m
TEXT BOOK
ON
RAILROAD SURVEYING
BY
GEORGE WELLINGTON PICKELS, C.E.
INSTRUCTOR IN CIVIL ENGINEERING UNIVERSITY OF ILLINOIS
AND
CARROLL CARSON WILEY, C.E.
ASSOCIATE IN CIVIL ENGINEERING UNIVERSITY OF ILLINOIS
FIRST EDITION FIRST THOUSAND
NEW YORK JOHN WILEY & SONS, INC.
LONDON : CHAPMAN & HALL, LIMITED 1914
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Copyright, 1913, by G. W. PICKELS AND C. C. WILEY
PUBLISHERS PRINTING COMPANY 207-217 West Twenty-fifth Street, New York
PREFACE
THIS book was written primarily for the use of students in Railroad Surveying, and is practically a summary of the notes used by the authors in their classes for a number of years.
The aim throughout has been to present the essentials of the subject in simple, concise form and to give modern practical methods only. To this end detailed mathematical solutions are omitted, obsolete methods abandoned, and only the more common problems outlined; consequently the subject-matter occupies considerably less space than the ordinary hand-book, but at the same time covers all phases of the subject thoroughly.
From the standpoint of the instructor, some of the essential characteristics of the book are:
(1) A co-ordination of the entire subject, indicating the general order and the solution of the various steps in the work.
(2) The explanation of reasons for or conditions under which the various problems arise.
(3) The assumption of a knowledge of elementary surveying and plane trigonometry on the part of the reader.
(4) The consequent omission of detailed mathematics. Out- lined solutions only are given, and hence the student must follow the solution of a problem through step by step instead of sub- stituting blindly in some formula which has the appearance of being suitable. The student is therefore more thoroughly trained in the plan of attack, and consequently can more readily handle the multitude of problems which he can not find "all worked out" in this or any other book.
Although designed as a book for student use, it is believed that it will appeal to the practicing engineer as well, and the latter's attention is respectfully called to the following features:
(1) The simplified curve nomenclature as recommended by the American Railway Engineering Association has been adopted.
(2) The " Spiral" has been co-ordinated with the circular curve, where it properly belongs under modern railroad practice. It will be noted that the spiral here given is of a general form and is
iii
287914
IV PREFACE
equally applicable with chords of any desired length as a so- called " Six-chord" or " Ten-chord" spiral.
(3) " Turnouts" are presented in practical form as actually used on steam roads in America, i.e., with straight frogs and switches.
Acknowledgment is hereby made of the courtesy of Prof. J. C. Nagle in permitting the use of Tables 5, 6, 8, and 9, which are taken from his " Field Manual for Railroad Engineers"; to Professor Carhart, for Table 7, which is taken from his "Field Book for Civil Engineers"; and to Prof. Walter Loring Webb, for Tables 9 and 10 from his work on "Railroad Construction," which appear as Tables 10 and 11 in this volume.
GEORGE WELLINGTON PICKELS, CARROLL CARSON WILEY.
University of Illinois, Urbana, 111., August, 1913.
CONTENTS
CHAPTER I RAILROAD SURVEYS
PARAGRAPH PAGE
1. Terminals and Intermediate Points Connected by
a Railroad 1
2. The Reconnoissance Survey 1
3. Reconnoissance in Prairie Country ...... 2
4. Reconnoissance in Rolling, Hilly Country .... 2
5. Reconnoissance in Mountainous Country .... 2
6. Preliminary Survey in Prairie Country 3
7. Preliminary Survey in Rolling, Hilly Country ... 3
8. Preliminary Survey in Mountainous Country ... 4
9. The Location Survey 4
10. Reference Stakes 4
11. Slope Stakes 5
12. Distribution Stakes 6
13. Borrow-Pit Stakes 6
14. The Location of Culverts and Trestles 6
15. The Time to Set Stakes 6
16. Monthly Estimate Surveys 6
17. Finishing Stakes 6
18. Center Stakes 6
19. Grade Stakes 6
20. Right of Way Stakes 6
21. Special Surveys 7
22. Maintenance Surveys 7
23. Monumenting 7
24. Suryej^s for Additional Tracks 7
25. The Transit Party 7
26. The Level Party 9
27. The Topography Party 9
28. The Land-line Party 9
29. Drafting 9
v
VI CONTENTS
PARAGRAPH PAGE
30. The Transit and Tape Method of Making Preliminary
Surveys 10
31. The Transit and Stadia Method of Making Preliminary
Surveys 10
32. The Plane Table Method of Making Preliminary
Surveys 10
33. Remarks 11
34. Bench Marks 11
CHAPTER II MAPS
35. The Reconnoissance Map 12
36. The Reconnoissance Profile 12
37. The First Preliminary Maps . 12
38. The Preliminary Profiles 12
39. The Preliminary Map (proper) ....'... 12
40. The Projected Location 13
41. Location Notes 13
42. The Location Map 13
43. The Location Profile 14
44. Additional Profiles 14
45. Legal Right of Way Maps 15
46. Maintenance of Way Right of Way Maps .... 15
47. Station Maps 15
48. Progress Profiles 15
49. Progress Photographs 15
CHAPTER III DISTANCE, CURVATURE, AND GRADES
50. Additional Distance 16
51. Effect of Curvature 17
52. Choice of Curvature 17
53. Minor Grades 18
54. Ruling Grades 18
55. Pusher Grades . 19
56. Choice of Grades 19
57. Vertical Curves 21
CONTENTS Vll
CHAPTER IV
CURVES Part 1. Circular Curves
PARAGRAPH PAGE
58. Functions of a Simple Curve 24
59. Relation between R and D 26
60. Field Work . 27
61. Fundamental Principles 32
62. Offsets from Chords Produced >33
63. Chord Offset Method . 34
64. Example 35
65. To Find New Radius for a Given Change in E . . 36
66. To Change T.C. to Make C.T. Fall on ParaUel Tangent 37
67. To Change R and T.C. to Make C.T. FaU on ParaUel
Tangent, on same Radial Line, Approximately . 38
68. To Change R to Make T.C. Fall on Parallel Tangent 38
69. To Shift C.T. so that Forward Tangent will Pass
Through Controlling Point 39
70. Compound Curves 41
71. Given the Central Angles and Radii to Find the
Tangents 43
72. Given both Tangents and one Radius to Find the Other
Radius 43
73. Field Work 45
74. To Change Location of C.C. so that C.T. will FaU
on ParaUel Tangent 45
75. To Change Second Radius and the Location of C.C.
so that C.T. wiU FaU on Parallel Tangent, on Same
Radial line, Approximately 46
76. Reversed Curves 49
Part 2. Spirals
77. Definition of Spiral '49
78. Functions of Spiral 50
79. Formulas 52
80. Length of Spiral 52
81. Field Work 55
82. Deflection-Angle Method 56
83. Offset Method 60
84. To Insert Spiral between the Branches of Compound
Curve •..,-.- 62
85. Deflection Angles from Point on Spiral 62
86. To Spiral Compound Curve at Each End and between
Branches ... 63
Vlll CONTENTS
PARAGRAPH PAGE
87. Application of Spiral to Existing Simple Curves . . 64
88. To Spiral Existing Simple Curve by Shifting Track
outward near Center 64
89. To Spiral Existing Simple Curve by Sharpening
Curve at Ends 66
90. To Spiral Existing Simple Curve by Compounding
Curve near Center 67
91. Application of Spiral to Existing Compound Curves . 68
CHAPTER V EARTHWORK •
92. Railroad Cross-Sections 73
93. Width of Roadbed 73
94. Ditches 74
95. Side Slopes 74
96. Borrow Pits 74
97. Shrinkage 75
98. Growth ' . . 75
99. Settlement 75
100. Slope Stakes 76
101. Cross-Sectioning 77
102. Field Work 77
103. Sections at Grade Points 80'
104. Side-Hill Sections 82
105. Uncompleted Sections 82
106. End Area Method of Computing Volumes ... 83
107. Prismoidal Method of Computing Volumes ... 84
108. Earthwork on Curves 85
109. Computation of Haul 88
110. Problem in the Distribution of Earth 87
111. Problem, to Find Limit of Profitable Haul ... 89
112. Effect of Trestle?, etc., on the Distribution of Earth 90
CHAPTER VI
TURNOUTS, CONNECTIONS, AND CROSSINGS
113. Outline of Subjects Treated 91
114. Definitions 91
115. Switches 92
116. Frogs 94
117. Frog Angles 96
118. Frog Numbers 96
CONTENTS IX PARAGRAPH PAGE
119. Location of Turnouts 96
120. Turnouts from Straight Track 96
121. Turnouts from Curved Track ., 97
122. Double Turnouts 98
123. Practical Leads 98
124. Diverging Tracks, from Straight Tracks .... 99
125. Diverging Tracks, from Curved Tracks .... 100
126. Sidings from Straight Tracks 104
127. Sidings from Curved Tracks 106
128. Crossovers between Straight Tracks 109
129. Crossovers between Curved Tracks Ill
130. Connection between Intersecting Straight Tracks 111
131. Connection between One Straight and One Curved
Intersecting Track . .113
132. Connection between Intersecting Curved Tracks . 115
133. Crossings 116
134. Crossing Data 117
135. Straight Crossings 118
136. Single-Curve Crossings . 119
137. Double-Curve Crossings 120
APPENDIX. THEORY OF SPIRAL
138. Derivation of 3 and A 121
139. Derivation of the Coordinates, x and y 121
140. Derivation of a, A, b, B ; . . 122
141. Derivation of 0 123
142. The Osculating Circle 124
143. Superelevation 124
TABLES
1. Spiral Table 70
2. Turnout Table 99
3. Siding Table 105
4. Crossover Table. 110
5. Table of Radii 128
6. Functions of a 1° Curve 131
7. Logarithms of Numbers 158
8. Logarithmic Sines and Cosines 176
9. Logarithmic Tangents and Cotangents 191
10. Natural Sines, Cosines, Tangents and Cotangents . . 206
11. Natural Versed Lines and External Secants . . . . 229
12. Cubic Yards per 100 ft. in Terms of Center Height . 252
13. Cubic Yards per 100 ft. in Terms of Sectional Area . 258
14. Trigonometric Formulas 262
TEXT BOOK ON RAILROAD SURVEYING
CHAPTER I RAILROAD SURVEYS
THE practice in railroad location surveys in one part of the United States is entirely different from that in another part, so that rules which will apply in one locality will not apply at all in others. All country can be broadly classed in three divisions: (1) level prairie country offering no obstacles in the way of hills, valleys, etc., and allowing the locating engineer much latitude in the placing of his line, and consequently re- ducing distance and curvature to a minimum; (2) rolling, hilly country through which several lines are possible, none of them departing to any great extent from the direct line between controlling points; and (3) mountainous country, which taxes the skill and ingenuity of 'the locating engineer to the utmost.
Reconnoissance Surveys
1. The terminals and intermediate points connected by a railroad are determined by its promoters with a view to the amount of traffic that can be expected from them. The nature and the amount of the traffic and the direction of heaviest haul determine the maximum gradients and curvature advisable. The first thing to be determined by the locating engineer is the directions of the lines joining controlling points. This informa- tion can usually be obtained with sufficient accuracy from a map of the territory which it is generally possible to obtain. The topographic maps published by the government are the best.
2. A reconnoissance is then made of the strip of country through which the road is to pass, as the result of which some of
1
2 TEXT BOOK ON RAILROAD SURVEYING
the routes are eliminated as impractical and one or more chosen for a more detailed survey.
3. If the country is of the first class, no reconnoissance is necessary and the survey is in the nature of a preliminary.
4. For country of the second class, the reconnoissance should be made across-country on horseback, following the direction of the line determined from the map. If in following the direct line between controlling points obstacles are met with which can not be surmounted, such as high hills, the engineer should explore on both sides of the obstacle and decide if possible which route offers the least resistance. Before deflecting from a straight line, the engineer must be sure that his reasons for so doing are justified from an economic standpoint. In country of the second class it is seldom that grades cause much trouble, and the main lookout of the engineer is to keep the amount of curvature as low as possible. The result of the reconnoissance through country of the second class is that one or more routes are selected for a more detailed survey.
5. It is in mountainous country — third class — that all the skill of the engineer is brought into play. The drainage of the country should be carefully studied, as it plays a very important part in the location of a railroad. If the controlling points are in the same valley, the main problem is solved; and the con- forming of the alinement to the topography is merely a matter of detail. But when the controlling points are in different valleys, the ridges between them have to be crossed, and the principal object of the reconnoissance is to discover the most favorable crossing places in the valleys and on the ridges. The saddles in the ridges and the most favorable river crossings become secondary controlling points. The location of all such points is platted on the map, and their elevations and distances apart are recorded. The most important and useful " instruments " used on reconnoissance are the judgment and experience of the locating engineer, as upon these depend the amount and cost of more detailed surveys and the cost of construction and of operation.
RAILROAD SURVEYS 3
Preliminary Surveys
6. In country of the first class, a preliminary line is run for direction. The magnetic bearing of the direct line between controlling points is scaled off the map, and a line having this direction is initiated from the first controlling point and pro- duced to the second controlling point. Since the direction of the line as obtained from the map and this direction as laid off in the field are subject to considerable error, the first line run will probably pass to one side of the second controlling point. The distance by which the transit line misses its mark is noted and the correction that must be applied to the first line is com- puted. The next line run will be the location.
In running the preliminary line stakes should be placed only at transit points. A straight line is the most difficult one to run, and particular care must be taken to avoid errors. It must be remembered that the preliminary is a reference line, and if it is not straight the purpose for which it is run is defeated. The distances between hubs can be determined with sufficient accuracy by means of the stadia.
7. In country of the second class, preliminary lines are run over each of the routes chosen by the locating engineer on the reconnoissance survey. The data taken are such that the several routes can be compared with respect to distance, grades, and curvature. Usually lines run with the transit and stadia will give sufficient data as regards distance and curvature; and the elevations of enough commanding points can be taken with the stadia to indicate the grades that will be required by the several routes. From these data one of the routes will usually appear superior to the others, and what is generally known as a preliminary survey is then made over the selected route. A preliminary survey as generally understood is a topographic survey of a narrow strip of country within which the road must pass. The purpose of this survey is to secure data from which a topographic map can be platted upon which the paper location is projected. The transit and stadia line already run over the chosen route is used as the base line from which the topography is taken. Although this line is usually measured with the tape, time used for this purpose is wasted, as it is impossible to plat the traverse distances to a consistent degree
TEXT BOOK ON RAILROAD SURVEYING
of accuracy. Spirit levels are then run over the line to determine the elevations of the transit points, and bench marks are es- tablished at half-mile intervals.
8. In country of the third class, several preliminary lines are required, each following one of the routes chosen by the locating engineer. The approximate grades of the lines between secondary controlling points are obtained from the data taken on the re- connoissance survey, and the preliminary line should be chosen so that the grade line so determined will conform as nearly as possible to the surface of the ground. If this is done, topography will not have to be taken as far on each side of the line as would otherwise be necessary. In mountainous country topography can be taken more accurately with the hand level than with the stadia, and line stakes are placed every 100 feet and their eleva- tions determined by spirit leveling so that this can be done. In other respects the methods of surveying in mountainous coun- try are the same as those used in country of the second class.
Location Survey
9. On location the line is run very carefully, stakes are driven every 100 feet, the plusses and angles of all property lines are taken, and curves are run in where indicated on the map. The distances from intersections with property lines to the nearest government section monument, or other legal monument, are carefully chained, so that accurate descriptions of the right of way can be drawn up. All buildings near the line which will be damaged by it must be located and an estimate of the damage be made. A level party follows the transit party taking profile levels and establishing bench marks unless previously established. From these data alinement maps, right of way maps, and pro- files are made; and after the grade line is established on the profile, construction can begin.
Construction Surveys
10. Reference stakes. After the location has been made and accepted, and just before construction begins, the beginning and end of all curves and intermediate points on long tangents are " tied-in " by reference stakes so that after the construction
RAILROAD SURVEYS 5
woik is completed these points can be re-located in their correct positions. There are several methods of referencing a point; the one shown in Fig. 1 is very satisfactory. A is the point to be referenced. First choose permanent points at C and E at least 300 feet from A, making the angle CAE as nearly a right angle as possible. A distant windmill or house-chimney makes an ideal point. If these are not to be had, a nail
FIG. i.
driven into the trunk of a tree about five feet from the ground is good. If hubs are used they should be made as permanent as possible, and located so that they will not be disturbed. Af- ter C and E have been determined, set a hub at point B on the line AC, and another one at D on the line AE. B and D should be placed far enough from the center line of the road so that they will not be disturbed during construction. Point A is re- located after construction by the intersection of the lines CB and ED, the transit being set-up at B and D. Care and judg- ment should be used in locating reference points, as they should be used after the roadbed has settled for locating per- manent monuments.
11. Slope stakes are then set at each station on each side of the center line at the points where the side slopes of the cut or fill will intersect the ground surface. These stakes are for the guidance of the contractor, and have marked on them the vertical distance from the ground at the stake to the level of the roadbed. (For method of setting slope stakes, see paragraph 100.)
6 TEXT BOOK ON RAILROAD SURVEYING
12. Distribution stakes are set to show the contractor the desired movement of the earth from the cuts into the fills. (See paragraph 108.)
13. Borrow-pit stakes are set to indicate to the contractor the limits within which he may borrow earth for making the fills.
14. The location of culverts and trestles must also be staked out. If possible, these should be constructed in advance of the grading so that openings will not have to be left in the fill to be completed later.
15. The time to set stakes is just before they are needed. If they are set too long a time ahead, some of them will invariably be knocked out and will require re-setting.
16. Monthly estimate surveys. During the last few days of every month surveys are made to determine the amount of earth moved by the contractor during the month, so that he can be paid.
17. Finishing stakes. From the slope stakes the contractor can construct the roadbed to within a few inches of the correct grade. At this stage of the work it is customary to give finishing stakes, which are stakes driven to grade at the edges of the roadbed at each station. From these the contractor is able to finish the roadbed to the correct grade and width.
18. Center stakes. After the earthwork is completed, the important points on the center line are re-located from the reference stakes, and center stakes (usually untacked) are driven from which the track is laid.
19. Grade stakes. After the track is laid, grade stakes are driven at every station and at those points where the grade changes with their tops to the grade of the final top or base or rail. Grade stakes are placed on the inside of curves.
20. Right of way stakes. The right of way fences are usually built as soon as the materials for construction can be hauled over the line. For the guidance of the fence foreman, stakes are placed on each right of way line (1) opposite the beginning and
RAILROAD SURVEYS 7
end of all curves, (2) opposite each station on curves, (3) from 300 to 500 feet apart on tangents, and (4) at all jogs in the right of way. These stakes should be long enough to be seen above the weeds, wheat, oats, etc. Laths are excellent for this purpose.
21. Special surveys. After the track is laid, special structures, such as station buildings, water tanks, cattle pens, etc., will require staking out. In addition, the parts of the right of way leased to coal, lumber, and grain companies must be staked.
Maintenance Surveys
22. Due to the fact that it takes two or three years for the roadbed to settle and for the track to become thoroughly em- bedded in the ballast, it will be necessary to re-set center and grade stakes frequently during this period. All center stakes which are set after the track is laid should be tacked.
23. Monumenting. After the track and roadbed have settled thoroughly, permanent monuments should be placed at the beginning and end of all spirals and circular curves, between the branches of compound curves, and at intermediate points on long tangents.
24. Additional tracks, such as side tracks, business tracks, •branch-line tracks, yard tracks of various kinds, cross-overs,
etc., are required to be staked out from time to time. There is no end to surveys of this kind, and all the large railroads employ maintenance parties who do nothing else.
Organization of Parties
The field corps is usually divided into (1) a transit party, (2) a level party, (3) a topography party, and sometimes (4) a land-line party.
25. TRANSIT PARTY.— The members of the transit party and their duties are as follows:
The Locating Engineer is the chief of the entire surveying corps, and receives his instructions from and reports to the Chief
8 TEXT BOOK ON RAILROAD SURVEYING
Engineer of the railroad company. His duties are: to direct all the surveys from the reconnoissance to the location, to pro- vide accommodations for his party, to pay all general expenses, and in case a camp is necessary to purchase all supplies and to manage the camp.
The Transitman is next in rank to the locating engineer, and in his absence is in charge of the party. His duties are: to do the transit work, which consists of lining in the chainmen, measuring the angles between successive tangents, noting the bearings of the tangents, measuring the angles which the line makes with all railways, highways, streams, and property lines, and record- ing the plusses at which they cross the line; and to keep the notes of the transit party. On construction the transitman usually becomes Resident Engineer and has charge of from 8 to 15 miles of construction.
The Head Chainman ranks next to the transitman in the transit party, and is directly in charge of the rear chainman, stakeman, and axmen. His duties are: to see that the distances are chained correctly; to see that the stakes are driven on line, that they are driven straight, and that they are marked cor- rectly; to direct the axmen where to cut in opening up the line; to set new transit points ; and to direct the taking of plusses. The head chainman has a very important position, as he regulates the speed of the entire party. In open country frequently the locating engineer takes this position. The head chainman carries the zero end of the tape.
The Rear Chainman's duties are : to hold his end of the tape on the last stake driven while the head chainman gets the distance; and to take and record all plusses which he turns over to the transitman at frequent intervals.
The Rear Flagman's duties are: to give the transitman a sight on the back sight station whenever he signals for it; and to carry excess baggage. The rear flagman should be a wide- awake man with good eyesight.
The Stakeman's duties are: to carry the stakes; to mark the station numbers on the stakes; and to drive the stakes as directed by the head chainman.
The Axmen do all the necessary clearing in order that the transit and level parties may have a clear path. They are sometimes required to make the stakes.
RAILROAD SURVEYS
26. THE LEVEL PARTY.— The members of the level party and their duties are as follows:
The Levelman is chief of the level party and ranks next to the transitman in the surveying corps. His duties are: to run profile levels over the line and to establish bench marks; and to keep the level notes.
The Rodman's duties are: to hold the rod vertical upon the ground at each station, and at those intermediate points where the longitudinal slope of the ground changes; and to keep " peg notes " as a check on the levelman's computations.
27. THE TOPOGRAPHY PARTY.— The members of the topography party and their duties are as follows:
The Topographer usually holds equal rank with the levelman in the surveying corps. This position is a very important one and should be filled by an experienced man. The duties of the topographer are: to take all data necessary for making an accurate contour map of a strip of country sufficiently wide to enable the engineer to make an intelligent projected location; and to record these data in such a way that they will be readily understood by the draftsman. The topographer is assisted in his work by a rodman and a tapeman.
28. THE LAND-LINE PARTY.— The duties of this party are : to measure the angles which the line makes with all railways, highways, streams, and property lines; to tie-in the line to the nearest government monuments so that legal descriptions may be prepared of the required right of way ; and to secure the names of the property owners.
29. Drafting. In addition to the above field parties there is the field draftsman, who does his work in camp. His duties are to plat the notes taken by all the parties the previous day, which necessitates the use of two sets of field note-books or else loose-leaf note-books. In some cases the draftsman, with the help of tha locating engineer and the transitman, plats the notes each night ; and the levelman plats the profile of the line over which he ran levels that day. Thus the map is kept up to date, and the locating engineer can project his location as the line advances.
10 TEXT BOOK ON RAILROAD SURVEYING
Methods of Making Preliminary Surveys
The preliminary survey is the most expensive survey, and is of primary importance since the location depends directly upon it. Hence the method of making it should be given considerable thought in order that it may be done with accuracy and economy. There are at present three general methods used: (1) the transit and tape method, (2) the transit and stadia method, and (3) the plane table method.
30. The transit and tape method is by far the most common. The transit party runs the line with transit and tape, the level party follows taking profile levels, and the topography party follows the level party; the land-line party may come in any- where after the transit party. This kind of a survey will require from six to fifteen men, depending on whether the several parties have a separate personnel and on the number of axmen required to open the line.
31. The transit and stadia method consists in running the line with the transit and stadia. Stakes are placed only at transit stations, and the elevations of these points are determined by transit and trigonometric leveling. The location and eleva- tions of important intermediate points along the line are de- termined in a similar manner. While the transit is at each station, the topography around that point is taken with the stadia. Thus all the needed data are taken as the line advances. These data may be recorded in the note-book and worked up later by the party draftsman; but it is much better if the draftsman plats the notes as the transitman takes them and draws in the contours while the landscape is before him. The draftsman holds a very important position in this party and should be an expert in that line of work. A survey by this method is very accurate as re- gards the contours, which are the most important item on a preliminary map; and, if good men are employed, it is more efficient than the first method. This method requires a transit- man, a draftsman, two rodmen, and as many axmen as the nature of the country may require.
32. The plane table method is very similar to the one just described and differs from it mainly in the use of instruments.
RAILROAD SURVEYS 11
The plane table takes the place of the transit, and the plane tableman does the drafting. Owing to the difficulty in handling and setting up the plane table, it is doubtful whether this method is as efficient as the transit and stadia method; and although the services of the draftsman are dispensed with, yet the progress is possibly not as rapid.
33. Remarks. For long lines that justify the employment of a large number of men the transit and tape method is probably the most efficient. In other cases, however, the transit and stadia method will prove the more economical. The latter method has not been used to any considerable extent, due to the fact that few engineers fully appreciate the advantages of the stadia method; but in the few cases in which it has been tried it has fully demonstrated its superiority, particularly for open country.
34. Bench marks. When spirit-levels are run over the line, bench marks should be established at half-mile intervals, ap- proximately, and should be placed far enough from the center line so that they will not be disturbed during construction. After construction, permanent bench marks should be established on all permanent structures, such as concrete bridges, and at every station building along the line. The common practice of using spikes driven in telephone poles and mile posts is a very dangerous one, as these are frequently moved and re-set. If the road has few concrete or steel structures, then bench marks may be established on trestles. When these are renewed, the elevations of the several parts will rarely be changed more than an inch; while a bench mark on a telephone pole may be changed several feet.
Note. — For further information on the subject of Railway Surveys and the Economics of Railway Location, see A. M. Wellington's "Economic Theory of the Location of Railways; " F. Lavis' " Railway Location Surveys and Estimates," or W. L. Webb's "Economics of Railroad Construction."
CHAPTER II
MAPS
Reconnoissance Maps
35. The reconnoissance map consists of a general sketch of the country which the locating engineer has investigated, and shows the several routes that are possible. Only controlling points, such as towns to be passed through, available stream crossings, saddles in the ridges, etc., are shown. If an existing map of the country is available, it is best to draw in the routes directly upon it. The notes taken on the reconnoissance survey regarding the geological formations, the cultural features of the country, the width, depth, and current of streams, etc., are considered part of the reconnoissance map, and frequently have great weight in the choice of routes.
36. The reconnoissance profile is made from the elevations of the controlling points and the distances between them. Pro- files are made for each of the several routes and are frequently placed on the same sheet, so that a more intimate comparison can be made. The purpose of the reconnoissance maps is to eliminate the impractical routes and to determine which ones will bear a more detailed investigation.
Preliminary Maps
37. The first preliminary maps show the transit and stadia lines run, and all railroads, highways* and streams that cross the lines.
38. The preliminary profiles corresponding to the first pre- liminary maps are made from the elevations of the traverse stations. From a study of these maps one route — occasionally two — will appear superior to the others, and the preliminary survey proper is then made over this route.
39. The preliminary map is generally made to a scale of from 200 to 400 feet to the inch, and is a complete topographic map of
12
MAPS 13
a strip of country from 100 to 1,000 feet wide. All highways, railways, streams, and buildings are shown. Frequently it is desirable to show the property lines, the names of land owners, and government monuments. Also all geological formations and other features that might affect the location of the line are indicated. Occasionally, special features may require an aux- iliary map to a scale of 50 or 100 feet to the inch over short stretches of the line.
40. The projected location is then made on the preliminary map. First project that line which will give the best alinement and grades. This will be the best line from the standpoint of operation, and the one to be used unless the cost of construction is prohibitive. In this case determine the line whose construction will come with- in the allowable cost and at the same time keeps within the allowable limits of curvature and grade. This can be done only by trial and requires a large amount of skill and judgment. In order to determine the grades and the amount of earthwork for the several projected lines, it will be necessary to construct a profile for each of them from the contour map. In locating grade lines on these profiles it must be remembered (1) that intersecting railways must be crossed either at grade or at a clearance distance above or below grade, (2) that highways can be raised or lowered within certain limits, and (3) that streams must be crossed a safe distance above high-water mark.
After satisfactory tangents have been projected, they are connected by curves which most nearly conform to the contour of the ground, and at the same time keep within the maximum curvature. If the curves are to be spiraled, allowance must be made at this time.
41. Location notes are then made from the accepted projected location. The bearings of tangents, the plusses of the be- ginnings and ends of all curves, the central angles of all curves, and the degrees of curve are scaled off the map and recorded. These condensed notes are used in making the final location.
Location Map
42. The location map is usually made to the same scale as the preliminary map, and shows all railways, highways, streams, and property lines that cross the line, together with their plusses;
14 TEXT BOOK ON RAILROAD SURVEYING
the names of the property owners and the amount of right of way required from each; the government subdivision lines and the numbers of sections, etc.; the distances from the line to govern- ment monuments; the boundaries of each field through which the line passes; the location and size of all openings; and any other data that will be of use to the construction engineer or to the right of way agent.
The location map can often be made by adding the necessary data to the preliminary map, and then making a new tracing, omitting the contours and such other features that are not de- sired on the final map.
43. The location profile is made from the profile levels which were run over the located line, and shows: the ground line; the grade line, including the per cent, of grade of the different por- tions and the elevations of all points where the grade changes and all points on vertical curves; the location and dimensions of all openings in the embankment ; the plusses of railways, highways, streams, and openings in the embankment ; the elevations of the top of rail of all intersecting railroads, and the high-water mark of streams; the descriptions and elevations of all bench marks; a rectified alinement map at the bottom of the profile sheet, con- taining practically all the data that are shown on the location map; the distribution diagram, which is drawn between the profile proper and the alinement; on the profile proper the econom- ical movement of the earth from the cuts into the fills; and the amount of excavation, overhaul, and borrow at all points along the line. In fact, the location profile contains practically all the information needed by the resident and construction engineers. It is used by them in staking out all the construction work, with the exception of large bridges and trestles, for which separate plans are made.
44. Additional profiles are made for any change in the eleva- tions of highways and railways. These profiles are short and are sometimes (and preferably) placed on the location profile opposite the points where the changes are made.
Right of Way Maps
Right of way maps are of two kinds: (1) legal maps and (2) maintenance of way maps.
MAPS 15
45. Legal right of way maps are made on sheets which are the same size as the sheets on which the conveyance deeds are drawn up (usually 8J x 13). A separate map is made for each de- scription, and a blue-print is attached to the deed and becomes a part of it and is recorded along with the deed. The railroad company preserves its copies of the deeds along with the right of way maps in the form of a book, which is known as the right of way book.
46. Maintenance of way right of way maps are made from the location map and a separate 'sheet (about 8J x 10) is used for each section (i.e., government section) or for each mile of track. These sheets are bound into a book and are used by the main- tenance of way department.
Construction Maps
47. Station maps are usually made to a scale of 50 or 100 feet to the inch, and show the proposed buildings and tracks at each station. Any changes in the plans which are made during con- struction are recorded on the map. Some railroads have stand- ard plans for station layouts, and these are followed as closely as conditions will permit.
48. Progress profiles. Each month after the monthly es- timate surveys have been made, the amount of grading done during the month is shown graphically on the location profile in colored pencil. Each month a different color is used, so that the chief engineer and other railroad officials can see at a glance the progress of the construction work and can compare the amount done each month with that of former months.
49. Progress photographs. For the same reason photographs should be taken each month or oftener of the various structures under construction, such as concrete arches, bridges, trestles, station buildings, etc. Photographs are excellent auxiliaries to a written report.
CHAPTER III
DISTANCE, CURVATURE, AND GRADES
IN the location of a railroad there are three factors that make for success or failure from a financial standpoint, namely, dis- tance, curvature, and grades. The best location is that in which each of these is a minimum. This would be when the line be- tween terminals was perfectly straight, and on a uniform grade. This ideal line involves a maximum expenditure for construction and a minimum outlay for operation. Such a line, of course, is a financial if not a physical impossibility. It must be re- membered that the first cost is a fixed amount, while the cost of operation continues as long as the road exists; and in time the additional cost of operating a cheaply located road will more than offset the amount saved in the construction. This state- ment is borne out by the fact that all the large railroads are spending huge amounts yearly for the reduction of curvature and grades, in order that operating expenses may be reduced. The locating engineer must take all of these things into con- sideration in making his location. Of the three named items, grades is by far the most important, while distance is the least important.
Distance
50. Additional distance in the length of a line affects the initial cost of construction, the cost of maintenance, and the cost of operation. The cost of construction and maintenance is proportional to the distance and may be readily determined. The cost of operation does not vary directly as the distance. The cost of operating a small additional distance will be only about one-third as much per train-mile as the average cost over tne whole line. When the additional distance becomes several miles, the cost is increased to about one-half of the average cost per train-mile.
16
DISTANCE, CURVATURE, AND GRADES 17
Curvature
51. Curvature affects the cost of construction, the cost of maintenance, and the cost of operation.
The cost of construction is increased since curvature means an increase in the length of the line; and also if structures such as trestles and bridges come on curves their cost is largely in- creased thereby.
The cost of maintenance is increased since curved track requires more care in alinement and surface than straight track, and also there is greater wear on both the track and the rolling stock due to the curvature.
The cost of operation is increased because more power is re- quired on curves than on straight track, and frequently a sharp curve will limit the weight of train that can be operated over the line. Also, sharp curves limit the speed of passenger trains, which may be an important item where there is a competing line. It has been determined by experiment that the additional tractive force required to draw a train around a one-degree curve is the same as that required by a grade of from 0.03 to 0.05 per cent. This resistance does not vary directly as the degree of curve, but decreases as the degree of curve increases. For curves up to about 8 degrees, however, the curvature resistance is usually taken as 0.04 per cent, per degree of curve; for curves from 8 to 15 degrees, 0.03 per cent, per degree; and for curves above 15 degrees, 0.02 per cent, per degree. The resistance to a train in starting is about double that given above, and must be considered if a stopping place comes on a curve. In general, curve resistance is not serious until it becomes so great that when added to grade resistance the total resistance limits the weight of train that can be hauled over the line. Therefore all the steeper grades should be compensated for curvature.
52. Choice of curvature. The total resistance offered by a curve depends directly upon the central angle, and is practically independent of the radius. Hence the important point is to keep the amount of curvature a minimum, and after the tangents have been decided upon the problem is to make the rate of curvature as uniform as the topography will permit. Little is gained by having a few flat curves and a number of sharp ones. The proof of this statement is in the fact that in the vast amount
18 TEXT BOOK ON RAILROAD SURVEYING
of re-alinement work that the railroads have been doing in the past few years there are very few, if any, cases where an increase in radius is the only benefit derived from the improvement. The object of all this work has been to reduce the total amount of central angles in curves and at the same time to reduce the maximum rate of curvature.
Grades
Grades may be classified as (1) minor grades, (2) ruling grades, and (3) pusher grades.
53. Minor grades are those which do not limit the weight of train which can be hauled over the line by one engine. Such grades are of three kinds according to their effect on the per- formance of the engine.
First, there are those grades whose drop (vertical height) is sufficiently small that a locomotive can operate without shutting off steam, or, in other words, will not reach a dangerous speed due to the down-grade while exerting a constant pull on the train. The effect of these grades on train operation is negligible, both as regards the effort required of the engine and the time required for the train to traverse a given distance, since the kinetic energy acquired in descending one grade is utilized in ascending the opposite grade.
The second kind of minor grades consists of those whose drop is so great that steam must be shut off to prevent the train from acquiring a dangerous velocity, and hence the effort of the engine must be increased on the opposite up-grade. Therefore there is a loss of power, since the engine is working intermit- tently and not at its greatest efficiency.
The third kind of minor grades consists of those which require the use of brakes in descending them. This causes an enormous loss of energy because part of the kinetic energy gained by the descent is absorbed by the brakes, and hence is not available on the next up-grade. Further, the engine is working at a dis- advantage, and there is considerable wear on equipment due to the action of the brakes.
54. Ruling grades are those which limit the weight of the train which can be hauled by one engine. Cars can not be picked up or dropped off along the line to make up a train in
DISTANCE, CURVATURE, AND GRADES 19
accordance with the grades met with, and hence a train must run through from one terminal of a division to the other. There- fore, excluding pusher grades, and such short steep grades which can always be operated by momentum, the maximum grade is the ruling grade on that division.
55. A pusher grade is one which is so steep that one or more extra engines are required to haul the train which one engine can handle on the remainder of the division. It will nearly always happen that some grades on each division will be con- siderably greater than the majority of the grades, and unless these can be reduced to the general average at a reasonable cost or a pusher engine is used, they limit the weight of train over the division and become the ruling grades.
A pusher grade adds enormously to the cost of operation since the auxiliary engines must be maintained; and, further, they pass twice over the line for each train handled, and hence do not operate at maximum efficiency. Obviously, therefore, a pusher grade must be considerably in excess of the ruling grade on the remainder of the division before its extra cost of operation would be justifiable.
56. Choice of grades. The total energy available to carry a moving train up a grade is the sum of the kinetic energy of the train due to its velocity (momentum) and that developed by the engine. The maximum amount of energy which the engine can develop is a fixed quantity, but the amount of kinetic energy which can be utilized depends on the initial speed of the train.
A given engine can just pull a train of given weight up such a grade that the sum of the frictional resistances and the grade resistances (including curvature resistances) equals the total force exerted by the engine. Or, conversely, the weight of train which a given engine can pull up a given grade is such that the sum of frictional and grade resistances again equals the effort of the engine. The frictional resistances are practically constant at about 8 pounds per ton for freight trains, while the grade resistance is 20 pounds per ton for each per cent, of grade. The length of such a grade is limited only by the endurance of the engine.
If the train approaches this grade at considerable speed, its kinetic energy may be utilized to overcome additional grade
20 TEXT BOOK ON RAILROAD SURVEYING
resistance, hence the engine can pull the train up a much steeper grade to the point where the additional vertical rise has absorbed all the kinetic energy. If the end of the grade is reached first, the train will pass over easily, suffering only a reduction in speed; if the grade extends further than this point, the train will be stalled.
Thus it is seen that for minor grades it is more the vertical height than the rate of slope which affects the operation. And also the ruling grade — the one which limits the train weight — may not be the one of steepest elope, provided that the heaviest trains can always approach it at sufficient speed to reach its top with the aid of momentum.
Therefore if a grade line can be established with alternate de- scents and ascents of such small amount that the train can always make use of its momentum, the rate of slope is of small importance. But, if the slopes are so long that momentum can not be utilized all the way, or the grade must be entered at very low speed, the rate of slope limits the train weight.
The first step in projecting a grade line on a profile is to determine approximately the ruling grade. The lowest value of the ruling grade is that of a uniform slope between terminals. The maximum value depends on the type and weight of locomo- tives, the weight of trains, etc., and can never be exactly de- termined, and therefore it is more usual to simply choose a maximum or ruling grade which will probably fit the territory through which the line runs. In assuming this maximum value, due consideration should be given to the direction of heaviest traffic, and easier grades secured if possible for trains in this direction.
A grade line is then laid out on the profile, keeping below this maximum if possible in such a way that the fills will balance the cuts and the total amount of earthwork will be kept as low as possible in order to reduce the cost of construction. The laying out of this line will require several trials, and each trial should be carefully studied as to its effect on operation as well as on first cost. After such a line has been laid out it may be found that the assumed maximum grade has been exceeded at some point, and study must be given as to whether it is possible to reduce this grade or whether it is justifiable to perhaps increase it suf- ficiently to be operated as a pusher grade. Or it may be found that only one grade approaches the chosen maximum, and again
DISTANCE, CURVATURE, AND GRADES 21
the line must be studied to determine if it is possible to reduce this grade to the general average. For example, the maximum grade on a division is found to be 1 per cent., while there are no others over 0.8 per cent., and possibly only two of these, the next lower being 0.5 per cent. The problem then is to decide the advisability of reducing the 1 per cent, grade to 0.8 per cent., and then possibly the three 0.8 per cent, grades to the average of 0.5 per cent. And this process of reducing the ruling grade could be continued until the additional cost of construction equals the sum which can profitably be spent for the purpose of reducing the ruling grade.
57. VERTICAL CURVES. — The intersections of the several portions of the grade line must be rounded off to avoid undue stress in the drawbars. The curve used for this purpose is a parab- ola because of its convenient characteristics. Such curves are termed vertical curves to distinguish them from the curves in the alinement.
The length of vertical curves depends on the total change in the grade which is the algebraic difference of the intersecting grades, Gi and G?., and on the rate of change of the vertical curve. Ascending grades are plus, and descending grades are minus.
The rate of change per station, r, of the vertical curve as rec- ommended by the American Railway Engineering Association is 0.1 foot for summits and 0.05 foot for sags for first-class rail- ways; and double these amounts for second-class and electric railways. It is to be noted, however, that a large number of first-class roads use the second-class rating. Since the change at the ends of the curve is from tangent to chord instead of from chord to chord, the rate of change of the first and last stations on the curve is just one-half the rate used on the remainder of the curve.
In solving a vertical curve problem, the first step is to find the length of the curve. This is done by dividing the algebraic difference of the grades by the assumed rate of change per station. This will usually give an odd length which is inconvenient to handle, and therefore the next higher even number of stations is chosen as the length of the curve.
The second step is to divide the algebraic difference of the grades by the length of curve as found in step one. The quotient
22 TEXT BOOK ON RAILROAD SURVEYING
will be the rate of change per station which is to be actually used.
The third step is to find the station numbers and elevations of the T.C. and C.T. (beginning and end of curve).
The fourth step is to find the elevations of the intermediate stations on the curve. This is done by starting at the T.C. and adding (or subtracting as the case may be) the changing grades successively until the C.T. is reached. The grade from the T.C. to the first station will be GI — \ r, from the second to the third station it will be GI — -f r, from the third to the fourth it will be GI — •§• r, and so on till the C. T. is reached. The elevation thus found for the C. T. should check with that determined from step three.
Example. A +0.8 per cent, grade meets a —0.6 per cent, grade at station 30 + 00, whose elevation is 750.50. It is de- sired to connect these grades by a vertical curve whose rate of change per station is approximately 0.2 foot.
GI — G2 (algebraically) Length of curve = — 2 v * ' . . .
f
L,W.s4,-,7
r - - - CD
Making L = 8,
r = -^ = 0.175
o
Taking everything into consideration it is better to make L = 800 feet (400 feet each side of apex), and to use a value of r = 0.175 than it is to make L = 700 ft. and use a value of r = 0.2.
Sta. of T.C. = 30 - 4 = 26 + 00.
Sta. of C.T. = 30 + 4 = 34 + 00.
Elev. of T.C. = Elev. P.I. - \LGi = 750.50 - 3.20 = 747.30
Elev. of C.T. = Elev. P.I. - \LGi = 750.50 - 2.40 = 748.10
Elevation Station 26 = 747.30 = 747.30
" 27 = 747.30 + (0.8 - 0.0875)
= 747.30 + 0.7125 = 748.01
DISTANCE, CURVATURE, AND GRADES 23
Elevation Station 28 = 748.01 + (0.7125 - 0.175) =
748.01 + 0.5375 = 748.55 " " 29 = 748.55 + (0.5375 - 0.175) =
748.55 -f 0.3625 = 748.91 " 30 = 748.91 -f (0.3625 - 0.175) =
748.91 +0.1875 = 749.10 " 31 = 749.10 + (0.1875 - 0.175) =
749.10 -h 0.0125 = 749.11 " " 32 = 749.11 + (0.0125 - 0.175) =
749.11 - 0.1625 = 748.95 " 33 = 748.95 + (-0.1625 - 0.175) =
748.95 - 0.3375 = 748.61 " " 34 = 748.61 + (-0.3375 - 0.175) =
748.61 - 0.5125 = 748.10
It should be noted that the highest point on the vertical curve comes at Sta. 31 instead of Sta. 30.
The elevation of each station on the vertical curve is shown on the location profile, and is used in setting slope stakes. If the distance from the sub-grade to the top of rail (from 1.5 to 2.0ft.) is added to the above elevations the results are the eleva- tions of the final top of rail. These elevations are used after the grading has been completed for setting grade stakes for sur- facing the track.
Note. — For a further discussion on the Economics of Railway Loca- tion, the student is referred to Wellington's "Economic Theory of the Location of Railways," or Webb's •• Economics of Railroad Construc- tion."
CHAPTER IV CURVES
Part I. Circular Curves
RAILWAY alinement consists of
1. Tangent, or straight track.
2. Curves, which unite the tangents.
Curves are of two kinds; (1) arcs of circles, and (2) arcs of spirals. The circle is employed for the body of all curves since it is more easily located with the transit and tape than any other form of curve. Spirals are used for easements at the ends of the circular arcs.
Circular curves are classified as Simple, Compound, and Reversed.
Simple Curves
58. FUNCTIONS.
A simple curve is an arc of a circle which unites two tangents
differing in direction. The functions of a simple curve are shown in Fig. 2.
24
CURVES 25
Point of Intersection — P.I. — is the point where the two tangents intersect.
Tangent to Curve — T.C. — is the end of the tangent and the beginning of the curve.
Curve to Tangent — C.T. — is the end of the curve and the beginning of the tangent.
Intersection Angle — 7 — is the deflection angle between the two tangents, and is equal to the angle at the center.
The Radius of the curve is denoted by R.
Tangent Distance — T — is the distance from the T.C. or the C.T. to the P.I.
T = R tan \I. .• ..... (2)
Long Chord— L.C.— is the chord from the T.C. to the C.T.
L.C. = 2fl sin i/ ....... (3)
Middle Ordinate — M — is the ordinate to the curve from the middle of the Long Chord.
M = R - R cos i/ = R vers JJ ... (4)
External Distance — E — is the distance from the middle of the curve to the P.I.
E = ~jR
Degree of Curve — D — is the angle at the center subtended by one 100-ft. chord, two 50-ft. chords, or four 25-ft. chords, de- pending upon the length of the radius. The intention is to make the difference between the length of the chord and the arc so small that it may be neglected.
Length of Curve — L — is the distance along the curve between the T.C. and the C.T.
L (in stations) = -yr ..... (6)
Deflection Angle — \D — From geometry the angle between two chords, or a chord and a tangent, intersecting on the circum-
26 TEXT BOOK ON HAILROAD SURVEYING
ference of a circle is measured by one-half the intercepted arc. For a chord 100 feet in length this angle is called the deflection angle, and therefore is JD.
Subdeflection Angle — d — is a similar angle for a chord of less than 100 feet.
If C is the length of the chord in feet,
Q d (in degrees) =^3^5 • • • • • (7)
d (in minutes) = 0.3CD (8)
Total Deflection Angle is the angle at the T.C. between the tangent and a chord to any point on the curve.
Total deflection angles are taken to the nearest 0.5 minute.
59. The relation between R and D. If the degree of curve be defined as the angle at the center subtended by a 100-ft. arc, an exact relation between R and D may be found, as follows. The circumference of a complete circle in terms of the radius is
O(\(\
2 nR'} and in terms of the degree of curve is 100 -~- , hence
100 X 360 5729.58 R= 2*D =-D~ ^
From (9) it is evident that R varies inversely as D. Therefore knowing the radius of a 1 degree curve, the radius of any other degree of curve can be found by simple proportion.
Since the chord is used instead of the arc, the value of R from
FIG. 3.
(9) can not be used, and a new value of R must be found which will agree with the chord-definition of the degree of curve.
CURVES 27
In Fig. 3, R sin JD = |C
Whence R = -^75 = iC cosec £D .... (10)
Dill 2 •*-'
When C is 100 ft., # = 50 cosec il> (11)
The difference in the values of R as computed from (9) and (11) becomes about 0.5 ft. when D is 7 degrees. Since a difference greater than this is objectionable, curves above 7 degrees are staked out with 50-ft. chords. When C is 50 ft.,
R = 25 cosec JD (12)
When D becomes 14 degrees, the difference in R as computed from (9) and (12) again become objectionable, and 25-ft. chords are used. When C is 25 ft.,
R = 12.5 cosec I D (13)
When D becomes 28 degrees, 10-ft. chords should be used. Table 5 of radii was computed from (11), (12*), and (13). It is customary to consider the radius of a 1 degree curve as 5730 ft., and to assume that R varies inversely as D. Hence
R = —p- (approx.) (14)
The difference between R as given in Table 5, and as computed from (14) is so small that it may be neglected.
By substituting R in terms of D in (2) to (6) it is seen that the various functions of a curve for any given value of 7 are approximately inversely proportional to D. Therefore, if these functions are known for any degree of curve, they can be found for any other degree of curve by simple proportion. Table 6 gives the functions of a 1 degree curve for intersection angles from 0 degree to 100 degrees.
60. FIELD WORK.
In laying out a curve successive points are located by a meas- urement from the preceding point and by line. The line is
28 TEXT BOOK ON RAILROAD SURVEYING
not the same for all points and is determined by the total de- flection angle calculated for each point. Thus in Fig. 4, point 1 is located by the chord T.C. — 1 and the total deflection angle A; point 2 by the chord 1-2 and the total deflection angle B] and point 3 by the chord 2-3 and the angle C.
FIG. 4.
Stakes are usually placed 100 feet apart except on sharp curves where the interval is reduced to 50 or 25 feet. However, the stationing is continued unbroken around the curve. The T.C. and the C.T. will therefore usually fall at a plus station, hence there will usually be a subdeflection angle at each end of the curVe.
The first step in the field work is to determine the station numbers of the T.C. and the C. T. and to compute the total de- flection angles for the entire curve. In Fig. 4, T.C. — 1 and 4- C.T. are odd distances, and 1-2, 2-3, and 3-4 are full stations. Then A is the subdeflection angle (di) for the chord T.C.-l, and is computed by Eq. (8).
A = di
Then B = A + $D = di + \D
And C = B + $D = d, + $D + |D
E = C + *£> = rfi + $D + $D + iD
F = E + d2 = di + \D -h JD + iD + & = \I
The total deflection angles are thus computed by successive additions, and the entire series of computations is checked if the last value is \I. If stakes are placed 50 feet apart the in- crements are \D, and if 25 feet apart they are \ D, instead of JD as above. The form of notes is shown in Fig. 5.
CURVES 29
On the ground the T.C. and the C.T. are located by measuring the tangent distance T from the P. 7. The curve can then be run in by means of angles and distances as explained above.
Since in turning off an angle with a transit, an error as large as 0.5 minute may easily be made— which amounts to 0.15 of a foot at 1000 feet from the transit — the length of sight on a curve should never exceed 1000 feet.
It has been found by experience that if the angle between the tape and the line of sight is more than about 30 degrees, the location of the point is inaccurate. Therefore the angle between the line of sight and the tangent at the transit station should never be more than 30 degrees, i.e., the product of the length of sight in stations and |D should be less than 30 degrees.
It is good practice in any case to run a portion of the curve from the C.T., since the errors of surveying can be adjusted more satisfactorily on the curve than at the C. T. There should be no more error, however, in either line or distance than is permissible in good chaining under the particular conditions.
If the entire curve can not be run in from the T.C. and the C.T., one or more intermediate set-ups on the curve will be necessary. There are, therefore, three possible positions of the transit in running in curves, viz.j the T.C., any intermediate point, and the C.T. The curve notes as computed above are used in all three cases, as follows:
At the T.C. Orient the transit by a sight along the tangent with the plates set at zero. Turn off the total deflection angle of each station, successively, and chain the corresponding dis- tances between them.
At any intermediate point. Orient the transit by a back- sight on the last transit station with the telescope inverted and the plates set at the total deflection angle of that station as recorded in the notes. To continue the curve, plunge the telescope * and set the plates at the total deflection angles of the succeeding stations and measure the corresponding distances between them.
At the C.T. Orient the transit by a sight along the tangent with the telescope normal and the plates set at the total de- flection angle of the C.T., i.e., J7. To run in the curve, set the
* The line of collimation must be in adjustment.
|
TRANSIT NOTES FOR LINE L |
|||||
|
STATION |
. ALINE- MENT |
TOTAL DEFL. ANGLE |
CALC. BEAR. |
MAG. BEAR. |
REMARKS |
|
-{- 55.8 |
O C.T. |
35°-4l' -f — |
NOO°-39'W |
NOO°-40V |
_*i 1=85-41' |
|
62 |
34 -34 |
||||
|
61 |
32 -34 |
||||
|
10560 |
30 -34 |
D = 4°00' |
|||
|
59 |
28 -34 |
1 = 71°22' |
|||
|
58 |
26-34 |
||||
|
57 58 55 |
24-34 22-34 20-34 |
CO 8 -f 5 »o g !o TH 0 II |
|||
|
54 |
0 |
18-34 |
PU |
||
|
53 |
^ |
16-34 |
|||
|
52 |
JA bo 3 |
14-34 |
|||
|
51 |
p |
12-34 |
|||
|
10550 |
** |
10-34 |
|||
|
43 |
8 -34 |
||||
|
48 |
6 -34 |
||||
|
47 |
4-34 |
||||
|
46 |
2-34 |
||||
|
45 |
0 -34 |
||||
|
H-71.6 |
O T.C. |
0°-00' |
N72°-Ol'W |
N72°-10'W |
|
|
44 |
|||||
|
43 |
FIG. 5.
