 8529 5368 8437 5515 8342 5659 8245 32. 29 5073 861 S 5223 8528 5371 8435 4517 8340 5662 8243 31 30 5075 8616 5225 8526 5373 8434 '5519 8339 5664 8241 30 31 5078 8615 5227 8525 5375 8432 5522 8337 5666 8240 29 32 5080 8613 5230 8523 5378 8431 5524 8336 5669 8238 28 33 5083 8612 5232 8522 5380 8429 5527 8334 5671 8236 27 34 5085 8610 5235 8520 5383 8428 5529 8332 5674 8235 26 35 5088 8609 5237 8519 5385 8426 5531 8331 5676 8233 25 36 5090 8607 5240 8517 5388 8425 5534 8329 5678 8231 24 37 5093 8606 5242 8516 5390 8423 5536 8328 5681 8230 23 38 5095 8604 5245 8514 5393 8421 5539 8326 5683 8228 ■ 22 39 509S 8603 5247 8513 5395 8420 5541 8324 5686 8226 21 40 5100 8601 5250 8511 5398 -8418 5544 8323 5688 8225 20 41 5103 8600 5252 8510 5400 8417 5546 8321 5690 8223 19 42 5105 8599 5255 8508 5402 8415 5548 8320 5693 8221 IS 43 5108 8597 5257 8507 5405 8414 5551 8318 5695 8220 17 44 5110 8596 5260 8505 5407 8412 5553 8316 5698 8218 16 45 5113 8594 5262 8504 5410 8410 5556 S315 5700 8216 15 46 5115 8593 5265 8502 5412 S409 5558 8313 5702 S215 14 47 5118 8591 5267 8500 5415. 8407 5561 8311 5705 8213 13 48 5120 8590 5270 8499 5417 8406 5563 8310 5707 8211 12 49 5123 8588 5272 8497 - 5420 8404 5565 8308 5710 8210 11 50 5125 8587 5275 8496 5422 8403 5568 8307 5712 8208 10 51 5128 8585 5277 8494 5424 8401 5570 8305 5714 8207 9 52 5130 8584 5279 8493 5427 8399 5573 S303 5717 8205 8 53 5133 8582 5282 8491 5429 839S 5575 8302 5719 8203 7 54 5135 8581 5284 8490 -5432 S396 5577 8300 5721 8202 6 55 5138 8579 5287 8488 5434 8395 5580 8299 5724 8200 5 56 5140 8578 52S9 8487 5437 8393 5582 S297 5726 8198 4 57 5143 8576 5292 8485 5439 8391 5585 8295 5729 8197 3 58 5145 8575 5294 8484 5442 8390 5587 8294 5731 8195 2 59 514S 8573 5297 S482 5444 8388 5590 8292 5733 8193 1 60 5150 8572 5299 8480 5446 8387 5592 8290 5736 8192 cos sin cos sin cos sin cos sin cos sin r 59° 58° 57° 56° 55° t NATURAL SINES AND COSINES. 59 / 35° 36° 37° 38° 39° t sin cos sin cos sin cos sin cos sin cos 5736 8192 5878 8090 6018 7986 6157 7880 6293 7771 60 1 5738 8190 5880 8088 6020 7985 6159 7878 6295 7770 59 2 5741 8188 5883 8087 6023 7983 6161 7877 6298 7768 58 3 5743 8187 5885 8085 6025 7981 6163 7875 6300 7766 57 4 5745 8185 5887 8083 6027 7979 6166 7873 6302 7764 56 5 5748 8183 5890 8082 6030 7978 6168 7871 6305 7762 55 6 5750 8181 5892 8080 6032 7976 6170 7869 6307 7760 54 7 5752 S180 5894 S07S 6034 7974 6173 7868 6309 7759 53 8 5755 8178 5897 8076 6037 7972 6175 7866 6311 7757 52 9 - 5757 8176 5899 S075 6039 7971 6177 7864 6314 7755 51 10 5760 8175 5901 8073 6041 7969 6180 7862 6316 7753 50 11 5762 8173 5904 8071 6044 7967 6182 7860 6318 7751 49 12 5764 S171 5906 8070 6046 7965 6184 7859 6320 7749 48 13 5767 8170 590S 8068 6048 7964 6186 7857 6323 7748 47 14 5769 8168 5911 8066 6051 7962 6189 7855 6325 7746 46 15 5771 8166 5913 8064 6053 7960 6191 7853 6327 7744 45 16 5774 8165 5915 8063 6055 7958 6193 7851 6329 7742 44 17 5776 8163 5918 8061 6058 7956 6196 7850 6332 7740 43 18 5779 8161 5920 8059 6060 7955 6198 7848 6334 7738 42 19 5781 8160 5922 8058 6062 7953 6200 7346 6336 7737 41 20 5783 8158 5925 8056 6065 7951 6202 7844 6338 7735 40 21 5786 8156 5927 8054 6067 7950 6205 7842 6341 7733 39 22 5788 8155 5930 8052 6069 7948 6207 7841 6343 7731 38 23 5790 8153 5932 8051 6071 7946 6209 7839 6345 7729 37 24 5793 8151 5934 8049 6074 7944 6211 7837 6347 7727 36 25 5795 8150 5937 8047 6076 7942 6214 7835 6350 7725 35 26 5798 8148 5939 8045 6078 7941 6216 7833 6352 7724 34 27 5800 8146 5941 8044 60S1 7939 6218 7832 6354 7722 33 28 - 5802 8145 5944 8042 6083 7937 6221 7830 6356 7720 32 29 5805 8143 5946 8040 6085 7935 6223 7828 6359 7718 31 30 5807 8141 5948 8039 6088 7934 6225 7826 6361 7716 30 31 5809 8139 5951 8037 6090 7932 6227 7824 6363 7714 29 32 5812 8138 5953 8035 6092 7930 6230 7822 6365 7713 28 33 5814 8136 5955 8033 6095 7928 6232 7821 6368 7711 27 34 5816 8134 5958 8032 6097 7926 6234 7819 6370 7709 26 35 5819 8133 5960 8030 6099 7925 6237 7817 6372 7707 25 36 '5821 8131 5962 8028 6101 7923 6239 7815 6374 7705 24 37 5824 8129 5965 8026 6104 7921 6241 7813 9376 7703 23 38 5826 8128 5967 8025 6106 7919 6243 7812 6379 7701 22 39 5828 8126 5969 8023 6108 7918 6246 7810 6381 7700 21 40 5831 8124 5972 8021 6111 7916 6248 7808 6383 7698 20 41 5833 8123 5974 8020 6113 7914 6250 7806 6385 7696 19 42 5835 8121 5976 8018 6115 7912 6252 7804 6388 7694 IS 43 5838 8119 5979 8016 6118 7910 6255 7802 6390 7692 17 44 5840 8117 5981 8014 6120 7909 6257 7801 6392 7690 16 45 5842 8116 5983 8013 6122 7907 6259 7799 6394 7688 15 46 5845 8114 5986 8011 6124 7905 6262 7797 6397 7687 14 47 5847 8112 5988 8009 6127 7903 6264 7795 6399 7685 13 48 5850 8111 5990 8007 6129 7902 6266 7793 6401 7683 12 49 5852 8109 5993 8006 6131 7900 6268 7792 6403 7681 11 50 5854 8107 5995 8004 6134 7898 6271 7790 6406 7679 10 51 5857 8106 5997 8002 6136 7896 6273 7788 6408 7677 9 52 5859 8104 6000 8000 6138 7894 6275 7786 6410 7675 8 53 5861 8102 6002 7999 6141 7893 6277 7784 6412 7674 7 54 5864 8100 6004 7997 6143 7891 6280 7782 6414 7672 6 55 5866 8099 6007 7995 6145 7889 6282 7781 6417 7670 5 56 5S68 8097 6009 7993 6147 7887 6284 7779 6419 7668 4 57 5871 8095 6011 7992 6150 7885 6286 7777 6421 7666 3 58 5873 8094 6014 7990 6152 7884 6289 7775 6423 7664 2 59 5875 8092 6016 7988 6154 7882 6291 7773 6426 7662 1 60 5878 8090 6018 7986 6157 7880 6293 7771 6428 7660 cos sin cos sin cos sin cos sin cos sin t 54° 53° 52° 51° 50° r 60 NATURAL SINES AND COSINES. / 40° 41° 42° 43° 44° t sin cos sin cos sin cos sin cos sin cos. 6428 7660 6561 7547 6691 7431 6820 7314 6947 7193 60 1 6430 7659 6563 7545 6693 7430 6822 7312 6949 7191 59 2 6432 7657 6565 7543 6696 7428 6824 7310 6951 7189 58 3 6435 7655 6567 7541 6698 7426 6826 7308 6953 7187 57 • 4 6437 7653 6569 7539 6700 7424 6828 7306 6955 7185 56 5 6439 7651 6572 7538 6702 7422 6831 7304 6957 7183 55 6 6441 7649 6574 7536 6704 7420 6833 7302 6959 7181 54 7 6443 7647 6576 7534 6706 7418 6835 7300 6961 7179 53 8 6446 7645 6578 7532 6709 7416 6837 7298 6963 7177 52 9 6448 7644 6580 7530 6711 7414 6839 7296 6965 7175 51 10 6450 7642 6583 7528 6713 7412 6841 7294 6967 7173 50 11 6452 7640 6585 7526 6715 7410 6843 7292 6970 7171 49 12 6455 7638 6587 7524 6717 7408 6845 7290 6972 7169 48 13 6457 7636 6589 7522 6719 7406 6848 7288 6974 7167 47 14 6459 7634 6591 7520 6722 7404 6850 7286 6976 7165 46 15 6461 7632 6593 7518 6724 7402 6852 7284 6978 7163 45 16 6463 7630 6596 7516 6726 7400 6854 ■7282 6980 7161 44 17 6466 7629 6598 7515 6728 7398 6856 7280 6982 7159 43 18 6468 7627 6600 7513 6730 7396 6858 7278 6984 7157 42 19 6470 7625 6602 7511 6732 7394 6860 7276 6986 7155 41 20 6472 7623 6604 7509 6734 7392 6862 7274 6988 7153 40 21 6475 7621 6607 7507 6737 7390 6865 7272 6990 7151 39 22 6477 7619 6609 7505 6739 7388 6867 7270 6992 7149 38 23 6479 7617 6611 7503 6741 7387 6869 7268 6995 7147 37 24 6481 7615 6613 7501 6743 7385 6871 7266 6997 7145 36 25 6483 7613 6615 7499 6745 7383 6873 7264 6999 7143 35 26 6486 7612 6617 7497 6747 7381 6875 7262 7001 7141 34 27 6488 7610 6620 7495 6749 7379 6877 7260 7003 7139 33 28 6490 760S 6622 7493 6752 7377 6879 7258 7005 7137 31 29 6492 7606 6624 7491 6754 7375 £831 7256 7007 7135 31 30 6494 7604 6626 7490 6756 7373 •68S4 7254 7009 7133 30 31 6497 7602 6628 7488 6758 7371 6886 72'52 7011 7130 29 32 6499 7600 6631 7486 6760 7369 6888 7250 7013 7128 28 33 6501 7598 6633 7484 6762 7367 6890 7248 7015 7126 27 34 6503 7596 6635 7482 6764 7365 6892 7246 7017 7124 26 35 6506 7595 6637 7480 6767 7363 6894 7244 7019 7122 25 36 6508 7593 6639 7478 6769 7361 6896 7242 7022 7120 24 37 6510 7591 6641 7476 6771 7359 6898 7240 7024 7118 23 38 6512 7589 6644 7474 6773 7357 6900 7238 7026 7116 22 39 6514 7587 6646 7472 6775 7355 6903 7236 7028 7114 21 40 6517 7585 6648 7470 6777 7253 6905 7234 7030 7112 20 41 6519 7583 6650 7468 6779 7351 6907 7232 7032 7110 19 42 6521 7581 6652 7466 6782 7349 6909 7230 7034 7108 IS 43 6523 7579 6654 7464 6784 7347 6911 7228 7036 7106 17 44 6525 7578 6657 7463 6786 7345 6913 7226 7038 7104 16 45 6528 7576 6659 7461 6788 7343 6915 7224 7040 7102 15 46 6530 7574 6661 7459 6790 7341 6917 7222 7042 7100 14 47 6532 7572 6663 7457 6792 7339 6919 7220 7044 7098 13 48 6534 7570 6665 7455 ■ 6794 7337 6921 7218 7046 7096 12 49 6536 7568 6667 7453 6797 7335 6924 7216 7048 7094 11 50 6539 7566 6670 7451 6799 7333 6926 7214 7050 7092 10 51 6541 7564 6672 7449 6S01 7331 6928 7212 7053 7090 9 52 6543 7562 6674 7447 6803 7329 6930 7210 7055 7088 8 53 6545 7560 6676 7445 6805 7327 6932 7208 7057 7085 7 54 6547 7559 6678 7443 -6807 7325 6934 7206 7059 7083 6 55 6550 7557 6680 7441 6809 7323 6936 7203 7061 7081 5 56 6552 7555 6683 7439 6811 7321 693S 7201 7063 7079 4 57 6554 7553 6685 7437 6814 7319 6940 7199 7065 7077 3 58 6556 7551 6687 7435 6816 7318 6942 7197 7067 7075 2 59 6558 7549 6689 7433 6818 7316 6944 7195 7069 7073 1 60 6561 7547 6691 7431 6820 7314 6947 7193 7071 7071 O cos sin cos sin cos sin cos sin cos sin t 49° 48° 47° 46° 45° r NATUKAL TANGENTS AND COTANGENTS. 