J.E.Schmidt— Inst.
R.Carr-H.C. C.E.Agg— R.C.
G.W.Pix— R.F.
C. Wiles — Ax
June 12, 13 Clear-Warm
C.T.
)P.O.C.
T.C.
FIG. 5.
31
32 TEXT BOOK ON RAILROAD SURVEYING
plates at the total deflection angle of each station as given in the notes, and measure the corresponding distances.
61. The FUNDAMENTAL PRINCIPLES are:
When sighting at any station the plates must read the total de- flection angle of that station. When on tangent at any station the plates must read the total deflection angle of that station.
If these principles are strictly observed a mistake in instrument work is impossible.
Example. The P.I. of two tangents is at Sta. 10555 + 00.3 and / = 71° 22'. It is desired to connect the tangents with a 4° curve.
Tforal0 curve for / = 71° 22'
D 4114.9 (from Table 6)
= 1028.7 ft.
Sta. T.C. = Sta. P.I. - T = (10555 + 00.3) - (10 + 28.7) =
10544 + 71.6
/ 71° 22' 71.367 L = -~- = — j — = — j— = 17.842 Stations.
Sta. C.T. = Sta. T.C. + L = (10544 + 71.6) + (17 + 84.2) =
10562 + 55.8
The distance from the T.C. to the first Sta. on the curve is 28.4 ft., hence
di = 0.3 CD = 0.3 X 28.4 X 4 = 34' Deflection angle = JD = 2° 00'
The distance from the last Sta. to the C.T. is 55.8 ft., hence d2 = 0.3 X 55.8 X 4 = 67' = 1° 07' \
Total Deflection Angle of T.C. = 0° 00'
" " Sta. 10545 = 0° 00' + 0° 34' = 0° 34'
" "" 10546 = 0° 34' + 2° 00' = 2° 34'
" " " " " 10547 = 2° 34' + 2° 00' = 4° 34'
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33
Total Deflection Angle of Sta. 10562 = = 34° 34'
" " " " C.T. = 34° 34' + 1°07' =
35° 41' = i/ (check)
These results are recorded in the form shown in Fig. 5.
62. Offsets from chords produced. In addition to his chain- ing duties the head chainman also sets the stakes on line as directed by the transitman. Obviously this work is much facilitated if the head chainman can quickly approximate the position of the stakes. This can be done by an offset from the line through the last two stations. For example, in Fig. 6, A and B are the last two stations set. Produce AB to E the distance C from B. F is located by the offset y from E and the distance C from B. y can be found by Eq. (16). If E is care- fully lined in and C and y measured with the tape, the point can be located with considerable accuracy; and, if a transit is not at hand, this method can be employed in locating an entire
FIG. 6.
curve. However, this method is most valuable as an aid to the head chainman in approximating the position of the stakes, and it should always be used. If E is only roughly lined in and y is paced, the points can be located within less than one foot, which is sufficient for the purpose. From Fig. 6,
\y : C: : J C : R
Whence
\y = p (C and R expressed in feet)
34 TEXT BOOK ON RAILROAD SURVEYING
Expressing R in terms of Z), we have
* ~ 1)1460 If n represents C expressed in stations, then
\y = 0.873 n*D (15)
\y is the tangent offset to the point F.
For C = 100 ft., n = 1,
and \y = 0.873 D, and y = 1.746 D = if D (approx.) (16,)
For C = 50 ft., n = \,
and Jy = 0.22 D, and y = 0.44 D
63. Chord Offset Method. There are some cases in which the deflection angle method of running in curves can not be used to advantage. For instance, in heavily wooded country it may not be economical to locate every station by the deflection method on account of the large amount of clearing necessary for the lines of sight. Fig. 7 illustrates this condition. If the stakes B, C, E, and F were all set from A it would necessitate the clearing
FIG. 7.
of a line to each or practically the entire area between the curve and the chord AF. If, on the other hand, F were set from A by its total deflection angle and the chord AF, and B, C, and E located by offsets from this chord, the only clearing required would be along AF and the short offsets. The transit would then be moved to F and the process repeated to J, and so on.
The chord AF is the L.C. of a curve whose value of / is the central angle of the curve ABCEF, and therefore can be de- termined from Eq. (3) or from Table 6. In chaining this chord, temporary stakes are set at the full station distances, although perpendicular offsets from these will not give the exact location
CURVES
35
of the curve stations since the chord AF is shorter than the line ABCEF. This error may be neglected for the following reasons: (1) the error at any point in practice will rarely exceed one foot; (2) the perpendicu- larity of the offsets is estab- lished by eye, hence is not exact; and (3) the approxi- mate location of these stations is sufficient since this method would be used only on first location to determine the profile. The offsets are com- puted as follows:
From geometry the pro- ducts of the segments of two intersecting chords are FlG 8
equal. Then from Fig. 8,
or
Si XS2 S1X
2R-S,
Since $3 is small compared with 2R it may be neglected in the denominator, and since in practice the difference between $3 and the offset will rarely -reach 0.05 ft., we may write
Si XS2 Si XS.2XD ,A Offset = nn — = —^^,r»^ (Approx.)
2R
2 X 5730
Reducing Si and $2 to stations, we have
Offset (in feet) = 0.873 SiS2D (Slide Rule)
(17)
64. Example. The T.C. of a 4° curve is at Sta. 67 + 82.7. Sta. 72 is set by its total deflection angle (8° 21') and the L.C. of a 4° curve for / = LD = 4.173 X 4 = 16° 41.5', which from Table 6 = 415.8 ft. While chaining this chord, temporary stakes are set at 17.3, 117.3, 217.3, and 317.3 ft. from the T.C. From Eq. (17),
The offset at Sta. 68 = 0.873 X 0.173 X 4 X 4 = 2.4 ft.
" " " 69 = 0.873 X 1.173 X 3 X 4 = 12.3 ft.
" " " 70 = 0.873 X 2.173 X 2 X 4 = 15.2 ft.
" " " 71 = 0.873 X 3.173 X 1 X 4 = 11.1 ft.
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TEXT BOOK ON RAILROAD SURVEYING
The stations on the curve are located by measuring these offsets from the temporary stakes already set.
Change of Location Problems
After the line is located according to the paper projection and a profile made, it may be found that, owing to inaccuracies in the platted topography, a considerable cut or fill comes on a hillside and may be eliminated by shifting a portion of the alinement. Occasionally other considerations than earthwork make euch a shift desirable.
65. Problem 1. In Fig. 9, the line as originally located (shown dotted) involves considerable earthwork which could
FIG. 9.
be eliminated by shifting the curve the distance p at or near its middle point.
The problem is to find the new degree of curve and the change in the position of the T.C. and the C. T. p is the difference in the external distances of the two curves, or
f^new curve ~ -^old curve i P
The new degree of curve may be computed from the new external by Eq. (5) or by means of Table 6, which is the quicker
CURVES
37
and more common method. The estimated value of p will usually give an odd value of D which is undesirable; hence the value of D to be used is taken only to the nearest ten minutes. The distance that the T.C. and the C.T. are shifted is equal to the difference in T for the two curves.
66. Problem 2, Case 1.
In Fig. 10, the line as originally located (shown dotted) in- volved considerable earthwork between A and B, which could
FIG. 10.
largely be eliminated by shifting the tangent the distance p parallel to its original position, which involves a change in the location of TWO curves.
The problem is to find the change in the T.C.s and the C.T.s of the two curves, the degree of curve remaining unchanged. In triangle 1, the sides m and I can be readily computed since / and p are known, m = n = the required change in the T.C. and P.I. p will rarely exceed 100 feet, hence the new tangent is best located by offsets from the old tangent. The new C.T. is then located from the old C.T. by rectangular coordinates one of which is p and the other is the side I of triangle 1.
The second curve is located similarly using triangle 2.
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TEXT BOOK ON RAILROAD SURVEYING
67. Problem 2, Case 2.
Owing to some special cause, for example a stream-crossing as shown in Fig. 11, it may be undesirable to move the C.T. for- ward as in Case 1. This condition can usually be met by placing
FIG. 11.
the new C.T. approximately on the same radial line as the old C.T. This involves a change in the degree of curve and in the position of the T.C.
In triangle 1, 7 and p are known, and I and m are computed.
7 new curve = 1 old curve '
whence the new D is easily found from Table 6 and, as in Problem 1, is taken only to the nearest 10 minutes. (The approximation in the position of the C.T. is due to thus not using the exact value of D.) A new value of T is then found which agrees with the D that is used. Then
^ = -* old curve ~{~ Wl — 2 new curve
68. Problem 2, Case 3. This case is similar to Case 2, except that the C.T. is on the fixed tangent instead of the one being changed, hence the solution is somewhat different.
Solve triangle 2 for the side m, then
-* new curve = Told curve — W
whence the new degree of curve is obtained from Table 6.
CURVES 39
Solve triangle 3 for the side 1. Then the new T.C. can be located from the old T.C. by the co-ordinates I and p.
As in the previous problem, D should be taken only to the nearest ten minutes. This necessitates a slight change in both the T.C. and the C.T., since T for this value of D is not the same as that used in the abpve computations. It must be remembered that the T.C. becomes the C.77., or vice versa, when the line is run in the opposite direction.
69. Problem 3. Sometimes curves are run in beginning at the T.C. without previously locating the P. I. and the C.T., and checking the direction of the forward tangent. On reaching the C.T. and projecting the forward tangent, it is found that the tangent does not pass through some controlling point. It is therefore necessary to change the direction of the tangent by shifting the C.T. This is most readily accomplished by measuring the necessary change of direction with the transit, and then changing the length of the curve to correspond. For example, in Fig. 12, the curve is run to B as a C.T. and the tangent is found to pass through x, whereas it is necessary to pass through A. The angle e is measured with the transit.
The length of curve corresponding to e is BC, whence the C.T. is moved back to C. The forward tangent then takes the position CA', parallel to BA, and misses A by the distance m, which is the middle ordinate of the curve BE.
40 TEXT BOOK ON RAILROAD SURVEYING
BE = 2BC =
m = -g-X X D = 0.875--
m will rarely reach 5 ft., hence the line CA' meets the require- ments.
Problems
1. If the P.I. is in a stream or is otherwise inaccessible, how can / and the positions of the T.C. and the C.T. be determined?
2. If the T.C. is inaccessible, how can the curve be run in and checked?
3. If the line of a curve passed through a building or similar obstruction, how can the curve be run in and checked?
4. Given I = 63° 43'. Find T, L, R, and E for each of the following values of D.— 0° 30', 2° 00', 5° 00', and 7° 30'. Solve by equation and check by Table 6.
5. Given the P.I. at Sta. 118 + 60.0, / = 57° 48', and D = 5° 00'. Find the station numbers of the T.C. and the C.T.
6. Write transit notes for the preceding problem.
7. Given, on original location, a 6° 00' curve with / = 78° 21' and the T.C. at Sta. 1041 + 72.6. Topography requires the middle point of the curve to be moved toward the center about 45 ft. What is the new degree of curve and the station number of its T.C.?
8. Given an established curve with 7 = 69° 38', D = 3° 00', and the T.C. at Sta. 982 + 41.1. It is desired to move the forward tangent outward a distance of 50 ft. Find the new station numbers of the T.C. and the C.T7., and the coordinates from the old C.T. to the new C.T.
Answer. T.C. = 982 + 94.4; C.T. = 1006 + 15.5; I = 18.6, and p = 50.0.
9. Data same as in Problem 8, except that the forward tangent is moved inward.
Answer. T.C. = 981 + 87.8; C.T. = 1005 + 08.9; I = 18.6, and p = 50.0.
10. Given an established curve with / = 47° 23', D = 2° 30', and the T.C. at Sta. 1841 + 83.7. It is desired to move the
CURVES 41
forward tangent outward a distance of 60 ft., keeping the C.T. on the same radial line approximately. Find the new degree of curve, the station number of the T.C., and the distance that the C.T. moves forward or backward due to using D to the near- est ten minutes only.
Answer. D, computed = 2° 38.7'; Z), used = 2° 40'; T.C. ~ 1843 + 28.0; C.T. moves 7.6 ft. backward.
11. Data same as in Problem 10, except that the forward tangent is moved inward.
Answer. D, computed = 2° 22.2'; D, used = 2° 20'; T.C. = 1840 + 30.3; C.T. moves 16.7 ft. forward.
12. Given an established curve with / = 50° 35', D = 4° 30', and the T.C. at Sta. 155 + 24.5. It is desired to move the initial tangent 35 ft. inward without changing the position of the C.T. (except the small amount due to using approx. value of D). Find the new degree of curve, the station numbers of the new T.C. and C.T., the coordinates of the new T.C. from the old T.C., and the small amount that the T.C. and the C.T. must shift due to the approx. value of D used.
Answer. .D, computed = 4° 52'; D, used = 4° 50'; T.C., computed = 155 + 98.7; T.C., used = 155 + 94.9; C.T7., com- puted = 166 + 38.1; C.T., used = 166 + 41.5; I = 70.3; p = 35.0; T.C. and C.T. shifted 3.8 ft.
13. Data same as in Problem 12 except that the tangent is moved outward.
Answer. D, computed = 4° 11'; D, used = 4° 10'; T.C., computed = 154 + 50.3; T.C., used = 154 + 47.5; C.T., com- puted = 166 + 59.2; C.T., used = 166 + 61.5; I = 77.0; p = 35.0; T.C. and C.T. shifted 2.8 ft.
14. After running in a 3° 00' curve to the right, using paper location notes, it is found that the forward tangent passes to the right of the governing point by 2° 20' as measured at the C.T. (a) What distance must the C.T. be shifted? (b) How much does the new tangent miss the controlling point?
Answer, (a) = 77.8ft.; (b) = 1.6ft.
Compound Curves
70. A compound curve is a combination of two or more simple curves in the same direction with a common tangent at the
42
TEXT BOOK ON iAILROAD SURVEYING
point of junction. A compound curve should never be used except under conditions where a simple curve will not meet the require- ments. In rough country it may happen that a large volume of earthwork can be avoided by making one part of a curve sharper than another, resulting in a compound curve.
For example, in Fig. 13, the line is located as a compound curve ABC, requiring little earthwork and keeping on the bank of the stream. If the simple curve AB had been produced to F to
end in a parallel tangent, it would have fallen in the river. Or if the simple curve CB had been prolonged to E, it would have pierced the cliff.
The degree of curve and the point of compound curve, C.C., are chosen to fit the contours and other governing conditions, and the central angles of the branches are scaled from the map.
This is one of many cases where a compound curve is ap- plicable.
From the standpoint of operation a compound curve is better than two simple curves separated by a short tangent, hence it should be used in such cases. In flat country a compound curve is inexcusable on main line. If the degrees of curve of two ad- jacent branches of a compound curve differ by more than 2° 00', an easement curve should be inserted between the branches, and provision for this should be made in locating the curve. (See Spirals, paragraph 84.)
CURVES
43
The nomenclature and positions of the functions are shown in Fig. 14.
71. Problem 1.
In new work / will be measured and /i, 72, A, and A will be determined from the preliminary maps. It is desired to know
the value of T\ and T2 in order to set the T.C. and the C.T. and to run in the curve.
In Fig. 14, BE is the common tangent at the C.C.
BE = BC + CE
BC = AB is the tangent distance for a A curve for an inter- section angle I\\ and CE = #G is the tangent distance for a A curve for an intersection angle 72 and are computed by Table 6. Then in the triangle BEF, one side and the adjacent angles are known from which the sides BF and EF are computed.
Tl = AB + BF, and T2 = EF + #£
72. Problem 2. Occasionally the positions of the T.C. and the C.T. are fixed within narrow limits, giving unequal tangent distances, which necessitates a compound curve.
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TEXT BOOK ON EAILROAD SURVEYING
The degree of curve of one branch must be chosen before the problem can be solved. The problem then is to determine the
FIG. 15.
degree of curve of the second branch and the central angles /i and 72.
In Fig. 15, /, Ti, Ti, and A are known. A H = HF = T0 = the tangent of A curve for the intersection angle /.
In triangle 1,
m = To - Tl
and hence the triangle can be solved for p and n. In triangle 2,
I = T0 + n - T2
Since p is known, the triangle can be solved for the angle at E, which is i/2.
/i = / - h
In triangle 3, since I and 72 are known, the side Oi02 = Ri — Rz can be solved for, whence Z>2 is determined from Table 5.
CURVES
45
73. Field Work.
A point on one branch of a compound curve can not be located with the transit set on a point on another branch, since in order to run in a circular curve with the transit and tape, the transit and the points to be located must be on the same circumference. Therefore each branch of a compound curve is run in indepen- dently as a simple curve. Thus the notes for the first branch are computed and the curve run in to the C.C. The transit is then placed at the C.C. and oriented as at the C.T. of a simple curve except that the plates read zero instead of ^1 when sighting along the tangent* The notes for the second branch are then com- puted and the curve run in to the C. T. or to the next C.C.
Change of Location Problems
74. Problem 1. This problem arises under conditions similar to those in Problem 2, Case 1, of simple curves, paragraph 66.
Given, as shown in Fig. 16, a located compound curve ABC. It is desired to move the forward tangent laterally a distance p.
FIG. 16.
The simplest solution of this problem is to retain the same degrees of curve and to shift the C.C. from B to E.
BE (in feet) = -^T 1Q0 L>i
* To orient at the C.C., back-sight on the last transit station with the plates set to read the difference between the total deflection angle of the C.C.,% Ji, and the total deflection angle of the back-sight sta- tion; turn the plates to zero and the line of sight is on tangent.
46
TEXT BOOK ON RAILROAD SURVEYING
Therefore the problem resolves itself into solving for the angle b.
In triangle 1, since a is known and the hypotenuse is the difference in the two radii, the base m can be computed. Then n = m — p.
In triangle 2, the hypotenuse and the base are known, whence the angle c is computed.
b = c — a
In triangle 3, e = 90° — J6 — a (prove)
whence the coordinates of M, the new C.T., from the old C.T. can be determined.
Three other cases of this problem arise, viz.: (1) the same as above, except that the tangent is moved outward; (2) the curve of longer radius may fall on the tangent to be moved inward; and (3) the curve of longer radius may fall on the tangent to be moved outward.
The solution of each of these cases is the same as that given above except that the various points take different relative positions. If the same relative construction lines are drawn and the corresponding points are used, no confusion should arise.
75. Problem 2. This problem arises under conditions similar to those in Problem 2, Case 2, of simple curves, paragraph 67.
\
FIG. 17.
Given, as shown in Fig. 17, a located compound curve ABC. It is desired to move the forward tangent laterally a distance p,
CURVES 47
and to keep the C.T. approximately on the same radial line, which involves a change in the degree of curve of the second branch and in the position of the C.C.
In triangle 1, a is known and the hypotenuse is the difference in the two given radii. Therefore the base m and the altitude n can be computed.
In triangle 2, the base n is now known and the altitude I can be determined since R\y R^ p, and m are known. The angle at p = |6 (Why?) can therefore be determined. Then
c = b — a
and the C.C. is shifted the distance BE (in feet) = -£- 100.
DI
In triangle 3, the angle b and the altitude n being known, the hypotenuse r can be computed from which Rx is determined, and the corresponding degree of curve Dx is found from Table 5, and is taken to the nearest ten minutes. Then since E and b are already fixed, this will change the value of p slightly and will shift the C.T. a short distance along the line EG from F, its theoretical location. The coordinates of this new position are given by the equations
x = h sin b, and y ' — x tan J6,
in which x is the movement along the tangent, y is the change in p, and h is the difference between the computed value of Rx and the value actually used.
Three other cases of this problem arise, depending on whether the longer or the shorter radius curve is on -the tangent to be moved, and on whether the tangent moves inward or outward. In all of these cases the solution is relatively the same.
Problems
1. Given the P. I. at Sta. 837 + 00, 7 = 64° 44', A = 29° 00', 72 = 35° 44', A = 4° 00', and D2 = 5° 30'. Find the station numbers of the T.C., C.C., and C.T.
Answer. T.C. = 828 + 73.4; C.C. = 835 + 98.4; C.T. = 842 + 73.4.
2. Given the P.I. at Sta. 1846 + 50.0, / = 57° 18', Ti = 835.0,
48 TEXT BOOK ON RAILROAD SURVEYING
T2 = 687.0, and A = 3° 00'. Find /i, 72, A, and the station numbers of the T.C., C.C., and C.T.
Answer, h = 16° 17'; 72 = 41° 01'; Z)2 = 4° 47.5'; T.C. = 1838 + 15.0; C.C. = 1843 + 57.8; C.T. = 1852 + 13.5.
3. A 2° 30' curve compounds with a 4° 00' curve at Sta. 8792 -f 27.6. The central angle of the 4° 00' curve = 26C 45'. It is desired to move the forward tangent inward 30 ft., but to re- tain the same degree of curve. Find the station number of the new C.C. and the coordinates of the new C.T. referred to the old C.T.
Answer. C.C. = 8790 + 61.6; I = 54.5 ft.; p = 30.0 ft.
4. Data the same as in Problem 3, except that the tangent is to be moved outward.
Answer. C.C. = 8794 + 22.0; I = 66.4 ft.; p = 30.0 ft.
5. A 5° 00' curve compounds with a 3° 00' curve at Sta. 147 + 63.3. The central angle of the 3° 00' curve is 19° 00'. The forward tangent is to be moved 25 ft. inward, but the same degree of curve is to be retained. Find the station number of the new C.C. and the coordinates of the new C.T. referred to the old C.T.
Answer. C.C. = 149 + 04.0; I = 90.2 ft.; p = 25.0 ft.
6. Data same as in Problem 5, except that the tangent is to be moved outward.
Answer. C.C. = 146 + 61.3; I = 63.3ft.; p = 25.0ft.
7. A 4° 30' curve compounds with a 7° 30' curve at Sta. 999 + 67.0. The central angle of the 7° 30' curve is 39° 24'. The forward tangent is to be moved inward 50 ft. and the C. T. is to be kept approximately on the same radial line. Find the new degree of curve for the second branch, the station number of the new C.C., and the coordinates of the new C.T. (actual) referred to the old C.T.
Answer. D, computed = 6° 33'; D, used = 6° 30'; C.C. = 996 + 36.2; x = 5.4 ft. forward; p' = 47.2 ft.
8. Data same as in Problem 7, except that the tangent is to be moved outward.
Answer. D, computed = 12° 51.3'; D, used = 12° 50'; C.C. = 1003 + 31.4; x = 0.3 ft. forward; P' = 50.0.
9. A 5° 30' curve compounds with a 3° 40' curve at Sta. 1888 + 36.2. The central angle of the 3° 40' curve is 27° 50'. The
CURVES 49
forward tangent is to be moved inward 30 ft. and the C.T. is to be kept approximately on the same radial line. Find the new degree of curve for the second branch, the station number of the new C.C., and the coordinates of the new C.T. (actual) referred to the old C.T.
Answer. D, computed = 2° 49.0r; D, used = 2° 50'; C.C. = 1890 + 84.4; x = 3 ft. backward; p' = 30.4 ft.
10. Data the same as in Problem 9, except that the tangent is to be moved outward.
Answer. D, computed = 4° 03.0'; D, used = 4° 00'; C.C. = 1886 + 01.5; x = 11.7 ft. forward; pf = 34.3 ft.
Reversed Curves
76. A reversed curve is a combination of two simple curves of opposite curvature with a common tangent at the point of junction.
A reversed curve should never be used on main lines on account of the shock due to the sudden reversal of curvature and also due to the fact that it is impossible to superelevate properly the outer rail at or near the point of reversal. If conditions require two curves of contrary curvature close together, they should be separated by sufficient tangent to run out the superelevation of each, or it should be provided with easement curves in which case the " points of spiral" may be coincident.
In yards and connections, reversed curves may be permissible, since the speed is low, and in some cases may be imperative. In nearly every case, however, they should be employed in con- junction with turnouts, therefore further discussion of reversed curves will be included with the problems of turnouts and con- nections in Chapter VI.
Part 2. Spirals
77. A spiral is a curve of varying radius which is used at the ends of circular curves in order that the change from rectilinear to circular motion, or vice versa, may be gradual and without shock. It is also used between the branches of a compound curve for similar reasons.
On tangents the track should be level transversely, but on curves the outer rail is elevated above the inner one to counter-
50
TEXT BOOK ON RAILROAD SURVEYING
ict the effect of centrifugal force. If this were carried out lit- erally, there would be a vertical jog in the outer rail at the T.C. and the C.T., which is impossible from the standpoint of opera- tion. It is evident then that the superelevation must be at- tained gradually; the distance in which this is done is called the " run-off." It is the custom on unspiraled curves to have the run-off either wholly or in part on the tangent with the result that there is a disagreeable tipping of the train upon entering and leaving curves. When a spiral is used this objec- tion is overcome since the superelevation is attained in its length, and at every point is correct for the degree of curve at that point. Thus the spiral may be defined as a curve whose degree of curve increases uniformly from zero at Us beginning to the degree of the main curve at its end.
Application to Simple Curves
78. The functions of the spiral are shown in Fig. 18, and are defined as follows:
T.S. — the point of change from tangent to spiral. S.C. — the point of change from spiral to circular curve.
FIG. 18.
C.S. — the point of change from circular curve to spiral. S.T. — the point of change from spiral to tangent.
a — the angle between the tangent at the T.S. and a chord to any point on the spiral — the spiral deflection angle.
CURVES 51
A — a for the S.C. — the spiral total deflection angle.
b — the angle at any point on the spiral between a tangent
at that point and a chord to the T.S. B—b at the S.C.
d — degree of curve of the spiral at any point. D — degree of curve of the central circular curve. / — the angle at any point on the spiral between a tangent
at that point and a chord to any other point (b is a
special case of /).
7 — the total central angle of the spiraled curve.
d — the central angle of the spiral from the T.S. to any point. A — the central angle of the spiral from the T.S. to the S.C. k — the rate of change in the degree of curve of the spiral per
station.
I — the length of the spiral in feet from the T.S. to any point.
L — the length of the spiral in feet from the T.S. to the S.C.
s — the length of the spiral in stations from the T.S. to any
point = JQJJ.
8 — the length of the spiral in stations from the T.S. to the
r — the radius of curvature of the spiral at any point (radius
corresponding to d).
R — the radius of curvature of the central circular curve. x — the abscissa of any point referred to the T.S. X— the abscissa of the 'S.C. referred to the T.S. y — the ordinate, or tangent offset, of any point. Y — the ordinate, or tangent offset, of the S.C. T.C. — the point of curve of central curve produced back to a
tangent parallel to the tangent at the T.S. o — the ordinate of the T.C. t— the abscissa of the T.C. referred to the T.S. P.I. — the point of intersection of the tangents of the spiraled
curve. Ts — the tangent distance of the spiraled curve (T.S. to P./.).
52 TEXT BOOK ON RAILROAD SURVEYING
T — the tangent distance of an unspiraled curve of the same
D and 7.
Es — the external distance of the spiraled curve. E — the external distance of the unspiraled curve of the same D and /.
79. Formulas.
From definition,
kl
d = ks = loo
The derivations of the following formulas require the use of the calculus and are given in the Appendix.
d (in degrees) = Jks2, A = |kS2 ....... (19)
a (in degrees) = J d = | ks2 ...... )
a (in minutes) = lOks2, >• (20)
A (in degrees) = f A = J kS2 )
b (in degrees) = f d = 2a,
B (in degrees) = f A = 2 A ' y = 0.291 ks3 - .00000158kV [ ( ^
Y = 0.291 kS3 - .00000158 k3S7 f
x = 1 - .000762 k2s ) /x
X = L - .000762 k2S5 f o = 0.0727 kS3 .......... . . (24)
t = iL - .000127 k2S5 ......... (25)
Ts= T + otan JI + t = (R +o) tanfl + t . . . (26)
ES = E + ^~Tf = (R + o) exsec JI + o . . . . (27)
COS 2-*-
80. Length of Spiral.
Since the function of a spiral is to ease the entrance to a cir- cular curve, D will always be known. Then from Eq. 18 it is only necessary to choose a value of k or L, and the spiral is fixed. Obviously any value of k could be chosen and the spiral would fit, but such a spiral may be so short as to require an excessive
CURVES 53
rate of superelevation, or, on the other hand, it may be needlessly long. It is therefore more logical to determine the length of spiral necessary to give the desired rate of superelevation and to make k to correspond.
The length of the spiral is a direct function of the rate of superelevation. The total superelevation depends upon the speed and the degree of curve and is found from the formula,
*e = 0.00069 DV2 (28)
in which e is the superelevation in inches and V the velocity in miles per hour, e should never exceed 8 inches on account of the effect on slowly moving trains, but the track should be super- elevated for the fastest tram up to this limit. Therefore the maximum train speed for any given curve is limited by this maximum superelevation. According to the American Railway Engineering Association, curves requiring less than 2 inches of superelevation are not generally spiraled, as the run-off may be placed on the tangent without objection.
The maximum rate at which the superelevation may be at- tained without discomfort to passengers is about 1 1-6 inches per second. f Therefore the minimum length of spiral is,
L = 6/7 ev where v is in feet per second. Reducing v to miles, per hour,
L = 1.26 eV
Substituting the value of e from Eq. 28,
L = . 00087 DV8 .... (29)
Substituting the value of D from Eq. 18, and solving for k, we have
115000., ,QrA
k = V3 (Approx.) .... (30)
The diagram, Fig. 19, is platted from values computed by the above formulas, and gives the length, superelevation, and k for
* For derivation, see Appendix, paragraph 143.
t American Railway Engineering Association, Bulletin 108, Feb., 1911.
TEXT BOOK ON RAILROAD SURVEYING
CURVES
55
curves from 0° 30' to 10° 00', and for speeds from 20 to 80 miles per hour. In this diagram, with any given value of D and F, the length of spiral, the corresponding value of ft, and the re- quired superelevation can be readily determined.
The consensus of opinion of 31 railroads of the United States as reported to the American Railway Engineering Association is that the theoretical speed for which the outer rail is superelevated, or the curve spiraled, may be exceeded about 20 per cent, without discomfort to passengers. Further, the maximum speed is never accurately known. Therefore, it is not necessary to use the exact values of k and L as determined for the assumed speed. Obviously, even values of k are desirable, and since considerable variation is permissible, such values may be chosen, provided the change does not increase the speed more than 20 per cent. An examination of the diagram, Fig. 19, will show that values of A; of i, 1, 2, and 4 will give a satisfactory length of spiral for practically all cases met in practice.
81. Field Work.
The first step in the field work is to determine the station numbers of the T.S., S.C., C.S., and S.T. The T.S. and the
FIG. 20.
S.T. are located on the ground by measuring the distance !Fs from the P.I. From Fig. 20,
Ts = T + o tan ^1 + t
(31)
56 TEXT BOOK ON RAILROAD SURVEYING
T is found from Table 6 (or Eq. 2); o is found from Table 1 (or Eq. 24); and t is found from Table 1 (or Eq. 25).
Example. Given:— P.I. = 21 + 21.1, D = 3° 40', / = 51° 20', and maximum speed about 45 miles per hour.
From diagram, Fig. 19.
Superelevation = 5 inches, k = 1, and L = 366.7 ft.
Sta. P.I = 21 +21.1
From Table 6, T = 750.9
From Table 1, o = 3.58, o tan \l = 1.7
From Table 1, t = 183.3
Ts = 9 35.9
Sta. T.S. = 11 +85.2 S = 3 66.7
Sta. S.C. = 15 + 51.9 Length of circular curve = — — - = r — S = 10 33.3
Sta. C.S. = 25 + 85.2 S= 3. 66.7
Sta. S.T. = 29 + 51.9 Spirals are staked out either by deflection angles or by offsets.
82. Deflection Angles. The process of staking out spirals by deflection angles is the same as that for simple curves. Spirals rarely exceed 600 ft. in length, and the total deflection angle to the S.C. rarely exceeds 5° 00 ', therefore the entire spiral can be run in from the T.S*
Since a spiral is more difficult to aline than a simple curve, stakes should be placed closer together; and since the spiral becomes sharper as it increases in length, stakes should be placed more closely together at the end than at the beginning.
* For running in spiral from an intermediate point on spiral, see paragraph 85.
CURVES
57
RULE: — Place stakes 50 ft. apart on all spirals up to the point where the degree of curve (d) becomes about 3°; beyond this point place them 25 ft. apart.
For ease in computation, stakes are placed the above distances apart beginning at the T.S.', hence in general all the stakes will fall at plusses.
The spiral deflection angles are
a (in minutes) = 10 ks2
(20)
Note that the spiral deflection angles vary with the square of the distance instead of the first power as in simple curves.
In Fig. 21 point 1 is located by a 50-ft. chord from the T.S. and the angle a\\ point 2 by a 50-ft. chord from 1 and the angle
T.S.
s.c.
FIG. 21.
02', and so on, noting the change in chord length when d becomes 3°. From Eq. 20, and
ai = 10' k (0.5 )2
a* = 10' k (1.0 )2 = 4ai
a3 = 10' k (1.5 )2 = 9ai
a4 = 10'k(1.75)2 = 49/4ai
a5 = 10' k (2.0 )2 = 16ai A = a6 = 10' k (2.25)2 = 81/4ai = 1/3A
It is thus seen that the deflection angle for the first station only needs to be determined from Eq. 20. The other values are found by multiplying this value by the square of the ratio of the first distance to the other distances.
|
TRANSIT NOTES FOR LINE L |
|||||
|
STATION |
ALINE- MENT |
TOTAL DEFL. ANGLE |
CALC. BEAR |
MAG. BEAR |
REMARKS |
|
1027 |
Tan. |
S 64°-14'W |
S 64°-10'W |
||
|
26+23.1 |
S.T. © |
o°-oo' |
|||
|
+73.1 25+23.1 +73.1 |
k =1°- in from S.T. |
0°-02.o 0-10 0-22.5 |
|||
|
24+23.1 +73.1 |
CQ C3 |
0-40 1-02.5 |
|||
|
+ 23.1 |
C.S. 0 |
1-30 |
|||
|
+23.1 |
c.s. © |
8-45' |
-Ho |
(check) |
|
|
23 |
8-24 |
||||
|
22 |
6-54 |
P.I. 1020+40 |
|||
|
21 |
.0 |
5-24 |
1 = 26-30' |
||
|
1020 |
°co |
3-54 |
D= 3-00' |
||
|
19 |
2-24 |
T8= 600 '2 |
|||
|
18 |
0-54 |
||||
|
17+39.8 |
s.c. © |
0-00' |
|||
|
17+39.8 |
1-30 |
k - 1- |
|||
|
+ 89.8 |
1-02.5 |
L= 300.'0 |
|||
|
16+39.8 |
7 |
0-40 |
A =4- 30' |
||
|
+89.8 15+39.8 |
2 "3. CO |
0-22.5 0-10 |
A= 1°-30' B = 3°_00' |
||
|
+89.8 |
0-02.5 |
||||
|
+39,8 |
T.S. © |
0-00' |
|||
|
1014 |
Tan. |
S 37- 44'\V |
S37°-50'W |
FIG. 22.
58
28 Mike McCarthy -last.
Heine Heinrichson-H.C.
01ey01sen-R.C. June 17, 1913
S.Garibaldi- R.F. Clear-Hot
Set up at S.T.plates at 0 °00'; B.S.along Tangent; Back in Spiral to C.S.
Ic=I-2A=17°-30'
B.S. at T.S., Plates at 3-00'. Plunge and turn to 0-00 'for Tangent.
FIG. 22. 59
60 TEXT BOOK ON RAILROAD SURVEYING
Example. Assume that in Fig. 21, T.S. is at Sta. 711 + 44.0, k = 2, and S = 2.25. Then D = 4° 30'.
Deflection angle of T.S., Sta. 711 + 44.0 = 0° 00'
" " 1 " 711 +94.0 = 0°05'
" " " 2 " 712+44.0 = 0°20'
" " 3 " 712 + 94.0 = 0° 45'
" " 4 " 713 + 19.0 = 1°01'
(1° 01. 25 'exact)
" " " 5 " 713 + 44.0 = 1° 20'
" "S.C.(A)" 713 + 69.0 = 1°41'
(1° 41. 25' exact) A - 1/3A, A = 5°-04'
(5° 03.75' exact) B = 2/3A = 2A =3° 22.5'
To orient the transit at the S.C., back-sight on the T.S. with the plates set at 3° 22.5' (angle B)', then turn the plates to zero and the telescope is on tangent and the circular curve is run in as from the T.C. of a simple curve, stakes being placed at the regular stations (in the above problem at 714 + 00, 714 + 50, etc.). After running in about half of the circular curve, move the transit to the S.T. and run in the second spiral with the same deflection angles. Then move to the C.S. and back-in the remainder of the circular curve, thus placing the adjustment of the errors of surveying at the center of the curve instead of at the end of the spiral as is usually but unwisely done. The form of notes is shown in Fig. 22.
This method is particularly applicable for locating spirals after the construction is completed and the track is to be brought to exact line and surface. For setting stakes during construction the offset method is preferable.
83. Offsets. Evidently the entire spiral can be located by means of the coordinates x and y (tangent offsets), and this is a satisfactory method for short flat spirals where y is less than about 10 feet. When y becomes greater than this, the spiral can not be located with sufficient accuracy unless the offsets are turned off with an instrument.
On location, since it is usually desirable to advance the line as rapidly as possible, the best method is to run-in the circular curve from the T.C. to the C.T. (offsetted curve, see Fig. 20),
CURVES 61
and to insert the spiral later by offsets from both the tangent and the circular curve.
Since the spiral departs from an osculating circle at any point at the same rate that it departs from the tangent at the T.S. (see Appendix, paragraph 142), it follows that the offsets from the circular curve to the spiral are the same as the offsets from the tangent at the T.S. for the same distances. Since the offset o and the spiral bisect each other (see Appendix, para- graph 141), it is evident that the maximum offset is Jo, and there- fore will be small, and also that it is necessary to compute offsets for half the spiral only. Half of the spiral is then located by offsets y from the tangent at the T.S., and the other half by the same offsets measured normal to the circular curve.
From Eq. 22 it is seen that the offsets vary approximately as the cube of the distances, and for this method of location can be taken so with inappreciable error. Since the maximum ordinate is £o, and o is determined to offset the T.C., it is seen that the offsets can be determined directly from o instead of from Eq. 22.
Application to Compound Curves
At the C.C. of a compound curve — as at the T.C. of a simple curve — there is a change in the rate of curvature and in the amount of superelevation, and if this is great enough to be ob- jectionable, a spiral should be inserted between the two branches.
Evidently only that part of the spiral of curvature intermediate between the degrees of the two curves is required, and — as at the T.C. of a simple curve — the two curves must be offsetted at the C.C.
84. Problem 1. In Fig. 23, HBC is a A curve and EFJ is a D2 curve having parallel tangents at C and E (the position of the C.C. if the curve were unspiraled). It is desired to con- nect the two curves by the spiral BF. Consider the spiral run backwards to its T.S. at A. Since the degree of curve of the spiral at B must be A and at F must be Z)2, then the spiral from B to F is that part of a regular spiral from where d = Di to where d = D2. The value of k depends upon the maximum speed permissible on the sharper curve and upon the difference in the two degrees of curve.
Since the spiral departs from every osculating circle at the
62
TEXT BOOK ON RAILROAD SURVEYING
same rate as from the tangent at the T.S., BC = CF, the spiral bisects CE, and CE is equal to o-for a spiral whose D = D2 — D\ for the chosen value of k.
FIG. 23.
To insert a spiral between the curves, find o for a Z>2 — A curve and make the offset from C to #. The length of the spiral in stations is
D2 - D!
Locate B and F by measuring J$i from C and E.
The curves may be staked out by continuing the first branch to C, offsetting to E, and running-in the second branch; and then inserting the spiral by offsets from the circular curves in ex- actly the same way as explained in paragraph 83.
85. Deflection angles may also be used; but, since the transit is at a point on the spiral, B or F, and not at the T.S., the reflec- tion angles to be used are values of / instead of a. From a tangent at B in Fig. 23, the deflection angle n to any point N' on the circular curve BCM is JA X BN'. Since the spiral departs from the osculating circle at the same rate as from the tangent at the T.S., the angle between the circular curve and a point N on the spiral is a = 1/6 k(BN)*. But BN and BN' are equal. Then
f = n + a =
(BN) + 1/6 k (BN)2.
CURVES 63
If the transit were set at F, the deflection angle to N would be f = JD2 (FN) - 1/6 k (FN)2
86. Problem 2. Fig. 24 shows a compound curve to be spiraled at each end and between the two branches. The
FIG. 24.
tangent distances Tsi and TS2 are required, and the solution is fully indicated in the figure.
Application to Existing Curves
To insert a spiral in an existing track, it is necessary to shift the ends of the curve inward to provide room for- the spiral. If the same degree of circular curve were retained, this would shift the entire curve inward. Since the amount of such shifting may be considerable (o sec. JJ at its center) the new alinement may not be on the old roadbed and considerable cost of earth- work would be entailed in making the change. To obviate this, the degree of curve may be changed in such a way that the new alinement will permit the insertion of the spiral and at the same time require little or no additional earthwork.
64
TEXT BOOK ON RAILROAD SURVEYING
87. SIMPLE CURVES. Existing simple curves may be spiraled in two ways.
(1) By shifting the center of the curve outward * a small amount, and by sharpening the curve sufficiently to give the desired offset. This method is particularly applicable for curves whose lengths are less than about four times the length of the spiral to be used.
(2) By sharpening the curve slightly at the ends to give the necessary offset, leaving the middle portion of the curve un- changed. This method is preferable for long curves.
88. First Method.
In Fig. 25, ABC is the existing unspiraled curve with B as its middle point. It is desired to shift the track outward at B
FIG. 25.
the assumed distance p, and to sharpen the curve to give the necessary offset o.
From the figure, p is the difference between the external dis- tances of the existing curve and the spiraled curve. Therefore from Eqs. 5 and 27, we have
p = R exsec JI — [(Ri -f o)exsec JI + o]
= (R - Ri - o) exsec JI - o ... (32)
*The shifting must be outward to make the change in alinement a minimum.
CURVES 65
The minimum change in radius (R — Ri) is that which will make p equal to zero. Then from Eq. 32,
Ri = R ^T- . (33)
vers il
(This is the maximum value of Ri that will satisfy the con- ditions.)
In any given problem first determine approximately (mentally) the maximum value of Ri from Eq. 33. This is used simply as a guide in estimating the value of RI to use. Choose a value of Ri less than this (preferably to agree with an even 10 minutes of degree of curve) and solve Eq. 32 for p. If this value agrees sufficiently close with the desired shifting of the track at Bt the solution is complete. If not, re-estimate Ri (using the previous value as a guide), and repeat until a satisfactory value of p is obtained.
The distance from the T.C. of the original curve to the T.S. is the difference between Ts for the new curve and T for the old curve. The T.S. and the S.T. are then located from the T.C. and the C.T., respectively, of the old curve, and the new curve is staked out as in new work.
Example. / = 40° 00', D = 4° 00', k = 1, and p = about 1.5 ft.
From Eq. 33, the maximum value of Ri = 1330 ft. (approx.) corresponding to DI = 4° 18' (approx.). Choose a trial value of Ri = 1322.2 ft. for A = 4° 20'. Then from Eq. 32, p = 0.8 ft. Choosing Ri = 1312.1 ft. for A =4° 22', p becomes 1.3 ft., showing that a change of 2' in D! increases p about 0.5 ft. Then to make p = 1.5 ft., DI would have to be about 4° 23'. Since an odd value of DI is undesirable, and since it is not necessary to make p exactly 1.5 ft., it is sufficient to take DI = 4° 22'.
In the foregoing discussion it was assumed that the degee of the existing curve was known and that the T.C. and C.T. were monumented. It will generally happen, however, that the degree of curve is unknown, that the track is in poor alinement, and that the T.C. and C.T. are not monumented. In this case, run out the tangents to an intersection and measure the inter- section angle. Then measure the external distance of the
*o should correspond with Ri which is unknown, therefore use 'a value of o corresponding to about 0.9 R.
66 TEXT BOOK ON RAILROAD SURVEYING
existing curve and from it determine the degree of the curve that will connect the tangents and pass through the middle point of the existing curve. Use the value of R corresponding to this value of D in solving Eqs. 32 and 33.
89. Second Method. Case 1. In Fig. 26, ABC is the exist- ing unspiraled curve, whose degree of curve, D, is known, whose alinement is good, and whose T.C. and C.T. are monumented. At some point on this curve, such as B, it is desired to compound with an assumed curve of slightly shorter radius, Ri, which, when run to a tangent parallel to the initial tangent, will be a distance from it equal to o for a Ri curve, thus providing room for the spiral.
In the figure, EFB is the Ri curve, and EG is o corresponding to
T.S. A T.C. G
FIG. 26.
it. It is required to find the location of the T.S., of the S.C., and of the C.C., B. From the figure,
o = EG = GL - EL = (R - Rx) vers Ii
vers Ii = ^ _ R (34)
The T.S. is located by measuring back from the old T.C.
T.C. to T.S. = t - (R - Ri - o) tan Ii. . . (35)
The S.C. is located by measuring the spiral length from the T.S. The C.C., J5, is located by measuring the distance FB from the
S.C.
FB (in feet) = --^ 10° • - • • (36)
CURVES
67
The location of the point B may be checked by measuring the distance AB along the old curve.
AB (in feet) = -g- 100
The distance from the T.S. to the C.C. along the new aline- ment is shorter than along the old alinement which will require the rails to be cut. This shortening is equal to the difference in the Sta. numbers of the C.C. as computed along the respective alinements.
The limits of RI are such as will make the point B come at the middle of the original curve, or will make B and F coincide. In general, R\ should be chosen between 0.8 R and 0.9 R.
Example. D = 3° 00', A (assumed) = 4° 00', k = 1, and o = 4.65. From Eq. 34, h = 12° 14.3'. From Eq. 35, the distance from the old T.C. to the T.S. is 156.5 ft. The spiral is 400 ft. long. From Eq. 36, the distance from the S.C. to the C.C. is 121.1 ft.
90. Second Method. Case 2. In Fig. 27, ABC is the
existing unspiraled curve, whose degree of curve is unknown, whose alinement may be poor, and whose T.C. and C. T. are no*, monumented. First set-up in the center of the track at some
_A_ G , O (P L --^F^fec^— -TN~~T V/LB
FIG. 27.
point C near the middle of the curve and by trial deflection angles find the degree of the curve, D, that will most nearly conform to the existing track. Then run-in this D curve to a point B which is about 500 ft. from the end of the curve. If this curve were continued, its T.C. would fall at / on a tangent parallel to the initial tangent QL and at a distance p from it.
68
TEXT BOOK ON RAILROAD SURVEYING
At B run-out the tangent to the D curve to an intersection with the initial tangent at L and measure the intersection angle IB and the distance BL. BN is the tangent distance of the curve corresponding to IB- Then,
p = NL sin IB
The D curve is to be compounded with a chosen D\ curve at some point F to give the required offset o.
EK = o — p = (R — Ri) vers IB, whence o — p
(37)
The T.S. is located at Q by measurement from L.
QL = QG + GL = t + JN - JK - NL cos IB
The S.C. and the C.C. are located as in Case 1, and the spirals are staked out as in new work.
J may fall outside of QL, in which case p and o are numerically added; again, p may be greater than o, and in this case Ri must be greater than R.
91. COMPOUND CURVES.
An existing compound curve can be spiraled in the following manner.
FIG. 28.
In Fig. 28, ABC is the existing compound curve with its C.C. Sit B. To make room for the spiral it is necessary to compound
CURVES 69
the sharper branch, D2, at some point C with a still sharper curve of chosen degree, D3, and to continue the first branch, DI, to the point E where its tangent is parallel to the tangent of the D3 curve at G. EG is the offset o for a spiral whose D = D3 - DI. The problem is to find BE = HI and CG = n2.
For small central angles the ordinates between two circular curves are equal to the difference in their tangent offsets. There- fore EF can be considered as the difference in the tangent offsets of the DI and D2 curves in the distance HI] similarly FG is the difference in the tangent offsets of the D2 and D3 curves for the distance n2.
Then from Eq. 15,
o = EF + FG = 0.873 (D2 - DI) ni2 + 0.873 (D3 - D2) n22.
Since the central angle of the arc EC equals the sum of the cen- tral angles of the arcs BE and CG,
D2 (ni + n2) = Dini + D3n2 or (D2- DI) ni = (D3- D2) n2.
Solving these simultaneous equations for HI and n2 we have
n - 1 07 I (D3 - P2) O /OON
L07\' (D2 - Dl) (Da-DJ-
n, = 1 07 !~~~ (E>2 - Di)o~ /oqi
\(D3-D2)(D3-D1)
C is located by measuring the distance n\ + nz along the D2 curve from B. The C.S. is located by running the DI curve from B the distance HI — t, and the S.C. is located by running the D3 curve from C the distance HZ — (Si — t). The spiral is staked out as usual for compound curves.
70
TEXT BOOK ON RAILROAD SURVEYING
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72 TEXT BOOK ON RAILROAD SURVEYING
Problems
1. What is the maximum speed for 10°, 7°, 3°, and 2° curves?
2. Given. P.I. at Sta. 741 + 60.0; / = 35° 42'; k = 2°; and D = 5° 00'. Determine the station numbers of the T.S., S.C., C.S., and S. T., and the external distance of the curve.
Answer. T.S. = 736 + 65.3, S.C. = 739 + 15.3, C.S. = 743 + 79.3, S.T. = 746 + 29.3.
3. Write transit notes for Problem 4.
4. Compute notes for locating the spiral in Problem 4 by offsets.
-5. On new location a 5° 00 ' curve is to be offsetted from a 2° 00' curve at station 333 + 00.0 f or a k = 1° spiral. Find the station numbers of the C.S. and the S.C. and the required offsets. Write notes for spiral.
6. Write notes to locate spiral in Problem 7 by offsets.
7. Given. P.I. at Sta. 267 + 00.0; / = 69° 20'; /i = 21° 40'; 72 = 47° 40'; A = 1° 30'; A = 4° 00'; ki = /c2 = 1°; /c3=2°. Find TA, TS2, and the Sta. numbers of the T.S., S.C., C.S., S.C., C.S., and S.T.
Answer. Tsl = 1883.3, T& = 1272.3, T.S. = 248 + 16.7, S.C. = 249 + 66.7, C.S. = 262 + 11.1, S.C. = 264 + 61.1, C.S. = 274 + 27.8, S.T. = 276 + 27.8.
8. Write transit notes for Problem 9.
11. An existing curve is to be spiraled. 7 = 39° 18', D = 3° 20', k = 1°. The track is to be shifted outward at the middle about 1.0 ft. Find A and the actual value of p.
Answer. A = 3° 30'; p = 1.24 ft.
9. Given an existing 2° 40' curve to be spiraled by compound- ing near the ends with a 3° 00' curve. The T.C. is at Sta. 66 + 66.6 and k = 1°. Find the station number of the T.S., S.C., and C.C., and the amount that the track will be shortened.
Answer. T.S. = 65 + 47.1, S.C. = 68 + 47.1, C.C. = 69 + 42.0. The track is shortened 0.1 ft.
10. An existing compound curve has its C.C. at Sta. 488+ 50.0. A = 4° 00', A = 7° 00', A = 7° 40', and k = 1°. Find the station numbers of the C.S., S.C., and C.C.
Answer. C.S. = 487 + 16.5, S.C. = 490 + 83.3, C.C. = 491 + 24.3.
CHAPTER V
EARTHWORK
Introduction
92. Railroad Cross -Sections. The forms of earthwork cross- sections in cut, fill, and side-hill work (both cut and fill) are shown in Figs. 29, 30, and 31, respectively. Fig. 32 shows the form a section in cut should take when it consists partly of earth and partly of rock.
FIG. 29.
FIG. 30.
FIG. 31.
FIG. 32.
93. Width of Roadbed. The width of roadbed for single track on fill varies from 14 to 22 feet, and in cut from 20 to 33 feet. However, the best practice is 18 or 20 feet on fill and 28 or 30 feet in cut. The greater width in cut is required to allow for side ditches for drainage.
For double track add to the above quantities the distance between track -centers.
Copyright, 1913, by G. W. Pickels and C. C. Wiley.
73
74 TEXT BOOK ON RAILROAD SURVEYING
94. Ditches. In order to provide drainage in cuts side ditches are constructed on each side of the track. The ditches should be of such cross-section that they can be easily constructed and maintained and not easily obstructed. For these reasons broad shallow ditches are better than narrow deep ones. The usual width of ditches is from 3 to 6 feet, depending on the size of the cut and the amount and rate of rainfall.
Where there is considerable ground water it may be necessary to construct tile sub-drains under one or both of the side ditches.
When there is likelihood of considerable surface water draining on to the roadbed, as for example in side-hill work, an open diversion ditch, termed a surface ditch, should be constructed outside the cut to carry this water to the end of the cut.
Side ditches are more expensive to excavate than the body of the cut, and therefore should preferably be included as a separate item in the contract.
95. Side Slopes. The slope of the sides of the cut or fill is expressed as the ratio of the -horizontal to the vertical distance and depends on the material through or of which they are made. The following are commonly used.
(1) Cut
Solid rock - vertical or J:l.
Loose rock — J:l to 1:1.
Hard earth - 1:1 to 11:1. Soft earth
or Sand - 1J:1 to 3:1.
(2) Fill
Loose rock — 1:1.
Earth -1:1 to 11:1.
Sand - 11:1 to 2:1.
96. Borrow Pits. It frequently happens that the earth from the adjacent cuts is not sufficient to make the intervening fill. In this case the contractor is allowed to borrow earth from along the right of way. The pits thus dug are called borrow pits, and are staked out by the engineer before the work is started. In staking out borrow pits care should be taken to leave a berm of at least 5 ft. between the foot of the embankment and the
EARTHWORK 75
edge of the borrow pit; a similar berm should also be left at the edge of the right of way. The contractor is required to leave all borrow pits in such a shape that water will not collect in them.
97. Shrinkage. Some soils become more compact when thoroughly compressed in an embankment than they were originally, and therefore a cubic yard of cut will ultimately make less than a cubic yard of fill. This does not take place until a year or two after the fill is made. This reduction of volume is called shrinkage. The amount of shrinkage varies with the kind of soil and hence the allowance for shrinkage should be left to the judgment of the engineer in the field and should not be made part of an arbitrary set of standards. Very few soils will shrink as much as 3 per cent.
98. Growth. Solid rock will increase in volume on excavation and hence a cubic yard in cut will make more than a cubic yard of fill. This is termed growth. The amount of growth de- pends on the uniformity of size of the fragments, and varies from 30 to 100 per cent., the average in railroad work being about 50 per cent.
99. Settlement. A newly built fill is never thoroughly com- pact and therefore will continue to settle for some time, possibly a year or two. The difference in height between the newly- built fill and the fill after fully settling is termed settlement. The amount of settlement depends on the nature of the soil and the method of forming the embankment. A fill of ordinary soil, well made with horses and scrapers or wagons, will settle about 5 per cent.; if simply dumped from a trestle, the settle- ment is greater and in some cases may reach 15 per cent. A rock fill will settle but little.
Allowance for settlement is made in the field by marking on the slope stake the theoretical fill plus the allowance for settlement. For example, if the fill is 10 feet and the settlement is 5 per cent.; the slope stake is set at the proper point for a fill of 10 feet, but is marked F 10.5.
Shrinkage and settlement are frequently confused, but it is to be noted that settlement includes shrinkage, and that the allowance in the field is for settlement.
76 TEXT BOOK ON RAILROAD SURVEYING
If a fill is short and high the full allowance for settlement may make a hump in the grade line which may be very objectionable from the standpoint of operation. Of course this hump would ultimately disappear, but it may be preferable to avoid the hump by reducing the allowance for settlement and later to bring the track up to grade by the addition of ballast.
In case a bridge is placed in a high fill, the full allowance for settlement can not be made at this point. Extra care should be taken to compact the fill immediately behind the abutments in order to reduce the amount of settlement, and the track should be carefully maintained at these points until the embankment
is fully settled.
»
Cross-Sectioning
100. Slope Stakes. Before construction work can be com- menced, slope stakes must be set for the guidance of the con- tractor (1) at every full station, (2) at those intermediate points where the longitudinal slope of the ground changes, and (3) at other points required by special structures.
A slope stake is a stake that is set on each side of the center line at the point where the side slope of the cut or fill will inter- sect the ground surface. It has the cut or fill at that point (see settlement) marked on one side and the station number on the
FIG. 33.
*
other. The numbers are written lengthwise of the stake be- ginning at the top, and the cut or fill is given in feet and tenths, prefixing C for cut and F for fill (see Fig. 33). The stakes are driven with the tops slanting outward, and the sides upon which the cuts or fills are marked facing the roadbed, as shown in Fig. 33.
EARTHWORK 77
101. Cross-Sectioning. Cross-sectioning consists in setting the slope stakes, which mark the limits of excavation or embank- ment, and in taking sufficient elevations between the slope stakes to compute the area of the section to be excavated or filled in.
The data needed for cross-sectioning are the sub-grade eleva- tion at every station, the width of the roadbed in both cut and fill, the side slopes for different materials, and the elevations of all bench marks. The sub-grade elevation for every station on the entire line can be obtained from the profile and should be written in the cross-section notebook opposite its station — as shown in the form of notes in Fig. 34 — and carefully checked before any cross-sectioning is done. Also the description and elevation of every bench mark that was established during the location should be written in the back of the notebook.
102. Field Work. Starting with the nearest bench mark, differential levels are run to the part of the line that is to be cross-sectioned. The back sights, fore eights, heights of in- strument, and elevations of turning points are recorded in the second column of the notes in such a way that the H.I. will be in the same line as the first station cross-sectioned from that set-up (see Fig. 34) . The sub-grade elevation in the third column is subtracted algebraically from the H.I. elevation in the second column and the difference is the grade rod and is recorded in the fourth column. A rod reading is then taken to the nearest tenth of a foot on the ground at the foot of the center stake. All the rod readings are considered negative. The rod reading and the grade rod are added algebraically and the sum represents the cut or fill at the point where the reading is taken, minus indicating fill and plus indicating cut. The cut or fill is marked on the back of the center stake and is recorded in the notes as the numerator of a fraction whose denominator is zero.
If the ground is level transversely of the line, the cut or fill at the slope stake will be the same as at the center, and the distance from the center stake to the slope stake is found by multiplying the center cut or fill by the ratio of the side slopes and adding one half the width of the roadbed. Such a section is called a level section (see Fig. 35a).
If the ground is not level transversely the cut or fill will be different for various points, and the problem is to find the point on each side of the center line whose distance from the center is
CROSS-SECTION NOTES.
|
Station. |
Turning Points. |
Grade. |
Grade Rod. |
L. |
C. |
R. |
|
55 56 57 58 59 10560 61 62 63 64 65 66 |
740.51 -11.63 |
727.50 727.00 726.50 726.00 725.50 725.00 724.50 724.00 723.50 723.00 ^ > 722.50 m m > 722.00 |
13.0 13.5 14.0 14.5 4.1 4.6 5.1 5.6 6.1 6.6 Vs ^0.3 |
+9.0 |
+9.8 |
+ 10.2 |
|
27.5 +7.3 |
0 +7.3 |
29.3 +7.8 |
||||
|
728.88 +0.72 |
||||||
|
729.60 -10.54 |
||||||
|
25.0 +5.5 |
0 +6.0 |
25.7 +6.4 |
||||
|
22.3 +4.2 |
0 +4.4 |
23.6 +4.4 |
||||
|
20.3 +2.2 |
0 +2.7 |
20.6 + 3.4 19.1 + 1.4 |
||||
|
17.3 + 1.0 |
0 + 1.2 |
|||||
|
719.06 +2.53 721.69 |
||||||
|
15.5 Grade -1.2 |
0 Point +65 -0.6 |
16.1 - 0.8 |
||||
|
10.8 -3.2 |
0 -2.4 |
10.2 - 2.1 |
||||
|
13.8 -4.8 |
0 -3.8 |
12.2 - 3.5 |
||||
|
16.2 -6.0 |
0 -5.2 |
14.3 - 5.0 16.5 - 6.6 |
||||
|
18.0 -6.8 |
0 -6.6 |
|||||
|
19.2 -8.5 |
0 -7.8 |
18.9 - 7.0 19.5 |
||||
|
21.8 |
0 |
FIG. 34.
78
|
End Areas. |
Volumes. |
Mass Curve Volumes. |
||
|
Cut. |
Fill. |
Cut. |
Fill. |
|
|
412.7 |
3653 |
|||
|
1303 |
||||
|
290.8 |
2350 |
|||
|
221.0 |
948 |
1402 |
||
|
150.2 |
687 |
715 |
||
|
88.3 |
442 |
273 |
||
|
230 |
||||
|
35.8 0.0 |
0.0 15.3 |
43 |
10 |
43 00 |
|
55.0 |
130 |
10 140 |
||
|
278 |
||||
|
95.3 |
418 |
|||
|
434 |
||||
|
139.2 |
852 |
|||
|
602 |
||||
|
186.0 |
1454 |
|||
|
230.8 |
772 |
2226 |
FIG. 34.
79
80
TEXT BOOK ON RAILROAD SURVEYING
equal to the cut or fill at that point multiplied by the slope ratio and added to one-half the roadbed. This is necessarily a cut- and-try method, but proficiency is soon attained in approxi- mating the correct position of the slope stak'^, and it is seldom that more than three trials are required. The cut or fill is marked
(a) Level Section
( t>) Three-Level Section
(c) Five-Level Section
(d) Irregulkr Section
FIG. 35.
FIG. 36.
on the slope stake and is recorded in the notebook as the numera- tor of a fraction whose denominator is the distance out from the center. Three-level, jive-level, and irregular sections come under this heading (see Figs. 35b-c-d).
103. Sections at Grade Points. Fig. 36 shows the junction between a cut and a fill. Stakes, marked " grade," are driven at A, B, C, and D, which are grade points. A cross-section is taken at B and D, and the distances x and y are measured.
EARTHWORK
81
Areas of Cross-Sections
Before the volume of earthwork can be computed, the area of each cross-section must be found. This is done as follows:
FIG. 37.
The cuts at A, B, C, E, F, and G (i.e., the vertical distances from the ground surface to the level of the roadbed), and the distances of these several points from the center, C, have been recorded in the field notebook. To each section annex the
fraction — and write plus and minus signs on each side of each b
numerator, thus:
q_ +C3 - + C2-
b D3 D2
C0+ ^
0
RULE 1. — To find the area (1) multiply each denominator by the algebraic sum of its adjacent numerators, using the sign facing the denominator; and (2) divide the algebraic sum of the resulting products by 2.
or,
IT b(C3+ c2) + D3C2+ D2(d- C,) +-] 2 L D!(CO - C2) + di(C0 - c2)+ d2Cl J
(Let the student prove this equation.)
After the student becomes familiar with this formula, it will not be necessarjr for him to actually write down the plus and minus signs in the notes.
82
TEXT BOOK ON RAILROAD SURVEYING
Eq. (40) can be used for either cut or fill, and for level, three- level, five-level, and irregular sections.
104. Side-hill Sections. When a section is partly in cut and partly in fill as shown in Fig. 38, the field work and the com- putation of the area are slightly modified.
\\Slope Stake
Slope Stake3
FIG. 38.
In this case, after the fill at the center has been determined, the grade point, A, is found by trial. Then all horizontal dis- tances are measured from A. The notes would be recorded as follows :
_0_ x
+Ci - + 0 + -
c2 d2
Di 0 di < Cut - X Fill - >
Notice that x and y are used as the denominators of the an- nexed fractions instead of b as in the former case.
The areas of the cut and fill are computed separately, and are recorded separately in the notes (see Fig. 34).
105. Uncompleted Sections. It is sometimes necessary to find the area of an uncompleted section — for example, for monthly estimates — or of an irregular-shaped borrow pit. The field work for this does not require that elevations be carried
EARTHWORK
83
from station to station, but at each set-up the plane of the horizon- tal line of sight is taken as the reference plane. For example, in Fig. 39, A B is the reference plane whose elevation is not
FIG. 39.
necessary for the determination of the area of the section. The notes should be written thus:
+ c4 - +C3- + C2^- +Ci - + C0 + - ci +
-_c2 d2
- c4
0
-c.
0
d,
Notice carefully the end fractions annexed in this case. The area is found by Rule 1.
Volumes of Earthwork
Earthwork is paid for by the cubic yard, and in order to compute the cost it is necessary to find the volume of the material handled. The total volume is the sum of the -volumes of the prismoids formed by adjacent cross-sections. The volume of the prismoid between two adjacent cross-sections may be found (1) by the end area method, and (2) by the prismoidal method.
106. End Area Method. In this method the prismoid is treated as a prism, whose cross-section is the mean of the two end areas of the prismoid.
Z
v (cu. yds.) =
27
(41)
where v is the volume, Ai and Ai the end areas in sq. ft., and I is the distance between cross-sections in feet.
84 TEXT BOOK ON RAILROAD SURVEYING
For I = 100 ft.,
v = 1.85 (Ai + A2) (41a)
This method is exact when the end areas are equal, but is only approximate when they are unequal. The result is usually too large and the maximum error occurs when one end area is zero, and is about 16 per cent.
Owing to its simplicity, and to the fact that sections usually do not change rapidly, this method is almost universally used.
Table 12 gives the cubic yards per 100 ft. for center depths from 1 to 60 ft.
Table 13 gives the cubic yards per 100 ft. for end areas from 1 to 1000 sq. ft.
107. Prismoidal Method. When the changes from cut to fill are frequent and abrupt or the work is in rock, greater accuracy may be required; in this case the prismoidal method is used.
From Simpson's rule,
. Ai + 4Am + A2 ,
Mean area ol a pnsmoiu = — — ^ — — , where A\ and
A 2 are the end areas and Am the area of a section midway be- tween the ends. Then,
I Z AI + 4 Am -h A2 V = 27 X " -6~ (42)
This is called the prismoidal formula. This form however is in- convenient to use since it requires the area of a mid-section. It is therefore more convenient to find the difference between the prismoidal and end area formulas and to apply this difference to the latter. Subtracting the prismoidal formula from the end area formula and reducing,
Prismoidal Correction = ^j (Ai — 2Am + A2)
Putting AI, A2, and Am in terms of their slope stake dimen- sions— remembering that the dimensions of Am are the average of those of AI and A2 — and reducing, we have
Pris. Cor. = (d - C2) (W2 - WO . . . (43)
EARTHWORK
85
in which Ci and Cz are the center cuts or fills at AI and A2, and Wi and Wz are the corresponding distances between slope stakes.
When 1= 100 ft., Pris. Cor. = 0.31 (Ci - C2) (W2 - Wi) (43a)
This correction is added algebraically to Eq. (41). The result is exact for three-level sections and is sufficiently accurate for any other form of cross-section.
108. Earthwork on Curves. The volume on curves is gen- erated by a section moving perpendicular to the center line of the curve. The section considered is the mid-section of the solid. The distance traveled by this section is the distance traveled by its center of gravity, and it is only when the center of gravity lies in a vertical line passing through the center line of the curve that the volume as computed by the prismoidal method is exact. If the center of gravity is inside the center line, the results ob- tained by the prismoidal method are too large; if outside, they are too small. The difference between the true volume and the volume determined by the prismoidal method is called the curvature correction.
If the volumes are computed by the end area method, it is inconsistent to apply the curvature correction ; but if the pris- moidal method is used, the curvature correction should be ap- plied, especially in rock work.
The curvature correction is computed as follows:
Fig. 40 represents the mid-section of the solid. Construct
FIG. 40.
BC with the same slope as CF. Then the center of gravity of the part shown shaded is in a vertical lins through C and there-
86 TEXT BOOK ON RAILROAD SURVEYING
fore there is no correction to be applied to this portion. The center of gravity of the triangle ABC is at G, which is the dis- tance x from the center, C.
The volume generated by the triangle ABC is
v = ABC X (R H-x) X I
in which / is the angle at the center expressed in radians. The volume computed by the prismoidal method is
vi = ABC X R X I The curvature correction then is
C. C. = v - vi = ABC X x X I
2 1 But x = g X -^ X (Di+di). Substituting this value of x and
expressing / in degrees, we have
C. C. = 0.006 ABCX (Dx + di) X 1° (44)
For 100 ft., 7 becomes D, the degree of the curve.
Haul and Overhaul
109. Haul. Haul is the work done in transporting the ma- terial from the excavation to its place in the embankment. Its unit is the yard-station, or the work done in transporting one cubic yard 100 ft. The term haul is frequently used to indicate either the yardage or the distance, but this must not be confused with the true meaning.
Contract prices are usually based on a maximum length of haul — generally 500 ft. — called the free-haul distance. If the material is transported a longer distance the extra work in- volved is termed overhaul and the contractor is allowed extra compensation at a certain price per yard-station. The con- tractor is therefore paid for all excavation and for overhaul, but he is not paid for making the fills nor for haul inside the free-haul distance.
The amount of excavation is readily determined from the cross-section notes, hence this portion of the contractor's re-
EARTHWORK 87
muneration presents no particular difficulties except when the excavation involves several different kinds of materials to be paid for at different prices. The amount of overhaul, however, depends on the plan of distributing the excavated material, and the problem is to determine an economical distribution. This problem is not of great difficulty, but unfortunately it has often been neglected, resulting in uneconomical work, misunder- standings with the contractor, and frequent law-suits.
The limit of profitable haul is that distance at which the cost of overhaul equals the cost of excavating a yard of earth. For example, if the contract price is 24 cents a yard for excavation and If cents a yard-sta. for overhaul, and the free-haul distance
24 is 500 ft., the limit of profitable haul is p -f 5 = 21 Sta.*
110. Case 1. Fig. 41 represents a fill between two cuts. It is readily seen that there is more than enough earth in the cuts to make the fill, and the question is how much of the fill shall be made from each cut.
The points B and D are the free-haul distance apart and are located on the profile so that the volume of cut between B and C equals the volume of fill between C and D. F and H are simi- larly located with respect to G.
Since the cut to the right is the deeper, it is evident that the fill can be made with the minimum haul if the greater volume of earth is taken from the right-hand cut. The problem is to locate A, E, and «/, which are the limits of the distribution from each of the two cuts. This can not be done by inspection nor
* A yard of earth excavated, hauled 700 ft., and dumped into the fill costs the railroad company 24 cts. plus 3 cts. overhaul. If the yard excavated had been hauled only a few feet to one side of the cut and dumped, and another yard of earth had been taken from a borrow pit along side of the fill and placed hi the fill, the cost would have been 48 cts. It is evident then that it is much cheaper for the railroad to pay the additional amount for overhaul.
In the above example, the saving was 21 cts. If the haul had been longer, the saving would have been less. But the railroad saves money up to the point where the cost of overhaul equals the cost of making a yard of fill from a borrow pit. Beyond this point there is an increasing loss, and when twice the limit of profitable haul is reached, this loss equals the previous saving. The limit of profitable haul is considered as that distance at which the profit is the largest.
88
TEXT BOOK ON RAILROAD SURVEYING
can it be accomplished easily from the cross-section notes. It can be done most easily and accurately by constructing a dis- tribution diagram.
The first step in making the distribution diagram is to construct the mass curve, which is done in the following manner :
FIG. 41.
Choose a horizontal base line near the bottom of the profile sheet, and project the grade points C and G onto it at C" and Gf as shown in Fig. 41.
Then beginning at C' plat to the chosen scale — usually 1,000 cu. yds. to the inch — a curve such that the ordinate to it at any point is equal to the total volume of earthwork between that point and C". From G' plat a similar curve to the same scale. The ordinates to these curves are computed at the regular stations from the cross-section notes. Allowance for shrinkage or growth must be made by increasing the fill volumes by the amount of shrinkage or decreasing them by the amount of growth.
The second step is to determine the limits of free haul. This is done by locating a horizontal line equal in length to the free- haul distance in such a position that its ends are in the mass curve as at B'D' and F' H'. These points are projected up to locate B, D, F, and H. The ordinate to B'D' is the free-haul yardage past C, and the ordinate to F'H' is the free-haul yardage past G.
The third step is to find the positions of A, E, and J so that the haul will be a minimum. For all practical purposes this occurs
EARTHWORK »9
when A E = EJ. Therefore in the distribution diagram find by trial the positions of the two horizontal lines A'E' and E"Jr of equal length, with Er and E" on the same vertical line. These points are projected onto the profile to locate A, E, and /. These points should be located in the field and distinctly marked for the guidance of the contractor.
The ordinates between B'D' and A'E' and also between F'H' and E"J' give the total volumes on which there is an overhaul charge. The total volume moved is given by the ordinates from the base line to A'E' and E"J'.
Since the mass curve is a curve between distance and total volumes, it follows that the area inside the curve represents haul in yard-stations. Consequently the overhaul is given by the shaded portion between the curves and the lines A'E' and E"J'.
If the ordinate B 'b is bisected — dividing the overhaul yardage into two equal parts — and the horizontal line M N is drawn, the two points M and N will be directly under the centers of fnass of the cut and the fill. Therefore M N minus the free-haul distance is the overhaul distance corresponding to B '&; and the overhaul can be found by multiplying B'b by this distance. This method is frequently easier of application than that of determining the areas direct. The overhaul past G can be determined similarly.
|
C' |
1 3 FIG. 42. |
G' |
111. Case 2. In Fig. 42, C and G are so far apart and the cuts are so long that it is evident that the limit of profitable haul will be reached. Construct the mass curve and locate the free-haul
90 TEXT BOOK ON RAILROAD SURVEYING
limits as before. Lay of A'E' and K'J' each equal to the limit of profitable haul. The centers of mass, M, N, P, and Q, are found as in Case 1. The points A', E', Kf, and /' projected onto the profile give the points A, #, K, and J \ which should be marked in the field.
The fill between E and K must be borrowed and the yardage required is given by the difference of the ordinates to Er and K" . The amount of overhaul is determined as in the former case. The complement of this case is the determination of waste in a long cut.
112. Case 3. In case earth can not be moved past some point, the distribution diagram is constructed as before except that the horizontal distribution lines (A'E' and E"J' in Fig. 41) must start at the fixed point. The remainder of the work is done as before. This condition frequently occurs— usually at stream crossings,
CHAPTER VI
TURNOUTS, CONNECTIONS, AND CROSSINGS 113. The subjects treated in this chapter are as follows.
, / Switches 1. Turnouts < ^
( Frogs
2. Connections
|
Diverging / From Tangents |
||
|
Tracks \ From Curves |
||
|
( From |
||
|
c,.,. Tangents Sidings { ^ 1 From |
||
|
Parallel |
Curves |
|
|
Tracks |
From |
|
|
Crossovers |
Tangents From |
|
|
Curves |
||
|
Intersecting (Tangents |
||
|
Tracks \ Curves |
3. Crossings
114. Definitions.
1. Turnouts
A switch is a device to deflect at will the wheels of a train from the track on which they are running.
A switch stand is a device for operating a switch (see Fig. 45).
A frog is a device at the intersection of two rails to permit the passage of the wheel flanges.
A guard rail is a short section of rail placed opposite the frog to guide the wheels so that the flanges will pass through the frog properly.
A turnout is a combination of a switch, a frog, and the necessary connecting. rails, etc., to permit rolling stock to pass from one track to another (see Fig. 45).
A siding is a secondary track parallel to the main track which is used for the storage of rolling stock or for the passing of trains.
91
92 TEXT BOOK ON RAILROAD SURVEYING
It is connected to the main track by a turnout at one or both ends.
A crossover is a connection at an intermediate point between two parallel adjacent tracks (see Fig. 45).
115. Switches. Switches are of three types, viz., Split Switches, Tongue Switches, and Stub Switches.
The Split Switch, Fig. 43a, is the form universally used on steam roads. It consists of two wedge-shaped sections of rails connected by tie rods and sliding on metal plates placed on the ties. The broad end or heel of each point rail acts as a pivot by being fastened to the lead rails by means of the usual splice bars. The point moves through a distance of about 5J inches, which is called the throw (t), and is controlled by a switch stand placed outside the track on a long tie (sometimes two) called a head- block. The distance between the gage lines at the heel is called the heel spread (h). The angle between the gage lines of the switch and the main rail is called the switch angle (s). The width of the point is usually \" (when new). From Fig. 43a it is seen that
sin s = *~ ...... (45)
where p is the width of the point, and I the length of the switch rail. Split switches vary in length from 10 to 33 feet, depending on the flatness of the turnout desired. The point rails are cut from rails of standard length so as to have no waste. For 30-ft. rails, 10, 12, 15, 18, 20, and 30-ft. switch points are used, and for 33-ft. rails, 11, 13, 16J, 20, 22, and 33-ft. The most common lengths are 15 and 16J ft.
The Tongue Switch, Fig. 43b, consists of a steel wedge or tongue pivoted at one end and moving in a heavy cast-iron frame so arranged that pavement may be built around it. This is the common form on street railways, where it is usually used singly with a rigid fitting called a mate in the opposite rail. Steam roads use them only for turnouts in pavement, and then usually in pairs, where the action is the same as in a split switch.
A Stub Switch, Fig. 43c, consists of a pair of ordinary rails fastened together with tie rods. The rails are spiked for part of their length, the remainder being thrown to match the stub ends of the lead rails. A stub switch differs from a split switch in that the toe is fixed and the heel moves. This form of switch may be
TURNOUTS, CONNECTIONS, AND CROSSINGS 93
rmnnnnnn
HjS.fi [fil J!L 15L__ J5L ALJ3LL _U3, -
LI U U U LJ
FIG. 43a.
MATE
SWITCH FIG. 43b.
FIG. 43c.
94
TEXT BOOK ON RAILROAD SURVEYING
employed to advantage on construction and mine tracks owing to its cheapness and ease of installation. A stub switch should never be used on a standard road.
116. Frogs. Frogs are of two types, viz., Rigid Frogs and Spring-rail Frogs. Frogs of either type are universally made with straight gage lines (except on street railways) . The point rails are finished with a blunt point usually \" wide. The dis- tance P between this actual and the theoretical point or intersection of gage lines equals the width multiplied by the frog number.
Fig. 44& shows the common form of rigid frog and the names of the various parts. The essential feature of the rigid frog is that both flangeways are open and must be jumped by passing wheel treads.
Theoretical Point -
^Actual Point
Flange way
Short Point Rail
Wing RaiK
FIG. 44a. Rigid Frog.
Main Point Rail
FIG. 44b. Spring-rail Frog.
Fig. 44b shows the common form of a Spring-rail Frog. In this type one wing rail (sometimes both) is made movable. It is normally held against the point rails by springs. A wheel on the main track therefore has an open flangeway and a con- tinuous support for the tread, while a wheel on the turnout must spring the wing-rail open to allow the flange to pass, and at the same time the treads lack continuous support as in a rigid frog. Guard rails are absolutely essential to the safe operation of a spring-
FIG. 45. Crossover.
96 TEXT BOOK ON RAILROAD SURVEYING
rail frog. Spring-rail frogs are used on main track turnouts, and rigid frogs in yards.
A special type of frog called the movable point frog is used in connection with crossings particularly with " slip switches."
117. Frog Angle, F. The frog angle is the angle between the gage lines at their point of intersection. Obviously the frog angle may have any value, but only values of about 2° to 8° are practical for turnouts. For turnouts a few standard values of the frog angle can be chosen which will meet all the practical requirements. These angles are chosen to agree with simple values of the Frog Number which is a more convenient method of designating frogs than by their angles.
118. Frog Number, N. The Frog Number is the ratio of the a .ial length to the spread, i.e., it is the distance measured along the bisector of the angle in which the gage lines diverge a unit distance. Reducing this ratio to a trigonometric function we have,
N = 1 cot JF (46)
Values of N from 7 to 15 are commonly used, but for special purposes values from 3 to 27 are occasionally used.
119. Location of Turnouts. The first step in staking out a turnout (whether on straight or curved track) is to locate the frog. The heul or toe of the frog should come, if possible, at a regular rail joint in order to avoid short pieces of rail in the track. This fixes the position of the P.F. (point of frog). The next step is to locate the P.S. (point of switch), which is done by measuring along the main track the distance L (the lead). The next step is to locate the outside rail of the turnout curve. This is done by offsets from the outside main rail at the middle and quarter points of the turnout curve. The inner turnout rail is set by gage from the outer.
120. Turnouts from Straight Track. Since the frogs and switches are straight, the alinement of a turnout is not a simple curve from a tangent, but consists of two short pieces of tangent making a fixed angle with the main track rails connected by a curve.
In triangle 1, Fig. 46, the hypotenuse and angles are known. Solve for m and n. In triangle 2, q = g — h — n and the angles
TURNOUTS, CONNECTIONS, AND CROSSINGS 97
are known. Solve for j and c. c is the chord of the outside lead rail and the central angle (F—s) is known, hence the radius of the outside rail is
- ..... (47)
The distance along the straight track from the P.P. to the P.S. is called the lead, L. From the figure
L = l+j+m + P ..... (48)
P.S.
h) (Vi I
'=N-x Width of frog point
FIG. 46.
To compute the offsets for the lead rail, consider its gage line produced back to a tangent parallel to the main rail. The distance between these tangents is
e = h — (R + ig) vers s
The offset from the main rail to the quarter point of the lead rail is then,
yi = e + (R + ig) vers [s + J(F - s)] (Slide Rule) For the middle point,
y2 = e + (R + ig) vers [s + J(F - s)] " " (49) For the three-quarters point,
y3 = e + (R + ig) vers [s + f (F - s)] " " '^
121. Turnouts from Curved Track. It can be shown (the solution is too involved to be included here) that the lead of a turnout from a curved track is almost identical with the lead of a turnout from straight track with the same frog number. And further, that the degree of curve of the lead rails is equal to the degree of curve of the turnout from straight track increased
98 TEXT BOOK ON RAILROAD SURVEYING
or diminished by the degree of the main curve depending on whether the turnout is on the inside or the outside of the main curve.
Therefore a turnout on a curve is staked out with the same dimen- sions as one with the same frog number on straight track.
122. Double Turnouts. Occasionally two turnouts to op- posite sides of the main track are located at the same point. This involves the use of two regular frogs in the main rails, a third or crotch frog at the intersection of the lead rails, and a three-throw switch. Such a switch is structurally weak and should never be used in a main track. And further, the condi- tions under which such arrangements are absolutely necessary are extremely rare. It is better practice to use two separate turnouts, placing one switch ahead of the other and if necessary using a sharper turnout to save distance, than to use a three-throw switch.
Double turnouts will therefore not be further considered.
123. Practical Leads. Since it is undesirable to use short pieces or odd lengths of rails, it is the universal practice to modify the theoretical leads as computed above (Eq. 48), so as to use convenient lengths of lead rails. The difference between the theoretical leads and the practical leads is never very great, and the turnout is located as above except for this modification in the lead. This has the effect of changing the turnout curve from a true circle, but the amount is inappreciable. There is also a difference in the length of the straight and the curved lead rails. The best practice is to correct this by making the toe length of the frog on the turnout side longer than on the main-track side.
Every, railroad has its standard turnouts, all dimensions of which are worked out and tabulated. The turnouts are then installed by the trackmen, the only duty required of the en- gineer being to locate the P.P. and occasionally the P.S. The engineer therefore has little occasion to use the functions of the turnout proper. His problem is to connect the turnout to the required track.
Table 2 gives the practical switch leads recommended by the American Railway Engineering Association; also the rectangular co-ordinates to the quarter and center points on the gage side of the curved rail, referred to the point of switch as origin.
TURNOUTS, CONNECTIONS, AND CROSSINGS
99
TABLE 2
Practical Leads as Recommended by the American Railway Engineering Association
|
8^ |
|||||||||
|
1 |
0.1 |
|| |
Rectangular Co-ordinates to the 8uarter and Center Points on |
I? |
|||||
|
y |
p |
age Side of Curved Rail, Re- |
<H 2 |
||||||
|
* |
ll |
!•§ |
ferred to Point of Switch as Origin |
"Sal |
|||||
|
£ |
gl |
°3 |
3J!s |
||||||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
7 |
362 . 08 |
15° 52' |
26.72 |
36.93 |
47.11 |
0.97 |
1.71 |
2.74 |
62.10 |
|
8 |
487 . 48 |
11 46 |
28.37 |
39.91 |
51.45 |
.02 |
1.78 |
2.91 |
67.98 |
|
9 |
605 . 18 |
9 29 |
28.75 |
40.98 |
53.19 |
.02 |
.76 |
2.75 |
72.28 |
|
10 |
790 . 25 |
7 15 |
30.28 |
44.05 |
57.81 |
.06 |
.84 |
2.85 |
77.93 |
|
11 |
922 . 65 |
6 13 |
40.74 |
56.47 |
72.19 |
.08 |
.84 |
2.87 |
94.31 |
|
1.3 |
1098 . 73 |
5 13 |
43.99 |
60.65 |
77.28 |
.15 |
.90 |
2.91 |
100.90 |
|
15 |
1744.38 |
3 17 |
55.49 |
77.95 |
100.41 |
.01 |
.78 |
2.85 |
133 . 28 |
|
IS |
2546.31 |
2 15 |
58.73 |
84.46 |
110.10 |
.04 |
.82 |
2.86 |
146.51 |
|
20 |
3257 . 26 |
1 46 |
61.84 |
90.21 |
118.50 |
.08 |
.88 |
2.93 |
157.42 |
|
24 |
4886.16 |
1 10 |
67.82 |
100.21 |
132.59 |
.27 |
.97 |
3.00 |
177.22 |
2. Connections DIVERGING TRACKS. 124. Case 1. From Straight Track.
FIG. 47. Given: 7 = the intersection angle between a diverging track and a
straight main track.
N = the frog number chosen for the turnout. R = the chosen radius of the connecting curve.
100 TEXT BOOK ON RAILROAD SURVEYING
K = the frog tangent, i.e., the distance from the actual P.P. to the T.C. of the connecting curve.
P = the distance between the theoretical and the actual point
of frog. It is required to locate the P.P., the T.C., and the C.T.
In triangle 1, Fig. 47, all the angles are known and the side m = gN + P + K + R tan i(/ — F), whence the sides n and j can be computed.
The point B and the C. T. of the connecting curve are located from A by the distances n andj + R tan J(7 — F), respectively. The P.P. is located from B by the co-ordinates g N + P and |gr = 2.35. The T.C. of the connecting curve is located from B by the angle F and the distance gN + P + -K-
125. Case 2. From Curved Track.
(a) Turnout from the inside of a curved main track.
The data and requirements of this problem are the same as in the preceding problem except that the main track is on a D° curve.
In triangle 1, Fig. 48, the hypotenuse and the angles are known and the other two sides are computed (as shown), whence,
In triangle 2, the base and altitude are found by arithmetic, and the triangle is solved for the hypotenuse and the angle a.
In triangle 3, the hypotenuse and angles are known and the other two sides are computed (as shown), whence,
In triangle 4, one side and the hypotenuse may be found by arithmetic, and the triangle solved for the third side and the angle b. Then,
x = a + b + (90° - I) - (90° - F)
= a + b-I + F (50)
The point H opposite the theoretical frog point is located from A by measuring along the center line the distance A H (in feet)
= -^ 100. The C.T. is located from A'by the distance AE =
AG - EG. (EG = JO.) The T.C. is best located as follows: set- up at H; back-sight on A', turn off \x to get on tangent; locate M for a temporary back-sight; plunge telescope and set point
TURNOUTS, CONNECTIONS, AND CROSSINGS 101
FIG. 48.
FIG. 49.
102
TEXT BOOK ON RAILROAD SURVEYING
B a distance gN from H] set-up at B and back-sight * on M; turn off frog angle and locate the T.C. on this line a distance gN + P + K from B] set point Q for a temporary back-sight. Set-up at the T.C., back-sight on Q, and run in the connecting curve.
(6) Same problem as (a) except that the main line curve ends between H and A.
In Fig. 49, A is the intersection of the diverging track tangent and the main line tangent. A' is the C.T. of the main track curve. The distance A A' is measured in the field. Then the angle x, the distance, HA' and A'E' are determined as in the preceding problem.
In triangle 5, the side A A' and the angles are known, hence I can be computed.
The C.T. (at E) is located from A by the distance A'E' - I.
(c) Turnout from the outside of a curved main track.
R ein I
FIG. 50.
*A back-sight is a sight taken on a point of known position for the purpose of orienting the instrument, and may be either back of or in front of the instrument.
TURNOUTS, CONNECTIONS, AND CROSSINGS 103
In triangle 1, Fig. 50, the hypotenuse and angles are known, and the other two sides are computed (as shown), whence,
In triangle 2, the base and altitude are found by arithmetic. The triangle is solved for the hypotenuse and the angle a.
In triangle 3, the hypotenuse and angles are known and the other two sides are computed (as shown), whence,
In triangle 4, one si^le and the hypotenuse can be found by arithmetic. The triangle is solved for the third side and the angle b. Then
x = b - (90° - I) - [a - (90° - F)]
= b + I-a-F (51)
The field work is identical with that of Problem (a).
(d) Same problem as (c) except that the main track curve ends at A' between A and H.
FIG. 51.
This problem, Fig. 51, bears the same relation to (c) that (6) bears to (a).
If / is greater than 90° in any of these four problems, the
104
TEXT BOOK ON RAILROAD SURVEYING
various lines used in the solution will have relatively different positions, but the general order of solution is the same, and if followed out no difficulty should arise.
PARALLEL TRACKS. SIDINGS. 126. Case 1. Straight Tracks.
(a) Tangent and simple curve.
The best way to connect a turnout to a parallel siding is to make the frog tangent of such a length that it can be connected to the siding by a simple curve of about the same radius as that of the lead rails. A connecting track of this kind is most easily located by co-ordinates from the actual point of frog.
FIG. 52.
In Fig. 52, xi, x2, and £3 are points on the main track op- posite the T.C., the middle point of the curve, and the C.77., respectively, and y\, 7/2, and ys are the corresponding offsets from the center line of the main track. From the figure,
yi = p — R vers F and xi = yi cot F — gN— P
y2 = p - R vers JF " x2 = Xi -f R (sin F - sin JF) > (52)
y3 = p " x3 = xi + R sin F
Table 3 gives the values of x and y for track centers from 12 to 16 ft. and for frog numbers from 7 to 15.
(b) Sometimes the connecting curve is commenced at the heel of the frog or a fixed distance beyond it. In this case x\
TABLE 3 105
Co-ordinates for Locating Parallel Sidings with Tape
|
fc |
£ § |
§3 |
fc |
||||||
|
0 |
§£ |
§ |
H |
||||||
|
% |
O II |
Xl |
X2 |
X3 |
yi |
y2 |
|| |
0 |
Variation |
|
1 |
EH |
a° |
2 £ |
||||||
|
7 |
12.0 |
23.31 |
50.45 |
77.73 |
8.12 |
11.03 |
15° 00' |
8° 10' |
&&>& |
|
12.5 |
26.79 |
53.93 |
81.21 |
8.62 |
11.53 |
||||
|
13.0 |
30.28 |
57.42 |
84.70 |
9.12 |
12.03 |
_« 2*Ji |
|||
|
13.5 |
33.76 |
60.90 |
88.18 |
9.62 |
12.53 |
O OO |
|||
|
14.0 |
37.24 |
64.38 |
91.66 |
10.12 |
13.03 |
v |
|||
|
14.5 |
40.73 |
67.87 |
95.15 |
10.62 |
13.53 |
iH X >> |
|||
|
15.0 |
44.21 |
71.35 |
98.63 |
11.12 |
14.03 |
O .^« |
|||
|
15.5 |
47.70 |
74.84 |
102.12 |
11.62 |
14.53 |
t, ao a |
|||
|
16.0 |
51.18 |
78 . 32 105 . 60 |
12.12 |
15.03 |
fe.So8 |
||||
|
8 |
12.0 |
25.33 |
57.73 |
90.26 |
7.94 |
10.98 |
11° 00' |
7° 09' |
0>® 35 |
|
12.5 |
29.32 |
61.72 |
94.25 |
8.44 |
11.48 |
||||
|
13.0 |
33.31 |
65.71 |
98.24 |
8.94 |
11.98 |
||||
|
13.5 |
37.29 |
69.69 |
102 . 22 |
9.44 |
12.48 |
€•§•9 |
|||
|
14, .0 |
41.28 |
73.68 |
106.21 |
9.94 |
12.98 |
v X >» |
|||
|
14.5 |
45.26 |
77.66 |
110.19 |
10.44 |
13.48 |
T~! |
|||
|
15.0 |
49.25 |
81.65 |
114.18 |
10.94 |
13.98 |
® -v ' . |
|||
|
15.5 |
53.24 |
85.64 |
118.17 |
11.44 |
14.48 |
f_ ao a |
|||
|
16.0 |
57.22 |
89.62 |
122.15 |
11.94 |
14.98 |
fe.So£ |
|||
|
9 |
12.0 |
29.59 |
64.87 |
100.26 |
8.07 |
11.02 |
9° 00' |
6° 22' |
©35© |
|
12.5 |
34.07 |
69.35 |
104 . 74 |
8.57 |
11.52 |
sf d 9 |
|||
|
13.0 |
38.55 |
73.83 |
109 . 22 |
9.07 |
12.02 |
_rt Ji J3 |
|||
|
13.5 |
43.03 |
78.31 |
113.70 |
9.57 |
12.52 |
yoy |
|||
|
14.0 |
47.51 |
82.79 |
118.18 |
10.07 |
13.02 |
v |
|||
|
14.5 |
51.99 |
87.27 |
122 . 66 |
10.57 |
13.52 |
r-J X r* |
|||
|
15.0 |
56.47 |
91.75 |
127.14 |
11.07 |
14.02 |
O -^' . |
|||
|
15.5 |
60.95 |
96.23 |
131.62 |
11.57 |
14.52 |
fc § |
|||
|
16.0 |
65.43 |
100.71 |
136.10 |
12.07 |
15.02 |
fc.S6rf |
|||
|
10 |
12.0 |
31.23 |
72.08 |
113.04 |
7.90 |
10.98 |
7° 00' 5° 44' |
&3*a |
|
|
12.5 |
36.21 |
77.06 |
118.02 |
8.40 |
11.48 |
||||
|
13.0 |
41.19 |
82.04 |
123 . 00 |
8.90 |
11.98 |
J*li |
|||
|
13.5 |
46.17 |
87.02 |
127.98 |
9.40 |
12.48 |
||||
|
14.0 |
51.15 |
92.00 |
132.96 |
9.90 |
12.98 |
^ l~l fl |
|||
|
14.5 15.0 |
56.13 61.11 |
96.98 101.96 |
137.94 142 . 92 |
10.40 10.90 |
13.48 13.98 |
Sail |
|||
|
15.5 |
66.09 |
106.94 |
147 . 90 |
11.40 |
14.48 |
o' _« 3 |
|||
|
16.0 |
71.07 |
111.92 |
152 . 88 |
11.90 |
14.98 |
fc.So£ |
|||
|
12 |
12.0 |
39.38 |
86.96 |
134 . 63 |
8.03 |
11.00 |
5° 00' |
4° 46' |
°3 *a |
|
12.5 |
45.38 |
92.96 |
140 . 63 |
8.53 |
11.50 |
C3 5 • «J |
|||
|
13.0 |
51.38 |
98.96 |
146.63 |
9.03 |
12.00 |
c3 Q «3 |
|||
|
13.5 |
57.37 |
104 . 95 |
152 . 62 |
9.53 |
12.50 |
"§ N ® |
|||
|
14.0 |
63.37 |
110.95 |
158 . 62 |
10.03 |
13.00 |
•^ r"1 CH |
|||
|
14.5 |
69.37 |
116.95 |
164.62 |
10.53 |
13.50 |
*"• ® J3 |
|||
|
15.0 |
75.36 |
122 . 94 |
170.61 |
11.03 |
14.00 |
® ft r? W |
|||
|
15.5 |
81.36 |
128 . 94 |
176.61 |
11.53 |
14.50 |
0 ^^ |
|||
|
16.0 |
87.35 |
134 . 93 |
182 . 60 |
12.03 |
15.00 |
Sail |
|||
|
15 |
12.0 |
48.38 |
111.08 |
173.85 |
7.87 |
10.97 |
3° 00' |
3° 46' |
®3*a |
|
12.5 |
55.97 |
118.67 |
181.44 |
8.37 |
11.47 |
jn'^J . M |
|||
|
13.0 |
63.57 |
126.27 |
189 . 04 |
8.87 |
11.97 |
CS £Q C3 |
|||
|
13.5 |
71.16 |
133.86 |
196.63 |
9.37 |
12.47 |
w^^S, |
|||
|
14.0 |
78.76 |
141.46 |
204 . 23 |
9.87 |
12.97 |
X fl |
|||
|
14.5 |
86.35 |
149 . 05 |
211.82 |
10.37 |
13.47 |
'"1 ® ?H |
|||
|
15.0 |
93.95 |
156.65 |
219.42 |
10.87 |
13.97 |
o agw |
|||
|
15.5 |
101.54 |
164.24 |
227.01 |
11.37 |
14.47 |
o ^3 |
|||
|
16.0 |
109.14 |
171.84 |
234.61 |
11.87 |
14.97 |
fe.Su'S |
106
TEXT BOOK ON RAILROAD SURVEYING
and 2/1 are known and the radius of the connecting curve must be computed. The other dimensions are then computed as before. Although this method flattens the connecting curve, it increases the distance from the P.P. to the T.C. There is nothing gained by making the connecting curve flatter than that of the turnout itself, and also the greater length of tangent is advantageous.
(c) Sometimes the connection is made in the form of a reversed curve with radii about the same as the radius of the turnout curve under the false idea that this saves distance between the P.P. and the T.C. The actual difference in z3 for such a connec- tion and for one of the form first given for a No. 10 turnout is only about 1.1 ft., an inappreciable amount considering the rel- ative riding qualities of the two layouts for heavy road engines.
127. Case 2. Curved Tracks.
A turnout and a connection to a parallel track on a curve may be staked out by the co-ordinates given in Table 3. Such a layout will have the following characteristics.
1. The degree of curve of the turnout will be increased or diminished by the degree of the main curve, depending on
FIG. 53.
whether the siding is inside or outside of the main track curve.
2. The degree of the connecting curve will be diminished or
increased by the degree of the main curve (approx.), depending
TURNOUTS, CONNECTIONS, AND CROSSINGS 107
on whether the siding is inside or outside of the main track curve.
3. The track between the frog point and the beginning of the connecting curve will become a curve of the same degree (ap- prox.) as the main curve.
On curves of about 1° this method is both satisfactory and convenient, but on sharper curves, or in case it is desired to maintain a frog tangent, it will be necessary to compute the connection for the particular case. Two general cases arise:
(a) Sidings on the outside of the main curve. In Fig. 53,
OA = (R + ig) cos F AB = (R + ig) sin F AC = AB + P + K = OiH OOi = R + p - Ri OH = OA - (Rx - ig) In triangle 2, (OOO2 = (OiH)2 + (OH)2
(R + p - RO2 = (AC)2 + (OA + ig - RO2 expanding and reducing,
(AC)2
R' = 2(OA + te 1 R _ p) + (OA + *8 + R + P) • (53) then
AC sm a = QQJ.
Since the central angle a and the radius R\ are now known, the length of the connecting curve can be computed.
The curve may be staked out' either by deflection angles from either end (orient how?) or by offsets from the main track. The latter method is the more rapid and convenient.
Since the connecting curve and the siding curve have a common tangent and since the angles are small, the offset between them at any point is equal to the difference of their tangent offsets. Then the offset from the center line of the main track to the center line of the connecting curve at any point is 7
p — 5- n2 (Di — Ds), in which DI and Z)s are the degrees of
o
curve of the connecting track and the siding, respectively, and n is the distance in stations along the connecting curve from the point where it joins the siding. These offsets should be measured
108
TEXT BOOK ON RAILROAD SURVEYING
radially to the main curve and the distances should be measured along the connecting curve.
(6) Sidings on the inside of the main curve.
FIG. 54a.
In Fig. 54a,
OA = (R - Jg) cos F AB = (R - Jg) sin F AC = AB - K - P = OH OOi = Ri + p - R OiH = Ri + ^g - OA
In triangle 2, (OOi)2 = (OH)2 + (OiH)2
(Ri + p - R)2 = (AC)2 + (Ri + Jg - OA)2
expanding and reducing,
then
AC
OOI
If Eq. 54 gives a positive value of RL, the layout is as shown in Fig. 54a.
If a negative value of #1 is obtained, the layout is as shown in Fig. 54b and the value of RI is numerically correct.
If (OA — %g) - R — p, Eq. 54 gives RI = infinity, and the
TURNOUTS, CONNECTIONS, AND CROSSINGS 109
frog tangent produced is tangent to the siding as shown in Fig. 54c.
These connections can be staked out by offsets as explained under case (a). It is to be noted, however, that if the layout is
FIG. 54b.
FIG. 54c.
as shown in Fig. 54b, the sum of the tangent offsets must be used.
PARALLEL TRACKS. CROSSOVERS.
Since a crossover is equivalent to an entry to a siding, and therefore both turnouts will be run over at practically the same speed, there is no valid reason for making one turnout flatter than the other, even when the crossover is between a main track
FIG. 55.
and a siding. A crossover should therefore always have frogs of the same number at both ends.
128. Case 1. Straight Tracks.
(a) Straight track between frogs of the same number.
110
TEXT BOOK ON RAILROAD SURVEYING
From Fig. 55, AC = P cot F
then x = AC - 2gN - 2P . . . . (55)
To locate the crossover one P.F. is set so that the heel or toe will be at a regular rail joint. The other P.F. is fixed by the distance x. These are the only stakes ordinarily required.
Table 4 gives the distance x between the frog points for track centers from 12 to 16 ft. for turnouts from No. 7 to 15.
TABLE 4
Distances along main track between frog points for crossovers between parallel tracks. Frogs of same number, straight track between frogs.
|
Track Centers |
||||||||||
|
N |
F |
|||||||||
|
12.0 |
12.5 |
13.0 |
13.5 |
14.0 |
14.5 |
15.0 |
15.5 |
16.0 |
||
|
7 |
8° 10' |
17.14 |
20.63 |
24.11 |
27.59 |
31.08 |
34.66 |
38.05 |
41.53 |
45.02 |
|
8 |
7° 09' |
19.66 |
23.64 |
27.61 |
31.62 |
35.60 |
39.59 |
43 . 57 |
47.56 |
51 . 55 |
|
9 |
6° 22' |
22.05 |
26.53 |
31.05 |
35.49 |
39.97 |
44.45 |
48.93 |
53.42 |
57.90 |
|
10 |
5° 44' |
24.52 |
29.50 |
34.48 |
39.46 |
44.45 |
49.43 |
54.41 |
59.39 |
64.37 |
|
12 |
4° 46' |
29.90 |
35.90 |
41.90 |
47.90 |
53.89 |
59.89 |
65.89 |
71.88 |
77.88 |
|
15 |
3° 49' |
37.38 |
44.88 |
52 . 37 |
59.86 |
67.36 |
74.85 |
82.35 |
89.84 |
97.34 |
(6) Simple curve between frogs of different number. Sometimes unequal frogs are used on crossovers, and in this
FIG. 56.
TURNOUTS, CONNECTIONS AND CROSSINGS 111
case the best form of layout to use is a connecting curve of about the same degree as the sharper turnout, tangent at the heel of the flatter frog. This will place a short piece of tangent between the curve and the heel of the sharper frog which is desirable.
In Fig. 56, F, Fi} p, g, and Ki are known. R is chosen to agree with the turnout curve of F.
In triangle 1, the hypotenuse and angle FI are known. Solve for the sides d\ and m.
In triangle 2, the altitude n = p — m and the angle F are known. Solve for the sides d and j. Then
K = j - gN - R tan \ (F - FI) The distance along the main tracks between frog points is
x = (d + dO - (gN + P + gNi + Pi) . . (56)
129. Case 2. Curved Tracks.
It can be shown that, if a crossover is located between curved tracks with the same frog numbers and a simple curve tangent to the heels of the frogs, the distance along the main tracks be- tween frog points is practically the same as for a straight cross- over between straight tracks; and also that the degree of curve of the connection is practically the same as that of the main tracks.
Therefore, a crossover on a curve is located with the same dimensions as one on tangent. It may be desirable, however, to locate points on the connecting curve. Usually one point at the middle is sufficient, and it will be seen that this point is midway between the frog points and on the center line between tracks.
Crossovers should be avoided on curves.
INTERSECTING TRACKS.
130. Case 1. Both Tracks Straight.
(a) Connection in form of simple curve.