61 t 0° 1° 2° 3° 4° r tan cot tan cot tan cot tan cot tan cot 0000 Infinite 0175 57.2900 0349 28.6363 0524 19.0811 0699 14.3007 60 1 0003 3437.75 0177 56.3506 0352 28.3994 0527 18.9755 0702 14.2411 59 2 0006 1718.87 0180 55.4415 0355 28.1664 0530 IS 8711 0705 14.1821 58 3 0009 1145.92 0183 54.5613 0358 27.9372 0533 18.7678 0708 14.1235 57 4 0012 859.436 0186 53.7086 0361 27.7117 0536 186656 0711 140655 56 5 0015 687.549 0189 52.8821 0364 27.4S99 0539 18.5645 0714 140079 55 6 0017 572.957 0192 52.0807 0367 27.2715 0542 1S.4645 0717 13.9507 54 7 0020 491.106 0195 51.3032 0370 27.0566 0544 18.3655 0720 13.8940 53 8 0023 429.718 0198 50.5485 0373 26.8450 0547 18.2677 0723 13 8378 52 9 0026 3S1.971 0201 49.8157 0375 26.6367 0550 18.1708 0726 13.7S21 51 10 0029 343.774 0204 49.1039 03 7S 26.4316 0553 18.0750 0729 13.7267 50 11 0032 312521 0207 48.4121 0381 26.2296 0556 179S02 0731 13.6719 49 12 0035 286.478 0209 47.7395 0384 26.0307 0559 17.8863 0734 13.6174 48 13 0038 264.441 0212 47.0S53 0387 25.S348 0562 17.7934 0737 13.5634 47 14 0041 245.552 0215 46.4489 0390 25.6418 0565 17.7015 0740 13.5098 46 15 0044 229.1S2 0218 45.8294 0393 25.4517 056S 17.6106 0743 13.4566 45 16 0047 214.858 0221 45.2261 0396 25.2644 0571 17.5205 0746 13.4039 44 17 0049 202.219 0224 44.6386 0399 25.0798 0574 17.4314 0749 13.3515 43 IS 0052 190.984 0227 44.0661 0402 24.8978 0577 17.3432 0752 13.2996 42 19 0055 180.932 0230 43.5081 0405 24.7185 0580 17.2558 0755 13.2480 41 20 0058 171.885 0233 42.9641 0407 24.5418 0582 17.1693 075S 13.1969 40 21 OOol 163.700 0236 42.4335 0410 24.3675 0585 17.0837 0761 13.1461 39 22 0064 156.259 0239 41.9158 0413 24.1957 05 88 16.9990 0764 13.0958 38 23 0067 149.465 0241 41.4106 0416 24.0263 0591 169150 0767 13.0458 37 24 0070 143.237 0244 40.9174 0419 23.8593 0594 16.8319 0769 12.9962 36 25 0073 137507 0247 40.435S 0422 23.6945 0597 16.7496 0772 12.9469 35 26 0076 132.219 0250 39.9655 0425 23.5321 0600 16.6681 0775 12.8981 34 27 0079 127.321 0253 395059 0428 23.3718 0603 16.5874 0778 12.8496 33 28 0081 122.774 0256 390568 0431 23.2137 0606 16.5075 0781 12.8014 32 29 0084 118.540 0259 38.6177 0434 23.0577 0609 16.4283 0784 12.7536 31 30 0087 114.589 0262 38.1885 0437 22.903S 0612 16 3499 0787 12.7062 30 31 0090 110.892 0265 37.7686 0440 22.7519 0615 16.2722 0790 12.6591 29 32 0093 107.426 0268 37.3579 0442 22.6020 0617 16.1952 0793 12.6124 28 33 0096 104.171 0271 36.9560 0445 224541 0620 16.1190 0796 12.5660 27 34 0099 101.107 0274 36.5627 0448 22.30S1 0623 16.0435 0799 12.5199 26 35 0102 9S.2179 0276 36 1776 0451 22.1640 0626 15.9687 0802 12.4742 25 36 0105 95.4895 0279 35 8006 0454 22.0217 "0629 15.8945 0805 12.4288 24 37 0108 92.9085 0282 35.4313 0457 21.8813 0632 15.8211 0808 12.3838 23 38 0111 90.4633 0285 35.0695 0460 21.7426 0635 15.7483 0810 12.3390 22 39 0113 8S.1436 02SS 34.7151 0463 21.6056 063S 15.6762 0813 12.2946 21 40 0116 85.939S 0291 34.3678 0466 21.4704 0641 15.6048 0816 12.2505 20 41 0119 83.8435 0294 34.0273 0469 21.3369 0644 15.5340 0819 12.2067 19 42 0122 81.8470 0297 33.6935 0472 21.2049 0647 15.4638 0822 12.1632 18 43 0125 79 9434 0300 33.3662 0475 21.0747 0650 15.3943 0S25 12.1201 17 44 0128 78.1263 0303 33.0452 0477 20.9460 0653 15.3254 0828 12.0772 16 45 0131 76.3900 0306 32.7303 0480 20.8188 0655 15.2571 0S31 12.0346 15 46 0134 74.7292 0308 32.4213 0483 20.6932 0658 15.1893 0834 11.9923 14 47 0137 73.1390 0311 32.1181 0486 20.5691 0661 15.1222 0837 11.9504 13 48 0140 71.6151 0314 31.8205 0489 20.4465 0664 15.0557 0840 11.9087 12 49 0143 70.1533 0317 31.5284 0492 20.3253 0667 14.9898 0843 11.8673 11 50 0146 6S.7501 0320 31.2416 0495 20.2056 0670 14.9244 0846 11.8262 10 51 0148 67.4019 0323 30.9599 0498 20.0S72 0673 14.8596 0S49 11.7853 9 52 0151 66.1055 0326 30.6833 0501 19.9702 0676 14.7954 0851 11.7448 8 53 0154 64.85S0 0329 30 4116 0504 19.8546 0679 14.7317 OS54 11.7045 7 54 0157 63.6567 0332 301446 0507 19.7403 0682 14.6685 0857 11.6645 6 55 0160 62.4992 0335 29.8823 0509 19.6273 0685 14.6059 0860 11.6248 5 56 0163 61.3829 0338 29.6245 0512 19.5156 0688 14.5438 0863 11.5853 4 57 0166 60.3058 0340 29.3711 0515 19.4051 0690 14.4823 0866 11.5461 3 58 0169 59.2659 0343 29.1220 0518 19.2959 0693 14.4212 0869 11.5072 2 59 0172 5S.2612 0346 28 8771 0521 19.1879 0696 14.3607 0S72 114685 1 60 0175 57.2900 0349 28.6363 0524 19.0811 0699 14.3007 0875 11.4301 r cot tan 89° cot tan 88° cot tan 87° cot tan 86° cot tan 85° i 62 NATURAL TANGENTS AND COTANGENTS. t 5° 6° 7° 8° 9° t tan cot tan cot tan cot tan cot tan cot o 0875 11.4301 1051 9.5144 1228 8.1443 1405 7.1154 1584 6.3138 60 1 0S78 11.3919 1054 9.4878 1231 8.1248 1408 7.1004 1587 6.3019 59 2 0SS1 11.3540 1057 9.4614 1234 S.1054 1411 7.0855 1590 6.2901 58 3 0SS4 11.3163 1060 9.4352 1237 8.0S60 1414 7.0706 1593 6.2783 57 •4 0887 11.2789 1063 9.4090 1240 8.0667 1417 7.0558 1596 6.2666 56 5 0890 11.2417 1066 9.3831 1243 8.0476 1420 7.0410 1599 6.2549 55 6 0S92 11.2048 1069 9.3572 1246 8.0285 1423 7.0264 1602 6.2432 54 7 0895 11.1681 10.72 9.3315 1249 8.0095 1426 7.0117 1605 6.2316 53 8 0898 11.1316 1075 9.3060 1251 7.9906 1429 6.9972 1608 6.2200 52 9 0901 11.0954 1078 9.2806 1254 7.9718 1432 6.9827 1611 6.2085 51 10 0904 11.0594 1080 9.2553 1257 7.9530 1435 6.9682 1614 6.1970 50 11 0907 11.0237 1083 9.2302 1260 7.9344 1438 6.9538 1617 6.1856 49 12 0910 10.9882 10S6 9.2052 1263 7.9158 1441 6.9395 1620 6.1742 48 13 0913 10.9529 1089 9.1803 1266 7.8973 1444 6.9252 1623 6.1628 47 14 0916 10.9178 1092 9.1555 1269 7.8789 1447 6.9110 1626 6.1515 46 15 0919 10.8829 1095 9.1309 1272 7.8606 1450 6.8969 1629 6.1402 45 16 0922 10.8483 1098 9.1065 1275 7.8424 1453 6.8828 1632 6.1290 44 17 0925 10.8139 1101 9.0821 1278 7.8243 1456 6.8687 1635 6.1178 43 18 0928 10.7797 1104 9.0579 1281 7.8062 1459 6.8548 1638 6.1066 42 19 0931 10.7457 1107 9.0338 1284 7.7883 1462 6.8408 1641 6.0955 41 20 0934 10.7119 1110 9.0098 1287 7.7704 1465 6.8269 1644 6.0844 40 21 0936 10.6783 1113 8.9860 1290 7.7525 1468 6.8131 1647 6.0734 39 22 0939 10.6450 1116 8.9623 1293 7.7348 1471 67994 1650 6.0624 38 23 0942 10.6118 1119 8.9387 1296 7.7171 1474 6.7S56 1653 6.0514 37 24 0945 10.5789 1122 S.9152 1299 7.6996 1477 6.7720 1655 6.0405 36 25 0948 10.5462 1125 8 8919 1302 7.6821 1480 6.7584 1658 6.0296 35 26 0951 105136 1128 8.8686 1305 7.6647 1483 6.7448 1661 6.0188 34 27 0954 10.4813 1131 8 8455 1308 7.6473 1486 6.7313 1664 6.0080 33 28 0957 10.4491 1134 8.8225 1311 7.6301 1489 6.7179 1667 5.9972 32 29 0960 10.4172 1136 8.7996 1314 7.6129 1,492 6.7045 1670 5.9865 31 30 0963 10.3854 1139 8.7769 1317 7.5958 1495 6.6912 1673 5.9758 30 31 0966 10.3538 1142 8.7542 1319 7.5787 1497 6.6779 1676 5.9651 29 32 0969 10.3224 1145 8.7317 1322 7.5618 1500 6.6646 1679 5.9545 28 33 0972 10.2913 1148 8.7093 1325 7.5449 1503 6.6514 1682 5.9439 27 34 0975 10.2602 1151 8.6870 1328 7.5281 1506 6.6383 1685 5.9333 26 35 0978 10.2294 1154 8 6648 1331 7.5113 1509 6.6252 1688 5.9228 25 36 0981 10.1988 1157 8.6427* 1334 7.4947 1512 6.6122 1691 5.9124 24 37 0983 10.1683 1160 8.6208 1337 7.4781 1515 6.5992 1694 5.9019 23 38 0986 10.1381 1163 8.5989 1340 7.4615 1518 6.5863 1697 5.8915 22 39 0989 10.1080 1166 8.5772 1343 7.4451 1521 6.5734 1700 5.8811 21 40 0992 10.07S0 1169 8.5555 1346 7.4287 1524 6.5606 1703 5.8708 20 41 0995 10.0483 . 1172 8.5340 1349 7.4124 1527 6.5478 1706 5.8605 19 42 0998 10.0187 1175 8.5126 1352 7.3962 1530 6.5350 1709 5.8502 18 43 1001 9.9893 1178 8.4913 1355 7.3800 1533 6.5223 1712 5.8400 17 44 1004 9.9601 1181 8.4701 135S 7.3639 1536 6.5097 1715 5.8298 16 45 1007 9.9310 1184 8.4490 1361 7.3479 1539 6.4971 1718 5.8197 15 46 1010 9.9021 1187 8.4280 1364 7.3319 1542 6.4846 1721 5.8095 14 47 1013 9.8734 1189 8.4071 1367 7.3160 1545 6.4721 1724 5.7994 13 48 1016 9.8448 1192 8.3863' 1370 7.3002 1548 6.4596 1727 5.7894 12 49 1019 9.8164 1195 8.3656 .1373 7.2844 1551 6.4472 1730 5.7794 11 50 1022 9.7882 1198 8.3450 1376 7.2687 1554 6.4348 1733 5.7694 10 51 1025 9.7601 1201 8.3245 1379 7.2531 1557 6.4225 1736 5.7594 9 52 1028 9.7322 1204 8.3041 . 1382 7.2375 1560 6.4103 1739 5.7495 8 53 1030 9.7044 1207 8.2S3S 1385 7.2220 1563 6.3980 1742 5.7396 7 54 1033 9.6768 1210 8.2636 .1388 7.2066 1566 6.3SS9 1745 5.7297 6 55 1036 9.6499 1213 8.2434 1391 7.1912 1569 6.3737 1748 5.7199 5 56 1039 9 6220 1216 8.2234 1394 7.1759 1572 6.3617 1751 5.7101 4 57 1042 9.5949 1219 8.2035 1397 7.1607 1575 6.3496 1754 5.7004 3 5S 1045 9.5679 1222 8.1837 1399 7.1455 1578 6.3376 1757 5.6906 2 59 1048 9.5411 1225 8.1640 1402 7.1304 1581 6.3257 1760 5.6809 1 60 1051 9.5144 1228 8.1443 1405 7.1154 1584 6.3138 1763 5.6713 r cot tan 84° cot tan 83° cot tan 82° cot tan 81° cot tan 80° t NATURAL TANGENTS AND COTANGENTS. 