Given in Fig. 57, the intersection angle, /; the frog angles, F and F\\ and the radius of the connecting curve.
Required: The distances, A and B, from the intersection of the center lines to points opposite the frog points.
112
TEXT BOOK ON RAILROAD SURVEYING
In triangle 1, the angles are known and one side, n, is readily obtainable. Solve for r and m.
FIG. 57.
In triangle 2, one side, .; + r, and the angles are now known, whence k and I can be computed. Then
A = k - gNi - Pi
B=Z+m -gN-P
(57)
(b) Connection in form of reversed curve.
Given in Fig. 58, the intersection angle, 7; the frog angles, F and Fi't the radii of the reversed curve, R and Ri'} and the location of one frog point, which is the distance, T, from the P.7. at A.
Required: The central angles, a and 6, of the reversed curve, the distance, T\t from the P.I. to the unknown frog point, and the distance x between frog points measured along the straight track.
In triangle 1 (CDB) CD and angle F are given. Solve for CB and DB, whence AB and OB can be found.
In triangle 2 (ABE) AB and the angles are known. Solve for BE and AE.
In triangle 3 (OEG) OE and the angles are known. Solve for OG and GE.
In triangle 4 (LHQ) LH and the angles are known. Solve for HQ and LQ = JM.
TURNOUTS, CONNECTIONS, AND CROSSINGS 113
In triangle 5 ( HJOi) HOi and the angle FI are known. Solve for OiJ and HJ.
In triangle 6 (OiOS) OiO = R + Ri and OiS = OJ + JM + GO are known. Solve for angles c and d, whence angles a and 6 are readily determined.
T! = AE + EG - OS - LM + gNi + PI . (58) x = T - AL cos I - gNi - Pi . . . . (59)
If Ti instead of T is known the plan of solution is the same.
If the tracks do not run to an intersection or if it is inadvisable to run out the tangents and determine 7, locate the point D, set-up and turn off 90° from the frog tangent, and measure DE. Then set-up at E and measure DEL. With these data the prob- lem can be solved in the same manner as before.
131. Case 2. One Straight and One Curved Track.
From Fig. 59,
In triangle 1, the hypotenuse and the angle F are known. Solve for the two sides. Whence,
In triangle 2, the two sides can be obtained by arithmetic. Solve for the hypotenuse and the angle a.
114
TEXT BOOK ON RAILROAD SURVEYING
FIG. 59.
In triangle 3, the hypotenuse and the angle 7 are known. Solve for the two sides.
In triangle 4, the altitude = Ri + \Q and the angle F\ are known. Solve for the hypotenuse and the base.
In triangle 5, the hypotenuse and the angle FI are known. Solve for the sides I and m. Whence,
In triangle 6, the altitude is found by arithmetic and the hypotenuse is known from triangle 2. Solve for the angle b. Then
x = a - b + (90° - I) - (90° - F)
and
= a -b - I + F
(curve) AB (in feet)
(60)
100 D
The P.P. is set at the distance AB - P from A. From triangles 3, 5, and 6, the distances AE, m, and OG are known. Then AC is found by arithmetic.
TURNOUTS, CONNECTIONS, AND CROSSINGS 115
The P.F.i is set at a distance AC — PI from A. The central angle of the connecting curve z = I -\- x — F\ — F.
Obviously such a connection can be placed in any of the four quadrants, but the one here shown gives the best alinement and should be used when possible.
In case a connection is to be placed in any other quadrant, the plan of solution is identical with that above, and if followed exactly no difficulty should arise.
132. Case 3. Both Tracks Curved.
From Fig. 60,
In triangle 1 (AOOi], the two sides, R and Ri, and the included angle / are known. Solve for the side 00 i and the angles a and 6.
In triangle 2 (BEO), the hypotenuse and angle F are known. Solve for the sides BE and EO.
Then in triangle 3 (OOaG), the two sides are found by arith- metic. Solve for the angle c and the side 002.
116 TEXT BOOK ON RAILROAD SURVEYING
In triangle 4 (CO\H) the hypotenuse and .the angle FI are known. Solve for the sides, CH and HOi.
Then in triangle 5 (Oi02/), the two sides are found by arith- metic. Solve for the angle d and the side OiOz.
In triangle 6 (00i02), the three sides are now known. Solve for the angles e and /. Then
x = b - f + c - (90° - F)
= b-f + c + F-90° . . . . (61) and
y = a - e + d + F! - 90° . . . (62)
curve AB (in ft.) = — ~— , and the'P.F. is set at a distance AB - P from A.
curve AC (in ft.) = — FT* an(^ the P-f-i is set at the dis- tance AC — PI from A.
Then the central angle of the connecting curve is
z=I+x + y-F-Fi . . . (63)
Obviously such a connection can be placed in any of the four quadrants, but the one here shown gives the best alinement and should be used when possible.
In case a connection is placed in any other quadrant the plan of solution is identical with that above, and if followed exactly no difficulty should arise.
3. Crossings
133. A crossing is a device used at the intersection of two tracks. It consists of four frogs and the necessary connecting rails. Any one of the frogs is a crossing frog. The crossing angle is the angle between the center lines of the tracks at their point of intersection.
Crossings are designated as single curve, double curve, or straight according as one, both, or neither of the tracks are curved.
Crossings are usually made of rolled rails fitted together. When the crossing angle is greater than about 25°, the various pieces are cut to fit against each other and are united by filling blocks and heavy straps well bolted. This is frequently termed
TURNOUTS, CONNECTIONS, AND CROSSINGS 117
solid construction. For angles under about 25°, regular frog point construction is used, and such crossings are termed frog crossings. Distinguish between frog crossing and crossing frog.
On street railway work hard steel (manganese) centers for frogs have been used for many years, and since 1905 such con- struction has been growing in use on steam roads both for standard frogs and for crossings. (This type is usually designat- ed as " manganese frogs or crossings.")
There have been numerous attempts to construct crossings with a revolving section or turntable at each frog so that the wheels will have no flange way to jump; but only one of these seems to give much promise of success.
The end frogs of a frog crossing are similar to a standard rigid frog in that there is a single point on which the wheels run. The middle frogs, however, have two running points and are therefore frequently termed " double-pointed frogs."
FIG. 61. Double Slip Switch.
When " slip switches " are used, the crossing is made to a standard frog number, and if located at an interlocking plant the middle frogs are frequently made with movable points. That is, with movable points joined in pairs and moving together similar to a split switch in such a way that the wheels have a solid bearing and no flangeway to jump.
A " slip switch " or " combination crossing " is a combination of a small angle crossing with a pair of connecting tracks placed entirely within the limits of the crossing. They are used in large yards and terminals (Fig. 61).
134. Crossing Data. Very few railroads construct their own crossings, but have them built by manufacturers who make a specialty of such work. The field engineer is rarely called on to compute the dimensions of a crossing, and to do so is a waste of time if the crossing is ordered from a manufacturer.
118
TEXT BOOK ON RAILROAD SURVEYING
It is far more important that the makers have all the data, and the field engineer is frequently required to furnish the data. The information required is:
1. The crossing angle.
2. The gage of each track.
3. The curvature — degree of curve, radii, or the equivalent.
4. The direction of curvature.
5. The length along each gage line from one gage line in- tersection (theoretical P.P.) to the nearest rail joint.
6. Length over all along each gage line.
7. The height, weight, and style of rail of which the crossing is to be made.
8. The height, weight, and style of rail in intersecting track if offset splices are to be furnished.
9. The spacing and size of holes for splice bars.
10. The type of crossing, etc., unless covered by general specifications.
This information can best be given by means of a small sketch. Field dimensions should be taken to the nearest 1/8" (0.01 ft.).
Occasionally the field engineer is called on to compute the di- mensions of a crossing. The values which are required are the frog angles, FI, F2, F3, F^ the length of sides along the gage lines, and the two diagonals. The computations should be made with sufficient accuracy to give results which are correct to the nearest 1/16", which is the working limit of the manufacturers.
The solutions of the three kinds of crossings are outlined as follows :
135. Straight Crossings.
FIG. 62.
(a) Unequal Gages. In Fig. 62, git g2, and I are given, and the sides and diagonals are required.
TURNOUTS, CONNECTIONS, AND CROSSINGS 119
In triangle 1, the altitude gi and the angle 7 are known. Solve for si and 61.
Similarly solve for $2 and 62 in triangle 2.
In triangle 3, the altitude gi and the base s2 + 61 are known. Solve for the hypotenuse, which is the long diagonal of the crossing.
In triangle 4, the altitude 02 and the base si — b2 are known. Solve for the hypotenuse, which is the short diagonal of the crossing.
(6) Equal Gages. In this case, triangles 1 and 2 are identical and all four sides are equal. The angle between the hypotenuse and the base of triangle 3 becomes J7, and of triangle 4 becomes 90 — ^7 which simplifies the solution.
136. Single-curve Crossings.
Given, in Fig. 63, 0i, 02, and 7 to find the frog angles, length of sides, and both diagonals.
FIG. 63
Project the radius on a perpendicular to the straight track.
Then OB = R cos 7, whence OE and OC are known.
In triangle FiCO, the base and hypotenuse are known. Solve for FiC and the angle FI.
Similarly solve for F2 and FZC, Fs and FSE, and F4 and F*E from corresponding triangles. Then the straight sides F\F* and FzFi can be found by subtraction. The curved sides FiFt and F2F3 can be determined since their radii are known and their central angles can be found by subtraction.
120 TEXT BOOK ON RAILROAD SURVEYING
The long diagonal is the hypotenuse of a triangle whose altitude is g\ and whose base is F$E — FiC, and the short diagonal is the hypotenuse of a triangle whose altitude is g\ and whose base is F2C - F4E.
137. Double-curve Crossings.
In Fig. 64, #1, R2, gl} g2) and / are given, and it is required to find the frog angles, length of sides, and both diagonals.
In triangle A0i02, two sides and the included angle are known. Solve for the distance between centers, 0\02.
Then in the four triangles formed on Oi02 by the radii from Fi, F2, FS} and F4 the three sides of each are known, and the
o,
FIG. 64.
angles can be solved for. From the angles at 0\ and 02 determine the central angles of the arcs, FiF2, F2F3, FSF4, and F4Flt from which the lengths of the arcs can be computed since their radii are known. The long diagonal is found from the triangles
or Fi02Fz, and the short diagonal from the triangles
or
APPENDIX . THEORY OF SPIRAL 138. Derivation of o and A.
From definition, d = ks] fortheS.C., D = kS . . . . (18)
The radius of curvature, r = -r^
do
Substituting for r its value, -j- , and then for d its value from Eq. 18, and solving,
ad - kldl
5730
kl2 ks2
Integrating, d =
in which o is in circular measure. Changing d to degrees,
d = iks2 ........ (19)
For the S.C., A = JkS2
139. Derivation of the Co-ordinates x and >.
The differential equations for the co-ordinates of a spiral are:
dx =vds cos d dy = ds sin d
Expanding the sin and cos into series,
/ fc 64
dx - ds 1 - " + T ~
/* <*3 A5 \
dy = ds (d - IT + IF - etc-|
? E. 12- '
ks2 Substituting TTT-^ for d
114.6 J
/ k2s4
dx = ds ^1 — ;
121
122 TEXT BOOK ON RAILROAD SURVEYING
. / ks2 k3s6 ^
dy = ds \U4f> ~ 6(114:6? ~
k2s5 • Integrating, x = s - T^-TJ-^ + etc.
ks3 k3s7
"' 3(114.6) 42(114.6)3 *
in which x and y are in stations. Reducing to feet and dropping small terms,
x = 100 s - 0.000762 k2s5 . . . (23) y = 0.291 ks3 - 0.00000158 k3s7 . (22)
140. Derivation of a, A, b, and B.
ks3 . kV
x 3X114.6 42X(114.6)3 + etc' tan a = — = - V^2o5
+ etc. f etc.
10 X (114.6)2 ks2 k3s6
Substituting d for
3 X H4.6 (114.6)3 X 105 ks2
114.6
t I
A 6 Is-
tan-^- = — + "gT" ^3 + etc. (tangent series).
1 24
Whence, tan a = tan -- o — Oz
Reducing to degrees,
tan a = tan -j d - 0.000000015 o3
Investigating the second term, it is found that o must be about 25° before there is an error of one minute in a by considering it as ^ $; and since 0 rarely reaches 25° and any error of direction is corrected at the S.C., it is sufficient to write
a = -^- d = lOks2 (in minutes)
.... (20)
A = -^-A = 10kS2 (in minutes) <> J
THEORY OF SPIRAL 123
and,
b = y 3 = 2a, and B = J- A = 2A . . (21)
141. Derivation of O.
From Fig. 65,
o = Y - R vers A
Substituting for Y its value, 0.291- kS3, for R its value, -j-g-, and expanding the vers series,
o = 0.291 kS3 - 0.00000158 k3S7 -
5730 / k2S4 k4S8 \
730 /_
kS \2
kS \2 X (114.6)2 24(114.6)4/
o = 0.291 kS3 - 0.00000158 k3S7 - 5730
/ kS3 k3S7 \
\2(114.6)2 24(114.6)V
Reducing,
o = 0.0727 kS3 - 0.0000002 k3 S7
Evidently the second term is very small, hence,
o = 0.0727 kS3 (24)
From figure,
t = X - R sin A
Substituting for X its value from Eq. 23, and for R its value,
5730 , ,. ., .
~r^-j and expanding the sin series,
t = 100 s- 0.000762 k2S5
- ^~ /A - ^ + etc. )
- 1008 - 0.000762 k«S- - Reducing,
t = 50 S - 0.000127 k2S5 ..... (25)
124
TEXT BOOK ON RAILROAD SURVEYING
Substituting J S in Eq. 23, the abscissa of the middle of the spiral is 50S - 0.000024 k2S5. The difference between this and Eq. 25 is only 0.0001 k2S5, showing that the spiral is practically bisected by the ordinate to the T.C.
FIG. 65.
Substituting J$ in Eq. 24, the ordinate for the middle of the spiral is 0.0364 kS3.
Jo = 0.0363 kS3
showing that o is bisected by the spiral. If the second term of Eq. 24 had been used the difference would have been still less.
142. Osculating Circle.
The fact that o and the spiral mutually bisect shows that the deflection of the circle from the spiral between the S.C. and the T.C. is the same as the deflection of the spiral from the tangent in half its length. Since the S.C. can be at any point on a spiral of given k, and the circular curve has the same radius as the spiral at that point, it follows that in general the spiral departs from an osculating circle at the same rate as from the initial tangent.
143. Superelevation.
From mechanics,
F -
Wv2 2gR
THEORY OF SPIRAL
125
where F is the centrifugal force, W is the weight, v is the velocity in feet per second, R is the radius of curvature, and g is the ac- celeration of gravity (equal to 16.08).
In Fig. 66, AB represents the horizontal distance between rail heads, which for standard gage is about 4.9 ft.; CB, the
FIG. 66.
superelevation; EH, the weight W', and GE, the centrifugal force. Then from similar triangles,
Substituting the above value of F in this equation, we have
Wv2 _ We 2gR ~ AB
whence,
e (in feet) =
ABv2 _ 4.9 v2 2gR ~ 32.16 R
5730,
Reducing v to miles per hour, substituting — g- for R, and reducing,
e (in inches) = 0.00069 D V2 .... (28)
TABLES
128
TABLE 5. — RADII.
|
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
|
0° 0' |
Infinite |
1° 0' |
5729.65 |
2° 0/ |
2864.93 |
3° 0' |
1910.08 |
4° 0' |
1432.69 |
|
1 |
313:75. |
3 |
5635.72 |
1 |
2841.26 |
1 i |
1899.53 |
1 |
1426.74 |
|
2 |
171887. |
2 |
5544.83 |
2 |
2817.97 |
2 |
1889.09 |
2 |
142(K85 |
|
3 |
114595. |
3 |
5456.82 |
3 |
2795.06 |
3 |
1878.77 |
3 |
1415^01 |
|
4 |
85943.7 |
4 |
5371.56 |
4 |
2772.53 |
4 |
1868.56 |
4 |
1409.21 |
|
5 |
68754.9 |
5 |
5388.92 |
5 |
2750.35 |
5 |
1858.47 |
5 |
1403^46 |
|
6 |
57595.8 |
6 |
5208.79 |
6 |
2728 52 |
6 |
1848.48 |
6 |
1397176 |
|
7 |
49110.7 |
7 |
5131.05 |
7 |
2707.04 |
7 |
1838.59 |
7 |
1392.10 |
|
8 |
42971.8 |
8 |
5055.59 |
8 |
2685.89 |
8 |
1828.82 |
8 |
1386.49 |
|
9 |
38197.2 |
9 |
4982.33 |
9 |
2665.08 |
9 |
1819.14 |
9 |
1380 92 |
|
10 |
34377.5 |
10 |
4911.15 |
10 |
2644.58 |
10 |
1809.57 |
10 |
1375.40 |
|
11 |
31252.3 |
11 |
4841.98 |
11 |
2624.39 |
11 |
1800.10 |
11 |
1369.92 |
|
12 |
28G47.8 |
12 |
4774.74 |
12 |
2604.51 |
12 |
1790.73 |
12 |
1364.49 |
|
13 |
26444.2 |
13 |
4709.33 |
13 |
2584.93 |
13 |
1781.45 |
13 |
1359.10 |
|
14 |
24555.4 |
14 |
4645.69 |
14 |
2565.65 |
14 |
1772.27 |
14 |
1:353.75 |
|
15 |
22918.3 |
15 |
4583.75 |
15 |
2546.64 |
15 |
1763.18 |
15 |
1348.45 |
|
16 |
21485.9 |
16 |
4523.44 |
16 |
2527.92 |
16 |
1754.19 |
16 |
1343.15 |
|
17 |
20222.1 |
17 |
4464.70 |
17 |
2509.47 |
17 |
1745.26 |
17 |
1337.65 |
|
18 |
19098.6 |
18 |
4407.46 |
18 |
2491.29 |
18 |
1736.48 |
18 |
1332.77 |
|
19 |
18093.4 |
19 |
4351.67 |
19 |
2473.37 |
19 |
1727.75 |
19 |
1327 63 |
|
20 |
17188.8 |
20 |
4297.28 |
20 |
2455.70 |
20 |
1719.12 |
20 |
1322! 53 |
|
21 |
16370.2 |
21 |
4244.23 |
21 |
2438.29 |
21 |
1710.56 |
21 |
1317.46 |
|
2:2 |
15626.1 |
22 |
4192.47 |
22 |
2421.12 |
22 |
1702.10 |
22 |
1312.43 |
|
23 |
14946.7 |
23 |
4141.96 |
23 |
2404.19 |
23 |
1693.72 |
23 |
1307.45 |
|
24 |
14323.6 |
24 |
4092.66 |
24 |
2387.50 |
24 |
1685.42 |
24 |
1302 50 |
|
25 |
13751.0 |
25 |
4044.51 |
25 |
2371.04 |
25 |
1677.20 |
25 |
1297.58 |
|
26 |
13222.1 |
26 |
3997.49 |
26 |
2354.80 |
26 |
1669.06 |
26 |
1292 71 |
|
27 |
12732.4' |
27 |
3951.54 |
27 |
2338.78 |
27 |
1661.00 |
27 |
1287.87 |
|
28 |
12277.7 |
28 |
3906.54 |
28 |
2322.98 |
28 |
1653.01 |
28 |
1283.07 |
|
29 |
11854.3 |
29 |
3862.74 |
29 |
2307.39 |
29 |
1645.11 |
29 |
1278 30 |
|
30 |
11459.2 |
30 |
3819.83 |
30 |
2292.01 |
30 |
1637.28 |
30 |
1273.57 |
|
31 |
11089.6 |
31 |
3777.85 |
31 |
2276.84 |
31 |
1629.52 |
31 |
1268.87 |
|
32 |
10743 0 |
32 |
3736.79 |
32 |
2261.86 |
32 |
1621.84 |
32 |
1264.21 |
|
33 |
10417.5 |
33 |
3696.61 |
33 |
2247.08 |
33 |
1614.22 |
33 |
1259^58 |
|
34 |
10111.1 |
34 |
3657.29 |
34 |
2232.49 |
34 |
1606.68 |
34 |
1254.98 |
|
35 |
9822.18 |
35 |
3618.80 |
35 |
2218.09 |
35 |
1599.21 |
35 |
1250.42 |
|
36 |
9549.311 |
36 |
3581.10 |
36 |
2203.87 |
36 |
1591.81 |
36 |
1245.89 |
|
37 |
9291.29 |
37 |
3544.19 |
37 |
2189.84 |
37 |
1584.48 |
37 |
1241.40 |
|
38 |
9046.75 |
38 |
3508.02 |
38 |
2175.98 |
38 |
1577.21 |
38 |
1236 94 |
|
39 |
8814.78 |
39 |
3472.59 |
39 |
2162.30 |
39 |
1570.01 |
39 |
1232.51 |
|
40 |
8594.42 |
40 |
3437.87 |
40 |
2148.79 |
40 |
1562.88 |
40 |
1228.11 |
|
41 |
8384.80 |
41 |
3403.83 |
41 |
2135.44 |
41 |
1555.81 |
41 |
1223 74 |
|
42 |
8185.16 |
42 |
3370.46 |
42 |
2122.26 |
42 |
1548.80 |
42 |
1219.40 |
|
43 |
7994.81 |
43 |
3337.74 |
43 |
2109.24 |
43 |
1541.86 |
43 |
1215 30 |
|
44 |
7813.11 |
44 |
3305.65 |
44 |
2096.39 |
44 |
1534.98 |
44 |
1210.82 |
|
45 |
7639.49 |
45 |
3274.17 |
45 |
2083.68 |
45 |
1528.16 |
45 |
1206.57 |
|
46 |
7473.42 |
46 |
3243.29 |
46 |
2071.13 |
46 |
1521.40 |
46 |
1202.36 |
|
47 |
7314.41 |
47 |
3212.98 |
47 |
2058.73 |
47 |
1514.70 |
47 |
1198.17 |
|
48 |
7162.03 |
48 |
31&3.23 |
48 |
2046.48 |
48 |
1508.06 |
48 |
1194.01 |
|
49 |
7015.8? |
49 |
3154.03 |
49 |
2034.37 |
49 |
1501.48 |
49 |
1189 88 |
|
50 |
6875.55 |
50 |
3125.36 |
50 |
2022.41 |
50 |
1494.95 |
50 |
1185.78 |
|
61 |
6740.74 |
51 |
3097.20 |
51 |
2010.59 |
51 |
1488.48 |
51 |
1181.71 |
|
62 |
6611.12 |
52 |
3069.55 |
52 |
1998.90 |
52 |
1482.07 |
52 |
1177.66 |
|
53 |
6486.38 |
53 |
3042.39 |
53 |
1987.35 |
53 |
1475.71 |
53 |
1173.65 |
|
54 |
6366.26 |
54 |
3015.71 |
54 |
1975.93 |
54 |
1469.41 |
54 |
1169 66 |
|
55 |
6250.51 |
55 |
2989.48 |
55 |
1964.64 |
55 |
1463.16 |
55 |
1165.70 |
|
56 |
6138.90 |
56 |
2963.71 |
56 |
1953.48 |
56 |
1456.96 |
56 |
1161.76 |
|
57 |
6031.20 |
57 |
2938.39 |
57 |
1942.44 |
57 |
1450.81 |
57 |
1157.85 |
|
58 |
5927.22 |
58 |
2913.49 |
58 |
1931.53 |
58 |
1444.72 |
58 |
1153.97 |
|
59 |
5826.76 |
59 |
2889.01 |
59 |
1920.75 |
59 |
1438.68 |
59 |
1150 11 |
|
60 |
5729.65 |
60 |
2864.93 |
60 |
1910.08 |
60 |
1432.69 |
60 |
1146.28 |
TABLE 5.— RADII.
129
|
1 — Deg |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
|
6°0 |
1146.28 |
6°0 |
955.37 |
7°0 |
818. G4 |
8°0' |
716.34 |
9°0/ |
G36.78 |
|
I |
1142.47 |
1 |
952.72 |
1 |
816.70 |
1 |
714.85 |
1 |
635.61 |
|
2 |
1138.69 |
2 |
950.09 |
2 |
814.76 |
2 |
713.37 |
2 |
634.44 |
|
3 |
1134.94 |
3 |
947.48 |
3 |
812.83 |
3 |
711.90 |
8 |
633.27 |
|
4 |
1131.21 |
4 |
944 . 83 |
4 |
810.92 |
4 |
710.43 |
4 |
632.10 |
|
5 |
1127.50 |
5 |
942.29 |
5 |
809.01 |
5 |
708.96 |
5 |
630.94 |
|
6 |
1123.82 |
6 |
939.72 |
6 |
807.11 |
6 |
707.51 |
6 |
629.79 |
|
7 |
1120.16 |
7 |
937.16 |
7 |
805.22 |
7 |
706.05 |
7 |
628.64 |
|
8 |
1116.52 |
8 |
934.62 |
8 |
803.34 |
8 |
704.60 |
8 |
627.49 |
|
9 |
1112.91 |
9 |
932.09 |
9 |
801.47 |
9 |
703.16 |
9 |
626. 35 |
|
10 |
1109.33 |
10 |
929.57 |
10 |
799.61 |
10 |
701.73 |
10 |
625.21 |
|
11 |
1105.76 |
11 |
927.07 |
11 |
797.75 |
11 |
700.30 |
11 |
624.08 |
|
12 |
1102.22 |
12 |
924.58 |
12 |
795.91 |
12 |
G98.88 |
12 |
622.95 |
|
13 |
1098.70 |
13 |
922.10 |
13 |
794.07 |
13 |
697.46 |
13 |
621.82 |
|
14 |
1095.20 |
14 |
919.64 |
14 |
79^.24 |
14 |
696.05 |
14 |
620.70 |
|
15 |
1091.73 |
15 |
917.19 |
15 |
790.42 |
15 |
694.65 |
15 |
619.58 |
|
16 |
1088.28 |
16 |
914.75 |
16 |
788.61 |
16 |
693.24 |
16 |
618.47 |
|
17 |
1084.85 |
17 |
912.33 |
17 |
786.80 |
17 |
691.85 |
17 |
617.30 |
|
18 |
1081.44 |
18 |
909.92 |
18 |
785.01 |
18 |
690.46 |
18 |
616.25 |
|
19 |
107§.05 |
19 |
907.52 |
19 |
783.22 |
19 |
689.08 |
19 |
615 15 |
|
20 |
1074.68 |
20 |
905.13 |
20 |
781.44 |
20 |
687.70 |
20 |
614.05 |
|
21 |
1071.34 |
21 |
902.76 |
21 |
779.67 |
21 |
686.33 |
21 |
612.96 |
|
22 |
1068.01 |
22 |
900 .40 |
22 |
777.91 |
22 |
684.96 |
22 |
611.87 |
|
23 |
1064.71 |
20 |
898.05 |
23 |
776.15 |
23 |
G83.60 |
23 |
610.78 |
|
24 |
1061.43 |
24 |
895.71 |
24 |
774.40 |
24 |
682.25 |
24- |
609.70 |
|
25 |
1058.16 |
25 |
893.39 |
2:> |
772.66 |
25 |
680.89 |
25 |
608.62 |
|
26 |
1054.92 |
26 |
891.08 |
26 |
770.93 |
26 |
679.55 |
26 |
607.55 |
|
27 |
1051.70 |
27 |
'888.78 |
27 |
769.21 |
27 |
678.21 |
27 |
606.48 |
|
28 |
1048.48 |
28 |
886.49 |
28 |
767.49 |
28 |
676.88 |
28 |
605.41 |
|
29 |
1045.31 |
29 |
884.21 |
29 |
765.78 |
29 |
675.54 |
29 |
604.35 |
|
30 |
1042.14 |
30 |
881.95 |
30 |
764.08 |
30 |
674.22 |
30 |
603.29 |
|
31 |
1039.00 |
31 |
879.69 |
31 |
762.39 |
31 |
672.90 |
31 |
602.23 |
|
32 |
1035.87 |
32 |
877.45 |
32 |
700.70 |
32 |
671.59 |
32 |
601.18 |
|
33 |
1032.76 |
33 |
875.22 |
33 |
759.02 |
33 |
670.28 |
33 |
600.13 |
|
34 |
1029.67 |
34 |
873.00 |
34 |
757.35 |
34 |
668.98 |
34 |
599.09 |
|
35 |
1026.60 |
85 |
870.80 |
35 |
755.69 |
35 |
607.68 |
35 |
598.04 |
|
36 |
1023.55 |
36 |
868.60 |
36 |
754.03 |
36 |
666.39 |
36 |
597.01 |
|
37 |
1020.51 |
37 |
866.41 |
37 |
752.38 |
37 |
665.10 |
37 |
595.97 |
|
38 |
1017.49 |
38 |
864.24 |
38 |
750.74 |
38 |
603.82 |
38 |
594.94 |
|
39 |
1014.50 |
39 |
862.08 |
39 |
749.10 |
39 |
662.54 |
39 |
593.91 |
|
40 |
1011.51 |
40 |
859.92 |
40 |
747.48 |
40 |
661.26 |
40 |
592.89 |
|
41 |
1008.55 |
41 |
857.78 |
41 |
745.86 |
41 |
659.99 |
41 |
591.87 |
|
42 |
1005.60 |
42 |
855.65 |
42 |
744.24 |
42 |
658.73 |
42 |
590.85 |
|
43 |
1002.67 |
43 |
853.53 |
43 |
742.63 |
43 |
657.47 |
43 |
589.84 |
|
44 |
999.76 |
44 |
851.42 |
44 |
741.03 |
44 |
656.22 |
44 |
588.83 |
|
45 |
996.87 |
45 |
849.32 |
45 |
739.44 |
45 |
654.97 |
45 |
587.83 |
|
46 |
993.99 |
46 |
847.23 |
46 |
737.80 |
46 |
653.72 1 |
46 |
586.82 |
|
47 |
991.13 |
47 |
845.15 |
47 |
736.28 |
47 |
652.48 |
47 |
585.83 |
|
48 |
988.28 |
48 |
843.08 |
48 |
734.70 |
48 |
651.25 |
48 |
584.83 |
|
49 |
985.45 |
49 |
841.02 |
49 |
733.14 |
49 |
650.02 |
49 |
583.84 |
|
50 |
982.64 |
50 |
838.97 |
50 |
731.53 |
50 |
648.79 |
50 |
582.85 |
|
51 |
979.84 |
51 |
836.93 |
51 |
730.03 |
51 |
647.57 |
51 |
581.86 |
|
52 |
977.06 |
52 |
834.90 |
52 |
728.48 |
52 |
646.35 |
52 |
580.88 |
|
53 |
974.29 |
53 |
832.89 |
53 |
726.94 |
53 |
645.14 |
53 |
579.90 |
|
54 |
971.54 |
54 |
830.88 |
54 |
725.41 |
54 |
643.94 |
54 |
578.92 |
|
55 |
968.81 |
55 |
828.88 |
55 |
723.88 |
55 |
642.73 |
55 |
577.95 |
|
56 |
966.09 |
56 |
826.89 |
56 |
722.36 |
56 |
641.53 |
56 |
576.98 |
|
57 |
963.39 |
57 |
824.91 |
57 |
720.85 |
57 |
640.34 |
57 |
576.02 |
|
58 |
960.70 |
58 |
822.93 |
58 |
719.34 |
58 |
639.15 |
58 |
575.06 |
|
59 |
958.03 |
59 |
820.97 |
59 |
717.84 |
59 |
637.96 |
59 |
574.10 |
|
60 |
955.37 |
60 |
819.02 |
60 |
716.34 |
60 |
636.78 |
60 |
573.14 |
130
TABLE 5.— RADII.
|
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
Deg. |
Radius. |
|
10° 0' |
573.14 |
12»0' |
477.68 |
14° 0' |
409.32 |
16° 0' |
358.17 |
18° 0' |
318.39 |
|
2 |
571.24 |
2 |
476.36 |
2 |
408.35 |
2 |
357.43 |
2 |
317.80 |
|
4 |
569.35 |
4 |
475.05 |
4 |
407.38 |
4 |
356.69 |
4 |
317.22 |
|
6 |
567.47 |
6 |
473.74 |
6 |
406.42 |
6 |
355.95 |
6 |
316.63 |
|
8 |
565.60 |
8 |
472.44 |
8 |
405.46 |
8 |
355.21 |
8 |
316.05 |
|
10 |
563.75 |
10 |
471.15 |
10 |
404.51 |
10 |
354.48 |
10 |
315.47 |
|
12 |
561.91 |
12 |
469.86 |
12 |
403.56 |
12 |
353.75 |
12 |
314.89 |
|
14 |
560.08 |
14 |
468.58 |
14 |
402.61 |
14 |
353.03 |
14 |
314.32 |
|
16 |
558.26 |
16 |
467.31 |
16 |
401.67 |
16 |
352.30 |
16 |
313.75 |
|
18 |
556.45 |
18 |
466.04 |
18 |
400.74 |
18 |
351.58 |
18 |
313.18 |
|
20 |
554.66 |
20 |
464.78 |
20 |
399.80 |
20 |
350.86 |
20 |
312.61 |
|
22 |
552.88 |
22 |
463.53 |
22 |
398.88 |
22 |
350.15 |
22 |
312.04 |
|
24 |
551.11 |
24 |
462.29 |
24 |
397.95 |
24 |
349.44 |
24 |
311.47 |
|
26 |
549.35 |
26 |
461.05 |
26 |
397.03 |
26 |
348.72 |
26 |
310.91 |
|
28 |
547.60 |
28 |
459.82 |
28 |
396.13 |
28 |
348.02 |
28 |
310.35 |
|
30 |
545.87 |
30 |
458.59 |
30 |
395.21 |
30 |
347.32 |
30 |
309.79 |
|
32 |
544.14 |
32 |
457.88 |
32 |
394.30 |
32 |
346.62 |
32 |
309.23 |
|
34 |
542.42 |
34 |
456.16 |
34 |
393.40 |
84 |
345.93 |
34 |
308.68 |
|
36 |
540.72 |
36 |
454.96 |
36 |
392.50 |
36 |
345.23 |
36 |
808.13 |
|
38 |
539.03 |
38 |
453.76 |
38 |
391.61 |
38 |
344.54 |
38 |
307.58 |
|
40 |
537.34 |
40 |
452.57 |
40 |
390.72 |
40 |
343.85 |
40 |
307.03 |
|
42 |
535 67 |
42 |
451.38 |
42 |
389.83 |
42 |
343.16 |
42 |
306.48 |
|
44 |
534.01 |
44 |
450.20 |
44 |
388.95 |
44 |
342.48 |
44 |
305.93 |
|
46 |
532.36 |
46 |
449.02 |
46 |
388.07 |
46 |
341.80 |
46 |
305.39 |
|
48 |
530.71 |
48 |
447.86 |
48 |
387.20 |
48 |
841.12 |
48 |
304.85 |
|
50 |
529.08 |
50 |
446.69 |
50 |
386.33 |
50 |
340.45 |
50 |
304.31 |
|
52 |
527.46 |
52 |
445.54 |
52 |
385.47 |
52 |
339.78 |
52 |
303.77 |
|
54 |
525.85 |
54 |
444.39 |
54 |
384.60 |
54 |
339.11 |
54 |
303.24 |
|
56 |
524.25 |
56 |
443.24 |
56 |
383.75 |
56 |
338.44 |
56 |
302.70 |
|
58 |
522.65 |
58 |
442.11 |
58 |
382.89 |
58 |
337.77 |
58 |
302.17 |
|
11° 0' |
521.07 |
18° 0' |
440.97 |
16° 0' |
382.04 |
17°0' |
337.11 |
19° 0' |
301.64 |
|
2 |
519.50 |
2 |
439.85 |
2 |
381.19 |
2 |
336.45 |
2 |
301.12 |
|
4 |
517.93 |
4 |
438.73 |
4 |
380.35 |
4 |
335.80 |
4 |
800.59 |
|
6 |
516.38 |
6 |
437.61 |
6 |
379.51 |
6 |
335.14 |
6 |
800.07 |
|
8 |
514.84 |
8 |
436.50 |
8 |
378.68 |
8 |
334.49 |
8 |
299. E4 |
|
10 |
513.30 |
10 |
435.40 |
10 |
377.84 |
10 |
333.84 |
10 |
299.02 |
|
12 |
511.77 |
12 |
434.30 |
12 |
377.0:2 |
12 |
333.19 |
12 |
298.50 |
|
14 |
510.26 |
14 |
433.21 |
14 |
376.19 |
14 |
332.55 |
14 |
297.99 |
|
16 |
508.75 |
16 |
432.12 |
16 |
375.37 |
16 |
331.91 |
16 |
297.47 |
|
18 |
507.25 |
18 |
431.04 |
18 |
374.55 |
18 |
331. 27 |
18 |
296.96 |
|
20 |
505.76 |
20 |
429.96 |
20 |
373.74 |
20 |
330.63 |
20 |
296.45 |
|
22 |
504.28 |
22 |
428.98 |
22 |
372.93 |
22 |
330.00 |
22 |
295.94 |
|
24 |
502.80 |
24 |
427.82 |
24 |
372.12 |
24 |
329.37 |
24 |
295.43 |
|
26 |
501.34 |
26 |
426.76 |
26 |
371.32 |
26 |
328.74 |
26 |
294.92 |
|
28 |
499.88 |
28 |
425.71 |
28 |
370.52 |
28 |
328.11 |
28 |
294 42 |
|
30 |
498.43 |
30 |
424.66 |
30 |
369.72 |
30 |
327.48 |
30 |
293.91 |
|
32 |
496.99 |
32 |
423.61 |
32 |
368.93 |
32 |
326.86 |
32 |
293.41 |
|
34 |
495.56 |
34 |
422.57 |
34 |
368.14 |
34 |
326.24 |
34 |
292.91 |
|
36 |
494.14 |
36 |
421.54 |
36 |
367.35 |
3G |
325.62 |
36 |
292.41 |
|
38 |
492.73 |
38 |
420.51 |
38 |
306.57 |
38 |
325.01 |
38 |
291.92 |
|
40 |
491.32 |
40 |
419.49 |
40 |
365.79 |
40 |
324.40 |
40 |
291.42 |
|
42 |
489.92 |
42 |
418.47 |
42 |
365.01 |
42 |
323.79 |
42 |
290.93 |
|
44 |
488.53 |
44 |
417.45 |
44 |
364.24 |
44 |
323.18 |
44 |
290.44 |
|
46 |
487.15 |
46 |
416.44 |
46 |
863.47 |
46 |
322.57 |
40 |
289.95 |
|
48 |
485.77 |
48 |
415.44 |
48 |
362.70 |
48 |
321.97 |
48 |
289.46 |
|
50 |
484.40 |
50 |
414.44 |
50 |
361.94 |
50 |
321.37 |
50 |
288.98 |
|
52 |
483.05 |
52 |
413.44 |
52 |
361.18 |
52 |
320.77 |
52 |
288.49 |
|
54 |
481.69 |
54 |
412.45 |
54 |
360.42 |
54 |
320.17 |
54 |
288.01 |
|
56 |
430.35 |
56 |
411.47 |
56 |
359.67 |
56 |
319.57 |
56 |
287.53 |
|
58 |
479.01 |
58 |
410.49 |
58 |
358.9-3 |
58 |
318.98 |
58 |
287.05 |
|
60 |
477.68 |
60 |
409.51 |
60 |
358.17 |
60 |
318.39 |
60 |
28(5.57 |
131
TABLE 6. —FUNCTIONS OF A ONE-DEGREE CURVE.
The Long Chords, Mid-Ordinates, Externals, and Tangent Distances of this table are for a curve of 5730 feet radius. To find the corresponding functions of any other curve divide the tabular values by the degree of curve.