63 r 10° 11° 12° 13° 14° t tan cot tan cot tan cot tan cot tan cot 1763 5.6713 1944 5.1446 2126 4.7046 2309 4.3315 2493 4.0108 60 1 1766 5.6617 1947 5.1366 2129 4.6979 2312 4.3257 2496 4.0058 59 2 1769 5.6521 1950 5.1286 2132 4.6912 2315 4.3200 2499 4.0009 58 3 1772 5.6425 1953 5.1207 2135 4.6845 2318 4.3143 2503 3.9959 57 4 1775 5.6330 1956 5.1128 2138 4.6779 2321 4.3086 2506 3.9910 56 5 177S 5.6234 1959 5.1049 2141 4.6712 2324 4.3029 2509 3.9861 55 6 17S1 5.6140 1962 5.0970 2144 4.6646 2327 4.2972 2512 3.9812 54 7 17S4 5.6045 1965 5.0892 2147 4.6580 2330 4.2916 2515 3.9763 53 S 17S7 5.5951 1968 5.0814 2150 4.6514 2333 4.2859 2518 39714 52 9 1790 5.5857 1971 5.0736 2153 4.6448 2336 4.2803 2521 3.9665 51 10 1793 5.5764 1974 5.065S 2156 4.6382 2339 4.2747 2524 3.9617 50 11 1796 5.5671 1977 5.0581 2159 4.6317 2342 4.2691 2527 3.9568 49 12 1799 5.5578 19S0 5.0504 2162 4.6252 2345 4.2635 2530 3.9520 48 13 1802 5.5485 1983 5 0427 2165 4.6187 2349 4.2580 2533 3.9471 47 14 1805 5.5393 19S6 5.0350 2168 4.6122 2352 4.2524 2537 3.9423 46 15 1808 5.5301 1989 5.0273 2171 4.6057 2355 4.2468 2540 3.9375 45 16 1811 5.5209 1992 5.0197 2174 4.5993 2358 4.2413 2543 3.9327 44 17 1814 5.5118 1995 5.0121 2177 4.5928 2361 4.2358 2546 3.9279 43 IS 1817 5.5026 1998 5.0045 2180 4.5864 2364 4.2303 2549 3.9232 42 19 1820 5.4936 2001 4.9969 2183 4.5800 2367 4.2248 2552 3.9184 41 20 1823 5.4S45 2004 4.9894 2186 4.5736 2370 4.2193 2555 3.9136 40 21 1826 5.4755 2007 4.9819 2189 4.5673 2373 4.2139 2558 3.9089 39 22 1S29 5.4665 2010 4.9744 2193 4.5609 2376 4.2084 2561 3.9042 38 23 1832 5.4575 2013 4.9669 2196 4.5546 2379 4.2030 2564 3.8995 37 24 1835 5.4486 2016 4.9594 2199 4.5483 23S2 4.1976 2568 3.8947 36 25 1838 5.4397 2019 4.9520 2202 4.5420 2385 4.1922 2571 3.8900 35 26 1841 5. 4308 2022 4.9446 2205 4.5357 2388 4.1868 2574 3.8854 34 27 1844 5.4219 2025 4.9372 2208 4.5294 2392 4.1814 2577 3.8807 33 28 - 1847 5.4131 2028 4.929S 2211 4.5232 2395 4.1760 2580 3.8760 32 29 1850 5.4043 2031 4.9225 2214 4.5169 2398 4.1706 2583 3.8714 31 30 1853 5.3955 2035 4.9152 2217 4.5107 2401 41653 2586 3.8667 30 31 1856 5.3868 2038 4.9078 2220 4.5045 2404 4.1600 2589 3.8621 29 32 1859 5.3781 2941 4.9006 2223 4.4983 2407 4.1547 2592 3.8575 28 33 1862 5.3694 2044 4.8933 2226 4.4922 2410 4.1493 2595 3.8528 27 34 1865 5.3607 204-7 4.8860 2229 4.4860 2413 4.1441 2599 3.8482 26 35 186S 5.3521 2050 4.S788 2232 4.4799 2416 4.1388 2602 3.8436 25 36 1S71 5.3435 2053 4.8716 2235 4.4737 2419 4.1335 2605 3.8391 24 37 1874 5.3349 2056 4.8644 2238 4.4676 2422 4.1282 2608 3.8345 23 38 1877 5.3263 2059 4.8573 2241 4.4615 2425 4.1230 2611 3.8299 22 39 1880 5.3178 2062 4.8501 2244 4.4555 2428 4.1178 2614 3.8254 21 40 1883 5.3093 2065 4.8430 2247 4.4494 2432 4.1126 2617 38208 20 41 1887 5.3008 2068 4.8359 2251 4.4434 2435 4.1074 2620 3.8163 19 42 1890 5.2924 2071 4.8288 2254 4.4374 2438 4.1022 2623 3.8118 18 43 1893 5.2839 2074 48218 2257 4.4313 2441 4.0970 2627 3.8073 17 44 1896 5.2755 2077 4.8147 2260 4.4253 2444 4.0918 2630 3.8028 16 45 1899 5.2672 20S0 4.8077 2263 4.4194 2447 40867 2633 3.7983 15 46 1902 5.2588 2083 4.8007 2266 4.4134 2450 4.0815 2636 3.7938 14 47 1905 5.2505 2086 4.7937 2269 4.4075 2453 4.0764 2639 3.7893 13 48 1908 5.2422 2089 4.7867 2272 4.4015 2456 4.0713 2642 3.7848 12 49 1911 5.2339 2092 4.7798 2275 4.3956 2459 4.0662 2645 3.7804 11 50 1914 5.2257 2095 4.7729 2278 4.3897 2462 4.0611 2648 3.7760 10 51 1917 5.2174 209S 4.7659 2281 4.3838 2465 4.0560 2651 3.7715 9 52 1920 5.2092' 2101 4.7591 2284 4.3779 2469 4.0509 2655 3.7671 8 53 1923 5.2011 2104 4.7522 2287 4.3721 2472 4.0459 2658 3.7627 7 54 1926 5.1929 2107 4.7453 2290 4.3662 2475 4.0408 2661 3.7583 6 55 1929 5.1848 2110 4.7385 2293 4.3604 2478 4.0358 2664 3.7539 5 56 1932 5 1767 2113 4.7317 2296 4.3546 2481 4.0308 2667 3.7495 4 57 1935 5.1686 2116 4.7249 2299 4.3488 2484 4 0257 2670 3.7451 3 58 1938 5.1606 2119 4.7J81 2303 4.3430 2487 4 0207 2673 3.7408 2 59 1941 5.1526 2123 4.7114 2306 4.3372 2490 4.015S 2676 3.7364 1 60 1944 5.1446 2126 4.7046 2309 4.3315 2493 4.0108 2679 3.7321 t cot tan 79° cot tan 78° cot tan cot tan 76° cot tan 75° 77° / (34 NATURAL TANGENTS AND COTANGENTS. t 15° 16° 17° 18° 19° r tan cot tan cot tan cot tan cot tan cot 2679 3.7321 2S67 3.4S74 3057 3.2709 3249 3.0777 3443 2.9042 60 1 26S3 3.7277 2871 3.4S36 3060 3.2675 32:^2 3.0746 3447 2.9015 59 2 26S6 3.7234 2S74 3.4798 3064 3.2641 3256 30716 3450 2.8987 58 3 26S9 3.7191 2S77 3.4760 3067 3.2607 3259 3.06S6 3453 2.S960 57 '4 2692 3.714S 2SS0 3.4722 3070 3.2573 3262 3.0655 3456 2.S933 56 5 2695 3.7105 2SS3 3.46S4 3073 3.2539 3265 3.0625 3460 2.S905 55 6 269S 3.7062 2SS6 3.4646 3076 3.2506 3269 3 0595 3463 2.8878 54 7 2701 3.7019 2S90 3.460S 30S0 3.2472 3272 3.0565 3466 2.S851 53 S 2704 3.6976 2S93 3.4570 30S3 3.2438 3275 3.0535 3469 2.SS24 52 9 270S 3.6933 2S96 3.4533 30S6 3.2405 327S 3.0505 3473 2.S797 51 10 2711 3.6S91 2S99 3.4495 30S9 3.2371 32S1 3.0475 3476 2.S770 50 11 2714 3.6S4S 2902 3.4458 3092 3.233S 32S5 3 0445 3479 2.8743 49 12 2717 3.6S06 2905 3.4420 3096 3.2305 32SS 3.0415 3482 2.S716 4S 13 2720 3.6764 290S 3.43S3 3099 3.2272 3291 3.03S5 3486 2.S6S9 47 14 2723 3.6722 2912 3.4346 3102 3.223S 3294 3.0356 34S9 2.8662 46 15 2726 3.66S0 2915 3.430S 3105 3.2205 329S 3.0326 3492 2.S636 45 16 2729 3.663S 291S 3.4271 310S 3.2172 3301 3.0296 3495 2.8609 44 17 2733 3.6596 2921 3.4234 3111 3.2139 3304 3.0267 3499 2.S5S2 43 IS 2736 3.6554 2924 3.4197 3115 3.2106 3307 3.0237 3502 2.S556 42 19 2739 3.6512 2927 3.4160 3118 3.2073 3310 3.020S 3505 2.8529 41 20 2742 3.6470 2931 3.4124 3121 3.2041 3314 3.01 7S 3508 2.S502 40 21 2745 3.6429 2934 3.40S7 3124 3.200S 3317 3 0149 3512 2.S476 39 22 274S 3.63S7 2937 3.4050 3127 3.1975 3320 30120 3515 2.S449 3S 23 2751 3.6346 2940 3.4014 3131 3.1943 3323 3.0090 35 IS 2.S423 37 24 2754 3.6305 2943 3.3977 3134 3.1910 3327 3.0061 3522 2.S397 36 25 275S 3.6264 2946 3.3941 3137 3.1S7S 3330 3.0032 3525 2.S370 35 26 2761 3 6222 2949 3.3904 3140 3.1845 3333 3.0003 352S 2.S344 34 27 2764 3.61S1 2953 3.3S6S 3143 3.1813 3336 2.9974 3531 2.S31S 33 2S 2767 3.6140 2956 3.3S32 3147 3.17SO 3339 2.9945 3535 2.8291 32 29 2770 3.6100 2959 3.3796 3150 3.1748 3343 2 9916 3538 2.8265 31 30 2773 3.6059 2962 3.3759 3153 3.1716 3346 2.9SS7 3541 2.S239 30 31 2776 3.601S 2965 3.3723 3156 3.16S4 3349 2.9S5S 3544 2.8213 29 32 27S0 3.597S 296S 3.36S7 3159 3.1652 3352 2.9S29 354S 2.S1S7 2S 33 27S3 3.5937 2972 3.3652 3163 3.1620 3356 2.9S00 3551 2.8161 27 34 27S6 3.5S97 2975 3.3616 3166 3.15SS 3359 2.9772 3554 2.S135 26 35 27S9 3.5S56 2978 3.35S0 3169 3.1556 3362 2.9743 3558 2.8109 25 36 2792 3.5S16 29S1 3.3544 3172 3.1524 3365 2.9714 3561 2.S0S3 24 37 2795 3.5776 29S4 3.3509 3175 3.1492 3369 2.96S6 3564 2.S057 23 3S 2793 3.5736 2987 3.3473 3179 3.1460 3372 2.9657 3567 2.S032 22 39 2S01 3.5696 2991 3.3438 31S2 3.1429 3375 2.9629 3571 2.S006 21 40 2S05 3.5656 2994 3.3402 31S5 3.1397 337S 2.9600 3574 2.79S0 20 41 2S0S 3.5616 2997 3.3367 31SS 3.1366 33S2 2.9572 3577 2.7955 19 42 2S11 3.5576 3000 3.3332 3191 3.1334 33S5 2.9544 35S1 2.7929 IS 43 2814 3.5536 3003 3.3297 3195 3.1303 33SS 2.9515 3584 2.7903 17 44 2S17 3.5497 3006 3.3261 319S 3.1271 3391 2.94S7 35S7 2.7S7S 16 45 2S20 3.5457 3010 3.3226 3201 3.1240 3395 2.9459 3590 2.7S52 15 46 2S23 3.541S 3013 3.3191 3204 3.1209 339S 2.9431 3594 2.7827 14 47 2S27 3.5379 3016 3.3156 3207 3.1178 3401 2.9403 3597 2.7801 13 4S 2S30 3.5339 3019 3.3122 3211 3.1146 3404 2.9375 3600 2.7776 12 49 2S33 3.5300 3022 3.30S7 3214 3.1115 340S 2.9347 3604 2.7751 11 50 2S36 3.5261 3026 3.3052 3217 3.10S4 3411 2.9319 3607 2.7725 10 51 2S39 3.5222 3029 3.3017 3220 3.1053 3414 2.9291 3610 2.7700 9 52 2S42 3.5183 3032 3.29S3 3223 3.1022 3417 2.9263 3613 2.7675 8 53 2845 3.5144 3035 3.294S 3227 3.0991 3421 2.9235 3617 2.7650 7 54 2849 3.5105 303S 3.2914 3230 3.0961 3424 2.920S 3620 2.7625 6 55 2S52 3.5067 3041 3.2SS0 3233 3.0930 3427 2.91S0 3623 2.7600 5 56 2855 3 502S 3045 3.2S45 3236 3.0S99 3430 2.9152 3627 2.7575 4 57 2S5S 3.49S9 304S 3.2S11 3240 3.0S6S 3434 2.9125 3630 2.7550 3 58 2S61 3.4951 3051 3.2777 3243 3.0S3S 3437 2.9097 3633 2.7525 2 59 2S64 3.4912 3054 3.2743 3246 3.0S07 3440 2.9070 3636 2 7500 1 60 2867 3.4S74 3057 3.2709 3249 3.0777 3443 2.9042 3640 2.7475 cot tan cot tan cot tan cot tan cot tan t 7 4° 73° 72° 7 1° 70° t NATURAL TANGENTS AND COTANGENTS. 65 t 20° 21° 22° 23° 24° t tan cot tan cot tan cot tan cot tan cot 3640 2.7475 3839 2.6051 4040 2.4751 4245 2.3559 4452 2.2460 60 1 3643 2.7450 3842 2.6028 4044 2.4730 4248 2.3539 4456 2.2443 59 2 3646 2.7425 3845 2.6006 4047 2.4709 4252 2.3520 4459 2.2425 58 3 3650 2.7400 3849 2.5983 4050 2.46S9 4255 2.3501 4463 2.240S 57 4 3653 2.7376 3852 2.5961 4054 2.4668 4258 2.3483 4466 2.2390 56 5 3656 2.7351 3855 2.593S 4057 2.4648 4262 2.3464 4470 2.2373 55 6 3659 2.7326 3859 2.5916 4061 2.4627 4265 2.3445 4473 2.2355 54 1 7 3663 2.7302 3862 2.5893 4064 2.4606 4269 2.3426 4477 2.2338 53 8 3666 2.7277 3865 2.5871 4067 2.4586 4272 2.3407 4480 2.2320 52 9 3669 2.7253 3869 2.584S 4071 2.4566 4276 2.3388 4484 2.2303 51 10 3673 2.722S 3872 2.5826 4074 2.4545 4279 2.3369 4487 2.2286 50 11 3676 2.7204 3875 2.5804 407S 2.4525 4283 2.3351 4491 2.2268 49 12 3679 2.7179 3879 2.57S2 4081 2.4504 4286 2.3332 4494 2.2251 48 13 3683 2.7155 38S2 2.5759 4084 2.4484 4289 2.3313 4498 2.2234 47 14 3686 2.7130 3885 2.5737 40SS 2.4464 4293 2.3294 4501 2.2216 46 15 3689 2.7106 3889 2.5715 4091 2.4443 4296 2.3276 4505 2.2199 45 16 3693 2.7082 3892 2.5693 4095 2.4423 4300 2.3257 450S 2.2182 44 17 3696 2.7058 3S95 2.5671 4098 2.4403 4303 2.3238 4512 2.2165 43 IS 3699 2.7034 3899 2.5649 4101 2.4383 4307 2.3220 4515 2.2148 42 19 3702 2.7009 3902 2.5627 4105 2.4362 4310 2.3201 4519 2.2130 41 20 3706 2.69S5' 3906 2.5605 4108 2.4342 4314 2.3183 4522 2.2113 40 21 3709 2.6961 3909 2.5533 4111 2.4322 4317 2.3164 4526 2.2096 39 22 3712 2.6937 3912 2.5561 4115 2.4302 4320 2.3146 4529 2.2079 38 23 3716 2.6913 3916 2.5539 4118 2.4282 4324 2.3127 4533 2.2062 37 24 3719 2.6SS9 3919 2.5517 4122 2.4262 4327 2.3109 4536 2.2045 36 25 3722 2.6865 3922 2.5495 4125 2.4242 4331 2.3090 4540 2.2028 35 26 3726 2.6841 3926 2.5473 4129 2.4222 4334 2.3072 4543 2.2011 34 27 3729 2.6S18 3929 2.5452 4132 2.4202 4338 2.3053 4547 2.1994 33 2S 3732 2.6794 3932 2.5430 4135 2.4182 4341 2.3035 4550 2.1977 32 29 3736 2.6770 3936 2.5408 4139 2.4162 4345 2.3017 4554 2.1960 31 30 3739 2.6746 3939 2.5386 4142 2.4142 4348 2.2998 4557 2.1943 30 31 3742 2.6723 3942 2.5365 4146 2.4122 4352 2.2980 4561 2.1926 29 32 3745 2.6699 3946 2.5343 4149 2.4102 4355 2.2962 4564 2.1909 28 33 3749 2.6675 3949 2.5322 4152 2.4083 4359 2.2944 4568 2.1892 27 34 3752 2.6652 3953 2.5300 4156 2.4063 4362 2.2925 4571 2.1876 26 35 3755 2.6628 3956 2.5279 4159 2.4043 4365 2.2907 4575 2.1859 25 36 3759 2.6605 3959 2.5257 4163 2.4023 4369 2.2889 4578 2.1842 24 37 3762 2.6581 3963 2.5236 4166 2.4004 4372 2.2871 4582 2.1825 23 38 3765 2.6558 3966 2.5214 4169 2.3984 4376 2.2853 4585 2.1808 22 39 3769 2.6534 3969 2.5193 4173 2.3964 4379 2.2835 4589 2.1792 21 40 3772 2.6511 3973 2.5172 4176 2.3945 4383 2.2817 4592 2.1775 20 41 3775 2.6488 3976 2.5150 41S0 2.3925 4386 2.2799 4596 2.1758 19 42 3779 2.6464 3979 2.5129 4183 2.3906 4390 22781 4599 2.1742 IS 43 3782 2.6441 3983 2 5108 4187 2.3886 4393 2.2763 4603 2.1725 17 44 3785 2.6418 3986 2.5086 4190 2.3867 4397 2.2745 4607 2.1708 16 45 3789 2.6395 3990 2.5065 4193 2.3847 4400 2.2727 4610 2.1692 15 46 3792 2.6371 3993 2.5044 4197 2.3828 4404 2.2709 4614 2.1675 14 47 3795 2.6348 3996 2.5023 4200 2.3808 4407 2.2691 4617 2.1659 13 48 3799 2.6325 4000 2.5002 4204 2.3789 4411 2.2673 4621 2.1642 12 49 3802 2.6302 4003 2.4981 4207 2.3770 4414 2.2655 4624 2.1625 11 50 3805 2.6279 4006 2.4960 4210 2.3750 4417 2.2637 4628 2.1609 io 51 3809 2.6256 4010 2.4939 4214 2.3731 4421 2.2620 4631 2.1592 9 52 3812 2.6233 ■ 4013 2.4918 4217 2.3712 4424 2.2602 4635 2.1576 8 53 3815 2.6210 4017 2.4897 4221 2.3693 4428 2.2584 4638 2.1560 7 54 3819 2.6187 4020 2.4876 4224 2.3673 4431 2.2566 4642 2.1543 6 55 3822 2.6165 4023 2.4855 4228 2.3654 4435 2.2549 4645 2.1527 5 56 3825 2 6142 4027 2.4834 4231 2.3635 4438 2.2531 4649 2.1510 4 57 3829 2.6119 4030 2.4813 4234 2.3616 4442 2.2513 4652 2.1494 3 58 3832 26096 4033 2.4792 423S 2.3597 4445 2.2496 4656 2.1478 2 59 3835 2.6074 4037 2.4772 4241 2.357S 4449 2.2478 4660 2.1461 1 60 3839 2.6051 4040 2.4751 4245 2.3559 4452 2.2460 4663 2.1445 t cot tan 69° cot tan 68° cot tan 67° cot tan 66° cot tan 65° t 66 NATURAL TANGENTS AND COTANGENTS. f 25° 26° 27° 28° 29° r tan cot tan cot tan cot tan cot tan cot 46b3 2.1445 4877 2.0503 5095 1.9626 5317 1.8807 5543 1.8040 60 1 4b67 2.1429 4881 2.0488 5099 1.9612 5321 1.8794 5547 1.802S 59 2 4670 2.1413 4885 2.0473 5103 1.9598 5325 1.S781 5551 1.8016 58 3 4674 2.1396 4888 2.0458 5106 1.95S4 532S 1.8768 5555 1.8003 57 4 4677 2.1380 4892 2.0443 5110 1.9570 5332 1.8755 5558 1.7991 56 5 4681 2.1364 4895 2.0428 5114 1.9556 5336 1.S741 5562 1.7979 55 6 4684 2.1348 4899 2.0413 5117 1.9542 5340 1.8728 5566 1.7966 54 7 46S8 2.1332 4903 2.0398 5121 1.9528 5343 1.S715 5570 1.7954 53 8 4691 2.1315 4906 2.0383 5125 1.9514 5347 1.8702 5574 1.7942 52 9 4695 2.1299 4910 2.0368 512S 1.9500 5351 1.8689 5577 1.7930 51 10 4699 2.1283 4913 2.0353 5132 1.9486 5354 1.8676 5581 1.7917 50 11 4702 2.1267 4917 2.033S 5136 1.9472 5358 1.S663 5585 1.7905 49 12 4706 2.1251 4921 2.0323 5139 1.9458 5362 1.8650 5589 1.7893 48 13 4709 2.1235 4924 2 0308 5143 1.9444 5366 1.8637 5593 1.7881 47 14 4713 2.1219 4928 2.0293 5147 1.9430 5369 1.8624 5596 1.7868 46 15 4716 2.1203 4931 2.0278 5150 1.9416 5373 .1.8611 5600 1.7856 45 16 4720 2.1187 4935 2.0263 5154 1.9402 5377 1.8598 5604 1.7844 44 17 4723 2.1171 4939 2.024S 5158 1.9388 5381 1.8585 560S 1.7832 43 IS 4727 2.1155 4942 2.0233 5161 1.9375 5384 1.S572 5612 1.7820 42 19 4731 2.1139 4946 2.0219 5165 1.9361 5388 1.8559 5616 1.7808 41 20 4734 2.1123 4950 2.0204 5169 1.9347 5392 1.8546 5619 1.7796 40 21 4738 2.1107 4953 2.0189 5172 1.9333 5396 1.8533 5623 1.7783 39 22 4741 2.1092 4957 2.0174 5176 1.9319 5399 1.8520 5627 1.7771 38 23 4745 2.1076 4960 2.0160 5180 1.9306 5403 1.8507 5631 1.7759 37 24 4748 2.1060 4964 2.0145 5184 1.9292 5407 1.8495 5635 1.7747 36 25 4752 2.1044 496S 20130 5187 1.9278 5411 1.8482 5639 1.7735 35 26 4755 2 1028 4971 2.0115 5191 1.9265 5415 1.8469 5642 1.7723 34 27 4759 2.1013 4975 2 0101 5195 1.9251 5418 1.8456 5646 1.7711 33 2S 4763 2.0997 4979 2.0086 5198 1.9237 5422 1.8443 5650 1.7699 32 29 4766 2.0981 4982 2.0072 5202 1.9223 .5426 18430 5654 1.7687 31 30 4770 2.0965 4986 2.0057 5206 1.9210 5430 1.8418 5658 1.7675 30 31 4773 2.0950 49S9 2.0042 5209 1.9196 5433 1.8405 5662 1.7663 29 32 4777 2.0934 4993 2.002S 5213 1.9183 5437 1.8392 5665 1.7651 28 33 4780 2.0918 4997 2.0013 5217 1.9169 5441 1.8379 5669 1.7639 27 34 4784 2.0903 5000 1.9999 5220 1.9155 5445 1.8367 5673 1.7627 26 35 4788 2.0887 5004 1.9984 5224 1.9142 5448 1.8354 5677 1.7615 25 36 4791 2.0872 5008 1.9970 5228 1.9128 5452 1.8341 5681 1.7603 24 37 4795 2.0856 5011 1.9955 5232 1.9115 5456 1.8329 5685 1.7591 23 38 4798 2.0840 5015 1.9941 5235 1.9101 5460 1.8316 5688 1.7579 22 39 4802 2.0825 5019 1.9926 5239 1.9088 5464 1.8303 5692 1.7567 21 40 4806 2.0809 5022 1.9912 5243 1.9074 5467 1.8291 5696 1.7556 20 41 4809 2.0794 5026 1.9897 5246 1.9061 5471 1.S278 5700 1.7544 19 42 4813 2.0778 5029 1.9883 5250 1.9047 5475 1.S265 5704 1.7532 18 43 4816 2.0763 5033 1.9868 5254 1.9034 5479 1.8253 5708 1.7520 17 44 4820 2.0748 5037 1.9854 5258 . 1.9020 5482 1.8240 5712 1.7508 16 45 4823 2.0732 5040 1.9840 5261 1.9007 5486 1.8228 5715 1.7496 15 46 4827 2.0717 5044 1.9825 5265 1.8993 5490 1.8215 5719 1.7485 14 47 4831 2.0701 5048 1.9811 5269 ' 1.8980 5494 1.8202 5723 1.7473 13 48 4834 2.0686 5051 1.9797 5272 1.8967 5498 1.8190 5727 1.7461 12 49 4838 2.0671 5055 1.9782 5276 1.8953 5501 1.8177 5731 1.7449 11 50 4841 2.0655 5059 1.976S 5280 1.8940 5505 1.8165 5735 1.7437 10 51 4845 2.0640 5062 1.9754 5284 1.8927 5509 1.S152 5739 1.7426 9 52 4849 2.0625 5066 1.9740 5287 1.8913 5513 1.8140 5743 1.7414 8 53 4S52 2.0609 5070 1.9725 5291 1.8900 5517 1.8127 5746 1.7402 7 54 4856 2.0594 5073 1.9711 5295 1.8887 5520 1.8115 5750 1.7391 6 55 4859 2.0579 5077 1.9697 5298 1.8873 5524 1.8103 5754 1.7379 5 56 4863 2 0564 5081 1.9683 5302 1.8860 5528 1.8090 575S 1.7367 4 57 4867 2.0549 5084 1.9669 5306 1.8847 5532 1.8078 5762 1.7355 3 5S 4870 2 0533 5088 1.9654 5310 1.8834 5535 1.8065 5766 1.7344 2 59 4874 2.0518 5092 1.9640 5313 1.8S20 5539 1.8053 5770 1.7332 1 60 4877 2.0503 5095 1.9626 5317 1.8807 5543 1.8040 5774 1.7321 t cot tan 64° cot tan 63° cot tan 62° cot tan 61° cot tan 60° t NATURAL TANGENTS AND COTANGENTS. 67 t 30° 31° 32° 33° 34° t tan cot tan cot tan cot tan cot tan cot 5774 1.7321 6009 1.6643 6249 1.6003 6494 1.5399 6745 1.4826 60 1 5777 1.7309 6013 1.6632 6253 1.5993 649S 1.53S9 6749 1.4S16 59 2 5781 1.7297 6017 1.6621 6257 1.59S3 6502 1.5379 6754 1.4807 58 3 5785 1.72S6 6020 1.6610 6261 1.5972 6506 1.5369 6758 1.479S 57 4 5789 1.7274 6024 1.6599 6265 1.5962 6511 1.5359 6762 1.4788 56 5 5793 1.7262 6028 1.65SS 6269 1.5952 6515 1.5350 6766 1.4779 55 6 5797 1.7251 6032 1.6577 6273 1.5941 6519 1.5340 6771 1.4770 54 7 5801 1.7239 6036 1.6566 6277 1.5931 6523 1.5330 6775 1.4761 53 8 5S05 1.722S 6040 1.6555 6281 1.5921 6527 1.5320 6779 1.4751 52 9 '5808 1.7216 6044 1.6545 62S5 1.5911 6531 1.5311 6783 1.4742 51 10 5812 1.7205 6048 1.6534 6289 1.5900 6536 1.5301 6787 1.4733 50 11 5816 1.7193 6052 1.6523 6293 1.5890 6540 1.5291 6792 1.4724 49 12 5820 1.7182 6056 1.6512 6297 1.5880 6544 1.5282 6796 1.4715 48 13 5824 1.7170 6060 16501 6301 1.5S69 6548 1.5272 6800 1.4705 47 14 5828 1.7159 6064 1.6490 6305 1.5859 6552 1.5262 6805 1.4696 46 15 5832 1.7147 6068 1.6479 6310 1.5849 6556 1.5253 6809 1.4687 45 16 5836 1.7136 6072 1.6469 6314 1.5S39 6560 1.5243 6813 1.467S 44 17 5840 1.7124 6076 1.645S 6318 1.5829 6565 1.5233 6S17 1.4669 43 18 5S44 1.7113 6080 1.6447 6322 1.5S1S 6569 1.5224 6822 1.4659 42 19 5S47 1.7102 6084 1.6436 6326 1.5808 6573 1.5214 6826 1.4650 41 20 5851 1.7090 60SS 1.6426 6330 1.579S 6577 1.5204 6830 1.4641 40 21 5855 1.7079 6092 1.6415 6334 1.5788 6581 1.5195 6S34 1.4632 39 22 5859 1.7067 6096 1.6404 633S 1.577S 6585 1.5185 6839 1.4623 38 23 5863 1.7056 6100 1.6393 6342 1.576S 6590 1.5175 6S43 1.4614 37 24 5867 1.7045 6104 1.6383 6346 1.5757 6594 1.5166 6847 1.4605 36 25 5871 1.7033 6108 1.6372 6350 1.5747 659S 1.5156 6851 1.4596 35 26 5875 1.7022 6112 1.6361 6354 1.5737 6602 1.5147 6S56 1.45S6 34 27 5879 1.7011 6116 1.6351 6358 1.5727 6606 1.5137 6860 1.4577 33 28 5883 1.6999 6120 1.6340 6363 1.5717 6610 1.5127 6864 1.4568 32 29 5SS7 1.69SS 6124 1.6329 ' 6367 1.5707 6615 1.5118 6S69 1.4559 31 30 5890 1.6977 6128 1.6319 6371 1.5697 6619 1.5108 6873 1.4550 30 31 5894 1.6965 6132 1.6308 6375 1.5687 6623 1.5099 6877 1.4541 29 32 5S9S 1.6954 6136 1.6297 6379 1.5677 6627 1.5089 6SS1 1.4532 28 33 5902 1.6943 6140 1.6287 6383 1.5667 6631 