For metric curves having 20-metre chords, multiply tne degree by 5 and enter the table with the result as a value of Z>, the tabu- lar values being taken as metres instead of feet
Thus for a 1° 30' metric curve having I— 45° the tangent dis- tance is T = — - — '— = 316.45 metres. Again, suppose J= 38° 1 . o X 5
and the long chord = 373.1 m. known and D required. The
tabular L. C. is 3731 m.; therefore D = 3731-° = 2° 0>
3.3.1 X 5
|
0° |
1° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
0.00 0.000 0.000 0.00 |
100.00 0.218 0.218 50.00 |
0 |
|
2 |
3.33 0000 0.000 1.67 |
103.33 0.233 0.233 51.67 |
2 |
|
4 |
6.6? 0 001 0.001 3.33 |
106.66 0.248 0.248 53.33 |
4 |
|
6 |
10.00 0.002 0.002 5.00 |
110.00 0.264 0.264 55.00 |
6 |
|
8 |
13.33 0.004 0.004 6.67 |
113.33 0.280 0.280 56.67 |
8 |
|
10 |
16.67 0.006 0.006 8.33 |
116.66 0.297 0.297 58.33 |
10 |
|
12 |
20.00 0.009 0.009 10.00 |
120.00 0.314 0.314 60.00 |
12 |
|
14 |
23.33 0.012 0.012 11.67 |
123.33 0.332 0.332 61.67 |
14 |
|
16 |
26.67 0.015 0.015 13.33 |
126.66 0.350 0.350 63.33 |
16 |
|
18 |
30.00 0.019 0.019 15.00 |
130.00 0.368 0.368 65.00 |
18 |
|
20 |
33.33 0.024 0.024 16.67 |
133.33 0.388 0.388 66.67 |
20 |
|
22 |
36.67 0.029 0.029 18.33 |
136.66 0.407 0.407 68.33 |
22 |
|
24 |
40.00 0.035 0.035- 20.00 |
140.00 0.427 0.427 l~0.00 |
24 |
|
26 |
43.33 0.041 0.041 21.67 |
143.33 0.448 0.448 "1.67 |
26 |
|
28 |
46.67 0.048 0.048 23.33 |
146.66 0.469 0.469 ^3.33 |
28 |
|
30 |
50.00 0.054 0.054 25.00 |
15000 0.491 0.491 "5.00 |
30 |
|
32 |
53 33 0.062 0.062 26.67 |
153.33 0.513 0.513 ^6.67 |
32 |
|
34 |
56 67 0.070 0.070 28.33 |
156.66 0.536 0.536 78.33 |
34 |
|
36 |
6000 0.079 0.079 30.00 |
160.00 0.559 0.559 80.00 |
36 |
|
38 |
63.33 0.088 0.088 31.67 |
163.33 0.582 0.582 81.67 |
38 |
|
40 |
66.67 0.097 0.097 33 33 |
16666 0.606 0.606 83.33 |
40 |
|
42 |
70.00 0.107 0.107 35.00 |
170.00 0.630 0.630 85.00 |
42 |
|
44 |
73.33 0.117 0.117 36.67 |
173.33 0.655 0.655 86.67 |
44 |
|
46 |
76.6? 0.128 0.128 38.33 |
176.66 0.681 0.681 88.33 |
46 |
|
48 |
80.00 0.140 0.140 40.00 |
180.00 0.706 0.706 90.00 |
48 |
|
50 |
83.33 0.151 0.151 41.67 |
183.33 0733 0.733 91.67 |
50 |
|
52 |
86 67 0.164 0.164 43.33 |
186.66 0.760 0.760 93.33 |
52 |
|
54 |
9000 0 176 O.J76 45.00 |
190.00 0.788 0.788 95.00 |
54 |
|
56 |
93 33 0.190 0.190 46.6? |
193.33 0.815 0.815 96.67 |
56 |
|
58 |
96.67 0.204 0.204 4833 |
196.66 0.844 0.844 98.33 |
58 |
|
tJB |
10000 0.218 0.218 5000 |
199.98 0.873 0 873 100.00 |
60 |
132 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
2° |
3° |
||
|
4 |
L. C. M. E. T. |
L. C. M. E. T. |
r |
|
0 |
"199.98 0.873 0.873 100.00 |
299.96 1.964 1.964 150.07 |
0 |
|
2 |
203.31 0.902 0.902 101.67 |
3U3.29 2.008 2.009 151.74 |
2 |
|
4 |
206.64 0 932 0.932 103.34 |
306.62 2.053 2.054 153.41 |
4 |
|
6 |
209.97 0.962 0.962 105.01 |
309.95 2.098 2.099 155.08 |
6 |
|
8 |
213.31 0.993 0.993 106.68 |
313.29 2.143 2.144 156.75 |
8 |
|
10 |
216.64 1.024 1.024 108.35 |
316.62 2.188 2.189 158.42 |
10 |
|
12 |
219.97 1.056 1.056 110.02 |
319.95 2.235 2.236 160.09 |
12 |
|
14 |
223.30 1.088 1.088 111.69 |
323.28 2.282 2.283 161.76 |
14 |
|
16 |
226.64 1.121 1.121 113.36 |
326.62 2.329 2.330 163.43 |
16 |
|
18 |
229.97 1.154 1.154 115.02 |
329.95 2.376 2.377 165.09 |
18 |
|
20 |
233.30 1.188 1.188 116.69 |
333.28 T.424 2.425 166.76 |
20 |
|
22 |
236.63 1.222 1.222 118.36 |
336.61 2.473 2.474 168.43 |
22 |
|
24 |
239.97 1.256 1.256 120.03 |
339.95 2.523 2.523 170.10 |
24 |
|
26 |
243.30 1.292 1.292 121.70 |
343.28 2.572 2.573 171.77 |
26 |
|
28 |
246.63 1.328 1.328 123.37 |
346.61 2.622 2.623 173 44 |
28 |
|
30 |
249.96 1.364 1.364 125.03 |
349.94 2.672 2.673 175.10 |
30 |
|
32 |
253.29 1.399 1.399 126.70 |
353.27 2.724 2.725 176.72 |
32 |
|
34 |
256.62 1.437 1.437 128.37 |
356.60 2.776 2.777 178.39 |
34 |
|
36 |
259.96 1.475 1.475 130.04 |
359.94 2.828 2.829 18006 |
36 |
|
38 |
263.29 1.513 1.513 131.71 |
363.27 2.880 2.881 181.73 |
38 |
|
40 |
266.62 1.552 1.552 133.38 |
366 60 2 933 2.934 183.40 |
40 |
|
42 |
269.96 1.592 1.592 135.05 |
369.94 2.987 2.988 185.07 |
42 |
|
44 |
273.29 1.632 1.632 136.72 |
373.27 3.042 3 043 186.74 |
44 |
|
46 |
276.62 1.672 1.672 138.38 |
376.60 3.096 3097 188.40 |
46 |
|
43 |
279.96 1.712 1.712 140.05 |
379.94 3.151 3.152 190.07 |
48 |
|
50 |
283.29 1.752 1.752 141.72 |
383.27 3.206 3.207 191.74 |
50 |
|
52 |
286.62 1.794 1.794 143.39 |
38660 3.263 3.264 193.41 |
52 |
|
54 |
289.96 1.836 1.836 145.06 |
389.94 3.320 3.321 195.08 |
54 |
|
56 |
293.29 1.878 1.878 146.73 |
393.27 3.377 3378 196.75 |
56 |
|
58 |
296.62 1.921 1.921 148.40 |
396.60 3.434 3.435 198.42 |
58 |
|
60 |
299.96 1.964 1.964 150.07 |
399.94 3.491 3.492 2uO 09 |
60 |
|
4° |
6° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
399.94 3.491 3.492 200.09 |
499.88 5.454 5.459 250.17 |
0 |
|
2 |
403.27 3.550 3.551 201.70 |
503.21 5.527 5.o33 251.84 |
2 |
|
4 |
406.60 3.609 3.610 203.43 |
506.54 5.601 5.607 253.51 |
4 |
|
6 |
409.93 3.668 3.670 205.10 |
509.87 5.675 5.681 255.18 |
6 |
|
8 |
413.26 3.727 3.730 206.77 |
513.20 5.749 5.755 256.85 |
8 |
|
10 |
416.59 3.787 3.790 208.44 |
51653 5.823 5.829 258.52 |
10 |
|
12 |
419.92 3.848 3.851 210.11 |
519.86 5.899 5.905 260.20 |
12 |
|
14 |
423.26 3.910 3.913 211.77 |
523.19 5.975 5981 261.86 |
14 |
|
16 |
426.59 3.972 3.975 213.45 |
526.52 6.052 6.058 263.54 |
16 |
|
18 |
429.92 4.034 4.037 215.11 |
529.85 6.129 6.135 265.20 |
18 |
|
20 |
433.25 4.096 4.099 216.78 |
533.18 6.206 6.212 266.87 |
20 |
|
22 |
436.58 4.160 4.163 218.45 |
536.51 6.284 6.290 208 54 |
22 |
|
24 |
439.91 4.224 4.227 220.12 |
539. 81 6.362 6.369 270.21 ' |
24 |
|
26 |
443.24 4.288 4.291 221.79 |
543.17 6.441 6.448 271.88 |
26 |
|
28 |
446.58 4.353 4.356 223.46 |
546.50 6.520 6.527 273.54 |
28 |
|
30 |
449.91 4.418 4.421 225.13 |
549.83 6.599 6.606 275.21 |
30 |
|
32 |
453.24 4.484 4.487 226.80 |
553 17 6.680 6.687 276.88 |
32 |
|
34 |
456.57 4.550 4.554 228.47 |
556.50 6.761 6.768 278.55 |
34 |
|
36 |
459.90 4.617 4.621 230.14 |
559.83 6.842 6.849 280.23 |
36 |
|
38 |
463.23 4.684 4.688 231.81 |
563.16 6.923 6.931 281.90 |
38 |
|
40 |
466.56 4.751 4.755 233.48 |
566.49 7.005 7.013 283.57 |
40 |
|
42 |
469.89 4.820 4.824 235.15 |
569.82 7.088 7.096 285.24 |
42 |
|
44 |
473.23 4.889 0.893 236.82 |
573.15 7 171 7.180 286.91 |
44 |
|
46 |
47656 4.958 4962 238.48 |
576.48 7.255 7.264 288.59 |
46 |
|
48 |
479.89 5.027 5.031 240.15 |
579.81 7.339 7.348 290.26 |
48 |
|
50 |
483.22 5.096 5100 241.82 |
583.14 7423 7.432 291.93 |
50 |
|
52 |
486.55 5.167 5.171 243.49 |
586.47 7.508 7.517 293.60 |
52 |
|
54 |
489.88 5.238 5.243 245.16 |
589.80 7.593 7.603 295.27 |
54 |
|
56 |
493.21 5.310 5.315 246.83 |
593.13 7.678 7 689 296 95 |
56 |
|
58 |
49654 5.382 5.387 248.50 |
596.46 7.764 7.775 298.62 |
58 |
|
60 |
499.88 5 454 5.459 250.17 |
599.80 7.850 7 861 300.30 |
60 |
6 —FUNCTIONS OF A ONE-DEGREE CURVE. 133
|
i 6° |
7° |
||
|
L C. M. E T. |
L. C. M. E. T. |
||
|
0 |
599.80 7.850 7.861 300.30 |
699.60 10.69 10.71 350.44 |
0 |
|
2 |
603.13 7.940 7.951 301.97 |
702.93 10.79 10.81 352.11 |
2 |
|
4 |
606 46 8.030 8.041 303.64 |
706.26 10.90 10.92 353.79 |
4 |
|
6 |
609.78 8.120 8.131 305. 31 |
709.58 11.00 11.02 355.46 |
6 |
|
8 |
613.11 8.210 8. 2:il 306.98 |
712.91 11.11 11.13 357.13 |
8 |
|
10 |
616 44 8.300 8.311 308.65 |
716.24 11.21 11.23 358.81 |
10 |
|
12 |
619.76 8.390 8.401 310.32 |
719.56 11.31 11.33 360.48 |
12 |
|
14 |
623.09 8.480 8,491 311.99 |
722.89 11.42 11.44 362.15 |
14 |
|
16 |
626.42 8.570 8.581 313.66 |
726.21 11.52 11.54 363 83 |
16 |
|
13 |
629.74 8.660 8.671 315.33 |
729.53 11.63 11.65 365.50 |
18 |
|
20 |
633.07 8.750 8.761 317.00 |
732.86 J1.73 11.75 367.17 |
20 |
|
'22 |
63(5.40 8.844 8.856 318.67 |
736.19 11.84 11.86 368.85 |
22 |
|
24 |
639.72 8.939 8.951 320.34 |
739.51 11.95 11.97 370.52 |
24 |
|
26 |
643.05 9.033 9.046 322.01 |
742.84 12.06 12.08 372.19 |
26 |
|
28 |
646.38 9.128 9.141 323.68 |
746.17 12.17 12.19 373.86 |
28 |
|
30 |
649.70 9.222 9.236 325.35 |
749.49 12.27 12.30 375.54 |
30 |
|
32 |
653.03 9.317 9.331 327.02 |
752.82 12.38 12.41 377.22 |
32 |
|
34 |
656.36 9.411 9.426 328.69 |
756.15 12.49 1252 378.89 |
34 |
|
36 |
659.69 9.506 9.521 330.37 |
759.47 12.60 12.63 380 57 |
36 |
|
38 |
663.02 9.600 9.616 332.04 |
762.80 12.71 12.74 382.24 |
38 |
|
40 |
666.34 9.695 9.712 333.71 |
766.13 12.82 12.85 383.92 |
40 |
|
42 |
669.67 9.794 9.812 335.38 |
769.45 12.93 12.96 385.60 |
42 |
|
44 |
673.00 9.894 9.912 337.05 |
772.78 13.04 13.08 387.27 |
44 |
|
46 |
676.32 9.993 10.01 338.73 |
776.11 13.15 13.19 388.95 |
46 |
|
48 |
679.65 10.09 10.11 340.40 |
779.43 13.26 13.31 390.62 |
48 |
|
50 |
682.98 10.19 10.21 342.07 |
782.76 13.37 13.42 392.30 |
50 |
|
52 |
686.30 10.29 10.31 343.74 |
786.09 13.48 13.53 393.98 |
52 |
|
54 |
689.63 10.39 10.41 345.41 |
789.41 13.59 13.65 395.65 |
54 |
|
56 |
692.96 10.49 10.51 347.08 |
792.74 13.70 13.76 397.33 |
56 |
|
58 |
696.28 10.59 10.61 348.76 |
796.07 13.81 13.88 399.01 |
58 |
|
60 |
699 60 10.69 10.71 850.44 |
799.40 13.96 13.99 400.70 |
60 |
|
8° |
9° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
/ |
|
|
0 |
799.40 13.96 13.99 400.70 |
899.10 17.66 17.71 450.95 |
0 |
|
2 |
802.72 14.07 14.10 402.37 |
902.42 17.79 17.84 452.63 |
2 |
|
4 |
806.04 14.19 14.22 404.05 |
905.74 17.92 17.98 454.31 |
4 |
|
6 |
809.37 14.31 14.34 405.72 |
909.07 18.06 18.11 455.98 |
6 |
|
8 |
812.69 14 43 14.46 407.39 |
912.39 18.19 18.25 457.66 |
8 |
|
10 |
816.01 14.55 14.58 409.06 |
915.71 18.32 18.38 459.34 |
10 |
|
12 |
819.34 14.66 14.70 410.74 |
919.04 18.46 18.52 461.02 |
12 |
|
14 |
822.66 14.78 14.82 412.41 |
922.36 18.59 18.65 462.70 |
14 |
|
16 |
825.98 14.90 14.94 414. OS |
925.68 18.72 18.79 464.37 |
16 |
|
18 |
829.31 15.02 15.06 415.75 |
929.01 18.86 18.92 466.05 |
18 |
|
20 |
832.63 15.14 15.18 417.43 |
932.33 18.99 19.06 467.73 |
20 |
|
22 |
83595 15.26 15.30 419.10 |
935.65 19.12 19.19 469.41 |
22 |
|
24 |
839.28 15.38 15.43 400.77 |
938.98 19.26 19.33 471.08 |
24 |
|
26 |
842.60 15.51 15.55 422.45 |
942.30 19.40 19.47 472.76 |
26 |
|
28 |
845.92 15.63 15.68 424.12 |
945.62 19.54 19.61 474.43 |
28 |
|
30 |
849.25 15.75 15.80 425.79 |
948.95 19.68 19.75 476.10 |
30 • |
|
32 |
852.57 15.88 15.93 427.47 |
952.27 19.82 19.89 477.78 |
32 |
|
34 |
855.89 16.00 16.05 429.15 |
955.59 19.96 20.03 479.46 |
34 |
|
36 |
859.22 16.12 16.18 430.82 |
958.92 20.10 20.17 481.14 |
36 |
|
38 |
862.54 16.25 16.30 432.50 |
962.24 20.24 20.31 482.83 |
38 |
|
40 |
865.86 16.38 16.43 434.18 |
965.56 20.38 20.45 484.51 |
40 |
|
42 |
869.19 16.50 16.55 435.86 |
968.89 20.52 20.59 486.19 |
42 |
|
1 44 |
872.51 16.63 16.68 437.54 |
972.21 20.66 20.74 487.87 |
44 |
|
46 |
875.83 16.76 16.81 439.21 |
975.53 20.80 20.88 489.56 |
46 |
|
1 48 |
879.16 16.89 16.94 440.89 |
97886 20.94 21.03 491.24 |
48 |
|
50 |
882.48 17.02 17.07 442.57 |
982.18 21.09 21.17 492.92 |
50 |
|
52 |
885.80 17.14 17.19 444.25 |
985.50 21.23 21.31 494.60 |
52 |
|
54 |
889.13 17.27 17.32 445.93 |
988.83 21.37 21.46 496.28 |
54 |
|
56 |
892.45 17.40 17.45 447.60 |
992.15 21.51 21.60 497.96 |
56 |
|
58 |
895.77 17.53 17.58 449.28 |
995.47 21.65 21.75 499.65 |
58 |
|
60 |
899.10 1766 17.71 450.95 |
998.80 21.80 21.89 501.32 |
60 |
134 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
10° |
11° |
||
|
L C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
998.8 21.80 21.89 501.32 |
1098.4 26.38 26.50 551.74 |
0 |
|
2 |
1002.1 21.94 22.03 503.00 |
1101.7 26.54 26.66 553.42 |
2 |
|
4 |
1005.4 22.09 22.18 504.68 |
1105.0 26.70 26.83 555.10 |
4 |
|
6 |
1008.8 22.24 22.33 506.36 |
1108.3 26.86 26.99 556.78 |
6 |
|
8 |
1012.1 22.39 22.48 508.04 |
1111.7 27.02 27.16 558.46 |
8 |
|
10 |
1015.4 22.54 22.63 509. ".2 |
1115.0 27.19 27.32 560.14 |
10 |
|
12 |
1018.7 22.68 22.78 511.40 |
1118.3 27.35 27.48 561.82 |
12 |
|
14 |
1022 0 22.83 22.93 513.08 |
1121.6 27.51 27.65 563.50 |
14 |
|
16 |
1025.4 22.98 23.08 514.76 |
1124.9 27.67 27.81 565.18 |
16 |
|
18 |
1028.7 23.13 23.23 516.44 |
1128.2 27.83 27.98 566.86 |
18 |
|
20 |
1032.0 23.28 23.38 518.12 |
1131.6 28.00 28.14 568.54 |
20 |
|
22 |
1035.3 23.43 23.53 519.80 |
1134.9 28.17 28.30 570.22 |
22 |
|
24 |
1038.6 23.58 23.68 521.48 |
1138.2 28.34 28.47 571.90 |
24 |
|
26 |
1042.0 23.73 23.84 523.16 |
1141.5 28.50 28.64 573.58 |
26 |
|
28 |
1045.3 23.88 23.99 524.85 |
1144.8 28.67 28.81 575.27 |
28 |
|
80 |
1048.6 24.04 24.14 526.53 |
1148.1 28.84 28.98 576.95 |
30 |
|
32 |
1051.9 24.19 24.30 528.21 |
1151.5 29.00 29.14 578.63 |
32 |
|
34 |
1055.2 24.34 24.45 529.89 |
1154.8 29.17 29.31 580.32 |
34 |
|
36 |
1058.6 24.49 24.60 531.57 |
1158.1 29.34 29.48 582.00 |
36 |
|
38 |
1061.9 24.64 24.76 533.25 |
1161.4 29.50 29.65 583.69 |
38 |
|
40 |
1065.2 24.80 24.91 534.93 |
1164.7 29.67 29.82 585.87 |
40 |
|
42 |
1068.5 24.95 25.06 536.61 |
1168.0 29.84 29.99 587.05 |
42 |
|
44 |
1071.8 25.11 25.22 538.29 |
1171.4 30.01 30.17 588.74 |
44 |
|
46 |
1075.2 25.27 25.38 539.97 |
1174.7 30.18 30.34 590.42 |
46 |
|
48 |
1078.5 25.43 25.54 541.65 |
1178.0 30.35 30.52 592.11 |
48 |
|
50 |
1081.8 25.59 25.70 543.33 |
1181.3 30.53 30.69 593.79 |
50 |
|
52 |
1085.1 25.74 25.86 545.01 |
11S4.6 30.70 30.86 595.47 |
52 |
|
54 |
1088.4 25.90 26.02 546. G9 |
1187.9 30.87 31.04 597.16 |
54 |
|
56 |
1091.8 26.06 26.18 548.37 |
1191.3 31.04 31.21 598.84 |
56 |
|
58 |
1095.1 26.22 26.34 550.06 |
1194.6 31.21 31.39 600.53 |
58 |
|
60 |
1098.4 26.38 26.50 551.74 |
1197.9 31.39 31.56 602.22 |
60 |
|
1*2° |
13° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
-0 |
1197.9 31.39 31.56 602.22 |
1297.3 36.83 37.07 652.87 |
0 |
|
2 |
1201.2 31.57 31.73 603.91 |
1300.6 37.02 37.26 654.56 |
2 |
|
4 |
1204.5 31.74 31.91 605.60 |
1303.9 37.21 37.46 656.25 |
4 |
|
6 |
1207.8 31.93 32.09 607.28 |
1307.2 37.40 37.65 657.93 |
6 |
|
8 |
1211.1 32.09 32.27 608.97 |
1310.5 37.59 37.85 659.62 |
8 |
|
10 |
1214.5 32.27 32.45 610.66 |
1313.8 37.79 38.04 661.31 |
10 |
|
12 |
1217.8 32.45 32.63 612.35 |
1317.2 37.98 38.23 663.00 |
12 |
|
14 |
1221.1 32.62 32.81 614.04 |
1320.5 38.17 38.43 664.69 |
14 |
|
16 |
1224.4 32.80 32.99 615.72 |
1323.8 38.36 38.62 666.37 |
16 |
|
18 |
1227.7 32.97 33.17 617.41 |
1327.1 38.55 38.82 668.06 |
18 |
|
20 |
1231.0 33.15 33.35 619.10 |
1330.4 38.75 39.01 669.75 |
20 |
|
22 |
1234.3 33.33 33.53 6v!0.79 |
1333.7 38.95 39.20 671.44 |
22 |
|
24 |
1237.7 33.51 33.72 622.48 |
1337.0 39.15 39.40 673.13 |
24 |
|
26 |
1241.0 33.69 33.90 624.16 |
1340.3 39.35 39.60 674.81 |
26 |
|
28 |
1244.3 33.87 34.09 6^5.85 |
1343.6 39.54 39.80 676.51 |
28 |
|
30 |
1247.6 34.06 34.27 627.55 |
1346.9 39.74 40.00 678.20 |
30 |
|
32 |
1250.9 34.24 34.45 629.24 |
1350.3 39.94 40.19 679.89 |
32 |
|
34 |
1254.2 34.42 34.64 630.93 |
1353.6 40.13 40.39 681.58 |
34 |
|
36 |
1257.5 34.60 34.82 632.61 |
1356.9 40.33 40.59 683.26 |
36 |
|
38 |
1260.8 34.78 35.01 634.30 |
1360.2 40.52 40.79 684.95 |
38 |
|
40 |
1264.2 3497 35.19 635.99 |
1363.5 40.71 40.99 686.64 |
40 |
|
42 |
1267.5 35.16 35.37 637.68 |
1366.8 40.91 41.19 68833 |
42 |
|
44 |
1270.8 35.34 35.56 639.37 |
1370.1 41.11 41.40 690.02 |
44 |
|
46 |
1274.1 35.53 35.75 641.05 |
1373.4 41.31 41.60 691.70 |
46 |
|
48 |
1277.4 35.71 35.94 642.74 |
1376.7 41.51 41.81 693.39 |
48 |
|
50 |
1280.7 35.90 36.13 644.43 |
1380.0 41.71 42.01 695.08 |
50 |
|
52 |
1284.0 36.09 36.31 646.12 |
1383.4 41.91 42.21 696.77 |
52 |
|
54 |
1287.4 36.27 36.50 647.81 |
1386.7 42.11 42.42 698.46 |
54 |
|
56 |
1290.7 36.46 36.69 649.49 |
1390.0 42.31 42.62 700.14 |
56 |
|
58 |
1294.0 36.64 36.88 651.18 |
1393.3 42.51 42.83 701.83 |
58 |
|
[60 |
1297.3 36.83 37.07 652.87 |
1396.6 42.71 43.03 703.53 |
60 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 135
|
14° |
15° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
1396.6 42.71 43.03 ?03.53 |
1495.9 49.02 49.44 754.85 |
0 |
|
2 |
1399.9 42.92 43.23 705.23 |
1499.2 49.24 49.66 756.05 |
2 |
|
4 |
1403.2 43.12 43.44 706.92 |
1502.5 49.46 49.89 757.74 |
4 |
|
6 |
1406.5 43.33 43.65 708.62 |
1505.8 49.68 50.11 759.44 |
6 |
|
8 |
1409.8 43.53 43.86 710.31 |
1509.1 49.90 50.34 761.13 |
8 |
|
10 |
1413.1 48.74 44.07 712.01 |
1512.4 50.12 50.56 762.88 |
10 |
|
12 |
1416.5 43.94 44.28 713.71 |
1515.7 50.34 50.78 764.53 |
12 |
|
14 |
1419.8 44.15 44.49 715.40 |
1519.0 50.56 51.01 766.22 |
14 |
|
16 |
1423.1 44.35 44.70 717.10 |
1522.3 50.78 51.23 767.92 |
16 |
|
18 |
1426.4 44.56 44.91 718.79 |
1525.6 51.00 51.46 769.61 |
18 |
|
20 |
1429.7 44.77 45.12 720.49 |
1528.9 51.22 51.68 771.31 |
20 |
|
22 |
1433.0 44.98 45.33 722.20 |
1532.2 51.44 51.90 773.01 |
22 |
|
24 |
1436.3 45.19 45.54 723.89 |
1535.5 51.67 52.13 774.70 |
24 |
|
26 |
1439.6 45.40 45.76 725.59 |
1538.8 51.89 52.36 776.40 |
26 |
|
28 |
1442.9 45.61 45.97 727.28 |
1542.1 52.12 52.59 778.09 |
28 |
|
30 |
1446.2 45.82 46.18 728.97 |
1545.4 52.34 52.82 779.79 |
30 |
|
32 |
1449.6 46.03 46.40 730.66 |
1548.7 52.57 53.05 781.49 |
32 |
|
34 |
1452.9 46.24 46.61 732.35 |
1552.0 52.79 53.28 783.19 |
34 |
|
36 |
1456.2 46.45 46.82 734.05 |
1555.3 53.02 53.51 784.89 |
36 |
|
38 |
1459.5 46.66 47.04 735.74 |
1558.6 53.24 53.74 786.59 |
38 |
|
40 |
1462.8 46.87 47.25 737.43 |
1561.9 53.47 53.97 788.29 |
40 |
|
42 |
146G.1 47.08 47.46 739.12 |
1505.2 53.69 54.20 789.99 |
42 |
|
44 |
1469.4 47.30 47.68 740.81 |
1568.5 53.92 54.44 791.69 |
44 |
|
46 |
1472.7 47.51 47.90 742.51 |
1571.8 54.15 54.67 793.39 |
46 |
|
48 |
1476. 0 47.73 48.12 744.20 |
1575.1 54.38 54.91 795.09 |
48 |
|
50 |
1479.3 47.94 48.34 745.89 |
1578.4 54.61 55.14 796.79 |
50 |
|
52 |
1482.7 48.16 48.56 747.58 |
1581.7 54.84 55.37 798.49 |
52 |
|
54 |
1486.0 48.37 48.78 749.27 |
1585.0 55.07 55 61 800.19 |
54 |
|
56 |
1489.3 48.59 49.00 750.97 |
1588.3 55.30 55.84 801.89 |
56 |
|
58 |
1492.6 48.80 49.22 752.66 |
1591.6 55.53 56.08 803.59 |
58 |
|
60 |
1495.9 49.02 49.44 754.35 |
1594.9 55.76 56.31 805.29 |
60 |
|
16° |
17° |
||
|
L C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
1594.9 55.76 56.31 805.29 |
1693.9 62.94 63.64 856.35 |
0 |
|
2 |
1598.2 55.99 56.54 806.99 |
1697.2 63.18 63.89 858.05 |
2 |
|
4 |
1601.5 56.23 56.78 808.64 |
1700.5 63.43 64.15 859.76 |
4 |
|
6 |
1604.8 56.46 57.02 810.39 |
1703.8 63.68 64.40 861.46 |
6 |
|
8 |
1608.1 56.70 57.26 812.09 |
1707.1 63.93 64.66 863.16 |
8 |
|
10 |
1611.4 56.93 57.50 813.79 |
1710.4 64.18 64.91 864.87 |
10 |
|
12 |
1614.7 57.17 57.74 815.49 |
1713.7 64.42 65.16 866.57 |
12 |
|
14 |
1618.0 57.40 57.98 817.19 |
1716.9 64.67 65.42 868.27 |
14 |
|
16 |
1621.3 57.64 58.22 818.89 |
1720.2 64.92 65.67 869.98 |
16 |
|
18 |
1624.6 57.87 58.46 820.59 |
1723.5 65.17 65.93 871.68 |
18 |
|
20 |
1627.9 58.11 58.70 822.29 |
1726.8 65.42 66.18 873.38 |
20 |
|
22 |
1631.2 58.34 58.94 823.99 |
1730.1 65.67 66.43 875.09 |
22 |
|
24 |
1634.5 58.58 59.19 825.69 |
1733.4 65.93 66.69 876.79 |
24 |
|
26 |
1637.8 58.82 59.43 827.39 |
1736.7 66.18 66.95 878.49 |
26 |
|
28 |
1641.1 59.06 59.68 829.09 |
1740.0 66.44 67.21 880.20 |
28 |
|
30 |
1644.4 59.30 59.92 830.79 |
1743.3 66.69 67.47 881.90 |
30 |
|
32 |
1647.7 59.54 60.16 832.49 |
1746.6 66.94 67.72 883.61 |
32 |
|
84 |
1651.0 59.78 60.41 834.20 |
1749.9 67.20 67.98 885.32 |
34 |
|
36 |
1654.3 60.02 60.65 835.90 |
1753.2 67.45 68.24 887.02 |
36 |
|
38 |
1657.6 60.26 60.90 837.61 |
1756.5 67.71 68.50 888.73 |
38 |
|
40 |
1660.9 60.50 61.14 839.31 |
1759.8 67.96 68.76 890.44 |
40 |
|
42 |
1664.2 60.74 61.39 841.01 |
1763.1 68.21 69.03 892.15 |
42 |
|
44 |
1667.5 60.99 61.64 842.72 |
1766.3 68.47 69.29 893.86 |
44 |
|
46 |
1670.8 61.23 61.89 844.42 |
1769.6 68.73 69.56 895.56 |
46 |
|
48 |
1674.1 61.48 62.14 846.13 |
1772.9 68.99 69.82 897.27 |
48 |
|
50 |
1677.4 61.72 62.39 847.83 |
1776 2 69.25 70.09 898.98 |
50 |
|
52 |
1680.7 61.96 62.64 849.53 |
1779.5 69.50 70.36 900.69 |
52 |
|
54 |
1684.0 62.21 62.89 851.24 |
1782.8 69.76 70.62 902.40 |
54 |
|
56 |
1687.3 62.45 63.14 852.94 |
1786.1 70.02 70.89 904.10 |
56 |
|
58 |
1690.6 62.70 63 39 854.65 |
1789.4 70.28 71.17 905.81 |
58 |
|
60 |
1693.0 62.94 63.64 856.35 |
1792.7 70.54 71.42 907.52 |
60 |
136 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
18° |
19° |
||
|
/ |
L. C. M. E. T. |
L. C. M. E. T. |
|
|
0 |
1792.7 70.54 71.42 907.52 |
1891.5 78.58 79.65 958.86 |
0 |
|
2 |
1796.0 70.80 71.69 909.23 |
1894.8 78.86 79.94 960.57 |
2 |
|
4 |
1799.3 71.06 71.96 910.94 |
1898.1 79.13 80.22 962.30 |
4 |
|
6 |
1802.6 71.33 72.23 912.65 |
1901.3 79.41 80.51 964.00 |
6 |
|
8 |
1805.9 71.59 72.50 914.36 |
1904.6 79.68 80.79 965.72 |
8 |
|
10 |
1809.2 71.85 72.77 916.07 |
1907.9 79.96 81.08 967.43 |
10 |
|
12 |
1812.5 72.12 73.04 917.78 |
1911.2 80.24 81.37 969.15 |
12 |
|
14 |
1815.7 72.38 73.31 919.49 |
1914.5 80.51 81.65 970.86 |
14 |
|
16 |
1819.0 72.64 73.58 921.20 |
1917.8 80.79 81.94 972.58 |
16 |
|
18 |
1822.3 72 91 73.85 922.91 |
1921.0 81.07 82.22 974.29 |
18 |
|
20 |
1825.6 73.17 74.12 924.63 |
1924.3 81.35 82.51 976.01 |
20 |
|
22 |
1828.9 73.43 74.39 926.34 |
1927.6 81.63 82.80 977.72 |
22 |
|
24 |
1832 2 73.70 74.67 928.05 |
1930.9 81.91 83.09 979.44 |
24 |
|
26 |
1835.5 73.97 74.94 929.76 |
1934.2 82.20 8338 981.15 |
26 |
|
28 |
1838.8 74.24 75.22 931.47 |
1937.5 82.48 83.67 982.86 |
28 |
|
30 |
1842.1 74.51 75.49 933.18 |
1940.7 82.76 83.97 984.58 |
30 |
|
32 |
1845.4 74.77 75.77 934.89 |
1944.0 83.05 84.26 986.30 |
32 |
|
34 |
1848.7 75.04 76.04 936.60 |
1947.3 83.33 84.55 988.02 |
34 |
|
36 |
1852.0 75.31 76.32 938.32 |
1950.6 83.61 84.84 989.74 |
36 |
|
38 |
1855.3 75.58 76.59 940.03 |
1953.9 83.90 85.13 991.46 |
38 |
|
40 |
1858.6 75.85 76.87 941.74 |
1957.2 84.18 85.43 993.18 |
40 |
|
42 |
1861.9 76.12 77.14 943.45 |
19604 84.47 85.73 994.90 |
42 |
|
44 |
1865.1 76.39 77.42 945.16 |
1903.7 84.75 80.02 996.62 |
44 |
|
46 |
1868.4 76.67 77.70 946.88 |
1967.0 85.04 86 32 998.34 |
46 |
|
48 |
1871.7 76.94 77.98 948.59 |
1970.3 85.32 86.61 1000.0 |
48 |
|
50 |
1875.0 77.21 78.26 950.30 |
1973.6 85.61 86.91 1001.8 |
50 |
|
52 |
1878.3 77.49 78.53 952.01 |
1976.9 85.90 87.21 1003.5 |
52 |
|
54 |
1881.6 77.76 78.81 953.72 |
1980.1 86.19 87.50 1005.2 |
54 |
|
50 |
1884.9 78.03 79.09 955.44 |
1983.4 86.47 87.80 1006.9 |
56 |
|
58 |
1888.2 78.31 79.37 957.15 |
19S6.7 86.76 88.09 1008.6 |
58 |
|
60 |
1891.5 78.58 79. (',5 958 86 |
1990.0 87.05 88.39 1010.4 |
60 |
|
20° |
21° |
||
|
L. C. M. E. T. |
L, C. M. E. T. |
/ |
|
|
0 |
1990.0 87.05 88.39 1010.4 |
2088.5 95.95 97.58 1062.0 |
0 |
|
2 |
1993.3 87.34 88.69 1012.1 |
2091.8 96.26 97.90 1063.7 |
2 |
|
4 |
1996.6 87. G3 88.99 1013.8 |
2095.0 96.56 98.21 1065.4 |
4 |
|
6 |
1999.8 87.92 89.29 1015.5 |
2098.3 96.87 98.53 1067.2 |
6 |
|
8 |
£003.1 88.21 89.59 1017.2 |
2101.6 97.17 98.84 1068.9 |
8 |
|
10 |
2006.4 88.50 89.89 1019.0 |
2104.9 97.48 99.16 1070.6 |
10 |
|
12 |
2009.7 88.79 90.19 1020.7 |
2108.1 97.79 99.48 1072.4 |
12 |
|
14 |
2013.0 89.08 90.49 1022 4 |
2111.4 98.09 99.79 1074.1 |
14 |
|
16 |
2016 3 89.37 90.79 1024.1 |
2114.7 98.40 100.1 1075.8 |
16 |
|
18 |
2019.5 89.66 91.09 1025.8 |
2118.0 98.70 100.4 1077.5 |
18 |
|
20 |
2022.8 89.96 91.40 1027.6 |
2121.2 99.00 J00.7 1079.3 |
20 |
|
22 |
2G26.1 90.25 91.71 1029.3 |
2124.5 99.30 J01.1 1081.0 |
22 |
|
24 |
2029-4 90.55 92.01 1031.0 |
2127.8 99.60 J01.4 1082.7 |
24 |
|
26 |
2032.7 90.85 92.32 1032.7 |
2131.0 99.90 101.7 1084.4 |
26 |
|
28 |
2036.0 91.15 92. G2 1034.4 |
2134.3 100.2 102.0 1086.2 |
28 |
|
30 |
2039.2 91.45 92.93 1036 1 |
2137.6 100.5 102.3 1087.9 |
30 |
|
32 |
2042.5 91.74 93.24 1037.9 |
2140.9 100.8 102.7 1089.6 |
32 |
|
34 |
2045.8 92.04 93.54 1039.6 |
2144.1 101.1 1030 1091.3 |
34 |
|
36 |
2049.1 92.34 93.85 1041.3 |
2147.4 101.4 103.3 1093.1 |
36 |
|
38 |
2052.4 92.64 94.15 1043.0 |
2150.7 101.7 103.6 1094.8 |
88 |
|
40 |
2055.7 92.94 94.46 1044.8 |
2154.0 102.1 104.0 1096.5 |
40 |
|
42 |
2058.9 93.24 94.78 1046.5 |
2157.2 102.4 104.3 1098.3 |
42 |
|
44 |
2062.2 93.54 95.09 1048.2 |
2160.5 102.7 104.6 1100.0 |
44 |
|
46 |
2065.5 93.84 95.40 1049.9 |
2163.8 103.0 104.9 1101.7 |
46 |
|
48 |
2068.8 94.14 95.71 1051.7 |
2167.1 103.3 105.3 1103.4 |
48 |
|
50 |
2072.1 94.44 96.03 1053.4 |
2170.3 103.6 105.6 1105.2 |
50 |
|
52 |
2075.4 94.74 96.34 1055.1 |
2173.6 103.9 105.9 1106.9 |
52 |
|
54 |
2078.6 95.04 96.65 1056.8 |
2176.9 104.2 106.3 1108.6 |
54 |
|
56 |
2081.9 95.34 96 96 1058.6 |
2180.1 104.5 106.6 1110.3 |
56 |
|
58 |
2085.2 95.64 97 27 10G0.3 |
2183.4 104.8 106.9 1112.1 |
58 |
|
60 |
2088.5 95.95 97.58 1062.0 |
2186.7 105.2 107.2 1118.8 |
60 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 137
|
22° |
23° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
2186.7 103.2 107.2 1113.8 |
2284.8 115.0 117.4 1165.8 |
0 |
|
2 |
2190.0 105.6 107.6 1115.5 |
2288.1 115.3 117.7 1167.5 |
2 |
|
4 |
2193.2 105.9 107.9 1117.3 |
2291.3 115.-7 118.1 1169.2 |
4 |
|
6 |
2196.5 106.2 108.2 1119.0 |
2294.6 116.0 118.4 1171.0 |
6 |
|
8 |
2199.8 106.5 108.6 1120.7 |
2297.8 116.4 118.8 1172.7 |
8 |
|
10 |
2203.0 106.8 108.9 1122.4 |
2301.1 116.7 119.1 1174.4 |
10 |
|
12 |
2206.3 107.1 109.2 1124.2 |
2304.4 117.0 119.5 1176.2 |
12 |
|
14 |
2209.6 107.4 109.6 1125.9 |
2307.6 117.4 119.8 1177.9 |
14 |
|
16 |
2212.9 107.7 109.9 1127.6 |
2310.9 117.7 120.2 1179.7 |
16 |
|
18 |
2216.1 108.0 110.2 1129.4 |
2314.1 118.1 120.5 1181.4 |
18 |
|
20 |
2219.4 108.4 110.6 1131.1 |
2317.4 118.4 120.9 1183.1 |
20 |
|
22 |
2222.7 108.7 110.9 1132.8 |
2320.7 118.7 121.2 1184.9 |
22 |
|
24 |
2-225.9 109.0 111.2 1134.6 |
2323.9 119.1 121 6 1186.6 |
24 |
|
26 |
2229.2 109.4 111.6 1136.3 |
2327.2 119.4 121.9 1188.4 |
26 |
|
28 |
2232.5 109.7 111.9 1138.0 |
2330.4 119.8 122.3 1190.1 |
28 |
|
30 |
2235.7 110.0 112.3 1139.7 |
2333.7 120.1 122.6 1191.8 |
30 |
|
32 |
2239.0 110.4 112.6 1141.5 |
2337.0 120.4 123.0 1193.6 |
32 |
|
34 |
2242.3 110.7 112.9 1143.2 |
2340.2 120.8 123.3 1195.3 |
34 |
|
36 |
2245.6 111.0 113.3 1144.9 |
2343.5 121.1 123.7 1197.1 |
36 |
|
38 |
2248.8 111.4 113.6 1146.7 |
2346.7 121.5 124.1 1198.8 |
38 |
|
40 |
2252.1 111.7 113.9 1148.4 |
23500 121.8 124.4 1200.5 |
40 |
|
42 |
2255.4 112.0 114.3 1150.1 |
2353.3 122.1 124.8 1202.3 |
42 |
|
44 |
2258.6 112.3 114.6 1151.9 |
2356.5 122.5 125.1 1204.0 |
44 |
|
46 |
2261.9 112.7 115.0 1153.6 |
2359.8 122.8 125.5 1205.8 |
46 |
|
48 |
2265.2 113.0 115.3 1155.4 |
2303.0 123.2 125.8 1207.5 |
48 |
|
50 |
2268.4 113.3 115.7 1157.1 |
2306.3 123.5 126.2 1209.2 |
50 |
|
52 |
2271.7 113.7 116.0 1158.8 |
2369.6 123.8 126.6 1211.0 |
52 |
|
54 |
2275.0 114.0 116.3 1160.6 |
2372.8 124.2 126.9 1212.7 |
54 |
|
56 |
2278.3 114.3 116.7 1162.3 |
2376.1 124.5 127.3 1214.5 |
56 |
|
58 |
2281.5 114.7 117.0 1164.0 |
2379.3 124.9 127.6 1216.2 |
58 |
|
60 |
2284.8 115.0 117.4 1165.8 |
2382.6 125.2 128.0 1218.0 |
60 |
|
24° |
25° |
||
|
/ |
L. 0. M. E. T. |
L C. M. E. T. |
|
|
0 |
23S2.6 125.2 128.0 1218.0 |
2480.4 135.8 139.1 1270.3 |
0 |
|
2 |
2385.9 125.5 128.4 1219.7 |
2483.6 186.2 139.5 1272.0 |
2 |
|
4 |
2389.1 125.9 128.7 1221.4 |
2486.9 136.5 139.9 1273.8 |
4 |
|
6 |
2392.4 126.2 129.1 1223.2 |
2400.1 136.9 140.3 1275.5 |
6 |
|
8 |
2395.6 126.6 129.5 1224.9 |
2493.4 137.2 140.6 1277.3 |
8 |
|
10 |
2398.9 126.9 129.8 1226.7 |
2496.6 137.6 141.0 1279.0 |
10 |
|
12 |
2402.2 127.3 130.2 1228.4 |
2499.9 138.0 141.4 1280.8 |
12 |
|
14 |
2405.4 127.6 130.6 1230.2 |
2503.1 138.3 141.8 1282.5 |
14 |
|
Ifl |
2408.7 128.0 130.9 1231.9 |
2506.4 138.7 142.2 1284.3 |
16 |
|
18 |
2411.9 128.3 131.3 1233/6 |
2509.6 139.0 142.5 1286.1 |
18 |
|
20 |
2415.2 128.7 131.7 1235.4 |
2512.9 139.4 142.9 1287.8 |
20 |
|
22 |
2418.5 129.0 132.0 1237.1 |
2516.1 139.8 143.3 1289.6 |
22 |
|
24 |
2421.7 129.4 132.4 123S.9 |
2519.4 140.1 143.7 1291.3 |
24 |
|
26 |
2425.0 129.7 132.8 1240.6 |
2522.6 140.5 144.1 1293.1 |
26 |
|
28 |
2428.2 130.1 133.1 1242.4 |
2525.9 140.8 144.5 1294.8 |
28 |
|
30 |
2431.5 130.4 133.5 1244.1 |
2529.1 141.2 144.9 1296.6 |
30 |
|
32 |
2434.8 130.8 133.9 1215.8 |
2532.4 141.6 145.3 1298.3 |
32 |
|
34 |
2433.0 131.1 134.2 1247.6 |
2535.6 142.0 145.6 1300.1 |
34 |
|
36 |
2441.3 131.5 134.8 1249. 3 |
2538.9 142.3 146.0 1301.8 |
36 |
|
38 |
2444.5 131.8 135.0 1251.1 |
2542.1 142.7 146.4 1303.6 |
38 |
|
40 |
2447.8 132.2 135.4 1252.8 |
2545.4 143.1 146 8 1305.3 |
40 |
|
42 |
2451.1 132.6 135.7 1254.6 |
2548. d 143.5 147.2 1307.1 |
42 |
|
44 |
2454.3 132.9 136.1 1256.3 |
2551.9 143.8 147.6 1308.8 |
44 |
|
46 |
2457.6 133.3 136.5 1258.1 |
2555.1 144.2 148.0 1310.6 |
46 |
|
48 |
2460. S 133.6 136.9 1259.8 |
2558.4 144.5 148.4 1312.4 |
48 |
|
50 |
2464.1 134.0 137.2 1261.5 |
2561.6 144.9 148.8 1314.1 |
50 |
|
52 |
2467.4 134.4 137.6 1263.3 |
2564.9 145.3 149.2 1315.9 |
52 |
|
54 |
2470.6 134.7 138.0 1265.0 |
2568.1 145.7 149.5 1317.6 |
54 |
|
56 |
2473.9 135.1 138.4 1266.8 |
2571.4 146.0 149.9 1319.4 |
56 |
|
58 |
2477.1 135.4 138.7 1263.5 |
2574.6 146.4 150.3 1321.1 |
58 |
|
60 |
2480.4 135.8 139.1 1270.3 |
2577.9 1468 150.7 1322.9 |
60 |
138 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
26° |
27* |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
I |
|
|
0 |
2577.9 146.8 150.7 1322.9 |
2675.3 158.3 162.8 1375.6 |
0 |
|
2 |
2581.1 147.1 151.1 1324.6 |
2678.5 158.6 163.2 1377.4 |
2 |
|
4 |
2584.4 147.5 151.5 1326.4 |
2681.8 159.0 163.7 1379.2 |
4 |
|
6 |
2587.6 147.9 151.9 1328.1 |
2685.0 159.4 164.1 1380.9 |
6 |
|
8 |
2590.9 148.3 152.3 1329.9 |
2688.2 159.8 164.5 1882.7 |
8 |
|
10 |
2594.1 148.7 152.7 1331.6 |
2691.5 160.2 164.9 1384.5 |
10 |
|
12 |
2597.4 149.1 153.1 1333.4 |
2694.7 160.6 165.3 1386.2 |
12 |
|
14 |
2600.6 149.4 153.5 1335.2 |
2698.0 161.0 165.7 1388.0 |
14 |
|
16 |
2603.9 149.8 153.9 1336.9 |
2701.2 161.4 166.1 1389.8 |
16 |
|
18 |
2607.1 1502 154.3 1338.7 |
2704.4 161.8 166.5 1391.5 |
18 |
|
20 |
2610.4 1506 154.7 1340.4 |
2707.7 162.2 167.0 1393.3 |
20 |
|
22 |
2613.6 151 0 155.1 1342.2 |
2710.9 162.6 167.4 1395.0 |
22 |
|
24 |
2616.9 151.4 155.5 1343.9 |
2714.1 163.0 167.8 1396.8 |
24 |
|
26 |
2620.1 151.7 155.9 1345.7 |
2717.4 163.4 168.2 1398.6 |
26 |
|
28 |
2623.4 152.1 156.3 1347.4 |
2720.6 168.8 168.6 1400.3 |
28 |
|
30 |
2626.6 152.5 156.7 1349.2 |
2723.8 164.2 169.1 1402.1 |
30 |
|
32 |
2629.8 152.9 157.1 1351.0 |
2727.1 164.6 169.5 1403.9 |
32 |
|
34 |
2633.1 153.3 157.5 1352.7 |
2730.3 165.0 169.9 1405.6 |
34 |
|
36 |
2636.3 153.7 157.9 1354 5 |
2733.6 165.4 170.3 1407.4 |
36 |
|
38 |
2639.6 154.0 158.3 1356.2 |
2736.8 165.8 170.8 1409.2 |
38 |
|
40 |
2642.8 154.4 158.7 1358.0 |
2740.0 166.2 171.2 1410.9 |
40 |
|
42 |
2646.1 154.8 159.1 1359.8 |
2743.3 166.6 171.6 1412.7 |
42 |
|
44 |
2649.3 155.2 159.5 1361.5 |
2746.5 167.0 172.0 1414.5 |
44 |
|
46 |
2652.6 155.6 160.0 1363.3 |
2749.7 167.4 172.5 1416.3 |
46 |
|
48 |
2655.8 156.0 160.4 1365.1 |
2753.0 167.8 172.9 1418.0 |
48 |
|
50 |
2659.1 156.3 160.8 1366.8 |
2756.2 168.2 173.3 1419.8 |
50 |
|
52 |
2662.3 156.7 161.2 1368.6 |
2759.5 168.6 173.7 1421.6 |
52 |
|
54 |
2665.6 157.1 161.6 13~0.4 |
2762.7 169.0 174.1 1423.3 |
54 |
|
56 |
2668.8 1575 162.0 13~2.1 |
2765.9 169.4 174.6 1425.1 |
56 |
|
58 |
2672.1 157.9 162.4 1373.9 |
2769.2 169.8 175.0 1426.9 |
58 |
|
60 |
2675.3 158.3 162.8 1375.6 |
2772.4 170.2 175.4 1428.6 |
60 |
|
28° |
29° |
1 |
|
|
/ |
L. C. M. E. T. |
L. C. M. E. T. |
|
|
0 |
2772.4 170.2 175.4 1128.6 |
2869.4 182.5 188.5 1481.9 |
0 |
|
2 |
2775.6 170.6 75.8 1430.4 |
2872.6 182.9 189.0 1483.7 |
2 |
|
4 |
2778.9 171.0 76.3 1432.2 |
2875.8 183 3 189.4 1485.4 |
4 |
|
6 |
2782.1 171.4 76.7 1434.0 |
2879.1 183.7 189.9 1487.2 |
6 |
|
8 |
2785.3 171.8 77.1 1435.7 |
2882.3 18^.2 190.3 1489.0 |
8 |
|
10 |
2788.6 172.2 77.6 1437.5 |
2885.5 184.6 190.8 1490.8 |
10 |
|
12 |
2791.8 172.6 78.0 1439.3 |
2888.7 185.0 191.2 1492.6 |
12 |
|
14 |
2795.0 173.0 78.4 1441.1 |
2892.0 185.4 191.7 1494.3 |
14 |
|
16 |
2798.3 173.4 78.9 1442.8 |
2895.2 185.8 192.1 1496.1 |
16 |
|
18 |
2801.5 173.8 79.3 1444.6 |
2898.4 186.3 192.5 1497.9 |
18 |
|
20 |
2804.7 74.3 179.7 1446.4 |
2901.6 186.7 193.0 1499.7 |
20 |
|
22 |
2808.0 74.7 180.2 1448.2 |
2904.8 187.1 193.5 1501.5 |
22 |
|
24 |
2811.2 75.1 180.6 1449.9 |
2908.1 187.5 193.9 1503.2 |
24 |
|
26 |
2814.4 75.5 181.0 1451.7 |
2911.3 188.0 194.4 1505.0 |
26 |
|
28 |
2817.7 75.9 181.5 1453.5 |
2914.5 188.4 194.8 1506.8 |
28 |
|
30 |
2820.9 76.3 181.9 1455.2 |
2917.7 188.8 195.3 1508-6 |
30 |
|
32 |
2824.1 176.7 182.3 1457.0 |
2921.0 189.2 195.7 1510.4 |
32 |
|
34 |
2827.4 177.1 182.8 1458.8 |
2924.2 189.7 196.2 1512.1 |
34 |
|
36 |
2830.6 177.5 183.2 1460.6 |
2927.4 190.1 196.7 1513.9 |
36 |
|
38 |
2833.8 177.9 J83.6 1462.3 |
2930.6 190.5 197.1 1515.7 |
38 |
|
40 |
2837.1 178.4 184.1 1464.1 |
2933.9 190.9 197.6 1517.5 |
40 |
|
42 |
2840 3 178.8 184.5 1465. 9 |
2937.1 191.4 198.0 1519.3 |
42 |
|
44 |
28435 179.2 185.0 H67.7 |
2940.3 191.9 198.5 1521.0 |
44 |
|
46 |
2846.8 179.6 185.4 1469.5 |
2943.5 192.4 198.9 1522.8 |
46 |
|
48 |
2850.0 1800 185.9 1471.2 |
2946.8 192.8 199.4 1524.6 |
48 |
|
50 |
2853.2 180.4 186.3 1473.0 |
2950.0 193.2 199.8 1526.4 |
50 |
|
52 |
2856.5 180.8 186.8 1474.8 |
2953.2 193.6 200.3 1528.2 |
52 |
|
54 |
2859.7 181.2 187.2 1476.6 |
2956.4 194.0 200.8 1530.0 |
54 |
|
56 |
2862.9 181.6 187.6 1478.3 |
2959.6 194.4 201.2 1531.7 |
56 |
|
58 |
2866.2 182.0 183.1 1480.1 |
2962.9 194.8 201.7 1533.5 |
58 |
|
60 |
2869.4 182 5 188.5 1481.9 |
2966.1 195.2 202.1 1535 3 |
60 1 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 139
|
30° |
31° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
2966.1 195.2 202.1 1535.3 |
3062.6 208.4 216 3 1589.0 |
0 |
|
2 |
2969.3 195.6 202.6 1537.1 |
3065.8 208.8 216.8 1590.8 |
2 |
|
4 |
2972.5 196.1 203.1 1538.9 |
3069.0 209.3 217 2 1592.6 |
4 |
|
6 |
2975.7 196.5 203.5 1540.7 |
3072.2 209.7 217.7 1594.4 |
6 |
|
8 |
2979.0 197.0 204.0 1542.5 |
3075.4 210.2 218.2 1596.2 |
8 |
|
10 |
2982.2 197.4 204.5 1544 3 |
3078.6 210.6 218.7 1598.0 |
10 |
|
12 |
2985.4 197.8 204.9 1546.0 |
3081.8 211.1 219.2 1599.8 |
12 |
|
14 |
2988.6 198.2 205.4 1547.8 |
3085.0 211.5 219.6 1601.6 |
14 |
|
16 |
2991.8 198.6 2059 1549.6 |
3088.3 212.0 220.1 1603.4 |
16 |
|
18 |
29950 199.1 2063 1551.4 |
3091.5 212.4 220.6 1605.2 |
18 |
|
20 |
2998.3 199 5 206.8 1553.2 |
3094.7 212.9 221 1 1607.0 |
20 |
|
22 |
3001.5 199.9 207.3 1555.0 |
3097.9 213.3 221.6 1608.8 |
22 |
|
24 |
3004.7 200.4 207.7 1556.8 |
3101.1 213.8 222.1 1610.6 |
24 |
|
26 |
3007.9 200.8 208.2 1558.6 |
3104.3 214.2 222.6 1612.4 |
26 |
|
28 |
3011 1 201.3 208.7 1560.4 |
3107.5 214.7 223.0 1614.2 |
28 |
|
30 |
3014.3 201.7 209.1 1562.2 |
3110.7 215.1 223.5 1616.0 |
30 |
|
32 |
30176 2021 209.6 1564.0 |
3113.9 215.6 224.0 1617.8 |
32 |
|
34 |
3020.8 202 6 210 1 1565.7 |
3117.1 216.0 224.5 1619.6 |
34 |
|
36 |
3024.0 203.0 210.5 1567.5 |
3120.3 216.5 225.0 1621.4 |
36 |
|
38 |
3027.2 203.5 211.0 1569.3 |
3123.5 216.9 225.5 1623.2 |
33 |
|
40 |
3030.4 203.9 211 5 1571.1 |
3126.7 217.4 226.0 1625.0 |
40 |
|
42 |
3033.6 204.3 212 0 1572.9 |
3129.9 217.8 226.5 1626.8 |
42 |
|
44 |
3036.9 204.8 212.4 1574.7 |
3133.1 218.3 227.0 1628.6 |
44 |
|
46 |
3040.1 205.2 212.9 1576.5 |
3136.4 218.7 227.5 1630.5 |
46 |
|
48 |
3043.3 205.7 213.4 1578.3 |
3139.6 219.2 228.0 1632.3 |
48 |
|
50 |
3046.5 206.1 213.9 1580.1 |
3142.8 219.6 228.4 1634.1 |
50 |
|
52 |
3049.7 206.5 214.4 1581.9 |
3146.0 220.1 228.9 1635.9 |
52 |
|
54 |
3052.9 207 0 214.8 1583.7 |
3149.2 220.5 229.4 1637.7 |
54 |
|
56 |
3056.2 207.4 215.3 1585.5 |
3152.4 221.0 2.9.9 1639.5 |
56 |
|
58 |
3059.4 207.9 215.8 1587.2 |
3155.6 221.5 230.4 1641.3 |
58 |
|
60 |
3062 6 208.4 216 3 1589.0 |
3158.8 222.0 230.9 1643.1 |
60 |
|
32° |
33° |
||
|
L. C. M. E. T. |
L. C M. E. T. |
/ |
|
|
0 |
3158.8 222.0 230.9 1643.1 |
3254.0 236.0 246.1 1697 3 |
0 |
|
2 |
3162.0 222 5 231.4 1644 9 |
3258.1 236.4 246.6 1699.1 |
2 |
|
4 |
3165.2 222.9 231.9 1646.7 |
3261.3 236.9 247.1 17009 |
4 |
|
6 |
3168.4 223.4 232.4 1648.5 |
3264.5 237.4 247.7 1702.7 |
6 |
|
8 |
3171.6 223.8 232.9 1650.3 |
3267 7 237.9 248.2 1704.5 |
8 |
|
10 |
3174.8 224.3 233.4 1652.1 |
3270.8 238.4 248.7 1706.4 |
10 |
|
12 |
3178.0 224 8 233.9 1653.9 |
3274 0 238.9 249.2 1708 .-2 |
12 |
|
14 |
3181.2 225.2 234.4 1655 7 |
3277.2 2393 249.7 1710.0 |
14 |
|
16 |
3184.4 225.7 234.9 1657.5 |
3280.4 239.8 250.2 1711.8 |
16 |
|
18 |
3187.6 226.1 235.4 1659.3 |
3283.6 240.3 250.8 1713.6 |
18 |
|
20 |
3190.8 226.6 2359 1661.1 |
3286.8 240.8 251.3 1715.5 |
20 |
|
22 |
3194.0 227.1 236.4 1662.9 |
3290 0 241.2 251.8 1717.3 |
22 |
|
24 |
3197 2 227.5 236 9 1664.7 |
3293.2 241.7 252.3 1719.1 |
24 |
|
26 |
3200.4 228.0 237.4 1666 5 |