1.5080 6886 1.4523 27 34 5906 1.6932 6144 1.6276 63S7 1.5657 6636 1.5070 6S90 1.4514 26 35 5910 1.6920 6148 1.6265 6391 1.5647 6640 1.5061 6894 1.4505 25 36 5914 1.6909 6152 16255 6395 1.5637 6644 1.5051 6899 1.4496 24 37 5918 1.6S9S 6156 1.6244 6399 1.5627 6648 1.5042 6903 1.4487 23 3S 5922 1.6S87 6160 1.6234 6403 1.5617 6652 1.5032 6907 1.4478 22 39 5926 1.6875 6164 1.6223 6408 1.5607 6657 1.5023 6911 1.4469 21 40 5930 1.6S64 6168 1.6212 6412 1.5597 6661 1.5013 6916 1.4460 20 41 5934 1.6853 6172 1.6202 6416 1.5587 6665 1.5004 6920 1.4451 19 42 5938 1.6842 6176 1.6191 6420 1.5577 6669 1.4994 6924 1.4442 18 43 5942 1.6831 61S0 1.6181 6424 1.5567 6673 1.4985 6929 1.4433 17 44 5945 1.6820 6184 1.6170 6428 1.5557 6678 1.4975 6933 1.4424 16 45 5949 1.6S0S 61SS 1.6160 6432 1.5547 6682 1.4966 6937 1.4415 15 46 5953 1.6797 6192 1.6149 6436 1.5537 6686 1.4957 6942 1.4406 14 47 5957 1.6786 6196 1.6139 6440 1.5527 6690 1.4947 6946 1.4397 13 48 5961 1.6775 6200 1.6128 6445 1.5517 6694 1.4938 6950 1.4388 12 49 5965 1.6764 6204 1.6118 6449 1.5507 6699 1.4928 6954 1.4379 11 50 5969 1.6753 620S 1.6107 6453 1.5497 6703 1.4919 6959 1.4370 io 51 5973 1.6742 6212 1.6097 6457 1.54S7 6707 1.4910 6963 1.4361 9 52 5977 1.6731 6216 1.6087 6461 1.5477 6711 1.4900 6967 1.4352 8 53 5981 1.6720 6220 1.6076 6465 1.5468 6716 1.4891 6972 1.4344 7 54 5985 1.6709 6224 1.6066 6469 1.5458 6720 1.4SS2 6976 1.4335 6 55 5989 1.6698 6228 1.6055 6473 1.5448 6724 1.4872 69S0 1.4326 5 56 5993 166S7 6233 1.6045 6478 1.543S 672S 1.4863 69S5 1.4317 4 57 5997 1.6676 6237 1.6034 6482 1.5428 6732 1.4854 6989 1.4308 3 58 6001 16665 6241 1.6024 64S6 1.5418 6737 1.4844 6993 1.4299 2 59 6005 1.6654 6245 1.6014 6490 1.5408 6741 1.4835 6998 1.4290 1 60 6009 1.6643 6249 1.6003 6494 1.5399 6745 1.4826 7002 1.4281 t cot tan 59° cot tan 58° cot tan 57° cot tan 56° cot tan 55° t NATURAL TANGENTS AND COTANGENTS. t 35° 36° 37° 38° 39° t tan cot tan cot tan cot tan cot tan cot 7002 14281 7265 1.3764 7536 1.3270 7813 1.2799 8098 1.2349 60 1 7006 1.4273 7270 1.3755 7540 1.3262 7818 1.2792 8103 1.2342 59 2 7011 1.4264 7274 1.3747 7545 1.3254 7822 1.2784 8107 1.2334 58 3 7015 1.4255 7279 1.3739 7549 1.3246 7827 1.2776 8112 1.2327 57 4 7019 1.4246 7283 1.3730 7554 1.3238 7832 1.2769 8117 1.2320 56 5 7024 1.4237 7288 1.3722 7558 1.3230 7836 1.2761 8122 1.2312 55 6 7028 1.4229 7292 1.3713 7563 1.3222 7841 1.2753 8127 1.2305 54 7 7032 1.4220 7297 1.3705 7568 1.3214 7846 1.2746 8132 1.2298 53 8 7037 1.4211 7301 1.3697 7572 1.3206 7850 1.2738 8136 1.2290 52 9 7041 1.4202 7306 1.3688 7577 1.3198 7855 1.2731 8141 1.2283 51 io 7046 1.4193 7310 1.3680 7581 1.3190 7860 1.2723 8146 1.2276 50 11 7050 1.4185 7314 1.3672 7586 1.3182 7865 1.2715 8151 1.2268 49 12 7054 1.4176 7319 1.3663 7590 1.3175 7869 1.2708 8156 1.2261 48 13 7059 1.4167 7323 1.3655 7595 1.3167 7874 1.2700 8161 1.2254 47 14 7063 1.4158 7328 1.3647 7600 1.3159 7879 1.2693 8165 1.2247 46 15 7067 1.4150 7332 1.3638 7604 1.3151 7883 12685 8170 1.2239 45 16 7072 1.4141 7337 1.3630 7609 1.3143 7888 1.2677 8175 1.2232 44 17 7076 1.4132 7341 1.3622 7613 1.3135 7893 1.2670 8180 1.2225 43 IS 7080 1.4124 7346 1.3613 7618 1.3127 7898 1.2662 8185 1.2218 42 19 7085 1.4115 7350 1.3605 7623 1.3119 7902 1.2655 8190 1.2210 41 20 7089 1.4106 7355 1.3597 7627 1.3111 7907 1.2647 8195 1.2203 40 21 7094 1.4097 7359 1.3588 7632 1.3103 7912 1.2640 8199 1.2196 39 22 7098 1.4089 7364 1.3580 7636 1.3095 7916 1.2632 8204 1.2189 38 23 7102 1.4080 7368 1.3572 7641 1.3087 7921 1.2624 8209 1.2181 37 24 7107 1.4071 7373 1.3564 7646 1.3079 7926 1.2617 8214 1.2174 36 25 7111 1.4063 7377 1.3555 7650 1.3072 7931 1.2609 8219 1.2167 35 26 . 7115 1.4054 7382 1.3547 7655 1.3064 7935 1.2602 8224 1.2160 34 27 7120 1.4045 7386 1.3539 7659 1.3056 7940 1.2594 8229 1.2153 33 28 7124 1.4037 7391 1.3531 7664 1.3048 7945 1.2587 8234 1.2145 31 29 7129 1.4028 7395 1.3522 7669 1.3040 7950 1.2579 8238 1.2138 31 30 7133 1.4019 7400 1.3514 7673 1.3032 7954 1.2572 8243 1.2131 30 31 7137 14011 7404 1.3506 7678 1.3024 7959 1.2564 8248 1.2124 29 32 7142 1.4002 7409 1.3498 7683 1.3017 7964 1.2557 8253 1.2117 28 33 7146 1.3994 7413 1.3490 7687 1.3009 7969 1.2549 8258 1.2109 27 34 7151 1.3985 7418 1.3481 7692 1.3001 7973 1.2542 8263 1.2102 26 35 7155 1.3976 7422 1.3473 7696 1.2993 7978 1.2534 8268 1.2095 25 36 7159 1.3968 7427 1.3465 7701 1.2985 7983 1.2527 8273 1.2088 24 37 7164 1.3959 7431 1.3457 7706 1.2977 7988 1.2519 8278 1.2081 23 38 716S 1.3951 7436 1.3449 7710 1.2970 7992 1.2512 8283 1.2074 22 39 7173 1.3942 7440 1.3440 7715 1.2962 7997 1.2504 8287 1.2066 21 40 7177 1.3934 7445 1.3432 7720 1.2954 8002 1.2497 8292 1.2059 20 41 7181 1.3925 7449 1.3424 7724 1.2946 8007 1.2489 8297 1.2052 19 42 7186 1.3916 7454 1.3416 7729 1.2938 8012 1.2482 8302 1.2045 18 43 7190 1.3908 7458 1.3408 7734 1.2931 8016 1.2475 8307 1.2038 17 44 7195 1.3S99 7463 1.3400 7738 1,2923 8021 1.2467 8312 1.2031 16 45 7199 1.3891 7467 1.3392 7743 1.2915 8026 1.2460 8317 1.2024 15 46 7203 1.3882 7472 1.3384 7747 1.2907 8031 1.2452 8322 1.2017 14 47 7208 1.3874 7476 1.3375 -7752 1.2900 8035 1.2445 8327 12009 13 4S 7212 1.3865 7481 1.3367 7757 1.2892 8040 1.2437 8332 1.2002 12 49 7217 1.3857 7485 1.3359 7761 1.2S84 8045 1.2430 8337 1.1995 11 50 7221 1.3848 7490 1.3351 7766 1.2876 8050 1.2423 8342 1.1988 10 51 7226 1.3840 7495 1.3343 7771 1.2869 8055 1.2415 8346 1.1981 9 52 7230 1.3831 7499 1.3335 7775 1.2861 8059 1.2408 8351 1.1974 8 53 7234 1.3823 7504 1.3327 77S0 1.2853 8064 1.2401 8356 1.1967 7 54 7S39 1.3814 7508 1.3319 7785 1.2846 8069 1.2393 8361 1.1960 6 55 7243 1.3806 7513 1.3311 7789 1.2838 8074 1.2386 8366 1.1953 5 56 7248 1.3798 7517 1.3303 7794 1.2S30 8079 1.2378 8371 1.1946 4 57 7252 1.3789 7522 1.3295 7799 1.2822 8083 1.2371 8376 1.1939 3 58 7257 1.3781 7526 1.3287 7803 1.2815 S088 1.2364 8381 1.1932 2 59 7261 1.3772 7531 1.3278 7808 1.2807 8093 1.2356 8386 1.1925 1 60 7265 1.3764 7536 1.3270 7813 1.2799 809S 1.2349 8391 1.1918 ' cot tan 54° cot tan 53° cot tan ' 52° cot tan 51° cot tan 50° i NATURAL TANGENTS AND COTANGENTS. 69 t 40° 41° 42° 43° 44° t tan cot tan cot tan cot tan cot tan cot 8391 1.1918 8693 1.1504 9004 1.1106 9325 1.0724 9657 1.0355 60 1 8396 1.1910 8698 1.1497 9009 1.1100 9331 1.0717 9663 1.0349 59 2 8401 1.1903 8703 1.1490 9015 1.1093 9336 1.0711 9668 1.0343 58 3 8406 1.1896 870S 1.1483 9020 1.1087 9341 1.0705 9674 1.0337 57 4 8411 1.1889 8713 1.1477 9025 1.1080 9347 1.0699 9679 1.0331 56 5 8416 1.1882 8718 1.1470 9030 1.1074 9352 1.0692 9685 1.0325 55 6 8421 1.1875 8724 1.1463 9036 1.1067 9358 1.0686 9691 1.0319 54 7 8426 1.1868 8729 1.1456 9041 1.1061 9363 1.0680 9696 1.0313 53 8 -8431 1.1861 8734 1.1450 9046 1.1054 9369 1.0674 9702 1.0307 52 9 8436 1.1854 8739 1.1443 9052 1.1048 9374 1.0668 9708 1.0301 51 io 8441 1.1847 8744 1.1436 9057 1.1041 9380 1.0661 9713 1.0295 50 11 8446 1.1840 8749 1.1430 9062 1.1035 9385 1.0655 9719 1.0289 49 12 8451 1.1833 8754 1.1423 9067 1.1028 9391 1.0649 9725 1.0283 48 13 8456 1.1826 8759 1.1416 9073 1.1022 9396 1.0643 9730 1.0277 47 14 8461 1.1819 8765 1.1410 9078 1.1016 9402 1.0637 9736 1.0271 46 15 8466 1.1S12 8770 1.1403 9083 1.1009 9407 1.0630 9742 1.0265 45 16 8471 1.1806 8775 1.1396 9089 1.1003 9413 1.0624 9747 1.0259 44 17 8476 1.1799 8780 1.1389 9094 1.0996 9418 1.0618 9753 1.0253 43 IS 8481 1.1792 8785 1.1383 9099 1.0990 9424 1.0612 9759 1.0247 42 19 8486 1.1785 8790 1.1376 9105 1.0983 9429 1.0606 9764 1.0241 41 20 8491 1.1778 8796 1.1369 9110 1.0977 9435 1.0599 9770 1.0235 40 21 8496 1.1771 8801 1.1363 9115 1.0971 9440 1.0593 9776 1.0230 39 22 8501 1.1764 8806 1.1356 9121 1.0964 9446 1.0587 9781 1.0224 38 23 8506 1.1757 8811 1.1349 9126 1.0958 9451 1.0581 9787 1.0218 37 24 8511 1.1750 8816 1.1343 9131 1.0951 9457 1.0575 9793 1.0212 36 25 8516 1.1743 8821 1.1336 9137 1.0945 9462 1.0569 9798 1.0206 35 26 8521 1.1736 8827 1.1329 9142 1.0939 9468 1.0562 9804 1.0200 34 27 8526 1.1729 8832 1.1323 9147 1.0932 9473 1.0556 9810 1.0194 33 28 8531 1.1722 8837 1.1316 9153 1.0926 9479 1.0550 9816 1.0188 31 29 8536 1.1715 8842 1.1310 9158 1.0919 9484 1.0544 9821 1.0182 31 30 8541 1.1708 8847 1.1303 9163 1.0913 9490 1.0538 9827 1.0176 30 31 8546 1.1702 8852 1.1296 9169 1.0907 9495 1.0532 9833 1.0170 29 32 8551 1.1695 8858 1.1290 9174 1.0900 9501 1.0526 9838 1.0164 28 33 8556 1.1688 8863 1.1283 9179 1.0894 9506 1.0519 9844 1.0158 27 34 8561 1.1681 8868 1.1276 9185 1.0888 9512 1.0513 9850 1.0152 26 35 8566 1.1674 8873 1.1270 9190 1.0881 9517 1.0507 9856 1.0147 25 36 8571 1.1667 887S 1.1263 9195 1.0875 9523 1.0501 9861 1.0141 24 37 8576 1.1660 8884 1.1257 9201 1.0869 9528 1.0495 9867 1.0135 23 38 8581 1.1653 8SS9 1.1250 9206 1.0S62 9534 1.0489 9873 1.0129 22 39 8586 1.1647 8894 1.1243 9212 1.0856 9540 1.0483 9879 1.0123 21 40 8591 1.1640 8899 1.1237 9217 1.0850 9545 1.0477 9884 1.0117 20 41 8596 1.1633 8904 1.1230 9222 1.0843 9551 1.0470 9890 1.0111 19 42 8601 1.1626 8910 1.1224 9228 1.0837 9556 1.0464 9896 1.0105 18 43 8606 1.1619 8915 1.1217 9233 1.0831 9562 1.0458 9902 1.0099 17 44 8611 1.1612 8920 1.1211 9239 1.0824 9567 1.0452 9907 1.0094 16 45 8617 1.1606 8925 1.1204 9244 1.0818 9573 1.0446 9913 1.0088 15 46 8622 1.1599 8931 1.1197 9249 1.0812 9578 1.0440 9919 1.00S2 14 47 8627 1.1592 8936 1.1191 9255 1.0805 95S4 1.0434 9925 1.0076 13 48 8632 1.1585 8941 1.1184 9260 ] .0799 9590 1.0428 9930 1.0070 12 49 8637 1.1578 8946 1.1178 9266 1.0793 9595 1.0422 9936 1.0064 11 50 8642 1.1571 8952 1.1171 9271 1.0786 9601 1.0416 9942 1.0058 10 51 8647 1.1565 8957 1.1165 9276 1.0780 9606 1.0410 9948 1.0052 9 52 8652 1.1558 8962 1.1158 9282 1.0774 9612 1.0404 9954 1.0047 8 53 8657 1.1551 8967 1.1152 9287 1.0768 9618 1.039S 9959 1.0041 7 54 8662 1.1544 8972 1.1145 9293 1.0761 9623 1.0392 9965 1.0035 6 55 8667 1.1538 8978 1.1139 9298 1.0755 9629 1.0385 9971 1.0029 5 56 8672 1.1531 8983 1.1132 9303 1.0749 9634 1.0379 9977 1.0023 4 57 8678 1.1524 8988 1.1126 9309 1.0742 9640 1.0373 9983 1.0017 3 58 8683 1.1517 8994 1.1119 9314 1.0736 9646 1.0367 9988 1.0012 2 59 8688 1.1510 8999 1.1113 9320 1.0730 9651 1.0361 9994 1.0006 1 60 8693 1.1504 9004 1.1106 9325 1.0724 9657 1.0355 1.000 1.0000 O cot tan cot tan cot tan cot tan cot tan t 49° 48° 47° 46° 45° / 70 TABLE VII. ■ -TRAVEKSE TABLE. Bearing, Distance 1. Distance 2. Distance 3. Distance 4. Distance 5. Bearing. o t Lat, Dep, Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o t 15 1.000 0.004 2.000 0.009 3.000 0.013 4.000 0.017 5.000 0.022 89 45 30 1.000 0.009 2.000 0.017 3.000 0.026 4.000 0.035 5.000 0.044 30 45 1.000 0.013 2.000 0.026 3.000 0.039 4.000 0.052 5.000 0.065 15 1 1.000 0.017 2.000 0035 3.000 0.052 3.999 0.070 4.999 0.0S7 89 15 1.000 0.022 2.000 0.044 2.999 0.065 3.999 0.087 4.999 0.109 45 30 1.000 0.026 1.999 0.052 2.999 0.079 3.999 0.105 4.998 0.131 30 45 1.000 0.031 1.999 0.061 2.999 0.092 3.998 0.122 4.998 0.153 15 2 0.999 0.035 1.999 0.070 2.998 0.105 3.998 0.140 4.997 0.174 88 15 0.999 0.039 1.998 0.079 2.998 0.118 3.997 0.157 4.996 0.196 45 30 0.999 0.044 1.998 0.087 2.997 0.131 3.996 0.174 4.995 0.218 30 45 0.999 0.048 1.99S 0.096 2.997 0.144 3.995 0.192 4.994 0.240 15 3 0.999 0.052 1.997 0.105 2.996 0.157 3.995 0.209 4.993 0.262 87 15 0.998 0.057 1.997 0.113 2.995 0.170 3.994 0.227 4.992 283 45 30 0.998 0.061 1.996 0.122 2.994 0.183 3.993 0244 4.991 0.305 30 45 0.998 0065 1.996 0.131 2.994 0.196 3.991 0.262 4.989 0.327 15 4 0.998 070 1.995 0.140 2.993 0.209 3.990 0.279 4.988 349 86 15 0.997 0.074 1.995 0.148 2.992 0.222 3.989 0.296 4.986 0.371 45 30 0.997 0078 1.994 0.157 2.991 0.235 3.988 0.314 4.985 0.392 30 45 0.997 0.0S3 1.993 0.166 2.990 0.248 3.986 0.331 4.983 0.414 15 5 0.996 0.087 1.992 0.174 2.989 0.261 3.985 0.349 4.981 0.436 85 15 0.996 092 1.992 0.183 2.987 0.275 3.983 0.366 4.979 0.458 45 30 0.995 096 1.991 0192 2.986 0.288 3.9S2 0383 4.977 0.479 30 45 0.995 0100 1.990 0.200 2.985 0.301 3.980 0.401 4.975 0.501 15 6 0.995 0.105 1.989 209 2.984 0.314 3.978 0.418 4.973 0.523 84 15 0.994 0.109 1.9SS 0.218 2.982 0.327 3.976 0.435 4.970 0.544 45 30 0.994 0.113 1.987 0.226 2.981 0.340 3.974 0.453 4.968 0.566 30 45 0.993 0.118 1.986 0.235 2.979 0.353 3.972 0.470 4.965 0.5S8 15 7 0.993 0.122 1.985 0.244 2.978 0.366 3.970 0.487 4.963 0.609 83 15 0992 0126 1.984 0.252 2.976 0.379 3.966 0.505 4.960 0631 45 30 0.991 0.131 1.983 0.261 2.974 0.392 3.966 0.522 4.957 0.653 30 45 0.991 0.135 1.982 0.270 2.973 0.405 3.963 0.539 4.954 0.674 15 8 0.990 0.139 1.981 278 2.971 0.418 3.961 0.557 4.951 0.696 82 15 0.990 0.143 1.979 0.287 2.969 0.430 3.959 0574 4.948 0.717 45 30 0.989 0.148 1.978 0.296 2.967 0.443 3.956 0.591 4.945 0.739 30 45 0.988 0152 1.977 0.304 2.965 0.456 3.953 608 4.942 0.761 15 9 0.988 0.156 1.975 0.313 2.963 0.469 3.951 0.626 4.938 0.782 81 15 0.987 0.161 1.974 0.321 2.961 0.482 3.948 0.643 4.935 0.804 45 30 0.9S6 0.165 1.973 0.330 2.959 0.495 3.945 0.660 4.931 0.825 30 45 0.986 0.169 1.971 0.339 2.957 0.508 3.942 0.677 4.928 0.847 15 10 0.985 0.174 1.970 0.347 2.954 0.521 3.939 0.695 4.924 0.868 80 15 9S4 0.178 1.968 0.356 2.952 0.534 3.936 0.712 4.920 0.890 45 30 0.983 0.182 1.967 0.364 2.950 0.547 3.933 0.729 4.916 0.911 30 45 0.982 1S7 1.965 0.373 2.947 560 3.930 0.746 4.912 0.933 15 11 0.982 0.191 1.963 0.382 2.945 0.572 3.927 0.763 4.908 0.954 79 15 0.9S1 0.195 1.962 0.390 2.942 0:585 3.923 0.780 4.904 0.975 45 30 980 0.199 1.960 '0.399 2.940 0.598 3.920 0.797 4.900 0997 30 45 0979 0.204 1.95S 0.407 2.937 611 3.916 0.815 4.895 1.018 15 12 0.978 0.208 1.956 0.416 2.934 0624 3.913 0.832 4.891 1.040 78 15 0.977 0.212 1.954 0.424 2.932 0.637 3.909 0.S49 4 886 1.061 45 30 0.976 0.216 1.953 0.433 2.929 0.649 3.905 0.S66 4.881 1.082 30 45 0.975 0.221 1.951 0.441 2.926 662 3.901 0S83 4.877 1.103 15 13 974 0.225 1.949 0.450 2.923 0.675 3.897 0.900 4.872 1.125 77 15 0.973 0229 1.947 0.458 2.920 0.688 3.894 0.917 4.867 1.146 45 30 0.972 0.233 1.945 0.467 2.917 0.700 3.889 0.934 4.862 1.167 30 45 971 0.238 1.943 0.475 2.914 0.713 3.885 0.951 4.857 1.188 15 14 970 0242 1.941 0.484 2.911 0.726 3.8S1 0.968 4.851 1.210 76 15 0.969 0.246 1.938 0.492 2.90S 0.73S 3.877 0.985 4.846 1.231 45 30 968 0.250 1.936 0.501 2.904 0.751 3.873 1.002 4.841 1.252 30 45 0.967 0.255 1.934 0.509 2.901 0.764 3.868 1.01S 4.835 1.273 15 15 0.966 0.259 1.932 0.518 2.89S 0.776 3.864 1.035 4.830 1.294 75 o r Dep. Lat. Dep. Lat. Dep, Lat. Dep. Lat. Dep. Lat. o t Bearing Distance 1. Distance 2. Distance 3. Distance 4. Distance 5. Bearing. 75°-90 c o°- -15° 71 Bearing. Distance 6. Distance 7. Distance 8. Distance 9. Distance 10. Bearing, o r Lat. Dep, Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o r 15 6.000 026 7.000 0.031 8.000 0.035 9 000 0.039 10.000 0.044 89 45 30 6000 0.052 7.000 0.061 8.000 0.070 9000 0.079 10.000 0.087 30 45 5.999 0.079 6.999 0.092 7.999 0.105 S.999 0.118 9.999 0.131 15 1 5.999 0.105 6.999 0.122 7.999 0.140 8.999 0.157 9.999 0.175 89 15 5.999 0.131 6.99S 0.153 7.99S 0.175 8.998 0.196 9.998 0.218 45 30 5.998 0.157 6.99S 0.183 7.997 0.209 8 997 0.236 9.997 0.262 30 45 5.997 0.1S3 6.997 0.214 7.996 0.244 8.996 0.275 9.995 0.305 15 2 5.996 0.209 6.996 0.244 7.995 0.279 8.995 0.314 9.994 0.349 88 15 5.995 0.236 6.995 0.275 7.994 0.314 8.993 0.353 9.992 0.393 45 30 5.994 0.262 6.993 0.305 7.992 0.349 8.991 0.393 9.991 0.436 30 45 5.993 0.2S8 6.992 0.336 7.991 0.384 8.990 0.432 9.989 0.4S0 15 3 5.992 0314 6.990 0.366 7.989 0.419 8.988 0.471 9.986 0.523 87 15 5.990 0.340 6.989 0.397 7.9S7 0.454 8.986 0.510 9.984 0.567 45 30 5.9S9 0.366 6.9S7 0.427 7.985 0.48S 8.983 0.549 9.981 0.611 30 45 5.9S7 0.392 6.985 0.458 7.983 0.523 8.981 0.589 9.979 0.654 15 4 5.9S5 0.419 6.983 0.4SS 7.981 0.558 8.978 0.628 9.976 698 86 15 5.9S4 0.445 6.9S1 0.519 7.978 0.593 8.975 0.667 9.973 0.741 45 30 5.9S2 0.471 6.97S 0.549 7.975 0.628 8.972 0.706- 9.969 0.785 30 45 5.979 0.497 6.976 0.580 7.973 0.662 8.969 0.745 9.966 0.828 15 5 5.977 '0.523 6.973 0.610 7.970 0.697 8.966 0.784 9.962 0.872 85 15 5.975 0549 6.971 0.641 7.966 0.732 8.962 0.824 9.958 0.915 45 30 5.972 575 6.968 0.671 7.963 0.767 8.959 0.863 9.954 0.959 30 45 5.970 601 6.965 0.701 7.960 0.802 8.955 0.902 9.950 1.002 15 6 5.967 0.627 6.962 0.732 7.956 0.836 8.951 0.941 9.945 1.045 84 15 5.964 0.653 6.958 0.762 7.952 0.871 S.947 0.980 9.941 1.089 45 30 5.961 0.679 6.955 0.792 7.949 0.906 8.942 1.019 9.936 1.132 30 45 5.95S 0.705 6.951 0.823 7.945 0.940 8938 1.058 9.931 1.175 15 7 5.955 0.731 6.948 0.853 7.940 0.975 8.933 1.097 9.926 1.219 83 15 5.952 0.757 6.944 0.883 7.936 1.010 8.928 1.136 9.920 1.262 45 30 5.949 0.7S3 6.940 0.914 7.932 1.044 8.923 1.175 9.914 1.305 30 45 5.945 0.809 6.936 0.944 7.927 1.079 8.918 1.214 9.909 1.349 15 8 5.942 0.835 6.932 0.974 7.922 1.113 8.912 1.253 9.903 1.392 82 15 5.93S 0.861 6.928 1.004 7.917 1.148 8.907 1.291 9.897 1.435 45 30 5.934 0.8S7 6 923 1.035 7.912 1.182 8.901 1.330 9.890 1.478 30 45 5.930 913 6.919 1.065 7.907 1.217 8.895 1.369 9.884 1.521 15 9 5.926 0.939 6.914 1.095 7.902 1.251 8.889 1.408 9.877 1.564 81 15 5.922 0.964 6.909 1.125 7.896 1.286 8.883 1.447 9.870 1.607 45 30 5.918 0.990 6.904 1.155 7.890 1.320 8.877 1.485 9.863 1.651 30 45 5.913 1.016 6.899 1.185 7.884 1.355 8.870 1.524 9.856 1.694 .15 10 5.909 1.042 6.894 1.216 7.878 1.389 8.863 1.563 9.848 1.737 80 15 5.904 1.068 6.88S 1.246 7.872 1.424 8.856 1.601 9.840 1.779 45 30 5.900 1.093 6.S83 1.276 7.866 1.458 8.849 1.640 9.833 1.822 30 45 5.895 1.119 6.877 1.306 7.860 1.492 8.842 1.679 9.825 1.865 15 11 5.S90 1.145 6.871 1.336 7.853 1.526 8.835 1.717 9.816 1.908 79 15 5.885 1.171 6.866 1.366 7.846 1.561 8.827 1.756 9.808 1.951 45 30 5. 880 1.196 6.859 1.396 7.839 1.595 8.819 1.794 9.799 1.994 30 45 5.874 1.222 6.853 1425 7.832 1.629 8.811 1.833 9.791 2036 15 12 5.869 1.247 6.S47 1.455 7.825 1663 8.803 1.871 9 782 2.079 78 15 5.S63 1.273 6.841 1.485 7.81S 1.697 8.795 1.910 9.772 2.122 45 30 5.858 1.299 6.834 1.515 7.S10 1.732 8.787 1.948 9.763 2.164 30 45 5.852 1.324 6.827 1.545 7.803 1.766 8.778 1.986 9.753 2.207 15 13 5.846 1.350 6.821 1.575 7.795 1.800 8.769 2.025 9.744 2.250 77 15 5.840 1.375 6.814 1.604 7.7S7 1.834 8.760 2.063 9.734 2.292 45 30 5.834 1.401 6.807 1.634 7.779 1.868 8.751 2.101 9.724 2.335 30 45 5.828 1.426 6.799 1.664 7.771 1.902 8.742 2139 9.713 2.377 15 14 5.822 1.452 6.792 1.693 7.762 1.935 8.733 2.177 9.703 2.419 76 15 5.S15 1.477 6.785 1.723 7.754 1.969 8.723 2.215 9.692 2.462 45 30 5.S09 1.502 6777 1.753 7.745 2.003 8.713 2.253 9.6S2 2.504 30 45 5.802 1.52S 6.769 1.7S2 7.736 2.037 8.703 2.291 9.671 2.546 15 15 5.796 1.553 6.761 1.812 7.727 2.071 S.693 2.329 9.659 2.588 75 o f Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o t Bearing. Distance 6. Distance 7. Distance 8. Distance 9. Distance 10. Bearing. 