3296.4 242.2 252.9 1720.9 |
26 |
|
28 |
3203.6 228.4 2379 1668.3 |
3299.6 242.7 253.4 1722.7 |
28 |
|
30 |
3206.8 228 9 238.4 1670.1 |
3302.7 243 2 253.9 1724.6 |
30 |
|
32 |
3210.0 229.4 239.0 1671.9 |
3305 9 243.6 254.4 1726.4 |
32 |
|
34 |
3213.2 229 8 239.5 1673 7 |
33091 244.1 255.0 1728.2 |
34 |
|
36 |
3216 5 230.3 240.0 1675.5 |
3312 3 244.6 255.5 1730.0 |
36 |
|
88 |
8219.7 230.7 240.5 1677.4 |
3315 5 245.1 256.0 1731.8 |
38 |
|
40 |
32229 231 2 241.0 1679.2 |
3318.7 245.6 256.5 1733.6 |
40 |
|
42 |
3226 1 231.7 241.5 1681.0 |
3321.9 246.0 257.1 1735.5 |
42 |
|
44 |
3629.3 232.2 242.0 1682 8 |
3325.1 246.5 257.6 1737.3 |
44 |
|
46 |
3232.5 232.6 242.5 1684.6 |
3328.3 247.0 258.1 1739.1 |
46 |
|
48 |
3235.7 233.1 243.0 16864 |
3331.5 247 5 258.6 1740.9 |
48 |
|
50 |
3238.9 233.5 243.5 16882 |
3334.6 248.0 259 2 1742.7 |
50 |
|
52 |
3242.1 234.0 244.1 1690.0 |
3337.8 248.4 259.7 1744.6 |
52 |
|
54 |
3245 3 234.5 244.6 1691.8 |
3341.0 248.9 2602 1746.4 |
54 |
|
66 |
3248.5 235 0 245.1 1693.7 |
3344.8 249.4 260.8 1748.2 |
56 |
|
58 |
3251.7 235.5 245.6 1695 5 |
3347.4 249.9 261.3 1750,0 |
53 |
|
60 |
3254.9 236.0 246 1 1697.3 |
3350-6 250.4 261 8 1751,8 |
An |
140 6.— FUNCTIONS OF A ONE-DEGREE CURVE
|
34° |
85° |
||
|
L. C. M. E. T. |
L. 0. M. E. T. |
, |
|
|
0 |
3350.6 250.4 261.8 1751.8 |
3446.1 265.2 278.1 1806.7 |
0 |
|
2 |
3353.8 250.8 262.3 1753.7 |
3449.3 265.7 278.6 1808.5 |
2 |
|
4 |
3357,0 251.2 262.9 1755.5 |
3452.5 266.2 279.2 1810.3 |
4 |
|
6 |
3360.1 251.7 263.4 1757.3 |
3455.6 266.7 279.7 1812.2 |
6 |
|
8 |
3363.3 252.2 2U4.0 1759.1 |
3458.8 267.2 280.3 1814.0 |
8 |
|
10 |
3366.5 252.7 264.5 1761.0 |
3462.0 267.7 280.8 1815.8 |
10 |
|
12 |
3369.7 253.2 265.0 1762.8 |
3465.2 268.2 281.4 1817.7 |
12 |
|
14 |
3372.9 253.7 265.6 1764.6 |
3468.3 268.7 281.9 1819.5 |
14 |
|
16 |
3376.1 254.2 266.1 1766.4 |
3471.5 269.2 282.5 1821.3 |
16 |
|
18 |
3379.2 254.7 266.7 1768.3 |
3474.7 269.7 283.0 1823.2 |
18 |
|
20' |
3382.4 255.2 267.2 1770.1 |
34V7.9 270.2 283.6 1825.0 |
20 |
|
22 |
3385.6 255.7 267.7 1771.9 |
3481.0 270.7 284.2 1820.8 |
22 |
|
24 |
3388.8 256.2 268.3 1773.7 |
3484.2 271.2 2S4.7 1828.7 |
24 |
|
26 |
3392.0 256.7 268.8 1775.6 |
3487.4 271.7 285.3 1830.5 |
26 |
|
28 |
3395.2 257.2 269.3 1777.4 |
3490.6 272.2 285.9 1832.3 |
28 |
|
30 |
3398.3 257.7 269.9 1779.2 |
3493.7 272.7 286.4 1834.2 |
30 |
|
83 |
3401.5 258.2 270.4 1781.0 |
3496.9 273.2 287.0 1830.0 |
32 |
|
34 |
3404.7 258.7 271.0 1782.9 |
3500.1 273. Y 287.5 1837.8 |
34 |
|
36 |
3407.9 2592 271.5 1784.7 |
3503.3 274.2 288.1 1839.7 |
8tf |
|
38 |
3411.1 259.7 272.0 1786.5 |
3506.5 274.7 288.7 1841.5 |
38 |
|
40 |
3414.3 260.2 272.6 1788.4 |
3509.6 275.2 289.2 1843.4 |
40 |
|
42 |
3417.4 260.7 273.1 1790.2 |
3512.8 275.7 289.8 1845.2 |
42 |
|
44 |
3420.6 261.2 273.7 1792.0 |
3516.0 276.2 290.4 1847.1 |
44 |
|
46 |
3423.8 261.7 274.2 1793.9 |
3519.2 -276.7 290.9 1848.9 |
46 |
|
48 |
3427.0 262.2 274.8 1795.7 |
3522.3 277.2 291.5 1850.7 |
48 |
|
50 |
3430.2 262.7 275.3 1797.5 |
3525.5 277.7 292.0 185;!. 6 |
50 |
|
52 |
3433.4 263.2 275.9 1799.3 |
3528.7 278.2 292.6 1854.4 |
52 |
|
54 |
3436.5 263.7 276.4 1801.2 |
3531.9 278.7 293.2 1856.3 |
54 |
|
56 |
3439.7 264.2 277.0 1803.0 |
3535.0 279.2 293.7 1858.1 |
56 |
|
58 |
3442.9 264.7 277.5 1804.8 |
3538.2 279.8 294.3 1859.9 |
58 |
|
00 |
3446 1 265.2 278.1 1806.7 |
3541.4 280.4 294.9 1801.8 |
60 |
|
36° |
37° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
3541.4 280.4 294.9 1861.8 |
3636.3 296.1 312.3 1917.3 |
0 |
|
2 |
3544.6 280 9 295.4 1863.6 |
3639.5 296.6 312.8 1919.1 |
2 |
|
4 |
3547.7 281.4 296.0 1865.5 |
3642 6 297 1 313.4 1921.0 |
4 |
|
6 |
3550.9 281.9 296.6 1867.3 |
3645.8 297.7 314.0 1922.8 |
6 |
|
8 |
3554.0 282. 5 297.2 3869.2 |
3648.9 298.2 314.6 1924.7 |
8 |
|
10 |
3557.2 2830 297.7 1871.0 |
3652.1 298.7 315.2 1926.5 |
10 |
|
12 |
3560.4 283.5 298.3 1872.9 |
3655.2 299.3 315.8 1928.4 |
12 |
|
14 |
3563 5 284.0 298.9 1874.7 |
3658.4 299.8 316.4 1930 2 |
14 |
|
16 |
3566.7 284.6 299.5 1876.5 |
3661.6 300.3 317.0 1932.1 |
16 |
|
18 |
3569.9 285.1 300.0 1878.4 |
3064.7 300.9 317.5 1933.9 |
18 |
|
20 |
3573.0 285.6 300.6 1880.2 |
3G67.9 301.4 318.1 1935.8 |
20 |
|
22 |
3576.2 286.1 301.2 1882.1 |
3671.0 301.9 318.7 1937.6 |
22 |
|
24 |
3579.4 286.7 301.8 1883.9 |
3674.2 302.5 319.3 1939.5 |
24 |
|
26 |
3582.5 2S7.2 302.3 1885.8 |
3677.3 303.0 319.9 1941.3 |
26 |
|
28 |
3585.7 287.7 302.9 1887.6 |
3680.5 303.5 320.5 1943.2 |
28 |
|
30 |
3588.8 288.2 303.5 1889.5 |
3683.6 304.1 321.1 1945.0 |
30 |
|
32 |
3592.0 288.8 304.1 1891.3 |
3686.8 304.6 321.7 1946.9 |
32 |
|
34 |
3595.2 289.3 304.6 1893.2 |
3690.0 305.1 322.3 1948.8 |
34 |
|
36 |
3598.3 289 8 305.2 1895.0 |
3693.1 305.7 322.9 1950.6 |
36 |
|
38 |
3601.5 290.3 305.8 1896.9 |
3696.3 306.2 323.5 1952.5 |
33 |
|
40 |
3604.7 290.9 306.4 1898.7 |
3699.4 306.7 324.2 1954.4 |
40 |
|
42 |
3607.8 291.4 307.0 1900.6 |
3702.6 307.3 324.8 1956.2 |
42 |
|
44 |
3611.0 291.9 307.5 1902.4 |
3705.7 307.8 325.4 1958.1 |
44 |
|
46 |
3614.1 292.4 308.1 1904.3 |
3708.9 308.3 326.0 1960.0 |
46 |
|
48 |
3617.3 293.0 308.7 1906.1 |
3712.1 308.9 326.6 1961.8 |
48 |
|
50 |
3620.5 293.5 309.3 1908.0 |
3715.2 309.4 327 2 1963.V |
50 |
|
52 |
3623 6 294.0 309.9 1909.8 |
3718.4 309.9 327.8 1965.5 |
52 |
|
54 |
3626.8 294.5 310.5 1911.7 |
37'21.5 310.5 328.4 1967.4 |
54 |
|
56 |
3630.0 295.1 311.1 1913.5 |
3724.7 311.0 329.0 1969.3 |
56 |
|
58 |
3633.1 295.6 311.7 1915.4 |
3727.8 311.6 329.6 1971.1 |
58 |
|
60 |
3636.3 296.1 312.3 1917.3 |
3731.0 312.2 330.2 1973.0 |
60 |
6. —FUNCTIONS OF A ONE-DEGREE CURVE. 141
|
38° |
39° |
||
|
L. C. M. E. T. |
L. G. M E. T. |
||
|
0 |
3731.0 312.2 330.2 19730 |
3825.5 328-7 348.7 2029.1 |
0 |
|
2 |
3734.1 312.7 330.8 1974.9 |
3828.6 329.2 349 3 2031.0 |
2 |
|
4 |
3737.3 313,3 331.4 1976-7 |
3831.8 329.8 349.9 20329 |
4 |
|
6 |
3740.4 313.8 332.0 1978-6 |
3834.9 330-3 350.8 2034.7 |
6 |
|
8 |
3743.6 314.4 332.6 1980.5 |
3838.0 330.9 351.2 2036.6 |
8 |
|
10 |
3746.7 314.9 333.2 1982.3 |
3841.2 331 5 351.8 2038.5 |
10 |
|
12 |
3749.9 315.5 333.8 1984.2 |
3844 3 332.0 352.4 2040 4 |
12 |
|
14 |
37530 3160 334-5 1986.1 |
3847.4 332.6 353.1 2042 3 |
14 |
|
16 |
37562 316.6 335.1 1987.9 |
3850.5 333.2 353.7 2044.1 |
16 |
|
18 |
3759.3 317.1 335 7 1989.8 |
3853 7 333 7 354.3 2046.0 |
18 |
|
20 |
3762 5 317 7 336 3 1991.7 |
3856.8 334.3 354.9 2047.9 |
20 |
|
22 |
3765.6 318 2 336.9 1993-6 |
3860 0 334.9 355.6 2049.8 |
22 |
|
24 |
3768 8 318.8 337.5 1995.4 |
3863.1 335.4 356.2 2051.7 |
24 |
|
26 |
3771.9 319.3 338.1 1997.3 |
3866.2 336-0 356.9 2053.5 |
26 |
|
28 |
3775.1 319.9 338.7 1999.2 |
3869.4 336.6 357 5 2055.4 |
28 |
|
30 |
3778.2 3204 339.4 2001.0 |
3872.5 337.1 358.1 2057-3 |
30 |
|
32 |
3781.4 321.0 340.0 2002.9 |
3875 6 337 7 358.8 2059.2 |
32 |
|
34 |
3784 5 321.5 340-6 2004.8 |
3878.8 338.3 359 4 2061.1 |
34 |
|
36 |
3787.7 322.1 341.2 2006.6 |
3881.9 338.8 360.1 2063.0 |
36 |
|
38 |
37308 322.6 341.8 2008.5 |
3885.0 339 4 360.7 2064.8 |
38 |
|
40 |
3794.0 3'.'3 2 342.4 2010 4 |
3888.2 340.0 361.3 2066.7 |
40 |
|
42 |
3797 1 323.7 343.1 2012.3 |
3891.3 340.5 362.0 2068 6 |
42 |
|
44 |
3800.3 3','4.3 343.7 2014.1 |
3894.4 341 1 362.6 20^0.5 |
44 |
|
46 |
3803.4 324.8 344.3 2016 0 |
3897.6 341.7 363.3 2072.4 |
46 |
|
48 |
3806.6 325.4 344.9 2017.9 |
3900 7 342 2 363.9 2074 2 |
48 |
|
50 |
3809.7 325 9 345.6 2019.7 |
3903.8 342.8 364.5 2076 1 |
50 |
|
52 |
3812.9. 326.5 346.2 2021.6 |
3907.0 343 4 365.2 2078.0 |
52 |
|
54 |
3816.0 327.0 346.8 2023.5 |
3910.1 343.9 365.8 2079 9 |
54 |
|
56 |
3819.2 3-27.6 347.4 2025 4 |
3913.2 344.5 366.5 2081.8 |
56 |
|
68 |
3822.3 323.1 3481 2027.2 |
3916.4 345 1 367.1 2083.7 |
58 |
|
60 |
3825.5 328.7 34S. 7 ' 2029.1 |
3919 5 345.6 3(57.7 2085-5 |
60 |
|
40° |
41° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
3919.5 345.6 367.7 2085.5 |
4013.4 3G2.9 387.4 2142.3 |
0 |
|
2 |
3922.6 346.1 368.4 2087.4 |
4016.5 C63.4 388.1 2144.2 |
2 |
|
4 |
3925.8 346 7 369 0 2089.3 |
4019.6 364.0 388.8 2146.1 |
4 |
|
6 |
3928.9 347.2 369.7 2091.2 |
4022.7 36J.5 389.4 2148.0 |
6 |
|
8 |
3932 0 347 8 370.3 20^3.1 |
4025.9 365.1 390.1 2149.9 |
8 |
|
10 |
3935.1 348.4 371.0 2095 0 |
4029.0 365.6 390.7 2151.9 |
10 |
|
12 |
3938.3 348.9 371 6 2096 9 |
4032.1 366.2 391.4 2158.8 |
12 |
|
14 |
3941.4 349.5 372.3 2098.8 |
4035.2 366. 8 302.1 2155.7 |
14 |
|
16 |
3944.5 350.1 372.9 2i00.7 |
4038.3 307.4 392.7 2157.6 |
16 |
|
18 |
3947.7 350.7 373.6 21026 |
4041.4 368.0 393.4 2159.5 |
18 |
|
20 |
3950.8 351.3 374.3 2104.5 |
4044.6 3G8.6 394.1 2161.4 |
20 |
|
22 |
3953.9 351 8 374.9 2106.3 |
4047.7 369.2 394.7 2163.3 |
22 |
|
24 |
3957.1 352.4 375.6 2108.2 |
4050.8 369.8 395.4 2165.2 |
24 |
|
26 |
3960.2 353.0 376.2 2110.1 |
4053.9 370.4 396.1 2167.1 |
26 |
|
28 |
3963.3 353 6 376.9 21120 |
4057.0 371.0 396.8 2169.0 |
28 |
|
30 |
3966.4 354.2 377.5 2113 9 |
4060.1 371.6 397.5 21709 |
30 |
|
32 |
3969.6 354.7 378.2 2115.8 |
4063.3 372.2 398.1 2172.8 |
32 |
|
34 |
3972.7 355.3 378.8 21177 |
4066.4 372.8 309.8 2174.7 |
34 |
|
81 |
3975.8 355.9 379.5 2119 6 |
4069.5 373.4 399.5 2176.6 |
36 |
|
38 |
3979.0 356.5 380 1 2121.5 |
4072.6 374.0 400.2 2178.5 |
38 |
|
40 |
3982.1 357.1 380.8 2123.4 |
4075.7 374.6 400.9 2180.4 |
40 |
|
42 |
3985.2 357 6 381.4 2125 3 |
4078.8 375.2 401.5 2182.4 |
42 |
|
44 |
3988.4 358.2 382.1 2127.2 |
4082.0 375.8 402.2 2184.8 |
44 |
|
46 |
3991 5 358 8 882.8 2129.1 |
4085.1 376.4 402.9 2186.2 |
46 |
|
48 |
3994.6 359.4 383.4 2131.0 |
4088.2 377.0 403.6 2188.1 |
48 |
|
50 |
3997 7 860 0 384.1 2132.9 |
4091.3 377.6 404.3 2190.0 |
50 |
|
52 |
4000 9 360 5 384,8 2134.7 |
4094.4 378.2 404.9 2191.9 |
52 |
|
54 |
4004.0 361 1 385.4 2136.6 |
4097.5 378.8 405.6 2193.8 |
54 |
|
56 |
40071 361.7 386.1 2138.5 |
4100.7 379.4 406.3 2195.7 |
56 |
|
58 |
4010.3 362.3 386 8 2140 4 |
4103.8 380.0 407.0 2197.6 |
58 |
|
60 |
4013 4 3t52.9 387.4 2142.3 |
4106.9 380.6 407.7 2199.5 |
60 |
142 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
42° |
43° |
||
|
/ |
L. C. M. E. T. |
L. C. M. E. T. |
/ |
|
0 |
4106.9 380.6 407.7 2199.5 |
4200.1 398.7 428.6 2257.1 |
0 |
|
2 |
4110.0 381.2 408.3 2201.4 |
4203.2 399.3 429.3 2259.0 |
2 |
|
4 |
4113.1 381.8 409.0 2203.3 |
4206.3 399.9 430.0 2261.0 |
4 |
|
6 |
4116.2 382.4 409.7 2205.3 |
4209.4 400.5 430.7 2262.9 |
6 |
|
8 |
4119.3 383.0 410.4 2207.2 |
4212.5 401.1 431.4 2264.8 |
8 |
|
10 |
4122.4 383.6 411.1 2209.1 |
4215.6 401.7 432.1 2266.7 |
10 |
|
12 |
4125.5 384.2 411.8 2211.0 |
4218.7 402.4 432.8 2268.7 |
12 |
|
14 |
4128.6 384.8 412.5 2212.9 |
4221.8 403.0 433.5 2270.6 |
14 |
|
16 |
4131.8 385 4 413.2 2214.9 |
4224.9 403.6 434.2 2272.5 |
16 |
|
18 |
4134.9 38b 0 413.9 2216.8 |
4228.0 404.2 434.9 2274.5 |
18 |
|
20 |
4138.0 386 3 414.6 2218.7 |
4231.1 404.8 435.6 2276.4 |
20 |
|
22 |
4141.1 387.2 415.3 2220.6 |
4234.2 405.4 430. 3 2278.3 |
22 |
|
24 |
4144.2 387.8 416.0 2222.5 |
4237.3 406.1 437.0 2280.2 |
24 |
|
26 |
4147 3 388.4 416.6 2224.4 |
4240.4 406.7 437.8 2282.2 |
26 |
|
28 |
4150.4 389.0 417.3 2226.4 |
4243.5 407.3 438.5 2284.1 |
28 |
|
30 |
4153.5 389.6 418.0 2228.3 |
4246.5 407.9 439.2 2286.0 |
30 |
|
32 |
4156.6 390.2 418.7 2230.2 |
4249.6 408.5 439.9 2288.0 |
32 |
|
34 |
4159.7 390.8 419.4 223?. 1 |
4252.7 409.1 440.6 2289.9 |
34 |
|
36 |
4162.8 391.4 420.1 2234.0 |
4255.8 409.8 441.4 2291.8 |
36 |
|
38 |
4165.9 392.0 420.8 2236.0 |
4258.9 410.4 442.1 2293.8 |
38 |
|
40 |
4169.0 392.6 421.5 2237.9 |
4262.0 411.0 442.8 2295.7 |
40 |
|
42 |
4172.1 393.2 422.2 2239.8 |
4265.1 411.6 443.5 2297.7 |
42 |
|
44 |
4175.2 393.8 422.9 2241.7 |
4268.2 412.2 444.2 2299.6 |
44 |
|
46 |
4178.4 394.4 423.6 2243.6 |
4271.3 412.8 445.0 2301.5 |
46 |
|
48 |
4181.5 395.0 424.3 2245.6 |
4274.4 413.5 445.7 2303.5 |
48 |
|
50 |
4184.6 395.6 425.0 2247.5 |
4277.5 414.1 446.4 2305.4 |
50 |
|
52 |
4187.7 396.2 425.7 2249.4 |
4280.6 414.7 447.1 2307.3 |
52 |
|
54 |
4190.8 396.8 426.4 2251.3 |
4283.7 415.3 447.8 2309.3 |
54 |
|
56 |
4193.9 397.4 427.1 2253.3 |
4286.8 415.9 448.6 2311.2 |
56 |
|
58 |
4197.0 398.0 427.8 2255.2 |
4289.9 416.5 449.3 2313.1 |
58 |
|
60 |
4200.1 398.7 428.6 2257.1 |
4293.0 417.2 450.0 2315.1 |
60 |
|
44° |
45° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
4293.0 417.2 450.0 2315.1 |
4385.5 436.2 472.1 2373.4 |
0 |
|
2 |
4296 1 417.8 450.7 2317.0 |
4388.6 436.8 472.9 2375.4 |
2 |
|
4 |
4299.2 418.4 451.5 2319.0 |
4391.7 437.5 473.6 2377.3 |
4 |
|
6 |
4302.2 419.1 452.2 2320.9 |
4394.7 438.1 474.4 2379.3 |
6 |
|
8 |
4305.3 419.7 4529 2322.8 |
4397.8 438.8 475.1 2381.2 |
8 |
|
10 |
4308.4 420.3 453.7 2324.8 |
4400.9 439.4 475.9 2383.2 |
10 |
|
12 |
4311.5 421.0 454.4 2326.7 |
4404.0 440.0 4766 2385.2 |
12 |
|
14 |
4314.6 421.6 455.1 2328.7 |
4407.0 440.7 477.4 2387.1 |
14 |
|
16 |
4317.7 422.2 455.9 2330.6 |
4410.1 441.3 478.1 2389.1 |
16 |
|
18 |
4320.7 422.9 456.6 2332.6 |
4413.2 442.0 478.9 2391.0 |
18 |
|
20 |
4323.8 423 5 457.3 2334.5 |
4416.3 442.6 479.6 2393.0 |
20 |
|
22 |
4326.9 424.1 458.1 2336.4 |
4419.3 443.2 480.4 2394.9 |
22 |
|
21 |
4330.0 424 8 458.8 2338.4 |
4422.4 443.9 481.1 2396.9 |
24 |
|
26 |
4333.1 425.4 459.5 23403 |
4425.5 444.5 481.9 2398.8 |
26 |
|
28 |
4336.2 426.0 460.3 2342.3 |
4428.6 445.2 482.6 2400.8 |
28 |
|
30 |
4339.2 426.7 461 0 2344.2 |
4431.6 445.8 483.4 2402.8 |
30 |
|
32 |
4342.3 427.3 461.7 2346.1 |
443*. 7 446.4 484.2 2404.7 |
32 |
|
34 |
4345.4 427 9 462.5 2348.1 |
4437.8 447.1 484.9 2406.7 |
34 |
|
36 |
4348.5 428 6 463.2 2350.0 |
4440.9 447.7 485.7 2408.6 |
36 |
|
38 |
4351.6 429.2 463.9 2352.0 |
4444.0 448.3 486.5 2410.6 |
3u |
|
40 |
4354.7 429.8 464.7 2353.9 |
4447.0 448.9 487.2 2412.6 |
40 |
|
42 |
4357.7 430.5 465.4 2355.9 |
4450.1 449.5 488.0 2414.5 |
42 |
|
44 |
4360.8 431.1 466.2 2357.8 |
4453.2 450.2 488.7 2416.5 |
44 |
|
46 |
4363.9 431.7 466.9 2359.8 |
4456.3 450.8 489.5 2418.5 |
46 |
|
48 |
4367.0 432.4 467.7 2361.7 |
4459.3 451.5 490. 3 2420.4 |
48 |
|
50 |
4370.1 433.0 4684 2363.7 |
4462.4 452.1 491.0 2422.4 |
50 |
|
52 |
4373.2 433.6 469.1 2365.6 |
4465.5 452.7 491.8 2424.4 |
52 |
|
54 |
43762 434.3 469.9 2367.6 |
4468.6 453.4 492.5 2426.3 |
54 |
|
56 |
43^9.3 434.9 470. 6 2369.5 |
4471.6 454.1 493.3 2428.3 |
56 |
|
5b |
4382.4 435.6 471.4 23^1.5 |
4474.7 454.8 494.1 2430.2 |
58 |
|
60 |
4385.5 436.2 472.1 2373.4 |
4477.8 455.5 494.8 2432.2 |
60 |
6 —FUNCTIONS OF A ONE-DEGREE CURVE. 143
|
46° |
47° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
/ |
|
|
0 |
4477.8 455.5 494.8 2432.2 |
4569.7 475.2 518.3 2491.5 |
"~0~ |
|
2 |
4480.9 456.1 495.6 2434.2 |
4572.7 475.9 519.0 2493.4 |
2 |
|
4 |
4483.9 456.8 496.5 2436.1 |
4575.8 476.5 519.8 2495.4 |
4 |
|
6 |
4487.0 457.4 497.2 2438.1 |
4578.8 477.2 520.6 2497.4 |
6 |
|
8 |
4490.0 458.1 497.9 2440.1 |
4581.9 477.8 521.4 2499.4 |
8 |
|
10 |
4493.1 458.7 498.7 2442.1 |
4584.9 478.5 522.2 2501.4 |
10 |
|
12 |
4496.2 459.4 499.5 2444.0 |
4588.0 479.2 523.0 2508.4 |
12 |
|
14 |
4499.2 460.0 500.3 2446.0 |
4591.0 479.8 523.8 2505.4 |
14 |
|
16 |
4502.3 460.7 501.0 2448.0 |
45P4.1 480.5 524.6 2507.8 |
16 |
|
18 |
4505.4 461.3 501.8 2449.9 |
4597.1 481.1 525.4 2509.8 |
18 |
|
20 |
4508.4 462.0 502.6 2451.9 |
4600.2 481.7 526.2 2511.3 |
20 |
|
22 |
4511.5 462.7 503.4 2453.9 |
4603.2 482.3 527.0 2513.3 |
22 |
|
24 |
4514.6 463.3 504.1 2455.9 |
4606.3 483.0 527.8 2515.3 |
24 |
|
26 |
4517.6 464.0 504.9 2457.8 |
4609.3 483.7 528.6 2517.3 |
26 |
|
28 |
4520.7 464.6 505.7 2459.8 |
4612.4 484.8 529.4 2519.3 |
28 |
|
80 |
4523.7 465.3 506.5 2461.8 |
4615.4 485.0 530.2 2521.2 |
30 |
|
32 |
4526.3 466.0 507.3 2463. S |
4618.5 485.7 531.0 2523.2 |
32 |
|
34 |
4529.9 466.6 508.0 2465.7 |
4621.5 486.3 531.8 2525.2 |
34 |
|
36 |
4532.9 467.3 508.8 2467.7 |
4624.6 487.0 532.6 2527.2 |
86 |
|
88 |
4536.0 467.9 509.6 2469.7 |
4627.6 487.7 533.4 2529.2 |
38 |
|
40 |
4539.1 468.6 510.4 2471.7 |
4630.7 488.4 534.2 2531.2 |
40 |
|
42 |
4542.1 469.3 511.1 2473.6 |
4633.7 489.1 535.0 2533.2 |
42 |
|
44 |
4545.2 469.9 511.9 2475.6 |
4G36.8 489.8 535.8 2535.2 |
44 |
|
46 |
4548.2 470.6 512.7 2477.6 |
4639.8 490.5 536.6 2537.2 |
46 |
|
48 |
4551.3 471.2 513.5 2479.6 |
4642.9 491.2 537.4 2539.2 |
48 |
|
50 |
4554.4 471.9 514.3 2481.6 |
4645.9 491.9 538.2 2541.2 |
50 |
|
52 |
4557.4 472.6 515.1 2483.5 |
4649.0 492.6 539.0 2543.1 |
52 |
|
54 |
4560.5 473.2 515.9 2485.5 |
4652.0 493.3 539.8 2545.1 |
54 |
|
56 |
4563.6' 473.9 516.7 2487.5 |
4655.1 494.0 540.6 2547.1 |
56 |
|
58 |
4566.6 474.5 517.5 2489.5 |
4658.1 494.7 541.4 2549.1 |
58 |
|
60 |
4569.7 475.2 518.3 2491.5 |
4661.2 495.4 542.3 2551.1 |
60 |
|
48° |
49° |
||
|
/ |
L. C. M. E. T. |
L. C. M. E. T. |
|
|
0 |
4661.2 495.4 542.3 2551.1 |
4752.3 515.9 567.0 2611.3 |
0 |
|
2 |
46C4.2 496.0 543.1 2553.1 |
4755.3 516.5 567.8 2613.3 |
2 |
|
4 |
4667.3 496.7 543.9 2555.1 |
4758.4 517.2 568.7 2615.3 |
4 |
|
6 |
4670.3 497.4 544.7 2557.1 |
4761.4 517.9 569.5 2617.3 |
6 |
|
8 |
4673.3 498.1 545.5 2559.1 |
4764.4 518.6 570.3 2619.3 |
8 |
|
10 |
4676.4 498.8 546.4 2561.1 |
4767.4 519.3 571.2 2621.4 |
10 |
|
12 |
4679.4 499.4 547.2 2563.1 |
4770.5 520.0 572.0 2623.4 |
12 |
|
14 |
4682.5 500.1 548.0 2565.1 |
4773.5 520.7 572.8 2625.4 |
14 |
|
16 |
4685.5 500.8 548.8 2567.1 |
4776.5 521.4 573.7 2627.4 |
16 |
|
18 |
4688.5 501.5 549.6 2569.1 |
4779.6 522.1 574.5 2629.4 |
18 |
|
20 |
4691.6 502.2 550.5 2571.1 |
4782.6 522.8 575.3 2631.4 |
20 |
|
22 |
4694.6 502.8 551.3 2573.1 |
4785.6 523.5 576.2 2633.5 |
22 |
|
24 |
4697.6 503.5 552.1 2575.1 |
4788.7 524.2 577.0 2635.5 |
24 |
|
26 |
4700.7 504.2 552.9 2577.1 |
4791.7 524.9 677.9 2637.5 |
26 |
|
28 |
4703.7 504.9 553.7 2579.1 |
4791.7 525.6 578.7 2639.5 |
28 |
|
30 |
4706.7 505.6 554.6 2581.1 |
4797.7 526.3 579.6 2641.5 |
30 |
|
32 |
4709.8 506.2 555.4 2583.1 |
4800.8 527.0 580.4 2643.5 |
32 |
|
34 |
4712.8 506.9 556.2 2585.1 |
4803.8 527.7 581.3 2645.6 |
34 |
|
36 |
4715.9 507.6 557.0 2587.2 |
4806.8 528.4 582.1 2647.6 |
36 |
|
38 |
4718.9 508.3 557.8 2589.2 |
4809.9 529.1 583.0 2649.6 |
38 |
|
40 |
4721.9 509.0 558.7 2591.2 |
4812.9 529.8 583.8 2651.6 |
40 |
|
42 |
47-25.0 509.6 559.5 2593.2 |
4815.9 530.5 584.7 2653.7 |
42 |
|
44 |
4728.0 510.3 560.3 2595.2 |
4819.0 531.2 585.5 2655.7 |
44 |
|
46 |
4731.0 511.0 561.2 2597.2 |
4822.0 531.9 586.4 2657.7 |
46 |
|
48 |
4734.1 511.7 562.0 2599.2 |
4825.0 532.6 587.2 2659.7 |
48 |
|
50 |
4737.1 512.4 562.8 2601.2 |
4828.0 533.3 588.1 2661.8 |
50 |
|
52 |
4740.2 513.1 563.7 2603.2 |
4881.1 534.0 588.9 2663.8 |
52 |
|
54 |
4743.2 513.8 564.5 2605.2 |
4834.1 534.7 589.8 2665.8 |
54 |
|
56 |
4746.2 514.5 565.3 2607.2 |
4837.1 535.4 590.6 2667.8 |
56 |
|
58 |
4749.3 515.2 566.2 2609.3 |
4840.2 536.1 591.5 2669.9 |
58 |
|
60 |
4752.3 515.9 567.0 2611.3 |
4843.2 586.8 592.4 2671.9 |
60 |
144 6. -FUNCTIONS OF A ONE-DEGREE CURVE.
|
60° |
61° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
/ |
|
|
0 |
4843.2 536.8 592.4 2671. 9 |
4933 6 558.2 618.5 2733.0 |
0 |
|
2 |
4846.2 537.5 593.2 2673 9 |
4936.6 558.9 619.3 2735.1 |
2 |
|
4 |
4849.2 538.2 594.1 2676.0 |
4939.6 559.7 620.2 2737.1 |
4 |
|
6 |
4852.2 538.9 594.9 2678.0 |
4942.6 560.4 621.1 2739.2 |
6 |
|
8 |
4855.2 539.6 595.8 2680.0 |
4945.6 561.1 622.0 2741.2 |
8 |
|
10 |
4858.3 540.3 596.7 2682.1 |
4948.6 561.8 622.9 2743.3 |
10 |
|
12 |
4861.3 541.0 597.5 2684. 1 |
41)51.6 562.5 623.7 2745.3 |
12 |
|
14 |
4864.3 541. V 598.4 2686.1 |
4954.6 563.3 624.6 2747.4 |
14 |
|
16 |
4867.3 542.4 599.3 2688.2 |
4957.6 584.0 625.5 2749.4 |
16 |
|
18 |
4870.3 543.1 600.1 2690.2 |
4960.6 564.7 626.4 2751.5 |
18 |
|
20 |
4873.3 543.9 601.0 2692.3 |
49G3.6 565.4 627.3 2753.5 |
20 |
|
22 |
4876.3 544.6 601.9 2694.3 |
4966.6 566.2 628.2 2755.6 |
22 |
|
24 |
4879.4 545.3 602.7 2696.3 |
4969.6 566.9 629.9 2757.7 |
24 |
|
26 |
4882.4 546.0 603.6 2698.4 |
4972.6 567.6 630.0 2759.7 |
26 |
|
28 |
4885.4 546.7 604.5 2700.4 |
4975.6 568.3 630.9 2761.8 |
28 |
|
30 |
4888.4 547.4 605.3 2702.4 |
4978.6 569.1 631.8 2763.8 |
30 |
|
32 |
4891.4 548.1 606.2 2704.5 |
4981.6 569.8 632.7 2765.9 |
32 |
|
34 |
4894.4 548.8 607.0 2706.5 |
4984.6 570.5 633.6 2767.9 |
34 |
|
36 |
4897.4 549.5 607.9 2708.6 |
4987.7 571.2 634.5 2770.0 |
36 |
|
38 |
4900.4 550.2 608.8 2710.6 |
4990.7 572.0 635.3 2772.0 |
38 |
|
40 |
4903.5 551.0 609.7 2712.6 |
4993.7 572.7 636.2 2774.1 |
40 |
|
42 |
4906.5 551.7 610.5 2714.7 |
4996.7 573.4 637.1 2776.2 |
42 |
|
44 |
4909.5 552.4 611.4 2716.7 |
4999.7 574.1 638.0 2778.2 |
44 |
|
46 |
4912.5 553.1 612.3 2718.8 |
5002.7 574.9 638.9 2780.3 |
46 |
|
48 |
4915.5 553.8 613.2 2720.8 |
5005.7 575.6 639.8 2782.3 |
48 |
|
50 |
4918.5 554.5 614.1 2722.8 |
5008.7 5T6.3 640.7 2784.4 |
50 |
|
52 |
4921.5 555.2 614.9 2724.9 |
5011.7 577.0 611.6 2786.4 |
52 |
|
54 |
4924.6 555.9 615.8 2726.9 |
5014.7 577.8 642.5 2788.5 |
54 |
|
56 |
4927.6 556.6 616.7 2729.0 |
5017.7 578.5 643.4 2790.6 |
56 |
|
58 |
4930.6 557.4 617.6 2731.0 |
5020.7 579.2 644.3 2792.6 |
58 |
|
60 |
4933.6 558.2 618.5 2733.0 |
5023.7 579.9 645.2 2794.7 |
60 |
|
52° |
53° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
5023.7 579.9 645.2 2794.7 |
5113.5 602.0 672.7 2856.9 |
0 |
|
2 |
5026.7 580.6 6J6.1 2796.8 |
5116.5 602.8 673.7 2858.9 |
2 |
|
4 |
5029.7 581.3 647.0 2798.8 |
5119.4 603.5 674.6 2861.0 |
4 |
|
6 |
5032.7 582.1 647.9 2800.9 |
5122.4 604.3 675.5 2863.1 |
6 |
|
8 |
5035.7 582.8 648.9 2803.0 |
5125.4 605.0 676.4 2865.2 |
8 |
|
10 |
5038.7 583.5 649.8 2805.0 |
5128.4 605.8 677.4 2867.3 |
10 |
|
12 |
5041.7 584.3 650.7 2807.1 |
5131.3 606.5 678.3 2869.4 |
12 |
|
14 |
5044.7 585.0 651.6 2809.2 |
5134.3 607.3 6r9.2 2871.5 |
14 |
|
16 |
5047.7 585.7 652.5 2811.2 |
5137.3 608.0 680.2 2873.5 |
16 |
|
18 |
5050.7 586.5 653.4 2813.3 |
5140.3 608.8 681.1 2875.6 |
18 |
|
20 |
5053.6 587.2 654.3 2815.4 |
5143.2 609.5 682.0 2877.7 |
20 |
|
23 |
5056.6 587.9 655.2 2817.4 |
5146.2 610.3 683.0 2879.8 |
22 |
|
24 |
5059.6 588.7 656.2 2819.5 |
5149.2 611.0 683.9 2881.9 |
24 |
|
26 |
5062.6 589.4 657.1 2821.6 |
5152.1 611.8 684.9 2884.0 |
26 |
|
28 |
5065.6 590.1 658.0 2823.6 |
5155.1 612.5 685.8 2886.1 |
28 |
|
30 |
5068.6 590.9 658.9 2825.7 |
5158.1 613.3 686.7 2888.1 |
30 |
|
32 |
5071.6 591.6 659.8 2827.8 |
5161.1 614.0 687.7 2890.2 |
32 |
|
34 |
5074.6 592.3 660.7 2829.8 |
5164.0 614.8 688.6 2892.3 |
34 |
|
36 |
5077.6 593.1 661,6 2831.9 |
5167.0 615.5 689.6 2894.4 |
36 |
|
' 38 |
5080.6 593.8 662.5 2834.0 |
5170.0 616.3 690.5 2896.5 |
38 |
|
40 |
5083.6 594.5 663.5 2836.1 |
5173.0 617.0 691.5 2898.6 |
40 |
|
42 |
5086.6 595.3 664.4 2838.2 |
5175.9 617.8 692.4 2900.7 |
42 |
|
44 |
5089.6 596.0 665.3 2840.2 |
5178.9 613.5 693.4 2902.8 |
44 |
|
46 |
5092.6 596.7 666.2 2842.3 |
5181.9 619.3 694.3 2904.9 |
46 |
|
48 |
5095.6 597.5 667.2 2844.4 |
5184.9 620.1 695.3 2907.0 |
48 |
|
50 |
5098.6 598.2 668.1 2846.5 |
5187.8 620.8 696.2 2909.1 |
50 |
|
52 |
5101.6 598.9 669.0 2848.5 |
5190.8 621.5 697.1 2911.2 |
52 |
|
54 |
5104.6 599.7 669.9 2850.6 |
5193.8 622.3 698.1 2913.3 |
54 |
|
56 |
5107.6 600.4 670.9 2852.7 |
5196.7 623.0 699.0 2915.4 |
56 |
|
58 |
5110.6 601.2 671.8 2854.8 |
5199.7 623.8 700.0 2917.5 |
58 |
|
60 |
5113.5 602.0 672.7 2856.9 |
5202.7 624.6 700.9 2919.5 |
60 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 145
|
64° |
65° |
||
|
L. C. M. E. T. |
L. C, M. E. T. |
||
|
0 |
5202.7 624.6 700.9 2919.5 |
5291.7 647.4 729.9 2982.8 |
0 |
|
2 |
5205.7 625.4 701.9 2921.6 |
5294.6 648.1 730.9 2984.9 |
2 |
|
4 |
5208.6 626.1 702.8 2923.8 |
5297.6 648.9 731.9 2987.1 |
4 |
|
6 |
5211.6 626.9 703.8 2925.9 |
5300.5 649.6 732.9 2989.2 |
6 |
|
8 |
5214.6 627.6 704.8 2928.0 |
5303.5 650.4 733.8 2991.3 |
8 |
|
10 |
5217.5 628.4 705.7 2930.1 |
5306.4 651.2 734.8 2993.4 |
10 |
|
12 |
5220.5 629.2 706.7 2932.2 |
5309.4 652.0 735.8 2995.5 |
12 |
|
14 |
5223.5 629.9 707.7 2934.3 |
5312.3 652.7 736.8 2997.7 |
14 |
|
16 |
5226.4 630.7 708.6 2936.4 |
5315.3 653.5 737.8 2999.8 |
16 |
|
18 |
5229.4 631.4 709.6 2938.5 |
5318.2 654.3 738. 7 3001.9 |
18 |
|
20 |
5232.4 632.2 710.5 2940.6 |
5321.2 655.1 739.7 3004.0 |
20 |
|
22 |
5235.3 633.0 711.5 2942.7 |
5324.1 655.8 740.7 3006.2 |
22 |
|
24 |
5238.3 633.7 712.5 2944.8 |
5327.1 656.6 741.7 3008.3 |
24 |
|
26 |
5241.3 634.5 713.4 2946.9 |
5330.0 657.4 742.7 3010.4 |
26 |
|
28 |
5244.2 635.2 714.4 2949.0 |
5333.0 658.2 743.7 3012.5 |
28 |
|
30 |
5247.2 636.0 715.3 2951.1 |
5335.9 658.9 744.7 3014.7 |
30 |
|
32 |
5250.2 636.8 716.3 2953.2 |
5338.8 659.7 745.7 3016.8 |
32 |
|
34 |
5253.1 637.5 717.3 2955.3 |
5341.8 660.5 746.7 3018.9 |
34 |
|
36 |
5256.1 638.3 718.2 2957.5 |
5344.7 661.3 747.7 3021.1 |
36 |
|
38 |
5259.1 639.0 719.2 2959.6 |
5347.7 662.0 748.7 3023.2 |
38 |
|
40 |
5262.0 639.8 720.2 2961.7 |
5350.6 662.8 749.7 3025.3 |
40 |
|
42 |
5265.0 640.6 721.1 2963.8 |
5353.6 663 6 750.7 3027.5 |
42 |
|
44 |
5268.0 641.3 722.1 2965.9 |
5356.5 664.4 751.7 3029.6 |
44 |
|
46 |
5270.9 642.1 723.1 2968.0 |
5359.5 665.1 752.6 3031.7 |
46 |
|
48 |
5273.9 642.8 724.1 2970.1 |
5362.4 665.9 753.6 3033.8 |
48 |
|
50 |
5276.9 643.6 725.0 2972.2 |
5365.4 666,7 754.6 3036.0 |
50 |
|
52 |
5279.8 644.4 726.0 2974.4 |
5368.3 667.5 755.6 3038.1 |
52 |
|
54 |
5282.8 645.1 727.0 2976.5 |
5371.3 668.3 756.6 3040.2 |
54 |
|
56 |
5285.8 645.9 728.0 2978.6 |
5374.2 669.1 757.6 3042.4 |
56 |
|
58 |
5288.7 646.6 729.0 2980.7 |
5377.2 669.9 758.6 3044.5 |
58 |
|
60 |
5291.7 647.4 729 9 2932.8 |
5380.1 670.7 759.6 3046.6 |
60 |
|
66° |
57° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
/ |
|
|
0 |
5380.1 670.7 759.6 3016.6 |
5468.2 694.4 790.2 3111.1 |
0 |
|
2 |
5383.0 671.4 760.6 3048.8 |
5471.1 695.2 791.2 3113.3 |
2 |
|
4 |
5386.0 672.2 761.6 3050.9 |
5474.0 696.0 792.2 3115.4 |
4 |
|
6 |
5388.9 672.9 762.7 3053.1 |
5477.0 696.8 793.3 3117.6 |
6 |
|
8 |
5391.8 673.7 763.7 3055.2 |
5479.9 697.6 794.3 3119.7 |
8 |
|
10 |
5394.8 674.4 764.7 3057.4 |
5482.8 698.4 795.3 3121.9 |
10 |
|
12 |
5397.7 675.2 765.7 3059.5 |
5485.7 699.2 796.3 3124.1 |
12 |
|
14 |
5400.7 676.0 766.7 3061.6 |
5488.7 700.0 797.4 3126.2 |
14 |
|
16 |
5403.6 676.8 767.7 3063.8 |
5491.6 700.8 798.4 3128.4 |
16 |
|
18 |
5406.5 677.6 768.7 3065.9 |
5494.5 701.6 799.4 3130.6 |
18 |
|
20 |
5409.5 678.4 769.7 3068.1 |
5497.4 702.4 800.5 3132.7 |
20 |
|
22 |
5412.4 679.2 770.8 3070.2 |
5500.3 703.2 801.5 3134.9 |
22 |
|
24 |
5415.3 680.0 771.8 30^2.4 |
5503.3 704.0 802.6 3137.0 |
24 |
|
26 |
5418.3 680.8 772.8 3074.5 |
5506.2 704.8 803.6 3139.2 |
26 |
|
28 |
5421.2 681.6 773.8 3076.6 |
5509.1 705.6 804.7 3141.4 |
28 |
|
30 |
5424.1 682.4 774.8 3078.8 |
5512.0 706.4 805.7 3143.5 |
30 |
|
32 |
5427.1 683.2 775.8 3080.9 |
5515.0 707.2 806.8 3145.7 |
32 |
|
34 |
5430.0 684.0 776.8 3083.1 |
5517.9 708.0 807.8 3147.9 |
34 |
|
36 |
5433.0 684.8 777.8 3085.2 |
5520.8 708.8 808.8 3150.0 |
36 |
|
38 |
5435.9 685.6 778.9 3087.4 |
5523.7 709.6 809.9 3152.2 |
38 |
|
40 |
5438.8 686.4 779.9 3089.6 |
55-26.7 710.4 810.9 3154.4 |
40 |
|
42 |
5441.8 687.2 780.9 3091.7 |
5529.6 711.2 812.0 3156.6 |
42 |
|
44 |
5444.7 688.0 781.9 3093.9 |
5532.5 712.0 813.0 3158.7 |
44 |
|
46 |
5447.6 688.8 783.0 3096.0 |
5535.4 712.8 814.1 3160.9 |
46 |
|
48 |
5450.6 689.6 784.0 3098.2 |
5538.4 713.6 815.1 3163.1 |
48 |
|
50 |
5453.5 690.4 785.0 3100.3 |
5541.3 714.4 816.2 3165.3 |
50 |
|
52 |
5456.5 691.2 786.0 3102.5 |
5544.2 715.2 817.2 3167.4 |
52 |
|
54 |
5459.4 692.0 787.1 3104.6 |
5547.1 716.0 818.3 3169.6 |
54 |
|
56 |
5462.3 692.8 788.1 3106.8 |
5550.0 716.8 819.3 3171.8 |
56 |
|
58 |
5465.3 693.6 789.1 3108.9 |
5553.0 717.6 820.4 3174.0 |
58 |
|
60 |
5468.2 694.4 790.2 3111.1 |
5555.9 718.4 821.4 3176.1 |
60 |
146 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
68° |
69° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
5555.9 718.4 821.4 3176.1 |
5643.1 742.8 853.5 3241.9 |
0 |
|
2 |
5558.8 719.2 822.5 3178.3 |
5646.0 743.6 854.6 3244.1 |
2 |
|
4 |
5561.7 720.0 823.5 3180.5 |
5648.9 744.4 855.7 3246.3 |
4 |
|
6 |
5564.6 720.8 824.6 3182.7 |
5651.8 745.3 856.8 3248.5 |
6 |
|
8 |
5567.5 721.6 825.7 3184.9 |
5654.7 746.1 857.9 3250.7 |
8 |
|
10 |
5570.4 7224 826.7 3187.1 |
5657.6 746.9 859.0 3252.9 |
10 |
|
12 |
5573.3 723.2 827.8 3189.2 |
5660.5 747.7 860.0 3255.1 |
12 |
|
14 |
5576.2 724.0 828.9 3191.4 |
5663.4 748.6 861.1 3257.3 |
14 |
|
16 |
5579.2 724.8 829.9 3193.6 |
5666.3 749.4 862.2 3259.5 |
16 |
|
18 |
5582.1 725.6 831.0 3195.8 |
5669.2 750.2 863.3 3261.7 |
18 |
|
20 |
5585.0 726.5 832.1 3198.0 |
5672.1 751.1 864.4 3263.9 |
20 |
|
22 |
5587.9 727.3 833.1 3200.2 |
5675.0 751.9 865.5 3266.1 |
22 |
|
24 |
5590.8 728.1 834.2 3202.4 |
5677.9 752.7 866.6 3268 3 |
24 |
|
26 |
5593.7 728.9 835.3 3204.5 |
5680.8 753.5 867.7 3270.5 |
26 |
|
28 |
5596.6 729.7 836.3 3206.7 |
5683.7 754.4 868.8 3272.7 |
28 |
|
30 |
5599.5 730 5 837.4 3208.9 |
5686.5 755.2 869.9 3274.9 |
30 |
|
32 |
5602.4 731.3 838.4 3211.1 |
5689.4 756.0 871.0 3277.1 |
32 |
|
34 |
5605.3 732.1 839.5 3213.3 |
5692.3 756.9 872.1 3279.4 |
34 |
|
36 |
5608.2 732.9 840.6 3215.5 |
5695.2 757.7 873.2 3281 6 |
36 |
|
38 |
5611.1 733.7 841.6 3217.7 |
5698.1 758.5 874.3 3283.8 |
38 |
|
40 |
5614.0 734.6 842 7 3219.9 |
5701.0 759.4 875.4 3286.0 |
40 |
|
42 |
5616.9 735.4 843.8 3222.1 |
5703.9 760.2 876.5 3288.2 |
42 |
|
44 |
5619.8 736.2 844.9 3224.3 |
5706.8 761.0 877.6 3290.5 |
44 |
|
46 |
5622.8 737.0 846.0 3226.5 |
57097 761.9 878.7 3292.7 |
46 |
|
48 |
5625.7 737.8 847.0 3228.7 |
5712 6 762.7 879.8 3294.9 |
48 |
|
50 |
5628.6 738.6 848.1 3230.9 |
5715.5 763.5 880.9 3297.1 |
50 |
|
52 |
5631.5 739.4 849.2 3233.1 |
5718.4 764.4 882.0 3299.3 |
52 |
|
54 |
5634.4 740.2 850.3 3235.3 |
5721.3 765.2 883.1 3301.5 |
54 |
|
56 |
5637.3 741.0 851.4 3237.5 |
5724.2 766.0 884.2 8303.8 |
56 |
|
58 |
5640.2 741.9 852.5 32-39.7 |
5727.1 766.8 885.3 3306.0 |
58 |
|
60 |
5643.1 742.8 853.5 3241.9 |
5730.0 767.7 886.4 3308.2 |
60 |
|
60° |
61° |
||
|
L. C. M, E. T. |
L. C. M. E. T. |
||
|
0 |
5730.0 767.7 886.4 3303.2 |
5816.4 792.9 920.2 3375.2 |
0 |
|
2 |
5732.9 768.5 887.5 3310.4 |
5*19.3 793.7 921.4 3377.4 |
2 |
|
4 |
5735.8 769.4 888.7 3312.7 |
5822.1 794.6 922.5 3379.7 |
4 |
|
6 |
5738.6 770.2 889.8 3314.9 |
5825.0 795.4 923.6 3381.9 |
6 |
|
8 |
5741.5 771.1 890.9 3317.1 |
5827.9 796.3 924.8 3384,2 |
8 |
|
10 |
5744.4 771.9 892.0 3319.3 |
5830.7 797.1 9:25.9 3386. 4 |
10 |
|
13 |
5747.3 772.7 893.1 3321.6 |
5833.6 798.0 927.1 3388.7 |
12 |
|
14 |
5750.2 773.6 894.3 3323.8 |
5836.5 798.8 928.2 3390.9 |
14 |
|
16 |
5753.0 774.4 895.4 3326.0 |
5839.3 799.7 9'29.3 3393.2 |
16 |
|
18 |
5755.9 775.3 896.5 3328.3 |
5842.2 800.5 930.5 3395.4 |
18 |
|
20 |
5758.8 776.1 897.6 3330.5 |
5845.1 801.4 931.6 3397.7 |
20 |
|
22 |
5761.7 776.9 898.8 3332.7 |
5847.9 802.2 932.8 8399.9 |
22 |
|
24 |
5764.6 777.8 899.9 3334.9 |
5850.8 803.1 933.9 3402.2 |
24 |
|
26 |
5767.4 778.6 901.0 3337.2 |
5853.7 803.9 935.1 3404.4 |
26 |
|
28 |
5770.3 779.5 902.1 3339.4 |
5856.5 804.8 936.3 3406.7 |
28 |
|
30 |
5773.2 780.8 903.2 3341.6 |
5859.4 805.6 937.4 3408.9 |
30 |
|
32 |
5776.1 781.1 904.4 3343.9 |
5862.3 806.5 938.6 3411.2 |
32 |
|
34 |
5779.0 782.0 905.5 3346.1 |
5865.1 807.3 939.7 3413.5 |
34 |
|
36 |
5781.8 782.8 906.6 3348.3 |
5868.0 808.2 940.9 3415.7 |
36 |
|
38 |
5784.7 783.7 907.7 3350.6 |
5870.9 809.0 942.1 3418.0 |
38 |
|
40 |
5787.6 784.5 908.8 3352.8 |
5873.7 809.9 943.2 3420.3 |
40 |
|
42 |
5790.5 785.3 910.0 3355.0 |
5876.6 810.7 944.4 3422.5 |
42 |
|
44 |
5793.4 786.2 911.1 3357.3 |
5879.5 811.6 945.5 3424.8 |
44 |
|
46 |
5796.2 787.0 912.3 3359.5 |
5882.3 812.4 946.7 3427.1 |
46 |
|
48 |
5799.1 787.9 913.4 3361.8 |
5885.2 813.3 947.8 3429.3 |
48 |
|
50 |
5802.0 788.7 914.5 3364.0 |
5888.1 814.1 949.0 3431.6 |
50 |
|
52 |
5804.9 789.5 915.7 3366.2 |
5890.9 815.0 950.2 3433.9 |
52 |
|
54 |
5807.8 790.4 916.8 3368.5 |
5893.8 815.8 951.3 3436.1 |
54 |
|
56 |
5810.6 791.2 918.0 3370.7 |
5896.7 816.7 952.5 3438.4 |
56 |
|
58 |
5813.5 792.1 919.1 3373.0 |
5899.5 817.5 953.6 3440.7 |
58 |
|
L 60 |
5816.4 792.9 920.2 3375.2 |
5902.4 818.4 954.8 3442.9 |
60 , |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 147
|
62° |
63° |
||
|
/ |
L. C. M. E. T. |
L. C. M. E. T. |
|
|
0 |
5902.4 818.4 954.8 3442.9 |
5987.8 844.4 990.3 3511.3 |
0 |
|
2 |
5905.2 819.3 956.0 3445.2 |
5990.6 845.3 991.5 3513.6 |
2 |
|
4 |
5908.1 820.1 957.2 3447.5 |
5993.5 846.2 992.7 3515.9 |
4 |
|
6 |
5910.9 821.0 9583 3449.7 |
5996.3 847.1 993.9 3518.2 |
6 |
|
8 |
5913.8 821.8 959.5 3452.0 |
5999.1 847.9 995.1 3520.5 |
8 |
|
10 |
5916.6 822.7 960.7 3454.3 |
6002.0 848.8 996.3 3522.8 |
10 |
|
12 |
5919.5 823.6 961.9 3456.6 |
6004.8 849.7 997.5 3525.1 |
12 |
|
14 |
5922.3 824.4 963.0 3458.8 |
6007.7 850.6 998.7 3527.4 |
14 |
|
16 |
5925.2 825.3 964.2 3461.1 |
6010.5 851.4 999.9 3529.7 |
16 |
|
is |
5928.0 826.1 965.4 3463.4 |
6013.3 852.3 1001.1 3532.0 |
18 |
|
20 |
5930.9 827.0 966.6 3465.7 |
6016.2 853.2 1002.3 3534.3 |
20 |
|
22 |
5933.7 827.9 967.8 3167.9 |
6019.0 854.1 1003.5 3536.6 |
22 |
|
24 |
5936.6 828.7 968.9 3470.2 |
6021.8 854.9 1004.7 3538.9 |
24 |
|
26 |
5939.4 829.6 970.1 3472.5 |
6024.7 855.8 1005.9 3541.2 |
26 |
|
28 |
5942.3 830.4 971.3 3474.7 |
6027.5 856.7 1007.1 3543.5 |
28 |
|
30 |
5945.1 831.3 972.5 3477.0 |
6030.3 857.6 1008.4 3545.8 |
30 |
|
82 |
5947.9 832.2 973.6 3479.3 |
6033.2 858.4 1009.6 3548.1 |
32 |
|
34 |
5950.8 833.0 974.8 3481.6 |
6036. 0 859.3 1010.8 3550.4 |
34 |
|
36 |
5953.6 833.9 976.0 3483.9 |
6038.9 860.2 1012.0 3552.7 |
36 |
|
38 |
5956.5 834.7 977.2 3486.2 |
6041.7 861.1 1013.2 3555.0 |
38 |
|
40 |
5959.3 835.6 978.4 3488.5 |
6044.5 861.9 1014.5 3557.3 |
40 |
|
42 |
5962.2 836.5 979.6 3490.7 |
6047.4 862.8 1015.7 3559.6 |
42 |
|
44 |
5965.0 837.4 980.8 3493.0 |
6050.2 863.7 1016.9 3562.0 |
44 |
|
46 |
5967.9 838.3 982.0 3495.3 |
6053.0 864.6 1018.1 3564.3 |
46 |
|
48 |
5970.7 839.1 983.2 3497.6 |
0055.9 865.4 1019.3 3566.6 |
48 |
|
50 |
5973.6 840.0 984.4 3499.9 |
60f>8.7 866.3 1020.6 3568.9 |
50 |
|
52 |
5976.4 840.9 985.5 3502.2 |
6061.6 867.2 1021.8 3571.2 |
52 |
|
54 |
5979.3 84f.7 986.7 3504.5 |
60(54.4 868.1 1023.0 3573.5 |
54 |
|
56 |
5982.1 842.6 9S7.9 3506.8 |
6067.2 868.9 1024.2 3575.8 |
56 |
|
58 |
5985.0 843.5 989.1 3509.0 |
6070.1 869.8 1025.4 3578.1 |
58 |
|
60 |
5987.8 844.4 990.3 3511.3 |
6072.9 870.7 1026.7 3580.4 |
60 |
|
64°: |
65° |
||
|
L. C. M. ^ E. T. |
L. C. M. E. T. |
||
|
0 |
6072.9 870.7 1026.7 3580.4 |
6157.5 897.3 1064.0 3650.4 |
0 |
|
2 |
6075.7 871.5 1027.9 3582.8 |
6160.3 898.2 1065.2 3652.8 |
2 |
|
4 |
6078.5 872.4 1029.2 3585.1 |
6163.1 899.1 1066.5 3655.1 |
4 |
|
6 |
6081.4 873.3 1030.4 3587.4 |
6165.9 900.0 1067.7 3657.5 |
6 |
|
8 |
6084.2 874.2 1031.7 3589.7 |
6168.7 900.9 1069.0 3659.8 |
8 |
|
10 |
6087.0 875.1 1032.9 3592.1 |
6171.5 901.8 1070.2 3662.2 |
10 |
|
12 |
6089.8 875.9 1034.1 3594.4 |
6174.3 902.7 1071.5 3664.5 |
12 |
|
14 |
6092.6 876.8 1035.4 3596.7 |
6177.1 903.6 1072.7 3666.9 |
14 |
|
16 |
6095.5 877.7 1036.6 3599.1 |
6179.9 904.5 1074.0 3669.2 |
16 |
|
18 |
6098.3 878.6 1037.9 3601.4 |
6182.7 905.4 1075.2 3671.6 |
18 |
|
20 |
6101.1 879.5 1039.1 3603.7 |
6185.5 906.3 1076.6 3673.9 |
20 |
|
22 |
6103.9 880.3 1040.3 3606.0 |
6188.3 907.2 1077.8 3676.2 |
22 |
|
24 |
6106.7 881.2 1041.6 3608.4 |
6191.1 908.1 1079.1 3678.6 |
24 |
|
26 |
6109.6 882.1 1042.8 3610.7 |
6193.9 909.0 1080.4 3680.9 |
26 |
|
28 |
6112.4 883.0 1044.1 3613.0 |
6196.7 909.9 1081.7 3683.3 |
28 |
|
30 |
6115.2 883.9 1045.3 3615.3 |
6199.5 910.8 1083.0 3685.6 |
30 |
|
32 |
6118.0 884.7 1046.5 3617.7 |
6202.3 911.7 1084.2 3688.0 |
32 |
|
34 |
6120.8 8S5.6 1047.8 3620.0 |
6205.1 912.6 1085.5 3690.4 |
34 |
|
36 |
6123.7 886.5 1049.0 3622.3 |
6208.0 913.5 1086.8 3692.7 |
36 |
|
38 |
6126.5 887.4 1050.3 3624.7 |
6210.8 914.4 1088.1 3695.1 |
38 |
|
40 |
6129.3 888.3 1051.5 3627.0 |
6213.6 915.3 1089.4 3697.4 |
40 |
|
42 |
6132.1 889.2 1052.7 3629.4 |
6216.4 916.2 1090.6 3699.8 |
42 |
|
44 |
6134.9 890.1 1054.0 3631.7 |
6219.2 917.1 1091.9 3702.2 |
44 |
|
46 |
6137.8 891.0 1055.2 3634.0 |
6222.0 918.0 1093.2 3704.5 |
46 |
|
48 |
6140.6 891.9 1056.5 3636.4 |
6224.8 918.9 1094.5 3706.9 |
48 |
|
50 |
6143.4 892.8 1057.7 3638.7 |
6227.6 919.8 1095.8 3709-3 |
50 |
|
52 |
6146.2 893.7 1059.0 3641.1 |
6230.4 920.7 1097.0 3711.6 |
52 |
|
54 |
6149.0 894.6 1060.2 3643.4 |
6233.2 921.6 1098.3 3714.0 |
54 |
|
56 |
6151.9 895.5 1061.5 3645.7 |
6236.0 922.5 1099.6 3716.3 |
56 |
|
58 |
6154.7 896.4 1062.7 3648.1 |
6238.8 923.4 1100.9 3718.7 |
58 |
|
60 |
6157.5 897.3 1064.0 3650.4 |
6241.6 924.3 1102.2 3721.1 |
60 |
'148 6. -FUNCTIONS OF A ONE-DEGREE CURVE.