75°-90 c 72 15°- -30° Bearing. Distance 1. Distance 2. Distance 3. Distance 4. Distance 5. Bearing. o t Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. O f 15 15 0.965 0263 1.930 0.526 2.894 0.789 3.859 1.052 4.824 1.315 74 45 30 0.964 0.267 1.927 0.534 2.891 0.802 3.855 1.069 4.818 1.336 30 45 0.962 0.271 1.925 0.543 2.887 0.814 3.850 1.086 4.812 1.357 15 16' 0.961 0.276 1.923 0.551 2.8S4 0.827 3.845 1.103 4.806 1.378 74 15 0.960 0.280 1.920 0.560 2.880 0.839 3.840 1.119 4.800 1.399 45 30 0.959 0.284 1.918 0.568 2.876 0.852 3.835 1.136 4.794 1.420 30 45 0.958 0.288 1.915 0.576 2.873 0.865 3.830 1.153 4.788 1.441 15 17 0956 0.292 1.913 0.585 2.S69 0.877 3.S25 1.169 4.782 1.462 73 15 0.955 0.297 1.910 0.593 2.865 0.890 3.820 1.186 4.775 1.483 45 30 0.954 0.301 1.907 0.601 2.861 0.902 3.815 1.203 4.769 1.504 30 45 0.952 0.305 1.905 0.610 2.857 0.915 3.810 1.220 4.762 1.524 15 18 0.951 0.309 1.902 0.618 2.853 0.927 3.804 1.236 4.755 1.545 72 15 0.950 0.313 1.899 0.626 2.849 0.939 3.799 1.253 4.748 1.566 45 30 0.948 0.317 1.897 0.635 2.845 0.952 3.793 1.269 4.742 1.587 30 45 0.947 0.321 1.894 0.643 2.841 0.964 3 788 1.286 4.735 1.607 15 19 0.946 0.326 1.891 0.651 2.837 0.977 3.782 1.302 4.728 1.62S 71 15 0.944 0.330 1.S8S 0.659 2.S32 0.989 3.776 1.319 4.720 1.648 45 30 0.943 0.334 1.885 0.668 2.828 1.001 3.771 1.335 4.713 1.669 30 45 0.941 0.338 1.882 0.676 2.824 1.014 3.765 1.352 4.706 1.690 15 20 0.940 0.342 1.879 0.684 2.819 1.026 3.759 1.368 4.698 1.710 70 15 0.938 0.346 1.876 692 2.815 1.038 3.753 1.384 4.691 1.731 45 30 0.937 0350 1.873 0.700 2.810 1.051 3.747 1.401 4.683 1.751 30 45 0.935 0.354 1.870 0709 2.805 1.063 3.741 1.417 4.676 1.771 15 21 0.934 0.358 1.867 0.717 2.801 1.075 3.734 1.433 4.668 1.792 69 15 0.932 0.362 1.864 0.725 2.796 1.087 3.728 1.450 4.660 1.812 45 30 0.930 0.367 1.861 0.733 2.791 1.100 3.722 1.466 4.652 1.833 30 45 0.929 0.371 1.858 0.741 2.786 1.112 3.715 1.482 4.644 1.853 15 22 0.927 0.375 1.854 0.749 2.782 1.124 3.709 1.498 4.636 1.873 68 15 0.926 379 1.851 0.757 2.777 1.136 3.702__ 1.515 4.628 1.893 45 30 0.924 0.383 1.848 0.765 2.772 1.148 3.696,1.531 4.619 1.913 30 45 0.922 0.387 1.844 0.773 2.767 1.160 3.689 1.547 ' 4.611 1.934 15 23 0.921 0.391 1.841 0.781 2.762 1.172 3.682 1.563 4.603 1.954 67 15 0.919 0.395 1.S3S 0.789 2.756 1.184 3.675 1.579 4.594 1.974 45 30 0.917 0.399 1.834 0.797 2.751 1.196 3.668 1.595 4.585 1.994 30 45 0.915 403 1.831 0.805 2.746 1.208 3.661 1.611 4.577 2.014 15 24 0.914 0.407 1.827 0.813 2.741 1.220 3.654 1.627 4.568 2.034 66 15 0.912 0.411 1.824 0.821 2.735 1.232 3.647 1.643 4.559 2.054 45 30 0.910 0.415 1.820 0.S29 2.730 1.244 3.640 1.659 4.550 2.073 30 45 0.90S 0.419 1.816 0.837 2.724 1.256 3.633 1.675 4.541 2.093 15 25 0.906 0.423 1.813 0.845 2.719 1.26S 3.625 1.690 4.532 2.113 65 15 0.904 0.427 1.809 0.853 2.713 1.28*0 3.618 1.706 4.522 2.133 45 30 0.903 0.431 1.805 0.861 2.708 1.292 3.610 1.722 4.513 2.153 30 45 0.901 0.434 1.801 0.869 2.702 1.303 3.603 1.73S 4.503 2.172 15 26 0.S99 0.438 1.798 0.877 2.696 1.315 3.595 1.753 4.494 2.192 64 15 0S97 0.442 1.794 0.885 2.691 1.327 3.587 1.769 4.484 2.211 45 30 0.895 0.446 1.790 892 2.685 1.339 3.580 1.785 4.475 2.231 30 45 0.S93 0.450 1.786 0.900 2.679 1.350 3.572 1.800 4.465 2.250 15 27 0.891 0.454 1.782 0.908 2.-673 1.362 3.564 1.816 4.455 2.270 63 15 0.889 0.458 1.77S 0.916 2.667 1.374 3.556 1.831 4.445 2.289 45 30 0.8S7 0.462 1.774 0.923 2.661 1.385 3.548 1.847 4.435 2.309 30 45 0885 0.466 1.770 0.931 2.655 1.397 3.540 1.862 4.425 2.328 15 28 0.S83 0.469 1.766 0.939 2 649 1.40S 3.532 1.878 4.415 2.347 62 15 0.881 0.473 1.762 0.947 2.643 1.420 3.524 1.893 4.404 2.367 45 30 879 0.477 1.758 0.954 2.636 1.431 3.515 1.909 4.394 2.386 30 45 0.877 0.481 1.753 0.962 2.630 1.443 3.507 1.924 4.3S4 2.405 15 29 0.875 0.485 1.749 0.970 2.624 1.454 3.498 1.939 4.373 2.424 61 15 0.872 0.489 1.745 0.977 2.617 1.466 3.490 1.954 4.362 2.443 45 30 0.870 0.492 1.741 0.985 2.611 1.477 3.481 1.970 4.352 2.462 30 45 0.868 0.496 1.736 0.992 2.605 1.489 3.473 1.985 4.341 2.481 15 30 0.866 0.500 1.732 1.000 2.598 1.500 3.464 2.000 4.330 2.500 60 O f Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o r Bearing. Distance 1. Distance 2. Distance 3. Distance 4. Distance 5. Bearing. 60 o -75 ( 15°- -30 o 73 Bearing. Distance 6. Distance 7. Distance 8. Distance 9. Distance 10. Bearing. o t Lat. Dep, Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o r 15 15 5.7S9 1.578 6.754 1.S41 7.71S 2.104 8.683 2.367 9.64S 2.630 74 45 30 5.782 1.603 6.745 1.871 7.709 2.138 8.673 2.405 9.636 2.672 30 45 5.775 1.629 6.737 1.900 7.700 2.172 8.662 2.443 9.625 2.714 15 16 5.76S 1.654 6.729 1.929 7.690 2.205 8.651 2.481 9.613 2.756 74 15 5.760 1.679 6.720 1.959 7.6S0 2.239 8.640 2.518 9.601 2.798 45 30 5.753 1.704 6.712 1.988 7.671 2.272 S.629 2.556 9.5SS 2.840 30 45 5.745 1.729 6.703 2.017 7.661 2.306 8.618 2.594 9.576 2.882 15 17 5.73S 1.754 6.694 2.047 7.650 2.339 S.607 2.631 9.563 2.924 73 15 5.730 1.779 6.685 2.076 7.640 2.372 8.595 2.669 9.550 2.965 45 30 5.722 1.S04 6.676 2.105 7.630 2.406 8.583 2.706 9.537 3 007 30 45 5.714 1.829 6.667 2.134 7.619 2.439 8.572 2.744 9.524 3.049 15 18 5.706 1.854 6.657 2.163 7.608 2.472 8.560 2.781 9.511 3.090 72 15 5.698 1.S79 6.648 2.192 7.598 2.505 8.547 2.818 9.497 3.132 45 30 5.690 1.904 6.63S 2.221 7.5S7 2.538 8.535 2.856 9.483 3.173 30 45 5.6S2 1.929 6.629 2.250 7.575 2.572 8.522 2.893 9.469 3.214 15 19 5.673 1.953 6.619 2.279 7.564 2.605 8.510 2.930 9.455 3.256 71 15 5.665 1.978 6.609 2.30S 7.553 2.63S 8.497 2.967 9.441 3.297 45 30 5.656 2.003 6.598 2.337 7.541 2.670 8.484 3.004 9.426 3.338 30 45 5.647 2.02S 6.588 2.365 7.529 2.703 8.471 3.041 9.412 3.379 15 20 5.638 2.052 6.57S 2.394 7.518 2.736 8.457 3.078 9.397 3.420 70 15 5.629 2.077 6.567 2.423 7.506 2.769 8.444 3.115 9.382 3.461 45 30 5.620 2.101 6.557 2.451 7.493 2.802 8.430 3.152 9.367 3.502 30 45 5.611 2.126 6.546 2.480 7.481 2.834 8.416 3.189 9.351 3.543 15 21 5.601 2.150 6.535 2.509 7.469 2.867 8.402 3.225 9.336 3.584 69 15 5.592 2.175 6.524 2.537 7.456 2.900 8.388 3.262 9.320 3.624 45 30 5.582 2.199 6.513 2.566 7.443 2.932 8.374 3.299 9.304 3.665 30 45 5.573 2.223 6.502 2.594 7.430 2.964 8.359 3.335 9.2S8 3.706 15 22 5.563 2.248 6.490 2.622 7.417 2.997 8.345 3.371 9.272 3.746 68 " 15 5.553 2.272 6.479 2.651 7.404 3.029 8.330 3.408 9.255 3.787 45 30 5.543 2.296 6.467 2.679 7.391 3.061 S.315 3.444 9.239 3.827 30 45 5.533 2.320 6.455 2.707 7.378 3.094 8.300 3.480 9.222 3.867 15 23 5.523 2.344 6.444 2.735 7.364 3.126 8.285 3.517 9.205 3.907 67 15 5.513 2.368 6.432 2.763 7.350 3.158 8.269 3.553 9.188 3.947 45 30 5.502 2.392 6.419 2.791 7.336 3.190 8.254 3.589 9.171 3.988 30 45 5.492 2.416 6.407 2.819 7.322 3.222 8.238 3.625 9.153 4.02S 15 24 0, 5.481 2.440 6.395 2.847 7.308 3.254 8.222 3.661 9.136 4.067 66 15 5.471 2.464 6.382 2.875 7.294 3.286 8.206 3.696 9.118 4.107 45 30 5.460 2.488 6.370 2.903 7.280 3.318 8.190 3.732 9.100 4.147 30 45 5.449 2.512 6.357 2.931 7.265 3.349 8.173 3.768 9.0S1 4.187 15 25 5.43S 2.536 6.344 2.95S 7.250 3.381 8.157 3.804 9.063 4.226 65 15 5.427 2.559 6.331 2.9S6 7.236 3.413 8140 3.839 9.045 4.266 45 30 5.416 2.5S3 6.318 3.014 7.221 3.444 8.123 3.875 9.026 4.305 30 45 5.404 2.607 6.305 3.041 7.206 3.476 8.106 3.910 9.007 4.345 15 26 5.393 2.630 6.292 3.069 7.190 3507 8089 3.945 S.9SS 4.3S4 64 15 5.3S1 2.654 6.278 3.096 7.175 3.538 8.072 3.9S1 8.969 4.423 45 30 5.370 2.677 6.265 3123 7.160 3.570 8.054 4.016 8.949 4.462 30 45 5.358 2.701 6.251 3.151 7.144 3.601 8.037 4.051 8.930 4.501 15 27 5.346 2.724 6.237 3.178 7.128 3.632 8.019 4.0S6 8 910 4.540 63 15 5.334 2.747 6.223 3.205 7.112 3.663 8.001 4.121 8.890 4.579 45 30 5.322 2.770 6.209 3.232 7.096 3.694 7.983 4.156 8.870 4.618 30 45 5.310 2.794 6.195 3.259 7.080 3.725 7.965 4.190 8.850 4.656 15 28 5.298 2.817 6.181 3.286 7.064 3.756 7.947 4.225 8.829 4.695 62 15 5.285 2.840 6.166 3.313 7.047 3.787 7.928 4.260 S.809 4.733 45 30 5.273 2.863 6.152 3.340 7.031 3.817 7.909 4.294 8.788 4.772 30 45 5.260 2.886 6.137 3.367 7.014 3.848 7.S91 4329 8.767 4.810 15 29 5.248 2.909 6.122 3.394 6.997 3.878 7.872 4.363 8.746 4.848 61 15 5.235 2.932 6.107 3.420 6.9S0 3.909 7.852 4.398 8.725 4.8S6 45 30 5.222 2.955 6 093 3.447 6.963 3.939 7.833 4.432 8.704 4.924 30 45 5.209 2.977 6.077 3.474 6.946 3.970 7.814 4.466 8.682 4.962 15 30 5.196 3.000 6.062 3.500 6.928 4.000 7.794 4.500 8.660 5.000 60 O f Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. t Bearing. Distance 6. Distance 7. Distance 8. Distance 9. Distance 10. Bearing. 