|
! , |
66° |
67° |
|
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
6241.6 924.3 1102.2 3721.1 |
6325.2 951.8 1141.5 3792.6 |
0 |
|
2 |
6244.4 925.2 1103.5 3723.4 |
6328.0 952.7 1142.8 3795.0 |
2 |
|
4 |
6247.2 926.1 1104.8 3725.8 |
6330.7 953.6 1144.1 3797.4 |
4 |
|
6 |
6250.0 927.0 1106.1 3728.2 |
6333.5 954.5 1145.4 3799.8 |
6 |
|
8 |
6252.7 927.9 1107.4 3730.6 |
6336.3 955.5 1146.7 3802.2 |
8 |
|
10 |
6255.5 928.8 1108.7 3732.9 |
6339.0 956.4 1148.1 3804.6 |
10 |
|
12 |
6258.3 929.8 1110.0 3735.3 |
6341.8 957.3 1149.4 3807.0 |
12 |
|
14 |
6261.1 930.7 1111.3 3737.7 |
6344.6 958.2 1150.7 3809.4 |
14 |
|
16 |
6263.9 931 6 1112.6 3740.1 |
6347.4 959.2 1152.0 3811.8 |
16 |
|
18 |
6266.7 932.5 1113.9 3742.4 |
6350.1 960.1 1153.3 3814.2 |
18 |
|
20 |
6269.5 933.4 1115.2 3744.8 |
6352.9 961.0 1154.7 3816.6 |
20 |
|
22 |
6272.3 934.3 1116.5 3747.2 |
6355.7 961.9 1156.0 3819.0 |
22 |
|
24 |
6275,0 935.3 1117.8 3749.6 |
6358.4 962.9 1157.4 3821.4 |
24 |
|
26 |
6277.8 936.2 1119.1 3751.9 |
6301.2 963.8 1158.7 3823.8 |
26 |
|
28 |
6280.6 937.1 1120.4 3754.3 |
6364.0 964.7 1160.1 3826.2 |
28 |
|
30 |
6283.4 938.0 1121.7 3756.7 |
6366.7 965.6 1161.4 3828.6 |
30 |
|
32 |
6286.2 938.9 1123.0 3759.1 |
6369.5 966.6 1162.8 3831.0 |
32 |
|
34 |
6289.0 939.8 1124.3 3761.5 |
0372.3 907.5 1164.1 3833.4 |
34 |
|
36 |
6291.8 940.8 1125.6 3763.9 |
6375.1 968.4 1165.5 3835.9 |
36 |
|
38 |
6294.5 941.7 1126.9 3766.3 |
6377.8 909.3 1166.8 3838.3 |
38 |
|
40 |
6297.3 942 6 1128.3 3768.7 |
6380.6 970.3 1168.2 3840.7 |
40 |
|
42 |
6300.1. 943.5 1129.6 3771.0 |
6383.4 971.2 1169.5 3843.1 |
42 |
|
44 |
6302.9 944.4 1130.9 3773.4 |
6386.1 972.1 1170.9 3845.5 |
44 |
|
46 |
6305.7 945.3 1132.2 3775.8 |
6388.9 973.0 1172.2 3847.9 |
46 |
|
1.48 |
6308.5 946.3 1133.5 3778.2 |
6391.7 974.0 1173.6 3850.4 |
48 |
|
50 |
6311.3 947.2 1134.9 3780.6 |
6394.4 974.9 1174.9 3852.8 |
50 |
|
52 |
6314.1 948.1 1136.2 3783.0 |
6397.2 975.8 1176.3 3855.2 |
52 |
|
54 |
6316.8 949.0 1137.5 3785.4 |
6400.0 976.8 1177.6 3857.6 |
54 |
|
56 |
6319.6 949.9 1138.8 3787.8 |
6402.8 977.7 1179.0 3860.0 |
56 |
|
58 |
6322.4 950.8 1140.1 3790.2 |
6405.5 978.6 1180.3 3862.5 |
58 |
|
60 |
6325.2 951.8 1141.5 3792.6 |
6408.3 979.6 1181.6 3864.9 |
60 |
|
68° |
69° |
||
|
L. C. M. E. T. |
L. C. M. * E. T. |
||
|
0 |
6408.3 979.6 1181.6 3864.9 |
6491.1 1007.7 1222.9 3938.1 |
0 |
|
2 |
6411.1 980.5 1183.0 3807.3 |
6493.8 1008.7 1224.3 3940.6 |
2 |
|
4 |
6413.8 981.4 1184.4 3869.7 |
6496.6 1009.6 1225.7 3943.0 |
4 |
|
6 |
6416. 6 982.4 1185.7 3372.2 |
6499.3 1010.6 1227.1 3945.5 |
6 |
|
8 |
G419.3 983.3 1187.1 3874.6 |
6502.1 1011.5 1228.5 3947.9 |
8 |
|
10 |
61-22.1 984.2 1188.5 3877.0 |
6504.8 1012.5 1229.9 3950.4 |
10. |
|
12 |
0421. 9 985.2 1189.8 3879.5 |
6507.5 1013.4 1231.3 3952.9 |
12 |
|
14 |
6427.6 986.1 1191.2 3881.9 |
6510.3 1014.4 1232.7 3955.3 |
14 |
|
10 |
6430.4 987.0 1192.6 3884.3 |
6513.0 1015.3 1234.1 3957.8 |
16 |
|
18 |
6433.1 988.0 1193.9 3886.8 |
6515.8 1016.3 1235.5 3960.2 |
18 |
|
20 |
6435.9 988.9 1195.3 3889.2 |
6518.5 1017.2 1236.9 3962.7 |
20 |
|
22 |
6438.7 980.8 1196.7 3891.6 |
6521.2 1018.2 1238.3 3965.2 |
22 |
|
24 |
6141.4 990.8 1198.0 3894.1 |
6524.0 1019.1 1239.7 3967.6 |
24 |
|
26 |
6444.2 991.7 1199.4 3896.5 |
0520.7 1020.1 1241.1 3970,1 |
26 |
|
28 |
6140.9 992.6 1200.8 3898.9 |
6529.5 1021.0 1242.5 3972.5 |
28 |
|
30 |
6149.7 99J. 6 1202.1 3901.4 |
0532.2 1022.0 1243.9 3975.0 |
30 |
|
32 |
6452.5 994.5 1203.5 3903.8 |
0534.9 10. '2. 9 1245.3 3977.5 |
32 |
|
34 |
6455.2 995.4 1204.9 3906.3 |
0537.7 1023.9 1246.7 3980.0 |
34 |
|
36 |
0458.0 996.4 1206.2 3908.7 |
0540.4 1024.8 1248.1 3982.4 |
36 |
|
38 |
6400.7 997.3 1207.6 3911.2 |
6543.2 1025.8 1249.5 3984.9 |
38 |
|
40 |
6463.5 908.2 1209.0 3913.6 |
0545.9 1026.7 1250.9 3987.4 |
40 |
|
42 |
0466.3 999.2 1210.3 3916.1 |
6548.6 1027.7 1252.3 3989.9 |
42 |
|
44 |
6469.0 1000.1 1211.7 3918.5 |
6551.4 1028.6 1253.7 3993.3 |
44 |
|
46 |
6471.8 1001.0 1213.1 3921.0 |
CS54.1 1029.6 1255.1 3994.8 |
46 |
|
48 |
6474.5 1002.0 1214.5 3923.4 |
6550.9 1030.5 1256.5 3997.3 |
48 |
|
50 |
6477.3 1002.9 1215.9 3925.9 |
6559.6 1031.5 1257.9 3999.8 |
50 |
|
52 |
6480.1 1003.8 1217.3 3928.3 |
6562.3 1032.4 1259.3 4002.2 |
52 |
|
54 |
6482.8 1004.8 1218.7 3930.8 |
6565.1 1033.4 1200.7 4004.7 |
54 |
|
56 |
6485.6 1005.7 1220.1 3933.2 |
6567.8 1034.3 1262.1 4007.2 |
56 |
|
58 |
6488.3 1006.7 1221.5 3935.7 |
6570.6 1035.3 1263.5 4009.7 |
58 |
|
60 |
6491.1 1007.7 1222.9 3938.1 |
6573.3 1036.3 1265.0 4012.1 |
60 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 149
|
70° |
71° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
t |
|
|
0 |
6573.3 1036.3 1265.0 4012.1 |
6654.9 1065.1 1308.4 4087.1 |
0 |
|
2 |
6576.0 1037.3 1266.4 4014.6 |
6657.6 1066.1 1309.9 4089.7 |
2 |
|
4 |
6578.7 1038.2 1267.9 4017.1 |
6660.3 1067.0 1311.3 4092.2 |
4 |
|
6 |
6581.5 1039.2 1269.3 4019.6 |
6663.0 1068.0 1312.8 4094.7 |
6 |
|
8 |
6584.2 1040.1 1270.8 4022.1 |
6605.7 1068.9 1314.2 4097.2 |
8 |
|
10 |
6586.9 1041.1 1272.2 4024.6 |
6668.4 1069.9 1315.7 4099.8 |
10 |
|
12 |
6589.6 1042.1 1273.6 4027.1 |
6671.1 1070.9 1317.2 4102.3 |
12 |
|
14 |
6592.3 1043.0 1275.1 4029.6 |
6673.8 1071.9 1318.6 4104.8 |
14 |
|
16 |
6595.1 1044.0 1276.5 4032.1 |
6676.6 1072.9 1320.1 4107.3 |
16 |
|
18 |
6597.8 1044.9 1278.0 4034.6 |
6679.3 1073.8 1321.5 4109.8 |
18 |
|
20 |
6600.5 1045.9 1279.4 4037.1 |
6682.0 1074.8 1323.0 4112.4 |
20 |
|
22 |
6603.2 1046.9 1280.8 4039.6 |
6684.7 1075.8 1324.4 4114.9 |
22 |
|
24 |
6605.9 1047.8 1282.3 4042.1 |
6687.4 1076.8 1325.9 4117.4 |
24 |
|
26 |
6608.7 1048.8 1283.7 4044.6 |
6690.1 1077.7 1327.4 4119.9 |
26 |
|
28 |
6611.4 1049.7 1285.2 4047.1 |
6692.8 1078.7 1328.9 4122.4 |
28 |
|
30 |
6614.1 1050.7 1286.6 4049.6 |
6695.5 1079.7 1330.4 4125.0 |
30 |
|
32 |
6616.8 1051.7 1288.0 4052.1 |
6098.2 1080.7 1331.8 4127.5 |
32 |
|
34 |
6619.5 1052.6 1289.5 4054.6 |
6700.9 1081.6 1333.3 4130.1 |
34 |
|
36 |
6622.3 1053.6 1290.9 4057.1 |
6703.6 1082.6 1334.8 4132.6 |
36 |
|
38 |
6625.0 1054.5 1292.4 4059.6 |
6706.3 1083.6 1336.3 4135.1 |
38 |
|
40 |
6627.7 1055.5 1293.8 4062.1 |
6709.0 1084.5 1337.8 4137.7 |
40 |
|
42 |
6630.4 1056.5 1295.3 4004.6 |
6711.7 1085.5 1339.2 4140.2 |
42 |
|
44 |
6633.1 1057.4 1296.7 4067.1 |
6714.4 1086.5 1340.7 4142.7 |
44 |
|
46 |
6635.9 1058.4 1298.2 4069.6 |
6717.2 1087.5 1342.2 4145.3 |
46 |
|
48 |
6638.6 1059.3 1299.6 4072.1 |
6719.9 1088.4 1343.7 4147.8 |
48 |
|
50 |
6641.3 1060.* 1301.1 4074.6 |
6722.6 1089.4 1345.2 4150.4 |
50 |
|
52 |
6644. C 1061.3 1302.6 4077.1 |
6725.3 1090.4 1346.7 4152.9 |
52 |
|
54 |
6646.7 1062.2 1304.0 4079.6 |
6728.0 1091.3 1348.2 4155.4 |
54 |
|
56 |
6649.5 1063.2 1305.5 4082.1 |
6730.7 1092.3 1349.7 4158.0 |
56 |
|
58 |
6652.2 1064.1 1306.9 4084.6 |
6733.4 1093.3 1351.2 4160.5 |
58 |
|
60 |
6654.9 1065.1 1308.4 4087.1 |
6736.1 1094.3 1352.7 4163.1 |
60 |
|
1 1.° |
73° |
||
|
L. C. M. E. T. |
L. C. M, E. T. |
||
|
0 |
6736.1 1094.3 1352.7 4163.1 |
6816.6 1123.9 1398.1 4240.0 |
0 |
|
2 |
6738.8 1095.2 1354.2 4165.6 |
6819.3 1124.8 1399.6 4242.6 |
2 |
|
4 |
6741.5 1096.2 1355.7 4168.2 |
6821.9 1125.8 1401.2 4245.1 |
4 |
|
6 |
6744.1 1097.2 1357.2 4170.7 |
6824.6 1126.8 1402.7 4247.7 |
6 |
|
8 |
6746.8 1098.2 1358.7 4173.3 |
6827.3 1127.8 1404.2 4250.3 |
8 |
|
10 |
6749.5 1099.2 1360.2 4175.8 |
6830.0 1128.8 1405.8 4252.9 |
10 |
|
12 |
6752.2 1100.1 1361.7 4178.4 |
6832.6 1129.8 1407.3 4255.5 |
12 |
|
14 |
6754.9 1101.1 1303.2 4181.0 |
6835.3 1130.8 1408.8 4258.1 |
14 |
|
16 |
6757.6 1102.1 1364.7 4183.5 |
6838.0 1131.8 1410.4 4260.7 |
16 |
|
18 |
6760.2 1103.1 1366.2 '4186.1 |
6840.7 1132.8 1411.9 4263.2 |
18 |
|
20 |
6762.9 1104.1 1367.7 4188.6 |
6843.3 1133.8 1413.5 4265.8 |
20 |
|
22 |
6765.6 1105.1 1369.2 4191.2 |
6846.0 1134.8 1415.1 4268.4 |
22 |
|
24 |
6768.3 1106.0 1370.7 4193.7 |
6848.7 1135.8 1416.6 4271.0 |
24 |
|
26 |
6771.0 1107.0 1372.2 4196.3 |
6851.3 1136.8 1418.2 4273.6 |
26 |
|
28 |
6773.7 1108.0 1373.7 4198.8 |
6854.0 1137.8 1419.7 4276.2 |
28 |
|
30 |
6776.3 1109.0 1375.2 4201.4 |
6856.7 1138.8 1421.3 4278.8 |
30 |
|
32 |
6779.0 1109.9 1376.7 4204.0 |
6859.4 1139.8 1422.9 4281.4 |
32 |
|
34 |
6781.7 1110.9 1378.2 4206.5 |
6862.0 1140.8 1424.4 4284.0 |
34 |
|
36 |
6784.4 1111.9 1379.7 4209.1 |
6804.7 1141.8 1426.0 4286.6 |
30 |
|
38 |
6787.1 1112.9 1381.2 4211.7 |
6867.4 1142.8 1427.5 4289.2 |
38 |
|
40 |
6789.8 1113.9 3382.8 4214.3 |
6870.1 1143.8 1429.1 4291.8 |
40 |
|
42 |
6792.4 1114.9 1384.3 4216.8 |
6872.7 1144.8 1430.7 4294.4 |
42 |
|
44 |
0795.1 1115.9 1385.8 4219.4 |
6875.4 1145.8 1432.2 4297.0 |
44 |
|
46 |
6797.8 1116.9 1387.4 4222.0 |
6878.1 1146.8 1433.8 4299.6 |
46 |
|
48 |
6800.5 1117.9 1388.9 4224.5 |
6880.8 1147.8 1435.3 4302.2 |
48 |
|
50 |
6803.2 1118.9 1390.4 4227.1 |
6883.4 1148 8 1436.9 4304.8 |
50 |
|
52 |
6805.9 1119.9 1392.0 4229.7 |
6886.1 1149.8 1438.5 4307.4 |
52 |
|
54 |
6808.5 1120.9 1393.5 4232.3 |
68S8.8 1150.8 1440.0 4310.0 |
54 |
|
56 |
6811.2 1121.9 1395.0 4234.8 |
6891.4 1151.8 1441.6 4312.6 |
56 |
|
58 |
6813.9 1122.9 1396.6 4237.4 |
6894.1 1152.8 1443.1 4315.2 |
58 |
|
80 |
6816.6 1123.9 1398.1 4240.0 |
6896.8 1153.8 1444.7 4317.8 |
60 |
150 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
74° |
75° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
6896.8 1153.8 1444.7 4317.8 |
6976.4 1184.1 1492.5 4396.7 |
0 |
|
2 |
6899.4 1154.8 1446.2 4320.5 |
6979.0 1185.1 1494.1 4399.4 |
2 |
|
4 |
6902.1 1155.8 1447.8 4323.1 |
6981.7 1186.1 1495.7 4402.1 |
4 |
|
6 |
6904.8 1156.8 1449.4 4325.7 |
6984.3 1187.1 1497.3 4404.7 |
6 |
|
8 |
6907.4 1157.8 1451.0 4328.3 |
6986.9 1188.1 1499.0 4407.4 |
8 |
|
10 |
6910.1 1158.8 1452.6 4330.9 |
6989.6 1189.2 1500.6 4410.0 |
10 |
|
18 |
6912.7 1159.8 1454.1 4333.6 |
6992.2 1190.2 1502.2 4412.7 |
12 |
|
14 |
6915.4 1160.8 1455.7 4336.2 |
6994.9 1191.2 1503.8 4415.3 |
14 |
|
16 |
6918.0 1161.8 1457.3 4338.8 |
6997.5 1192.2 1505.4 4418.0 |
16 |
|
18 |
6920.7 1162.8 1458.9 4341.4 |
7000.1 1193.2 1507.0 4420.7 |
18 |
|
20 |
6923.3 1163.9 1460.5 4344.0 |
7002.8 1194.3 1508.7 4423.3 |
20 |
|
22 |
6926.0 1164.9 1462.0 4346.7 |
7005.4 1195.3 1510.3 4426.0 |
22 |
|
24 |
6928.6 1165.9 1463.6 4349.3 |
7008.0 1196.3 1512.0 4428.6 |
24 |
|
26 |
6931.3 1166.9 1465!2 4351.9 |
7010.7 1197.3 1513.6 4431.3 |
26 |
|
28 |
6933.9 1167.9 1466.8 4354.5 |
7013.3 1198.3 1515.3 4434.0 |
28 |
|
30 |
6936.6 1168.9 1468.4 4357.1 |
7015.9 1199.4 1516.9 4436.6 |
30 |
|
32 |
6939.2 1169.9 1469.9 4359.8 |
7018.6 1200.4 1518.5 4439.3 |
32 |
|
34 |
6941.9 1170.9 1471.5 4362.4 |
7021.2 1201.4 1520.2 4442.0 |
34 |
|
36 |
6944.6 1171.9 1473.1 4365.1 |
7023.9 1202.4 1521.8 4444.6 |
36 |
|
88 |
6947.2 1172.9 1474.7 4367.7 |
7026.5 1203.4 1523.5 4447.3 |
38 |
|
40 |
6949.9 1174.0 1476.4 4370.3 |
7029.1 1204.5 1525.1 4450.0 |
40 |
|
42 |
6952.5 1175.0 1478.0 4373.0 |
7031.8 1205.5 1526.7 4452.7 |
42 |
|
44 |
6955.2 1176.0 1479.6 4375.6 |
7034.4 1206.5 1528.4 4455.3 |
44 |
|
46 |
6957.8 1177.0 1481.2 4378.3 |
7037.0 1207.5 1530.0 4458.0 |
46 |
|
48 |
6960.5 1178.0 1482.8 4380.9 |
7039.7 1208.5 1531.7 4460.7 |
48 |
|
50 |
6963.1 1179.0 1484.4 4383.5 |
7042.3 1209.6 1533.3 4463.4 |
50 |
|
52 |
6965.8 1180.0 1486.0 4386.2 |
7045.0 1210.6 1534.9 4466.0 |
52 |
|
54 |
6968.4 1181.0 1487.7 4388.8 |
7047.6 1211.6 1536.6 4468.7 |
54 |
|
56 |
6971.1 1182.0 1489.3 4391.5 |
7050.2 1212.6 1538.2 4471.4 |
56 |
|
58 |
6973.7 1183.0 1490.9 4394.1 |
7052.9 1213.6 1539.9 4474.1 |
58 |
|
60 |
6976.4 1184.1 1492.5 4396.7 |
7055.5 1214.7 1541.5 4476.7 |
60 |
|
76° |
77° |
||
|
L. C. M. E. T. |
L. C. M E. T. |
||
|
0 |
7055.5 1214.7 1541.5 4476,7 |
7134.0 1245.6 1591.7 4557.8 |
0 |
|
2 |
7058.1 1215.7 1543.2 4479.4 |
7136.6 1246.6 1593.4 4560.5 |
2 |
|
4 |
7060.7 1216.7 1544.9 4482.1 |
7139.2 1247.7 1595.1 4563.3 |
4 |
|
6 |
7063.3 1217.8 1546.5 4484.8 |
7141.8 1248.7 1596.8 4566.0 |
6 |
|
8 |
7066.0 1218.8 1548.2 4487.5 |
7144.4 1249.8 1598.5 4568.7 |
8 |
|
10 |
7068.6 1219.8 1549.9 4490.2 |
7147.0 1250.8 1600.2 4571.5 |
10 |
|
12 |
7071.2 1220.9 1551.5 4492.9 |
7149.6 1251.8 1601.9 4574.2 |
12 |
|
14 |
7073.8 1221.9 1553.2 4495.6 |
7152.2 1252.9 1603.6 4576.9 |
14 |
|
16 |
7076.4 1222.9 1554.9 4498.3 |
7154.8 1253.9 1605.3 4579.7 |
16 |
|
18 |
7079.0 1224.0-1556.5 4501.0 |
7157.4 1255 0 1607.0 4582.4 |
18 |
|
20 |
7081.7 1225.0 1558.2 4503.7 |
7160.0 1256.0 1608.7 4585.1 |
20 |
|
22 |
7084.3 1226.0 1559.9 4506.3 |
7162.6 1257.0 1610.4 4587.9 |
22 |
|
24 |
7086.9 1227.1 1561.5 4509.0 |
71C5.2 1258.1 1612.1 4590.6 |
24 |
|
26 |
7089.5 1228.1 1563.2 4511.7 |
7167.8 1259.1 1613.8 4593.3 |
26 |
|
28 |
7092.1 1229.1 1564.9 4514.4 |
7170.4 1260.2 1615.5 4596.0 |
28 |
|
80 |
7094.7 1230.2 1560.5 4517.1 |
7173.0 1261.2 1617.3 45988 |
30 |
|
32 |
7097.4 1231.2 1568.2 4519.8 |
7175.6 1262.2 1619.0 4601.5 |
32 |
|
31 |
7100.0 1232.2 1569.9 4522.5 |
7178.2 1263.3 1620.7 4604.3 |
34 |
|
36 |
7102.6 1233.3 1571.5 4525.3 |
7180.8 1264.3 1622.4 4607.0 |
36 |
|
38 |
7105.2 1234.8 1573.2 4528.0 |
7183.4 1265.4 1624.1 4609.8 |
38 |
|
40 |
7107.8 1235.3 1574.8 4530.7 |
7186.0 1266.4 1625.9 4612.5 |
40 |
|
42 |
7110.4 1236.4 1576.4 4533.4 |
7188.6 1267.4 1627.6 4615.3 |
4-> |
|
44 |
7113.1 1237.4 1578.1 4536.1 |
7191.2 1268.5 1629.3 4618.0 |
44 |
|
46 |
7115.7 1238.4 1579.8 4538.8 |
7193.8 1269.5 1631.0 4620.8 |
40 |
|
48 |
7118.3 1239.5 1581.5 4541.5 |
7196.4 1270.6 1632.7 4623.5 |
48 |
|
50 |
7120.9 1240.5 1583.2 4544.2 |
7199.0 3271.6 16345 4626.3 |
50 |
|
52 |
7123.5 1241.5 1584.9 4547.0 |
7201.6 1272.7 1636.2 4629.0 |
52 |
|
54 |
7126.1 1242.6 1586.6 4549.7 |
7204.2 1273.7 1637.9 4631.8 |
54 |
|
56 |
7128.8 1243.6 1588.3 4552.4 |
7206.8 1274.8 1639.6 4634.5 |
56 |
|
58 |
7131.4 1244.6 1590.0 4555.1 |
7209.4 1275.8 1641.3 4637.3 |
58 |
|
60 |
7134.0 1245.6 1591.7 4557.8 |
7212.0 1276.9 1643.1 4640.0 |
60 / |
6 —FUNCTIONS OF A ONE-DEGREE CURVE. 151
|
78° |
79° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
7212.0 1276.9 1643.1 4640.0 |
7289.5 130S.5 1696.0 4723.4 |
0 |
|
o |
7214.6 1278.0 1644.8 4642.8 |
7292.1 1309.5 1697.7 4726.2 |
2 |
|
4 |
7217.2 1279.0 1646.6 4645.6 |
7294.6 1310.6 1699.5 4729.0 |
4 |
|
6 |
7219.7 1280.1 1648.3 4648.3 |
7297.2 1311.7 1701.3 4731.8 |
6 |
|
8 |
7222.3 1281.1 1650.1 4651.1 |
7299.7 1312.7 1703.1 4734.7 |
8 |
|
10 |
7224.9 1282.2 1651.8 4653.9 |
7302.3 1313.8 1704.9 4737.5 |
10 |
|
12 |
7227.5 1283.2 1653.6 4656.7 |
7304.9 1314.9 1706.6 4740.3 |
12 |
|
14 |
7230.1 1284.3 1655.3 4659.4 |
7307.4 1315.9 1708.4 4743.1 |
14 |
|
16 |
7232.7 1285.3 1657.1 4662.2 |
7310.0 1317.0 1710.2 4745.9 |
16 |
|
18 |
7235.2 1286.4 1G58.8 4665.0 |
7312.6 1318.1 1712.0 4748.7 |
18 |
|
20 |
7237.8 1287.4 1660.6 4667.7 |
7315.1 1319.1 1713.8 4751.5 |
20 |
|
22 |
7240.4 1288.5 1662.3 4670.5 |
7317.7 1320*2 1715.6 4754.3 |
22 |
|
24 |
7243.0 1289.5 1664.1 4673.3 |
7320.3 1321.3 1717.4 4757.1 |
24 |
|
26 |
7245.6 1290.6 1665.8 4676.0 |
7322.8 1322.3 1719.2 4760.0 |
26 |
|
28 |
7248.2 1291.6 1667.6 4678.8 |
7325.4 1323.4 1721.0 4762.8 |
28 |
|
30 |
7250.7 1292.7 1669. 3 4681.6 |
7327.9 1324.5 1722.8 4765.6 |
30 |
|
32 |
7253.3 1293.7 1671.1 4684.4 |
7330.5 1325.5 1724.6 4768.4 |
32 |
|
34 |
7255.9 1294.8 1672.8 4687.2 |
7333.1 13:26.6 1726.4 4771.2 |
34 |
|
36 |
7258.5 1295.8 1674.6 4689.9 |
7335.6 1327.7 1728.2 4774.1 |
36 |
|
38 |
7261.1 1296.9 1676.3 4692.7 |
7338.2 1328.7 1730.0 4776.9 |
38 |
|
40 |
7263.7 1297.9 1678.2 4695.5 |
7340.8 1329.8 1731.9 4779.7 |
"40 |
|
42 |
7266.2 1299.0 1679.9 4698 3 |
7343.3 1330.8 1733.7 4782.6 |
42 |
|
44 |
7268.8 1300.0. 1681.7 4701.1 |
7345.9 1331.9 1735.5 4785.4 |
44 |
|
46 |
7271.4 1301.1 1683.5 4703.9 |
7348.4 1333.0 1737.3 4788.2 |
46 |
|
48 |
7274.0 1302.1 1685.3 470''.. 7 |
7351.0 1334.1 1739.1 4791.0 |
48 |
|
50 |
7276.6 1303.2 1687.1 4709.5 |
7353.6 1335.2 1740.9 4793.9 |
50 |
|
52 |
7279.2 1304.2 1688.8 4712.2 |
7356.1 1336.2 1742.7 4796.7 |
52 |
|
54 |
7281.7 1305.3 1690.6 4715.0 |
7358.7 1337.3 1744.5 4799.5 |
54 |
|
56 |
7284.3 1306.3 1692.4 4717.8 |
7361.3 1338.4 1746.3 4802.4 |
56 |
|
58 |
7286.9 13C7.4 1694.2 4720.6 |
73o3.8 1339.5 1748.1 4805.2 |
58 |
|
60 |
7289.5 1308.5 1696.0 4723.4 |
73G6.4 1340.6 1750.0 4808.0 |
60 |
|
80° |
81° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
7366.4 1340.6 1750 0 4808.0 |
7442.7 1372.8 1805.5 4893.9 |
0 |
|
2 |
7368 9 1341.7 1751.8 4810.9 |
7445.2 1373.9 1807.3 4896.8 |
2 |
|
4 |
7371.5 1342.7 1753.7 4813.7 |
7447.7 1375.0 1809.2 4899.7 |
4 |
|
6 |
7374.0 1343.8 1755.5 4816.6 |
7450.3 1376.1 1811.1 4902.6 |
6 |
|
8 |
7376.6 1344.9 1757.4 4819.4 |
7452.8 1377.1 1813.0 4905.4 |
8 |
|
10 |
7379.1 1346.0 1759.2 4822.3 |
7455.3 1378.2 1814.9 4908.3 |
10 |
|
12 |
7381.7 1347.0 1761.0 4825.1 |
7457.8 1379.3 1816.8 4911.2 |
12 |
|
14 |
7384.2 1348.1 1762.9 4828.0 |
7460.4 1380.4 1818.6 4914.1 |
14 |
|
16 |
7386.7 1349.2 1764.7 4830.8 |
7462.9 1381.4 1820.5 4917.0 |
16 |
|
18 |
7389.3 1350.3 1766.6 4833.7 |
7465.4 1382.5 1822.4 4919.9 |
•18 |
|
20 |
7391.8 1351.3 1768.4 4836.5 |
7467.9 1383.6 1824.2 4922.8 |
20' |
|
22 |
7394.4 1352.4 1770.2 4839.4 |
7470.4 1384.7 1826.1 4925.7 |
22 |
|
24 |
7396.9 1353.5 1772.1 4842.2 |
7473.0 1385.7 1828.0 4928.6 |
24 |
|
26 |
7399.5 1354.6 1773.9 4845.1 |
7475.5 1386.8 1829.9 4931.5 |
26 |
|
28 |
7402.0 1355.6 1775.8 4847.9 |
7478.0 1387.9 1831.8 4934.4 |
28 |
|
30 |
7404.5 1356.7 1777.6 4850.8 |
7480.5 1389.0 1833.7 4937.2 |
30 |
|
32 |
7407.1 1357.8 1779.4 4853.7 |
7483.1 1390.1 1835.6 4940.2 |
82 |
|
34 |
7409.6 1358.9 1781.3 4856.5 |
7485.6 1391.2 1837.5 4943.1 |
34 |
|
36 |
7412.2 1359.9 1783.1 4859.4 |
7488.1 1392.3 1839.4 4946.0 |
36 |
|
38 |
7414.7 1361.0 1785.0 4862.3 |
7490.6 1393.4 1841.3 4948.9 |
38 |
|
40 |
7417.3 1362.1 1786.8 4865.1 |
7493.2 1394.5 1843.2 4951.8 |
40 |
|
42 |
7419.8 1363.2 1788.6 4868.0 |
7495.7 1395.6 1845.1 4954.7 |
42 |
|
44 |
7422.3 1364.2 1790.5 4870.9 |
7498.2 1396.7 1847.0 4957.6 |
44 |
|
46 |
7424.9 1365.3 1792.4 4873.8 |
7500.7 1397.8 1848.9 4960.6 |
46 |
|
48 |
7427.4 1366.4 1794 3 4876.6 |
7503.3 1398.9 1850.8 4963.5 |
48 |
|
50 |
7430.0 1367.5 1796.2 4879.5 |
7505.8 1400.0 1852.7 4966.4 |
60 |
|
52 |
7432.5 1368.5 1798.0 4882.4 |
7508.3 1401.1 18546 4969.3 |
52 |
|
54 |
7435.1 1369.6 1799.9 4885 3 |
7510.8 1402.2 1856.5 4972.2 |
54 |
|
56 |
7437.6 1370 7 1801.8 4888.1 |
7513.3 1403.3 1858.4 4975.1 |
56 |
|
58 |
7440.1 1371 .8 1803.7 4891.0 |
7515.9 1404.4 1860.3 4978.0 |
58 |
|
60 |
7442.7 1372.8 1805.5 4893.9 |
7518.4 1405.5 18623 4981. C |
60 \ |
152 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
82° |
83° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
7518.4 1405.5 1862.3 4981.0 |
7593.6 1438.5 1920.6 5069.4 |
0 |
|
2 |
7520.9 1406.6 1§64.2 4983.9 |
7596.1 1439.6 1922.6 5072.4 |
2 |
|
4 |
7523.4 1407.7 1866.1 4986.8 |
7598.6 1440.7 1924.6 5075.4 |
4 |
|
6 |
7525.9 1408.8 1868.1 4989.8 |
7601.1 1441.8 1926.5 5078.4 |
6 |
|
8 |
7528.4 1409.9 1870.0 4992.7 |
7603.6 1442.9 1928.5 5081.4 |
8 |
|
10 |
7530.9 1411.0 1871.9 4995.7 |
7606.0 1444.0 1930.5 5084.4 |
10 |
|
12 |
7533.4 1412.1 1873 9 4998.6 |
7608.5 1445.1 1932.4 5087.3 |
12 |
|
14 |
7535.9 1413.2 1875.8 5001.5 |
7611.0 1446.2 1934.4 5090.3 |
14 |
|
16 |
7538.5 1414.3 1877.7 5004.5 |
7613.5 1447.3 1936.4 5093.3 |
16 |
|
18 |
7541.0 1415.4 1879.7 5007.4 |
7616.0 1448.4 1938.4 5096.3 |
18 |
|
20 |
7543.5 1416.5 1881.6 5010.3 |
7618.5 1449.6 1940.4 5099.3 |
20 |
|
22 |
7546.0 1417.6 1883.5 5013.3 |
7621.0 1450.7 1942.4 5102.3 |
22 |
|
24 |
7548.5 1418.7 1885.5 5016.2 |
7623.5 1451.8 1944.4 5105.2 |
24 |
|
26 |
7551.0 1419.8 1887.4 5019.2 |
7626.0 1452.9 1946.4 5108.2 |
26 |
|
28 |
7553.5 1420.9 1889.3 5022.1 |
7628.5 1454.0 1948.4 5111.2 |
28 |
|
30 |
7556.0 1422.0 1891.3 5025.0 |
7630.9 1455.1 1950.4 5114.2 |
30 |
|
32 |
7558.5 1423.1 1893.2 5028.0 |
7633.4 1456.2 1952.4 5117.2 |
32 |
|
34 |
7561.0 1424.2 1895.1 5031.0 |
7635.9 1457.3 1954.4 5120.2 |
34 |
|
36 |
7563.5 1425.3 1897.1 5033.9 |
7638.4 1458.4 1956.4 5123.2 |
36 |
|
38 |
7566.0 1426.4 1899.0 5036.9 |
7640.9 1459.5 1958.4 5126.2 |
38 |
|
40* |
7568.5 1427.5 1901.0 5039.8 |
7643.4 1460.7 1960.4 5129.2 |
40 |
|
42 |
.7571.0 1428.6 1902.9 5042.8 |
7645.9 1461.8 1962.4 5132.2 |
42 |
|
44 |
7573.5 1429.7 1904.9 5045.8 |
7648.4 1462.9 1964.4 5135.2 |
44 |
|
46 |
7576.1 1430.8 1906.9 5048.7 |
7650.9 1464.0 1966.4 5138.2 |
46 |
|
48 |
7578.6 1431.9 1908.8 5051.7 |
7653.4 1465.1 1968.4 5141.2 |
48 |
|
50 |
7581.1 1433.0 1910.8 5054.6 |
7655.8 1466.2 1970.4 5144.3 |
50 |
|
52 |
7583.6 1434.1 1912.8 5057.6 |
7658.3 1467.3 1972.4 5147.3 |
52 |
|
54 |
7586.1 1435.2 1914.7 5060.6 |
7660.8 1468.4 1974.4 5150.3 |
54 |
|
56 |
7588.6 1436.3 1916.7 5063.5 |
7663.3 1469.5 1876.4 5153.3 |
56 |
|
58 |
7591.1 1437.4 1918.7 5066.5 |
7665.8 1470.6" 1978.4 5156.3 |
58 |
|
60 |
7593.6 1438.5 1920.6 5069.4 |
7668.3 1471.8 1980.5 5159.3 |
60 |
|
84° |
85° |
||
|
t |
L. C. M. E. T. |
L. C. M. E. 1 |
|
|
0 |
7668.3 1471.8 1980.5 5159.3 |
7742.4 1505.4 2041.8 5250.6 |
0 |
|
2 |
7670.8 1472.9 1982.5 5162.3 |
7744.8 1506.5 2043.9 5253.6 |
2 |
|
4 |
7673.2 1474.0 1984.5 5165.3 |
7747.3 1507.6 2046.0 5256.7 |
4 |
|
6 |
7675.7 1475.1 1986.6 5168.4 |
7749.7 1508.8 2048.0 5259.8 |
6 |
|
8 |
7678.2 1476.2 1988.6 5171.4 |
7752.2 1509.9 2050.1 5262.9 |
8 |
|
10 |
7680.6 1477.4 1990.6 5174.4 |
7754.6 1511.0 2052.2 5266 0 |
10 |
|
12 |
7683.1 1478.5 1992.7 5177.5 |
7757.1 1512.2 2054.2 5269.0 |
12 |
|
14 |
7685.6 1479.6 1994.7 5180.5 |
7759.5 1513.3 2056.3 5272.1 |
14 |
|
16 |
7688.1 1480.7 1996.7 5183.5 |
7762.0 1514.4 2058.4 5275.2 |
16 |
|
18 |
7690.5 1481.8 1998.8 5186.6 |
7764.4 1515.6 2060.5 5278.3 |
18 |
|
"20 |
7693.0 1483.0 2000.8 5189.6 |
7766.9 1516.7 2062.6 5281.4 |
20 |
|
22 |
7695.5 1484.1 2002.8 5192.6 |
7769.3 1517.8 2064.7 5284.4 |
22 |
|
24 |
7697.9 1485.2 2004.9 5195.6 |
7771.8 1519.0 2066.8 5287.5 |
24 |
|
26 |
7700.4 1486.3 2006.9 5198.7 |
7774.2 1520.1 2068.9 5290.6 |
26 |
|
28 |
7702.9 1487.4 2008.9 5201.7 |
7776.7 1521.2 2071.0 5293.7 |
28 |
|
30 |
7705.3 1488.6 2011.0 5204.7 |
7779.1 1522.4 2073.1 5296.7 |
30 |
|
32 |
7707.8 1489.7 2013.0 5207.8 |
7781.5 1523.5 2075.2 5299.8 |
32 |
|
84 |
7710.3 1490.8 2015.0 5210.8 |
7784.0 1524.6 2077 3 5302.9 |
34 |
|
36 |
7712.8 1491.9 2017.0 5213.9 |
7786.4 1525.8 2079.4 5306.1 |
36 |
|
38 |
7715.2 1493.0 2019.1 5216.9 |
7788.9 1526.9 2081.5 5309.2 |
38 |
|
40 |
7717.7 1494.2 2021.2 5220.0 |
7791.3 1528.0 2083.7 5312.3 |
40 |
|
42 |
7720.2 1495.3 2023.2 5223.1 |
7793.8 1529.2 2085.8 5315.4 |
42 |
|
44 |
7722.6 1496.4 2025.3 5226.1 |
7796.2 1530.3 2087.9 5318.5 |
44 |
|
46 |
7725.1 1497.5 2027.4 5229.2 |
7798.7 1531.4 2090.0 5321.6 |
46 |
|
48 |
7727.6 1498.6 2029.4 5232.2 |
7801.1 1532.6 2092.1 5324.7 |
48 |
|
50 |
7730.0 1499.8 2031.5 5235.3 |
7803.6 1533.7 2094.2 5327.8 |
50 |
|
52 |
7732.5 1500.9 2033.6 5238.3 |
7806.0 1534.8 2096.3 5330 9 |
52 |
|
54 |
7735.0 1502.0 2035.6 5241 4 |
7808.5 1536.0 2098.4 5334.0 |
54 |
|
56 |
7737.5 1503.1 2037.7 5244.5 |
7810.9 1537.1 21.00.6 5337.1 |
56 |
|
58 |
7739 9 1504.2 2039.8 5247.5 |
7813 4 1538.2 2102.7 5340.2 |
58 |
|
60 |
7742.4 15054 2041.8 5250.6 |
7815.8 1539.3 2104.8 5343.3 |
60 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 153
|
86° |
87° |
||
|
L. C. M. E. ,T. |
L. C. M. E. T, |
/ |
|
|
0 |
7815.8 1539.3 2104.8 5343.3 |
7888.5 1573.6 2169.5 5437.5 |
b |
|
2 |
7818.2 1540.4 2106.9 5346.4 |
7890.9 1574.8 2171.6 5440.7 |
2 |
|
4 |
7820.6 1541.6 2109.1 5349.5 |
7893.3 1575.9 2173.8 5443.9 |
4 |
|
6 |
7823.1 1542.7 2111.2 5352.7 |
7895.7 1577.1 2176.0 5447.1 |
6 |
|
8 |
7825.5 1543.9 2113.4 5355.8 |
7898.1 1578.2 2178.2 5450.3 |
8 |
|
10 |
7827.9 1545.0 2115.5 5358.9 |
7900.5 1579.4 2180.4 5453.4 |
10 |
|
12 |
7830.3 1546.1 2117.6 5362.0 |
7903.0 1580.5 2182.5 5456.6 |
12 |
|
14 |
7832.8 1547.3 2119.8 5365.2 |
7905.4 1581.7 2184.7 5159.8 |
14 |
|
16 |
7835.2 1548.4 2121.9 5368.3 |
7907.8 1582.9 2186.9 5463.0 |
16 |
|
18 |
7837.6 1549.6 2124.1 5371.4 |
7910.2 1584.0 2189.1 5466.2 |
18 |
|
20 |
7840.0 1550.7 2126.2 5374.6 |
7912.6 1585.1 2191.3 5469.4 |
20 |
|
22 |
7842.4 1551.8 2128.3 5377.7 |
7915.0 1586.3 2193.5 5472.5 |
22 |
|
24 |
7844.9 1553.0 2130.5 5r80.8 |
7917.4 1587.4 2195.7 5475.7 |
24 |
|
26 |
7847.3 1554.1 2132.6 5383.9 |
7919.8 1588.6 2197.9 5478.9 |
26 |
|
28 |
7849.7 1555.3 2134.8 5387.1 |
7922.2 1589.7 2200.1 5482.1 |
28 |
|
30 |
7852.1 1556.4 2136.9 5390.2 |
7924.6 1590.9 2202.3 5485.3 |
30 |
|
32 |
7854.6 1557.5 2139.0 5393.4 |
7927.1 1592.0 2204.5 5488.5 |
82 |
|
34 |
7857.0 1558.7 2141.2 5396.5 |
7929.5 1593.2 2206.8 5491.7 |
34 |
|
36 |
7859.4 1559.8 2143.3 5399.7 |
7931.9 1594.3 2209.0 5494.9 |
36 |
|
38 |
7861.8 1561.0 2145.5 5402.8 |
7934.3 1595.5 2211.2 5498.1 |
38 |
|
40 |
7864.3 1562.1 2147.7 5406.0 |
7936.7 1596.6 2213.4 5501.3 |
40 |
|
42 |
7866.7 1563.2.2149.8 5409.1 |
7939.1 1597.8 2215.6 5504.5 |
42 |
|
44 |
7869.1 1564.4 2152.0 5412.3 |
7941.5 1598.9 2217.8 5507.7 |
44 |
|
46 |
7871.5 1565.5 2154.2 5415.4 |
7913.9 1600.1 2220.0 5510.9 |
46 |
|
48 |
7874.0 1566.7 2156.4 5418.6 |
7946.3 1601.2 2222.3 5514.1 |
48 |
|
50 |
7876.4 1567.8 2158.6 5421.8 |
7948.7 1602.4 2224.5 5517.3 |
50 |
|
52 |
7878.8 1568.9 2160.7 5424.9 |
7951.2 1603.5 2226.7 5520.5 |
52 |
|
54 |
7881.2 1570.1 2162.9 5428.1 |
7953.6 1604.7 2228.9 5523.7 |
54 |
|
56 |
7883.6 1571.2 2165.1 5431.2 |
7956.0 1605.8 2231.1 5526.9 |
56 |
|
58 |
7886.1 1572.4 2167.3 5434.4 |
7958.4 1607.0 2233.3 5530.1 |
58 |
|
60 |
7888.5 1573.6 2169.5 5437.5 |
7960.8 1608.2 2235.6 5533.3 |
60 |
|
88° |
89° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
7960.8 1608.2 2235.6 5533.3 |
8032.4 1643.0 2303.6 5630.8 |
0 |
|
2 |
7963.2 1609.4 2237.8 5536.6 |
8034.8 1644.1 2305.9 5631.1 |
2 |
|
4 |
7965.6 1610.5 2240.1 5539.8 |
8037.1 1645.3 2308.2 5637.4 |
4 |
|
6 |
7968.0 1611.7 2242.3 5543.1 |
8039.5 1646.5 2310.5 5640.7 |
6 |
|
8 |
7970.3 1612.8 2244.6 5546.3 |
8041.9 1647.7 2312.8 5644.0 |
8 |
|
10 |
7972.7 1614.0 2246.8 5549.5 |
8044.2 1648.9 2315.1 5647.3 |
10 |
|
1? |
7975.1 1615.2 2249.1 .5552.8 |
8046.6 1650.0 2317.4 5650.6 |
12 |
|
14 |
7977.5 1616.3 2251.3 5556.0 |
8049.0 1651.2 2319.7 5653.9 |
14 |
|
16 |
7979.9 1617.5 2253.6 5559.2 |
8051.4 1652.4 2322.0 5657.1 |
16 |
|
Ib |
7982.3 1618.6 2255.8 5562.5 |
8053.7 1653.6 2324.3 5660.4 |
18 |
|
20 |
7984.7 1619.8 2258.1 5565.7 |
8056.1 1654.8 2326.7 5663.7 |
20 |
|
22 |
7987.1 1621.0 2260.4 5568.9 |
8058.5 1655.9 2329.0 5667.0 |
22 |
|
24 |
7989.4 1622.1 2262.7 5572.2 |
8060.8 1657.1 2331.3 5670.3 |
24 |
|
26 |
7991.8 1623.3 2264.9 5575.4 |
8063.2 1658.3 2333.7 5673.6 |
26 |
|
28 |
7994.2 1624.4 2267.2 5578.6 |
8065.6 1659.5 2336.0 5676.9 |
28 |
|
30 |
7996.6 1625.6 2269.5 5581.9 |
8067.9 1660.7 2338.3 5680.2 |
30 |
|
32 |
7999.0 1626.8 2271.7 5585.1 |
8070.3 1661.8 2340.7 5683.5 |
32 |
|
34 |
8001.4 1627.9 2273.9 5588.4 |
8073.7 1663.0 2343.0 5686.8 |
34 |
|
36 |
8003.8 1629.1 2276.2 5591.7 |
8075.1 1664.2 2345.3 5690.2 |
36 |
|
38 |
8006.1 1630.2 2278.5 5594.9 |
8077.4 1665.4 2347.7 5693.5 |
38 |
|
40 |
8008.5 1631.4 2280.8 5598.2 |
8079.8 1666.6 2350.0 5696.8 |
40 |
|
42 |
8010.9 1632.6 2283.0 5601.4 |
8082.2 1667.7 2352.3 5700.1 |
42 |
|
44 |
8013.3 1633.7 2285.3 5604.7 |
8084.5 1668.8 2354.7 5703.4 |
44 |
|
46 |
8015.7 1634.9 2287.6 5608.0 |
8086.9 1670.0 2357.0 5706.8 |
46 |
|
48 |
8018.1 1636.0 2289.9 5611.2 |
8089.3 1671.2 2359.3 5710.1 |
48 |
|
50 |
8020.5 1637.2 2292.2 5614.5 |
8091.6 1672.4 2361.7 5713.4 |
50 |
|
52 |
8022.9 1638.4 2294.4 5617.8 |
8094.0 1673.5 2364.0 5716.7 |
52 |
|
54 |
8025.2 1639.5 2296.7 5621.0 |
8096.4 1674.7 2366.3 5720.0 |
54 |
|
56 |
8027.6 1640.7 2299.0 5624.3 |
8098.8 1675.9 2368.7 5723.4 |
56 |
|
58 |
8030.0 1641.8 2301.3 56-37.5 |
8101.1 1677.1 2371.0 5726.7 |
58 |
|
60 |
8032.4 1643.0 2303.6 5630.8 |
8103.5 1678.3 2373.4 5730.0 |
60 |
154 6.— FUNCTIONS OF A ONE-DEGREE CURVE.