60°-75 c 74 30°- -45 O Bearing. Distance 1. Distance 2. Distance 3. Distance 4. Distance 5. Bearing. o r Lat< Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o t 30 15 0.864 0.504 1.728 LOOS 2.592 1.511 3.455 2.015 4.319 2.519 59 45 30 0.862 0.508 1.723 1.015 2.585 1.523 3.447 2.030 4.308 2.538 30 45 0.859 0.511 1.719 1.023 2.578 1.534 3.438 2.045 4.297 2.556 15 31 0.857 0.515 1.714 1.030 2.572 1.545 3.429 2.060 4.286 2.575 59 15 0.855 0.519 1.710 1.038 2.565 1.556 3.420 2.075 4.275 2.594 45 30 0.853 0.522 1.705 1.045 2.558 1.567 3.411 2.090 4.263 2.612 30 45 0.850 0526 1.701 1.052 2.551 1.579 3.401 2.105 4.252 2.631 15 32 0.848 0.530 1.696 1.060 2.544 1.590 3.392 2.120 4.240 2 650 58 15 0.846 0.534 1.691 1.067 2.537 1.601 3.383 2.134 4.229 2.668 45 30 0.843 0.537 1.687 1.075 2.530 1.612 3.374 2.149 4.217 2.686 30 45 0.841 0.541 1.682 1.082 2.523 1.623 3.364 2.164 4.205 2.705 15 33 0.839 0.545 1.677 1.089 2.516 1.634 3.355 2.179 4.193 2.723 57 15 0.836 0.54S 1.673 1.097 2.509 1.645 3.345 2.193 4.181 2741 45 30 0.834 0.552 1.668 1.104 2.502 1.656 3.336 2.208 4.169 2.760 30 45 0.831 0.556 1.663 1.111 2.494 1.667 3.326 2.222 4.157 2.778 15 34 0.829 0.559 1.658 1.118 2.487 1.678 3.316 2.237 4.145 2.796 56 15 0.827 0.563 1.653 1.126 2.480 1.688 3.306 2.251 4.133 2.814 45 30 0.824 0.566 1.648 1.133 2.472 1.699 3.297 2.266 4.121 2.832 30 45 0.822 0.570 1.643 1.140 2.465 1.710 3.287 2.280 4.108 2.850 15 35 0.819 0.574 1.638 1.147 2.457 1.721 3.277 2.294 4.096 2.868 55 15 0.817 0.577 1.633 1.154 2.450 1.731 3.267 2.309 4.083 2.886 45 30 0.814 0.581 1.628 1.161 2.442 1.742 3.257 2.323 4.071 2.904 30 45 0.812 584 1.623 1.168 2.435 1.753 3.246 2.337 4.058 2.921 15 36 0.809 0.588 1.618 1.176 2.427 1.763 3.236 2.351 4.045 2.939 54 15 0.S06 0.591 1.613 1.183 2.419 1.774 3.226 2.365 4.032 2.957 45 30 0.804 0.595 1.608 1.190 2.412 1.784 3.215 2.379 4.019 2.974 30 45 0.801 0.598 1.603 1.197 2.404 1.795 3.205 2.393 4.006 2.992 15 37 0.799 0.602 1.597 1.204 2.396 1.805 3.195 2.407 3.993 3.009 53 15 0.796 0.605 1.592 1.211 2.388 1.816 3.184 2.421 3.980 3.026 45 30 0.793 0.609 1.587 1.218 2.380 1.826 3.173* 2.435 3.967 3.044 30 45 0.791 0.612 1.581 1.224 2.372 1.837 3.163' 2.449 • 3.953 3.061 15 38 0.788 0.616 1.576 1.231 2.364 1.847 3.152 2.463 3 940 3.078 52 15 0.785 0.619 1.571 1.238 2.356 1.857 3.141 2.476 3.927 3.095 45 30 0.783 0.623 1.565 1.245 2.348. 1.868 3.130 2.490 3.913 3.113 30 45 0.780 0.626 1.560 1.252 2.340 1.878 3.120 2.504 3.899 3.130 15 39 0.777 0.629 1.554 1.259 2.331 1.888 3.109 2.517 3.886 3.147 51 15 0.774 0.633 1.549 1.265 2.323 1.898 3.098 2.531 3.872 3.164 45 30 0.772 0.636 1.543 1.272 2.315 1.908 3.086 2.544 3.858 3.180 30 45 0.769 0.639 1.538 1.279 2.307 1.918 3.075 2.558 3.844 3.197 15 40 0.766 0.643 1.532 1.286 2.298 1.928 3 064 2.571 3.830 3.214 50 15 0.763 0.646 1.526 1.292 2.290 1.938 3 053 2.584 3.816 3.231 45 30 0.760 0.649 1.521 1.299 2.281 1.948 3.042 2.598 3.802 3.247 30 45 0.758 0653 1.515 1.306 2.273 1.958 3.030 2.611 3.788 3.264 15 41 0.755 656 1.509 1.312 2.264 1.968 3.019 2.624 3.774 3.280 49 15 0.752 0.659 1.504 1.319 2.256 1.978 3.007 2.637 3759 3.297 45 30 0.749 0.663 1.498 1325 2.247 1.988 2.996 2.650 3.745 3.313 30 45 0.746 0.666 1.492 1.332 2.238 1.998 2.984 2.664 3.730 3.329 15 42 0.743 0.669 1,486 1.338 2.229 2.007 2.973 2.677 3.716 3.346 48 15 0.740 0.672 1.480 1.345 2.221 2.017 2.961 2.689 3.701 3.362 45 30 0.737 0.676 1.475 1.351 2.212 2 027 2.949 2.702 3.686 3.378 30 45 0.734 0.679 1.469 1.358 2.203 2.036 2.937 2.715 3.672 3.394 15 43 0.731 682 1.463 1.364 2.194 2.046 2.925 2.728 3.657 3.410 47 15 0.728 0.685 1.457 1.370 2.185 2.056 2.913 2.741 3.642 3.426 45 30 0.725 0.688 1.451 1.377 2.176 2.065 2.901 2.753 3.627 3.442 30 45 0.722 0.692 1.445 1.383 2.167 2.075 2.889 2 766 3.612 3.458 15 44 0.719 0.695 1.439 1.389 2.158 2.084 2.877 2.779 3.597 3.473 46 15 0.716 0.698 1.433 1.396 2.149 2.093 2.865 2.791 3.582 3.489 45 30 0.713 0.701 1.427 1.402 2.140 2.103 2.853 2.804 3.566 3.505 30 45 0.710 0.704 1.420 1.408 2.131 2.112 2S41 2.816 3.551 3.520 15 45 0.707 0.707 1.414 1.414 2.121 2.121 2.828 2.828 3.536 3.536 45 o r Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. O f Bearing, Distance 1. Distance 2. Distance 3. Distance 4. Distance 5. Bearing. 45° -60°" 30°- -45 O 75 Bearing. Distance 6. Distance 7. Distance 8. Distance 9. Distance 10. Bearing. O f Lat, Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. o t 30 15 5.183 3.023 6.047 3.526 6.911 4.030 7.775 4.534 8.638 5.038 59 45 30 5.170 3.045 6.031 3.553 6.893 4.060 7.755 4.568 8.616 5.075 30 45 5.156 3.068 6.016 3.579 6.875 4.090 7.735 4.602 8.594 5.113 15 31 5.143 3.090 6.000 3.605 6.857 4.120 7.715 4.635 8.572 5.150 59 15 5.129 3.113 5.984 3.631 6.839 4.150 7.694 4.669 8.549 5.188 45 30 5.116 3.135 5.968 3.657 6.821 4.180 7.674 4.702 8.526 5.225 30 45 5.102 3.157 5.952 3.683 6.803 4.210 7.653 4.736 8.504 5.262 15 32 5.088 3.180 5.936 3.709 6.784 4.239 7.632 4.769 8.481 5.299 58 15 .5.074 3.202 5.920 3.735 6.766 4.269 7.612 4.802 8.457 5.336 45 30 5.060 3.224 5.904 3.761 6.747 4.298 7.591 4.836 8.434 5.373 30 45 5.046 3.246 5.887 3.787 6.728 4.328 7.569 4.869 8.410 5.410 15 33 5.032 3.268 5.871 3.812 6.709 4.357 7.548 4.902 8.387 5.446 57 15 5.018 3.290 5.854 3.838 6.690 4.386 7.527 4.935 8.363 5.483 45 30 5.003 3.312 5.837 3.864 6.671 4.416 7.505 4.967 8.339 5.519 30 45 4.989 3.333 5.820 3.889 6.652 4.445 7.483 5.000 8.315 5.556 15 34 4.974 3.355 5.803 3.914 6.632 4.474 7.461 5.033 8.290 5.592 56 15 4.960 3.377 5.786 3.940 6.613 4.502 7.439 5.065 8.266 5.628 45 30 4.945 3.398 5.769 3.965 6.593 4.531 7.417 5.098 8.241 5.664 30 45 4.930 3.420 5.752 3.990 6.573 4.560 7.395 5.130 8.217 5.700 15 35 4.915 3.441 5.734 4.015 6.553 4.5S9 7.372 5.162 8.192 5.736 55 15 4.900 3.463 5.716 4.040 6.533 4.617 7.350 5.194 8.166 5.772 45 30 4.885 3.484 5.699 4.065 6.513 4.646 7.327 5.226 8.141 5.807 30 45 4.869 3.505 5.681 4.090 6.493 4.674 7.304 5.258 8.116 5.843 15 36 4.854 3.527 5.663 4.115 6.472 4.702 7.281 5.290 8.090 5.878 54 15 4.839 3.548 5.645 4.139 6.452 4.730 7.258 5.322 8.064 5.913 45 30 4.823 3.569 5.627 4.164 6.431 4.759 7.235 5.353 8.039 5.948 30 45 4.808 3.590 5.609 4.188 6.410 4.787 7.211 5.385 8.013 5.983 15 37 4.792 3.611 5.590 4.213 6.389 4.815 7.188 5.416 7.986 6.018 53 15 4.776 3.632 5.572 4.237 6.368 4.842 7.164 5.448 7.960 6.053 45 30 4.760 3.653 5.554 4.261 6.347 4.870 7.140 5.479 7.934 6.088 30 45 4.744 3.673 5.535 4.286 6.326 4.898 7.116 5.510 7.907 6.122 15 38 4.728 3.694 5.516 4.310 6 304 4.925 7.092 5.541 7.880 6.157 52 15 4.712 3.715 5.497 4.334 6.283 4.953 7.068 5.572 7.853 6.191 45 30 4.696 3.735 5.478 4.358 6.261 4.980 7.043 5.603 7.826 6.225 30 45 4.679 3.756 5.459 4.381 6.239 5.007 7.019 5.633 7.799 6.259 15 39 4.663 3.776 5.440 4.405 6.217 5.035 6.994 5.664 7.772 6.293 51 15 4.646 3.796 5.421 4.429 6.195 5.062 6.970 5.694 7.744 6.327 45 30 4.630 3.816 5.401 4.453 6.173 5.089 6.945 5.725 7.716 6.361 30 45 4.613 3.837 5.382 4.476 6.151 5.116 6.920 5.755 7.688 6.394 15 40 4.596 3.857 5.362 4.500 6.128 5.142 6.894 5.785 7.660 6.428 50 15 4.579 3.877 5.343 4.523 6.106 5.169 6.869 5.815 7.632 6.461 45 30 4.562 3.897 5.323 4.546 6.083 5.196 6.844 5.845 7.604 6.495 30 45 4.545 3.917 5.303 4.569 6.061 5.222 6.818 5.875 7.576 6.528 15 41 4.528 3.936 5.283 4.592 6.038 5.248 6.792 5.905 7.547 6.561 49 15 4.511 3.956 5263 4.615 6.0.15 5.275 6.767 5.934 7.518 6.594 45 30 4.494 3.976 5.243 4 638 5.992 5.301 6.741 5.964 7.490 6.626 30 45 4.476 3.995 5.222 4.661 5.968 5.327 6.715 5.993 7.461 6.659 15 42 4.459 4.015 5.202 4.684 5.945 5.353 6.688 6022 7.431 6.691 48 15 4.441 4.034 5.182 4.707 5.922 5.379 6.662 6.051 7.402 6.724 45 30 4.424 4.054 5.161 4.729 5.898 5.405 6.635 6080 7.373 6.756 30 45 4.406 4.073 5.140 4.752 5.875 5.430 6.609 6.109 7.343 6.788 15 43 4.388 4.092 5.119 4.774 5.851 5.456 6.582 6.138 7.314 6.820 47 15 4.370 4.111 5.099 4.796 5.827 5.481 6.555 6.167 7.284 6.852 45 30 4.352 4.130 5.078 4.818 5.803 5.507 6.528 6.195 7.254 6884 30 45 4.334 4.149 5.057 4.841 5.779 5.532 6.501 6 224 7.224 6.915 15 44 4.316 4.168 5.035 4.863 5.755 5.557 6.474 6.252 7.193 6.947 46 15 4.298 4.187 5.014 4.885 5.730 5.582 6.447 6.280 7.163 6.978 45 30 4.280 4.206 4.993 4.906 5.706 5.607 6.419 6.308 7.133 7.009 30 45 4.261 4.224 4.971 4.928 5.681 5.632 6.392 6.336 7.102 7.040 15 45 4.243 4.243 4.950 4.950 5.657 5.657 6.364 6.364 , 7.071 7.071 45 o t Dep, Lat. Dep. Lat. Dep. Lat. Dep. Lat, Dep. Lat. o t Bearing, Distance 6. Distance 7. Distance 8. Distance 9. ] Distance 10. Bearing. 45°-60 c A TABLE OF THE ANGLES Which every Point and Quarter Point of the Compass makes with the Meridian. North.. Points. 0-14 o- 1 ! 0-% 1 t 11 2 48 45 5 37 30 8 26 15 11 15 Points. o-i| 0-34* South.. N. by E. N. by W. S. by E. S. by W. N.N.E. N.N.W. 1-% 1-34 2 14 3 45 16 52 30 19 41 15 22 30 I-V4 I-V2 l-3/ 4 2 S.S.E. S.S.W. N.E. by N. N.W. by N. 2-1/4 2-V2 2-34 3 25 18 45 28. 7 30 30 56 15 33 45 2-V4 2-V2 2-% 3 S.E. by S. S.W. by S. NE. N.W. 3-% 3-i| 3- 3 i 4 36 33 45 39 22 30 42 11 15 45 3-1/4 8-« 3-3/ 4 4 S.E. S.W. N.E. by E N.W.byW. 4-1/4 4-i/ 2 4-% 5 47 48 45 50 37 30 53 26 15 56 15 4-% 5 S.E. by E. S.W. by W. E.N.E. W.N.W. 5-V4 5- 1 ! 6-% 6 59 3 45 61 52 30 64 41 15 67 30 5-V4 5-% 6 E.S.E. W.S.W. E. by N. W. by N. 6-y 4 6-% 6-% 7 70 18 45 73 7 30 75 56 15 78 45 6-V4 6-i| «-% 7 E. by S. W. by S. East. West. 81 33 45 84 22 30 87 11 15 90 7-i/ 4 7-V, r-% 8 East. West. iPR 15 1903 WtVi LIBKAHY Ul- UUNtiKCSS 020 186 234 6