|
90° |
91° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
8103.5 1678.3 2373.4 5730.0 |
8173.9 713.8 2445.1 5830.9 |
0 |
|
2 |
8105.8 1679.5 2375.8 5733.3 |
8176.2 715.0 2447.5 5834.3 |
2 |
|
4 |
8108.2 1680.6 2378.2 5736.7 |
8178.5 716.2 2450.0 5837.7 |
4 |
|
6 |
8110.5 1681.8 2380.5 5740.0 |
8180.9 717.4 2452.4 5841.1 |
6 |
|
8 |
8112.9 1683.0 2382.9 5743.4 |
8183.2 718.6 2454.8 5844.5 |
8 |
|
10 |
8115.2 1684.2 2385.3 5746.7 |
8185.5 719.7 2457.2 5847.9 |
10 |
|
12 |
81176 1685.4 2387.6 5750.0 |
8187.9 720.9 2459.7 5851.3 |
12 |
|
14 |
8119.9 1686.5 2390.0 5753.4 |
8190.2 1722.1 2462.1 5854.7 |
14 |
|
16 |
8122.3 1687.7 2392.4 5756.7 |
8192.5 1723.3 2464.5 5858.1 |
16 |
|
18 |
8124.6 1688.9 2394.7 5760.1 |
8194.8 1724.5 2467.0 5861.5 |
18 |
|
20 |
8127.0 1690.1 2397.1 5763.4 |
8197.2 1725.7 2469.4 5864.9 |
20 |
|
22 |
8129.3 1691.3 2399.5 5766.8 |
8199.5 1726.9 2471.9 5868.3 |
22 |
|
24 |
8131.7 1692.5 2401.9 5770.1 |
8201.8 1728.1 2474.3 5871.8 |
24 |
|
26 |
8134.0 1693.6 2404.3 5773.5 |
8204.2 1729.3 2476.7 5875.2 |
26 |
|
28 |
8136.4 1694.8 2406.6 5776.9 |
8206.5 1730.5 2479.2 5878.6 |
28 |
|
30 |
8138.7 1696.0 2409.0 5780.2 |
8208.8 1731.7 2481.6 5882.0 |
30 |
|
32 |
8141.1 1697.2 2411.4 5783.6 |
8211.1 1732.9 2484.1 5885.4 |
32 |
|
34 |
8143.4 1698.4 2413.8 5787.0 |
8213.5 1734.1 2486.5 5888.9 |
34 |
|
36 |
8145.8 1699.6 2416.2 5790.3 |
8215.8 1735.3 2489.0 5892.3 |
36 |
|
38 |
8148.1 1700.7 2418.6 5793.7 |
8218.1 1736.4 2491.5 5895.7 |
38 |
|
40 |
8150.4 1701.9 2421.0 5797.1 |
8220.4 1737.6 2493.9 5899.2 |
40 |
|
42 |
8152.8 1703.1 2423.4 5800.4 |
8222.8 1738.8 2496.4 5902.6 |
42 |
|
44 |
8155.1 1704.3 2425.8 5803.8 |
8225.1 1740.0 2498.9 5906.0 |
44 |
|
46 |
8157.5 1705.5 2428.2 5807.2 |
8227.4 1741.2 2501.3 5909.4 |
46 |
|
48 |
8159.8 1706.7 2430.6 5810.6 |
8229.7 1742.4 2503.8 5912.9 |
48 |
|
50 |
8162.2 1707.9 2433.0 5814.0 |
8232.0 1743.6 2506.3 5916.3 |
50 |
|
52 |
8164.5 1709.0 2435.4 5817.3 |
8234.3 1744.8 2508.7 5919.8 |
52 |
|
54 |
8166.8 1710.2 2437.9 58:20.7 |
8236.7 1746.0 2511.2 5923.2 |
54 |
|
56 |
81G9.2 1711.4 2440.3 5824.1 |
8239.0 1747.2 2513.7 5926.7 |
56 |
|
58 |
8171.5 1712.6 2442.7 5827.5 |
8241.3 1748.4 2516.2 5930.1 |
58 |
|
60 |
8173.9 1713.8 2445.1 5830.9 |
8243.6 1749.6 2518.7 5933.6 |
60 |
|
92° |
93° |
||
|
/ |
L. C M. E. T. |
L. C. M. E. T. |
|
|
0 |
8243.6 1749.6 2518.7 5933.6 |
8312.8 1785.7 2594.2 603S.2 |
0 |
|
2 |
8245.9 1750.8 2521.2 5937.0 |
8315.1 1786.9 2596.8 6041.7 |
2 |
|
4 |
8248.2 1752.0 2523.6 5940.5 |
8317.4 1188.2 2599.3 6045.2 |
4 |
|
6 |
8250.6 1753.2 2526.1 5944.0 |
8319.7 1789.4 2G01.9 6048.7 |
6 |
|
\ |
8252.9 1754.4 2528.6 5947.4 |
8322.0 1790.6 2604.4 6052.2 |
8 |
|
10 |
8255.2 1755.6 2531.1 5950.9 |
8324.3 1791.8 2G07.0 6055.8 |
10 |
|
12 |
8257.5 1756.8 2533.6 5954.4 |
8326.6 1793.0 2609.6 6059.3 |
12 |
|
14 |
8259.8 1758.0 2536.1 5957.8 |
8328.8 1794.2 2612.1 6062.8 |
14 |
|
16 |
8262.2 1759.2 2538.6 5961.3 |
8331.1 1795.4 2614.7 6066.4 |
16 |
|
18 |
8264.5 1760.4 2541.1 5964.8 |
8333.3 1796.6 2617.3 6069.9 |
18 |
|
20 |
8266.8 1761.6 2543.6 5968.2 |
8335.6 1797.8 2619.8 6073.4 |
20 |
|
22 |
8269.1 17G2.8 2546.1 5971.7 |
8337.9 1799.1 2622.4 6077.0 |
22 |
|
24 |
8271.4 1764.0 2548.6 5975.2 |
8340.2 1800.3 2625.0 6080.5 |
24 |
|
26 |
8273.7 1765.2 2551.2 5978.7 |
8342.5 1801.5 2627.6 6084.1 |
26 |
|
28 |
8276.0 1766.4 2553.7 5982.2 |
8344.8 1802.7 2630.2 6087.6 |
28 |
|
30 |
8278.3 1767.6 2556.2 5985.6 |
8347.1 1803.9 2632.7 6091.2 |
30 |
|
32 |
8280.6 1768.8 2558.7 5989.1 |
8349.4 1805.1 2635.3 6094.7 |
32 |
|
34 |
8282.9 17^0.0 2561.2 5992.6 |
8351.7 1806.3 2637.9 6098.3 |
34 |
|
36 |
8285.2 1771.2 2563.8 5996.1 |
8354.0 1807.6 2640.5 6101.8 |
36 |
|
.38 |
8287.5 1772.5 2566.3 5999.6 |
8356.3 1808.8 2643.1 6105.4 |
38 |
|
40 |
8289.8 1773.7 2568.8 6003.1 |
8358.5 1810.0 2645.7 6109.0 |
40 |
|
42 |
8292.1 1774.9 2571.3 6006.6 |
8360.8 1811.2 2648.3 6112.5 |
42 |
|
44 |
8294.4 1776.1 2573.9 6010.1 |
8363.1 1812.4 2650.9 6116.1 |
44 |
|
46 |
8296.7 1777.3 2576.4 6013.6 |
8365.4 1813.6 2653.5 6119.7 |
46 |
|
48 |
8299.0 1778.5 2578.9 6017.1 |
8367.7 1814.9 2656.1 6123.2 |
48 |
|
50 |
8301.3 1779.7 2581.5 6020.6 |
8369.9 1816.1 2658.7 6126.8 |
50 |
|
52 |
8303.6 1780.9 2584.0 6024.1 |
8372.2 1817.3 2661.3 6130.4 |
52 |
|
54 |
8305.9 1782.1 2586.6 6027.6 |
8374.5 1818.5 2663.9 6133.9 |
54 |
|
56 |
8308.2 1783.3 2589.1 6031.1 |
8376.8 1819.7 2666.6 6137.5 |
56 |
|
58 |
8310.5 1784.5 2591.7 6034.6 |
8379.1 1820.9 2669.2 6141.1 |
58 |
|
GO |
8312.8 1785.7 2594.2 6038.2 |
8381.3 1822.2 2671.8 6144.7 |
60 |
6 —FUNCTIONS OF A ONE-DEGREE CURVE. 155
|
94° |
95° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
8381.3 1822.2 2671.8 6144.7 |
8449.2 1858.9 2751.5 6253.2 |
0 |
|
2 |
8383.6 1823.4 2674.4 6148.3 |
8451.5 1860.1 2754.2 6256.9 |
2 |
|
4 |
8385.9 1824.6 2677.0 6151.9 |
8453.7 1861.3 2756.9 6260.5 |
4 |
|
6 |
8388.1 1825.8 2679.7 6155.4 |
8456.0 1862.6 2759.6 6264.2 |
6 |
|
8 |
8390.4 1827.0 2682.3 6159.0 |
8458.2 1863.8 2762.3 6267.8 |
8 |
|
10 |
8392.7 1828.3 2684.9 6162.6 |
8460.4 1865.0 27650 6271.5 |
10 |
|
12 |
8395.0 1829.5 2687.6 6166.2 |
8462.7 1866.3 2767.7 6275.2 |
12 |
|
14 |
8397.2 1830.7 2690.2 6169.8 |
8464.9 1867.5 2770.4 6278.8 |
14 |
|
16 |
8399.5 1831.3 2692.8 6173.4 |
8467.2 1868.7 2773.1 6282.5 |
16 |
|
18 |
8401.7 1833.1 2695.6 6177.0 |
8469.4 1869.9 2775.8 6286.2 |
18 |
|
20 |
8404. C 1834.4 2698.1 6180.6 |
8471.7 1871.2 2778.5 6289.8 |
20 |
|
22 |
8406.3 1835.6 2700.8 6184.2 |
8473.9 1872.4 2781.2 6293.5 |
22 |
|
24 |
8408.5 1836.8 2703.4 6187.8 |
8476.2 1873.6 2784.0 6297.2 |
24 |
|
26 |
8410.8 1838.0 2706.1 6191.5 |
8478.4 1874.9 2786.7 6300.9 |
26 |
|
28 |
8413.1 18J9.3 2708.7 6195.1 |
8480.7 1876.1 2789.4 6304.6 |
28 |
|
30 |
8415.3 1840.5 2711.4 6198.7 |
8482.9 1877.3 2792.1 6308 2 |
30 |
|
32 |
8417.6 1841.7 2714.0 6202.3 |
8485.1 1878.6 2794.9 6311.9 |
32 |
|
34 |
8419.9 1842.9 2716.7 6205.9 |
8487.4 1879.8 2797.6 6315.6 |
34 |
|
36 |
8422.1 1844.2 2719.3 6209.5 |
8489.6 1881.0 280U.3 6319.3 |
36 |
|
38 |
8424.4 1845.4 2722.0 6213.2 |
8491.9 1882.3 2803.1 6323.0 |
38 |
|
40 |
8426.6 1846.6 2724.7 6216.8 |
8494.1 1883.5 2805.8 6326.7 |
40 |
|
42 |
8428.9 1847.8 itf27.3 6220.4 |
8496.3 1884.8 2808.6 6330.4 |
42 |
|
44 |
8431.2 1849.1 2730.0 6224.1 |
8498.6 1886.0 2811.3 6334.1 |
44 |
|
46 |
8433.4 1850.3 2732.7 6227.7 |
8500.8 1887.2 2814.1 6337.8 |
46 |
|
48 |
8435.7 1851.5 2735.4 6231.3 |
8503.0 1888.5 2816.8 6341.5 |
48 |
|
50 |
8437.9 1852.7 2738.0 6235.0 |
8505.3 1889.7 2819.6 6345.2 |
50 |
|
52 |
8440.2 1854.0 2740.7 6238.6 |
8507.5 1890.9 2822.3 6349.0 |
52 |
|
54 |
8442.4 1855.2 2743.4 6242.3 |
8509.8 1892.2 2825.1 6352.7 |
54 |
|
56 |
8444.7 1856.4 2746.1 6245.9 |
8512.0 1893.4 2827.8 6356.4 |
56 |
|
58 |
8447.0 1857.6 2748.8 6249.6 |
8514.2 1894.6 2830.6 6360.1 |
58 |
|
60 |
8449.2 1858.9 2751.5 6253.2 |
8516.4 1895.9 2833.4 6363.8 |
60 |
|
96° |
97° |
||
|
/ |
L. C. M. E. T. |
L. C. M. E. T. |
t |
|
0 |
8516.4 1895. S 2833.4 6363.8 |
8583.0 1933.2 2917.5 6476.6 |
0 |
|
2 |
8518.7 1897.1 2836.1 6367.5 |
8585.2 1934.4 2900.3 6480.4 |
2 |
|
4 |
8520.9 1898.4 2838.9 6371.3 |
8587.5 1935.7 2923.2 6484.2 |
4 |
|
6 |
8523.1 1899.6 2841.7 6375.0 |
8589.7 1936.9 2926.0 6488.0 |
6 |
|
8 |
8525.4 1900.8 2844.5 6378.7 |
8591.9 1938.2 2928.9 6491.8 |
8 |
|
10 |
8527.6 1902.1 2847.2 6382.5 |
8594.1 1939.4 2931.7 6495.6 |
10 |
|
12 |
8529.8 1903.3 2850.0 6386.2 |
8596.3 1940.7 2934.6 6499.4 |
12 |
|
14 |
8532.0 19046 2852.8 6389.9 |
8598.5 1941.9 2937.5 6503 2 |
14 |
|
16 |
8534.3 1905.8 2855.6 6393.7 |
8600.7 1943.2 2940.3 6507.1 |
16 |
|
18 |
8536.5 1907.0 2858.4 6397.4 |
8602.9 1944.4 2943.2 6510.9 |
18 |
|
20 |
8538.7 1908.3 2861.2 6401.2 |
8605.1 1945.7 2946.1 6514.7 |
20 |
|
22 |
8540.9 1909.5 2864.0 6404.9 |
8607.3 1946.9 2948.9 6518.5 |
22 |
|
24 |
8543.2 1910.8 2866.7 6408.7 |
8609.5 1948.2 2951.8 6522.3 |
24 |
|
26 |
8545.4 1912.0 2869.5 6412.4 |
8611.7 1949.4 2954.7 6526.2 |
26 |
|
28 |
8547. e 1913.3 2872.3 6416.2 |
8613.9 1950.7 2957.6 6530.0 |
28 |
|
30 |
8549.8 1914.5 2875.1 6419.9 |
8616.1 1952:0 29G0.4 6533.8 |
30 |
|
32 |
8652.0 1915.7 2877.9 6423.7 |
8618.3 1953.2 2963.3 6537.7 |
32 |
|
34 |
8554.3 1917.0 2880.8 6427.5 |
8620.5 1954.5 2966.2 6541.5 |
' 34 |
|
36 |
8556.5 1918.2 2883.6 6431.2 |
8622.7 1955.7 2969.1 6545.3 |
36 |
|
38 |
8558.7 1919.5 2886.4 6435.0 |
8624.9 1957.0 2972.0 6549.2 |
38 |
|
40 |
8560.9 1920.7 2889.2 6438.8 |
8627.1 1958.2 2974.9 6553.0 |
40 |
|
42 |
8563.1 1922.0 2892.0 6442 5 |
8629.3 1959 5 2977.8 6556 9 |
42 |
|
44 |
8565 3 1923.2 2894.8 6446.3 |
8631.5 1960.7 2980.7 6560.7 |
44 |
|
46 |
8567 6 1924 5 2897.7 6450.1 |
8633.7 1962.0 2983.6 6564.6 |
46 |
|
48 |
8569 8 1925.7 2900.5 6453.9 |
8635.8 1963.2 2986.5 6568 4 |
48 |
|
50 |
8572.0 1927.0 2903.3 6457.6 |
8638.0 1964.5 2989.4 6572.3 |
50 |
|
52 |
8574.2 1928.2 2906.1 6461.4 |
8040.2 1965.8 2992.3 6576.2 |
52 |
|
54 |
8576.4 1929 4 2W9.0 6465.2 |
8642.4 1967.0 2995.2 6580.0 |
54 |
|
56 |
8578.6 1930.7 2911.8 6-169.0 |
8644.6 1968.3 2998.1 6583.9 |
56 |
|
58 |
8580.8 1931.9 2914.7 6472.8 |
8646.8 1969.5 3001.1 6587.7 |
58 |
|
60 |
8583.0 1933.2 2917.5 6476.6 |
8649 0 1970.8 3004 0 6591.6 |
60 |
156 6.— FUNCTIONS OF A. ONE-DEGREE CURVE.
|
98° |
99° |
||
|
L. C. M. B. T. |
L. C. M. E. T. |
||
|
0 |
8649.0 1970.8 3004.0 6591.6 |
8714.3 2008.7 3092.9 6709.0 |
0 |
|
2 |
8651.2 1972.0 3006.9 6595.5 |
8716.4 2009.9 3095.9 6712.9 |
2 |
|
4 |
8653.3 1973.3 3009.8 6599.4 |
8718.6 2011.2 3098.9 6716.9 |
4 |
|
6 |
8655.5 1974.6 3012.8 6603.2 |
8720.7 2012.5 3101.9 6720.8 |
6 |
|
8 |
8657.7 1975.8 3015.7 6607.1 |
8722.9 2013.7 3104.9 6724.8 |
8 |
|
10 |
8659.9 1977.1 3018.6 6611.0 |
8725.1 2015.0 3107.9 6728.8 |
10 |
|
12 |
8662.1 1978.3 3021.6 6614.9 |
8727.2 2016.3 3111.0 6732.7 |
12 |
|
14 |
8664.3 1979.6 3024.5 6618.8 |
8729.4 2017.5 3114.0 6736.7 |
14 |
|
16 |
8666.4 1980.9 3027.5 6622.7 |
8731.5 2018.8 3117.0 6740.7 |
16 |
|
18 |
8668.6 1982.1 3030.4 6626.6 |
8733.7 2020.1 3120.0 6744.6 |
18 |
|
20 |
8670.8 1983.4 3033.3 6630.5 |
8735.9 2021.4 3123.1 6748.6 |
20 |
|
22 |
8673.0 1984.6 3036.3 6634.4 |
8738.0 2022.6 3126.1 6752.6 |
22 |
|
24 |
8675.2 1985.9 3039.3 6638.3 |
8710.2 2023.9 3129.1 6756.6 |
24 |
|
26 |
8677.8 1987.2 3042.2 6642.2 |
8742.3 2025.2 3132.2 6760.6 |
26 |
|
28 |
8679.5 1988.4 3045.2 6646.1 |
8744.5 2026.4 3135.2 G764.6 |
28 |
|
30 |
8681.7 1989.7 3048.1 6650.0 |
8746.6 2027.7 3138.3 6768.6 |
30 |
|
32 |
8683.9 1991.0 3051.1 6653.9 |
8748.8 2029.0 3141.3 6772.6 |
32 |
|
34 |
8686.0 1992.2 3054.1 6657.8 |
8750.9 2030.3 3144.4 6776.6 |
34 |
|
36 |
8688.2 1993.5 3057.0 6661.7 |
8753.1 2031.5 3147.4 6780.6 |
36 |
|
38 |
8690.4 1994.7 3060.0 6665.7 |
8755.3 2032.8 3150.5 6784.6 |
38 |
|
40 |
8692.6 1996.0 3063.0 6669.6 |
8757.4 2034.1 3153.5 6788.6 |
40 |
|
42 |
8694.7 1997.3 3066.0 6673.5 |
8759.5 2035.4 3156.6 6792.6 |
42 |
|
44 |
8696.9 1998.5 3068.9 6677.4 |
8761.7 2036.6 3159.7 6796.6 |
44 |
|
46 |
8699.1 1999.8 3071.9 6681.4 |
8763.8 2037.9 3162.7 6800.6 |
46 |
|
48 |
8701.2 2001.1 3074.9 6685.3 |
8766.0 2039.2 3165.8 6804.6 |
48 |
|
60 |
8703.4 2002.3 3077.9 6689.2 |
8768.1 2040.5 3168.9 6808.6 |
50 |
|
52 |
8705.6 2003.6 3080.9 6693.2 |
8770.3 2041.7 3172.0 6812.6 |
52 |
|
54 |
8707.8 2004.9 3083.9 6697.1 |
8772.4 2043.0 3175.1 6816.7 |
54 |
|
56 |
8709.9 2006.1 3086.9 6701.1 |
8774.6 2044.3 3178.1 6820.7 |
56 |
|
58 |
8712.1 2007.4 3089.9 6705.2 |
8776.7 2045.6 3181.2 6824.7 |
58 |
|
60 |
8714.3 2008.7 3092.9 6709.0 |
8778.9 2046.8 3184.3 6828.8 |
60 |
|
100° |
101° |
||
|
L C. M. E. T. |
L. C. M. E. T. |
/ |
|
|
" |
8778.9 2046.8 3184.3 6828.8 |
8842.8 2085.3 3278.3 6951 0 |
0 |
|
2 |
8781.0 2048.1 3187.4 6832.8 |
8844.9 2086.6 3281.5 6955.2 |
2 |
|
4 |
8783.1 2049.4 3190.5 6836.8 |
8847.0 2087.8 3284.7 6959.3 |
4 |
|
6 |
8785.3 2050.7 3193.6 6840.9 |
8849.2 2089.1 3287.9 6963.4 |
6 |
|
8 |
8787.4 2051.9 3196.7 6844.9 |
8851.3 2090.4 3291.1 6967.6 |
8 |
|
10 |
8789.6 2053.2 3199.8 6,849.0 |
8853.4 2091.7 3294.3 6971.7 |
10 |
|
12 |
8791.7 2054.5 3:202.9 6853.0 |
8855.5 2093.0 3297.5 6975.8 |
12 |
|
14 |
8793.9 2055.8 3:206.0 6857.1 |
8857.6 2094.3 3300.7 6980.0 |
14 |
|
16 |
8796.0 2057.1 3209.1 6861.1 |
8859.8 2095.6 3303.9 6984 1 |
16 |
|
18 |
8798.9 2058.3 3212.2 6865.2 |
8861.9 2096.9 3307.1 6988.2 |
18 |
|
20 |
8800.3 2059.6 3215.4 6869.2 |
8864.0 2098.2 3310.3 6992.4 |
20 |
|
22 |
8802.4 2060.9 3218.5 6873.3 |
8866.1 2099.4 3313.5 6996.6 |
22 |
|
24 |
8804.5 2062.2 3221.6 6877.4 |
8868.2 2100.7 3316.7 7000.7 |
24 |
|
26 |
8806.7 2063.5 3224.7 6881.4 |
8870.3 2102.0 3319.9 7004.9 |
26 |
|
28 |
8808.8 2064.7 3227.9 6885.5 |
8872.4 2103.3 3323.1 7009.0 |
28 |
|
30 |
8810.9 2066.0 3231 0 6889.6 |
8874.5 2104.6 3326.4 7013.2 |
30 |
|
32 |
8813.1 2067.3 3234.1 6893.7 |
8876.7 2105.9 3329.6 7017.3 |
32 |
|
34 |
8815.2 2068.6 3237 3 6897.8 |
8878.8 2107.2 3332.8 7021.5 |
34 |
|
36 |
8817.3 2069.9 32404 6901.8 |
8880.9 2108.5 3336.0 7025.7 |
36 |
|
38 |
8819.5 2071.1 3243.5 6905.9 |
8883.0 2109.8 3339.3 7029.9 |
38 |
|
40 |
8821.6 2072.4 3246.7 6910.0 |
8885.1 2111.1 3342.5 7034.0 |
40 |
|
42 ' |
8823.7 2073.7 3249.8 6914.1 |
8887.2 2112.4 3345.8 7038.2 |
42 |
|
44 |
8825.8 2075.0 3253.0 6918.2 |
8889.3 2113.6 3349.0 7042.4 |
44 |
|
46 |
8828.0 2076.3 3256.2 6922.3 |
8891.4 2114.9 3352.3 7046.6 |
46 |
|
48 |
8830.1 2077.6 3259.3 6926.4 |
8893.5 2116.2 3355.5 7050.8 |
48 |
|
50 |
8832.2 2078.9 3262.5 6930.5 |
8895.6 2117.5 3358.8 7055.0 |
50 |
|
52 |
8834.3 2080.1 3265.7 6934.6 |
8897.7 2118.8 3362.0 7059.2 |
52 |
|
54 |
8836.4 2081.4 3268.8 6938.7 |
8899.8 2120.1 3365.5 70634 |
54 |
|
56 |
8838.6 2082.7 3272.0 6942.8 |
8901.9 2121.4 3368.7 7067.6 |
56 |
|
58 |
8340.7 2084.0 3275.2 6946.9 |
8904.0 2122.7 3372.0 7071.8 |
58 |
|
60 |
88428 2085.3 3278.3 6951.0 |
8906.1 2124.0 3375.1 7076.0 |
60 |
6.— FUNCTIONS OF A ONE-DEGREE CURVE. 157
|
102° |
103° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
||
|
0 |
8906.1 2124.0 3375.1 7076.0 |
8968.7 2163.0 3474.6 7203.6 |
0 |
|
2 |
8908.2 2125.3 3378.3 7080.2 |
8970.8 2164.3 3478.0 7207.9 |
2 |
|
4 |
8910.3 2126.6 3381.6 7084.4 |
8972.9 2165.6 3481.4 7212.2 |
4 |
|
6 |
8912.4 2127.9 3384.9 7088.6 |
8974.9 2166.9 3484.7 7216.5 |
6 |
|
8 |
8914.5 2129.2 3388.2 7092.8 |
8977.0 2168.2 3488.1 7220.8 |
8 |
|
10 |
8916.6 2130.5 3391.5 7097.1 |
8979.1 2169.5 3491.5 7225.1 |
10 |
|
12 |
8918.7 2131.8 3394.7 7101.3 |
8981.1 2170.8 3494.9 7229.5 |
12 |
|
14 |
8920.8 2133.1 3398.0 7105.5 |
8983.2 2172.1 3498.3 7233.8 |
14 |
|
16 |
8922.9 2134.4 3401.3 7109.7 |
8985.3 2173.4 3501.6 7238.1 |
16 |
|
18 |
8925.0 2135.7 3404.6 7114.0 |
8987.3 2174.7 3505.3 7242.4 |
18 |
|
20 |
8927.0 2137.0 3407.9 7118.2 |
8989.4 2176.1 3508.4 7246.8 |
20 |
|
22 |
8929.1 2138.3 3411.2 7122.4 |
8991.5 2177.4 3511.8 7251.1 |
30 |
|
24 |
8931.2 2139.6 3414.5 7126.7 |
8993.5 2178.7 3515.2 7255.4 |
24 |
|
26 |
8933.3 2140.9 3417.9 7130.9 |
6995.6 2180.0 3518.7 7259.8 |
26 |
|
28 |
8935.4 2142.2 3421.2 7135.2 |
8997.7 2181.3 3522.1 7264.1 |
28 |
|
30 |
8937.5 2143.5 3424.5 7139.4 |
8999.7 2182.6 3525.5 7268.5 |
30 |
|
32 |
8939.6 2144 8 3427.8 7143.7 |
9001.8 2183.9 3528.9 7272.8 |
32 |
|
34 |
8941.6 2146.1 3431.1 7148.0 |
9003.9 2185.2 3532.3 7277.2 |
34 |
|
36 |
8943.7 2147.4 3434.5 7152.2 |
9005.9 2186.5 3535.7 7281.5 |
36 |
|
38 |
8945.8 2148.7 3437.8 7156.5 |
9008.0 2187.8 3539.2 7285.9 |
38 |
|
40 |
8947.9 2150.0 3441.1 7160.7 |
9010.0 2189.1 3542.6 7290.3 |
40 |
|
42 |
8950.0 2151.3 3444.4 7165.0 |
9012.1 2190.5 3546.0 7294.6 |
42 |
|
44 |
8952.1 2152.6 3447.8 7169.3 |
9014.2 2191.8 3549.5 7299.0 |
44 |
|
46 |
8951.1 2153.9 3451.1 7173.6 |
9016.2 2193.1 3552.9 7303.4 |
46 |
|
48 |
8956.2 2155.2 3454.5 7177.9 |
9018.3 2194.4 3556.3 7307.7 |
48 |
|
50 |
8958.3 2156.5 3457.8 7182.1 |
9020.3 2195.7 3559.8 7312.1 |
50 |
|
52 |
8960.4 2157.8 3461.2 7186.4 |
9022.4 2197.0 3563.2 7316.5 |
52 |
|
54 |
8962.5 2159.1 3464.5 7190.7 |
9024.5 2198.3 3566.7 7320.9 |
54 |
|
56 |
8964.5 2160.4 3467.9 7195.0 |
9026.5 2199.6 3570.2 7325.3 |
56 |
|
58 |
8966.6 2161.7 3471.2 7199.3 |
9028.6 2200.9 3573.6 7329.7 |
58 |
|
60 |
8968.7 2163.0 3474.6 7203.6 |
9030.6 2202.3 3577.1 7334.1 |
60 |
|
104° |
105° |
||
|
L. C. M. E. T. |
L. C. M. E. T. |
i _ |
|
|
0 |
9030.6 2202.3 3577.1 7334.1 |
9091.8 2241.8 3682.6 7467.5 |
0 |
|
2 |
9032.7 2203.6 3580.5 7338.5 |
9093.9 2243.1 3686.1 7472.0 |
2 |
|
4 |
9034.7 2204.9 3584.0 7342.9 |
9095.9 2244.4 3689.7 7476.5 |
4 |
|
6 |
9036.8 2206.2 3587.5 7347.3 |
9097.9 2245.8 3693.3 7481.0 |
6 |
|
8 |
9038.8 2207.5 3591.0 7351.7 |
9099.9 2247.1 3696.9 7485.5 |
8 |
|
10 |
9040.9 2208.8 3594.4 7356.1 |
9102.0 2248.4 3700.4 7490.0 |
10 |
|
12 |
9042.9 2210.2 8597.9 7360.5 |
9104.0 2249.7 3704.0 7494.5 |
12 |
|
14 |
9045.0 2211.5 3601.4 7364.9 |
9106.0 2251.1 3707.6 7499.1 |
14 |
|
16 |
9047.0 2212.8 3604.9 7369.4 |
9108.0 2252.4 3711.2 7503.6 |
16 |
|
18 |
9049.1 2214.1 3608.4 7373.8 |
9110.1 2253.7 3714.8 7508.1 |
18 |
|
20 |
9051.1 2215.4 3611.9 7378.2 |
9112.1 2255.0 3718.4 7512.6 |
20 |
|
22 |
9053.1 2216.7 3615.4 7382.0 |
9114.1 2256.4 3722.0 7517.2 |
22 |
|
24 |
9055.2 2218.0 3618.9 7387.1 |
9116.1 2257.7 3725.6 7521.7 |
24 |
|
26 |
9057.2 2219.4 3622.4 7391.5 |
9118.1 22.-9.0 3729.3 7526.3 |
26 |
|
28 |
9059.3 2220.7 3625.9 7396.0 |
9120.2 2260.3 3732.9 7530.8 |
28 |
|
30 |
9061.3 2222.0 3629.4 7400.4 |
9122.2 2261.7 3736.5 7535.3 |
30 |
|
32 |
9063.3 2223.3 3G33.0 7404.8 |
9124.2 2263.0 3740.1 7539 9 |
32 |
|
34 |
9065.4 2224.6 3636.5 7409.3 |
9126.2 2264.3 3743.7 7544.4 |
34 |
|
36 |
9067.4 2226 0 3640.0 7413 8 |
9128.2 2265.7 3747.4 7549.0 |
36 |
|
38 |
9069.5 2227.3 3643.5 7418.2 |
9130.2 2267.0 3751.0 7553.6 |
88 |
|
40 |
9071.5 2228.6 3647.1 7422.7 |
9132.3 2268.3 3754.6 7558.1 |
40 |
|
42 |
9073.5 2229.9 3650.6 7427.1 |
9134.3 2269.6 3758.3 7562.7 |
42 |
|
44 |
9075.6 2231.2 3654.1 7431.6 |
9136.3 2271.0 3761.9 7567.3 |
44 |
|
46 |
9077.6 2232.6 3657.7 7436.1 |
9138.3 2272.3 3765.6 7571.8 |
46 |
|
48 |
9079.8 2233.9 3661.2 74406 |
9140.3 2273.6 3769.2 7576.4 |
48 |
|
50 |
9081.7 2235.2 3664.8 7445.0 |
9142.3 2275.0 3772.9 7581.0 |
50 |
|
52 |
9083.7 2236.5 3668.3 7449.5 |
9144.3 2276.3 3776.5 7585.6 |
52 |
|
54 |
9085.7 2237.8 3671.9 7454.0 |
9146.3 2277.6 3780.2 7590.2 |
54 |
|
56 |
9087.8 2239.2 3675.4 7458 5 |
9148.3 2278.9 3783.9 7594.8 |
56 |
|
58 |
9089.8 2240.5 3679.0 7463.0 |
9150.4 2280.3 3787.5 7599.4 |
58 |
|
60 |
9091.8 2241.8 3682.6 74675 |
9152.4 2281.6 3791.2 7604.0 |
60 |
158 TABLE 7. —LOGARITHMS OF NUMBERS.
N0123456789
100
1
2 3
4 5 6
7 8 9
110
1
4 5 6 7 8 9
120
1 2 3 4 5 6 7 8 9
130 1
2 3 4 5 6 7 8 9
140
1 2 3
4 5 6 7 8 9
150
00000 00043 00087 00130 00173 00217 00260 00303 00346 00389
0432 0475 0518 0561 0604 0647 0689 0732 0775 0817
0860 0903 0945 0988 1030 1072 1115 1157 1199 1242
1284 1326 1368 1410 1452 1494 1536 1578 1620 1662
1703 1745 1787 1828 1870 1912 1953 1995 2036 2078
2119 2160 2202 2243 2284 2325 2366 2407 2449 2490
2531 2572 2612 2653 2694 2735 2776 2816 2857 2898
2938 2979 3019 3060 3100 3141 3181 3222 3262 3302
3342 3383 3423 3463 3503 3543 3583 3623 3663 3703
3743 3782 3822 3862 3902 3941 3981 4021 4060 4100
04139 04179 04218 04258 04297 04336 04376 0441^ 04454 04493
4532 4571 4610 4650 4689 4727 4766 4805 4844 4883
4922 4961 4999 5038 5077 5115 5154 5192 5231 5269
6308 5346 5385 5423 6461 5500 5538 5576 5614 5652
5690 5729 5767 5805 5843 5881 5918 5956 5994 6032
6070 6108 6145 6183 6221 6258 6296 6333 6371 6408
6446 6483 6521 6558 6595 6633 6670 6707 6744 6781
6819 6856 6893 693Q 6967 7004 7041 7078 7115 7151
7188 7225 7262 7298 7335 7372 7408 7445 7482 7518
7555 7591 7628 7664 7700 7737 7773' 7809 7846 7882
07918 07954 07990 08027 08063 08099 08135 08171 08207 08243
8279 8314 8350 8386 8422 8458 8493 8529 8565 8600
8636 8672 8707 8743 8778 8814 8849 8884 8920 8955
8991 9026 9061 9096 9132 9167 9202 9237 9272 9307
9342 9377 9412 9447 9482 9517 9552 9587 9621 9656
9691 9726 9760 9795 9830 9864 9899 9934 9968 10003
10037 10072 10106 10140 10175 10209 10243 10278 10312 0346
0380 0415 0449 0483 0517 0551 0585 0619 0653 0687
0721 0755 0789 0823 0857 0890 0924 0958 0992 1025
1059 1093 1126 1160 1193 1227 1261 1294 1327 1361
11394 11428 11461 11494 11528 11561 11594 11628 11661 11694
1727 1760 1793 1826 1860 1893 1926 1959 1992 2024
2057 2090 2123 2156 2189 2222 2254 2287 2320 2352
2385 2418 2450 2483 2516 2548 2581 2613 2646 2678
2710 2743 2775 2808 2840 2872 2905 2937 2969 3001
3033 3066 3098 3130 3162 3194 3226 3258 3290 3322
3354 3386 3418 3450 3481 3513 3545 3577 3609 3640
3672 3704 3735 3767 3799 3830 3862 3893 3925 3956
3988 4019 4051 4082 4114 4145 4176 4208 4239 4270
4301 4333 4364 4395 4426 4457 4489 4520 4551 4582
14613 14644 14675 14706 14737 14768 14799 14829 14860 14891
4922 4953 4983 5014 5045 5076 5106 5137 5168 5198
5229 5259 5290 5320 5351 5381 5412 5442 5473 5503
5534 5564 5594 5625 5655 5685 5715 5746 5776 5806
5836 5806 5897 5927 5957 5987 6017 6047 6077 6107
6137 6167 6197 6227 6256 6286 6316 6346 6376 6406
6435 6465 6495 6524 6554 6584 6613 6643 6673 6702
6732 6761 6791 6820 6850 6879 6909 6938 6967 6997
7026 7056 7085 7114 7143 7173 7202 7231 7260 7289
7319 7348 7377 7406 7435 7464 7493 7522 7561 7580
17609 17638 17667 17696 17725 17754 17782 17811 17840 17869
TABLE 7.— LOGARITHMS OF NUMBERS. 159
N0123456789
150
1 2 3
4 5 6 7 8 9
3 4 5 6 7 8 9
180
1 2 3 4 5 6 7 8 9
17609 17638 17667 17696 17725 17754 17782 17811 17840 17869
7898 7926 7955 7984 8013 8041 8070 8099 8127 8156
8184 8213 8241 8270 8298 8327 8355 8384 8412 8441
8469 8498 8526 8554 8583 8611 8639 8667 8696 8724
8752 8780 8808 8837 8865 8893 8921 8949 8977 9005
9033 9061 9089 9117 9145 9173 9201 9229 9257 9285
9312 9340 9368 9396 9424 9451 9479 9507 9535 9562
9590 9618 9645 9673 9700 9728 9756 9783 9811 9838
9866 9893 9921 9948 99762000320030200582008520112
2014020167201942022220249 0276 0303 0330 0358 0385
20412 20439 20466 20493 20520 20548 20575 20602 20629 20656
0683 0710 0737 0763 0790 0817 0844 0871 0898 0925
0952 0978 1005.1032 1059 1085 1112 1139 1165 1192
1219 1245 1272 1299 1325 1352 1378 1405 1431 1458
1484 1511 1537 1564 1590 1617 1643 1669 1696 1722
1748 1775 1801 1827 1854 1880 1906 1932 1958 1985
2011 2037 2063 2089 2115 2141 2167 2194 2220 2246
2272 2298 2324 2350 2376 2401 2427 2453 2479 2505
2531 2557 2583 2608 2634 2660 2686 2712 2737 2763
2789 2814 2840 2866 2891 2917 2943 -2968 2994 3019
23045 23070 23096 23121 23147 23172 23198 23223 23249 23274
3300 3325 3350 3376 3401 3426 3452 3477 3502 3528
3553 3578 3603 3629 3654 3679 3704 3729 3754 3779
3805 3830 3855 3880 3905 3930 3955 3980 4005 4030
4055 4080 4105 4130 4155 4180 4204 4229 4254 4279
4304 4329 4353 4378 4403 4428 4452 4477 4502 4527
4551 4576 4601 4625 4650 4674 4699 4724 4748 4773
4797 4822 4846 4871 4895 4920 4944 4969 4993 5018
5042 5066 5091 5115 5139 5164 5188 5212 5237 5261
5285 5310 5334 6358 5382 5406 5431 5455 5479 6503
25527 25551 25575 25600 25624 25648 25672 25696 25720 25744
5768 6792 5816 6840 5864 5888 6912 5935 5959 5983
6007 6031 6055 6079 6102 6126 6150 6174 6198 6221
6245 6269 6293 6316 6340 6364 6387 6411 6435 6458
6482 6505 6529 6553 6576 6600 6623 6647 6670 6694
6717 6741 6764 6788 6811 6834 6858 6881 6905
6951 6975 6998 7021 7045 7068 7091 7114 7138 7161
7184 7207 7231 7254 7277 7300 7323 7346 7370 7393
7416 7439 7462 7485 7508 7531 7554 7577 7600 7623
7646 7669 7692 7715 7738 7761 7784 7807 7830 7852
27875 27898 27921 27944 27967 27989 28012 28035 28058 28081
8103 8126 8149 8171 8194 8217 8240 8262 8285 8307
8330 8353 8375 8398 8421 8443 8466 8488 8511 8533
8556 8578 8601 8623 8646 8668 8691 8713 8735 8758
8780 8803 8825 8847 8870 8892 8914 8937 8959 8981
9003 9026 9048 9070 9092 9115 9137 9159 9181 9203
9226 9248 9270 9292 9314 9336 9358 9380 9403 9425
9447 9469 9491 9513 9535 9557 9579 9601 9623 9645
9667 9688 9710 9732 9754 9776 9798 9820 9842 9863
9885 9907 9929 9951 9973 999430016300383006030081
30103 30125 30146 30168 30190 30211 30233 30255 30276 30298
160 TABLE 7. —LOGARITHMS OF NUMBERS.
N0123456789
200
1 2 3 4 5 6 7 8 9
210
1 2 3 4 5 6 7 8 9
220
1 2 3 4 5 6 7 8 9
280
1 2 3 4 5 6 7 8 9
240
1 2 3 4 5 6 7
30103 30125 30146 30168 30190 30211 30233 30255 30276 30298
0320 0341 0363 0384 0406 0428 0449 0471 0492 0514
0535 0557 0578 0600 0621 0643 0664 0685 0707 0728
0750 0771 0792 0814 0835 0856 0878 0899 0920 0942
0963 0984 1006 1027 1048 1069 1091 1112 1133 1154
1175 1197 1218 1239 1260 1281 1302 1323 1345 1366
1387 1408 1429 1450 1471 1492 1513 1534 1555 1576
1597 1618 1639 1660 1681 1702 1723 1744 1765 1785
1806 1827 1848 1869 1890 1911 1931 1952 1973 1994
2015 2035 2056 2077 2098 2118 2139 2160 2181 2201
32222 32243 32263 32284 32305 32325 32346 32366 32387 32408
2428 2449 2469 2490 2510 2531 2552 2572 2593 2613
2634 2654 2675 2695 2715 2736 2756 2777 2797 2818
2838 2858 2879 2899 2919 2940 2960 2980 3001 3021
3041 3062 3082 3102 3122 3143 3163 3183 3203 3224
3244 3264 3284 3304 3325 3345 3365 3385 3405 3425
3445 3465 3486 3506 3526 3546 3566 3586 3606 3626
3646 3666 3686 3706 3726 3746 3766 3786 3806 3826
3846 3866 3885 3905 3925 3945 3965 3985 4005 4025
4044 4064 4084 4104 4124 4143 4163 4183 4203 4223
34242 34262 34282 34301 34321 34341 34361 34380 34400 34420
4439 4459 4479 4498 4518 4537 4557 4577 4596 4616
4635 4655 4674 4694 4713 4733 4753 4772 4792 4811
4830 4850 4869 4889 4908 4928 4947 4967 4986 5005
5025 5044 5064 5083 5102 6122 5141 5160 5180 5199
5218 5238 5257 5276 5295 5315 5334 5353 5372 5392
5411 5430 5449 5468 5488 5507 5526 5545 5564 5583
5603 5622 5641 5660 5679 5698 5717 5736 5755 5774
5793 5813 5832 5851 5870 5889 5908 5927 5946 5965
5984 6003 6021 6040 6059 6078 6097 6116 6135 6154
36173 36192 36211 36229 36248 36267 36286 36305 36324 36342
6361 6380 6399 6418 6436 6455 6474 6493 6511 6530
6549 6568 6586 6605 6624 6642 6661 6680 6698 6717
6736 6754 6773 6791 6810 6829 6847 6866 6884 6903
6922 6940 6959 6977 6996 7014 7033 7051 7070 7088
7107 7125 7144 7162 7181 7199 7218 7236 7254 7273
7291 7310 7328 7346 7365 7383 7401 7420 7438 7457
7475 7493 7511 7530 7548 7566 7585 7603 7621 7639
7658 7676 7694 7712 7731 7749 7767 7785 7803 7822
7840 7858 7876 7894 7912 7931 7949 7967 7985 8003
38021 38039 38057 38075 38093 38112 38130 38148 38166 38184
8202 8220 8238 8256 8274 8292 8310 8328 8346 8364
8382 8399 8417 8435 8453 8471 8489 8507 8525 8543
8561 8578 8596 8614 8632 8650 8668 8686 8703 8721
8739 8757 8775 8792 8810 8828 8846 8863 8881 8899
8917 8934 8952 8970 8987 9005 9023 9041 9058 9076
9094 9111 9129 9146 9164 9182 9199 9217 9235 9252
9270 9287 9305 9322 9340 9358 9375 9393 9410 9428
9445 9463 9480 9498 9515 9533 9550 9568 9585 9602 9620 9637 9655 9672 9690 9707 9724 9742 9759 9777
250 39794 39811 39829 39846 39863 39881 39898 39915 39933 39950
TABLE 7.— LOGARITHMS OF NUMBERS. 161
O12345678
250 1
2 3
4 5 6 7 8 9
260 1
2 3
4 5 6 7 8 9
3 4 5 6 7 8 9
280
1 2 3 4 5 6 7 8 9
39794 39811 39829 39846 39863 39881 39898 39915 39933 39950
9967 9985 40002 40019 40037 40054 40071 40088 40106 40123
4014040157 0175 0192 0209 0226 0243 0261 0278 0295
0312 0329 0346 0364 0381 0398 0415 0432 0449 0466
0483 0500 0518 0535 0552- 0569 0586 0603 0620 0637
0654 0671 0688 0705 0722 0739 0756 0773 0790 0807
0824 0841 0858 0875 0892 0909 0926 0943 0960 0976
0993 1010 1027 1044 1061 1078 1095 1111 1128 1145
1162 1179 1196 1212 1229 1246 1263 1280 1296 1313
1330 1347 1363 1380 1397 1414 1430 1447 1464 1481
41497 41514 41531 41547 41564 41581 41597 41614 41631 41647
1664 1681 1697 1714 1731 1747 1764 1780 1797 1814
1830 1847 1863 1880 1896 1913 1929 1946 1963 1979
1996 2012 2029 2045 2062 2078 2095 2111 2127 2144
2160 2177 2193 2210 2226 2243 2259 2275 2292 2308
2325 2341 2357 2374 2390 2406 2423 2439 2455 2472
2488 2504 2521 2537 2553 2570 2586 2602 2619 263£
2651 2667 -2684 2700 2716 2732 2749 2765 2781 2797
2813 2830 2846 2862 2878 2894 2911 2927 2943 2959
2975 2991 3008 3024 3040 3056 3072 3088 3104 3120
43136 43152 43169 43185 43201 43217 43233 43249 43265 43281
3297 3313 3329 3345 3361 3377 3393 3409 3425 3441
3457 3473 3489 3505 3521 3537 3553 3569 3584 3600
3616 3632 3648 3664 3680 3696 3712 3727 3743 3759
3775 3791 3807 3823 3838 3854 3870 3886 3902 3917
3933 3949 3965 3981 3996 4012 4028 4044 4059 4075
4091 4107 4122 4138 4154 4170 4185 4201 4217 4232
4248 4264 4279 4295 4311 4326 4342 4358 4373 4389
4404 4420 4436 4451 4467 4483 4498 4514 4529 4545
4560 4576 4592 4607 4623 4638 4654 4669 4685 4700
44716 44731 44747 44762 44778 44793 44809 44824 44840 44855
4871 4886 4902 4917 4932 4948 4963 4979 4994 5010
5025 5040 5056 5071 5086 5102 5117 5133 5148 5163
5179 5194 5209 5225' 5240 5255 5271 5286 5301 5317
5332 5347 5362 5378 5393 5408 5423 5439 5454 5469
5484 5500 5515 5530 5545 5561 5576 5591 5606 5621
5637 5652 5667 5682 5697 5712 5728 5743 5758 5773
5788 5803 5818 5834 5849 5864 5879 5894 5909 5924
5939 5954 5969 5984 6000 6015 6030 6045 6060 6075
6090 6105 6120 6135 6150 6165 6180 6195 6210 6225
46240 46255 46270 46285 46300 46315 46330 46345 46359 46374
6389 6404 6419 6434 6449 6464 6479 6494 6509 6523
6538 6553 6568 6583 6598 6613 6627 6642 6657 6672
6687 6702 6716 6731 6746 6761 6776 6790 6805 6820
6835 6850 6864 6879 6894 6909 6923 6938 6953 6967
6982 6997 7012 7026 7041 7056 7070 7085 7100 7114
7129 7144 7159 7173 7188 7202 7217 7232 7246 7261
7276 7290 7305 7319 7334 7349 7363 7378 7392 7407
7422 7436 7451 7465 7480 7494 7509 7524 7538 7553
7567 7582 7596 7611 7625 7640 7654 7669 7683 7698
47712 47727 47741 47756 47770 47784 47799 47813 47828 47842
162 TABLE 7.— LOGARITHMS OF NUMBERS.
O12345678
300 1 2 3
4 5 6
7 8 9
310 1
2 3 4 5 6 7 8 9
320
1 2 3 4 5 6 7 0 9
330
1 2 3 4 5 G 7 8 9
340
1
2 3
4 5 6 7 8 9
350
47712 47727 47741 47756 47770 47784 47799 47813 47828 47842
7857 7871 7885 7900 7914 7929 7943 7958 7972 7986
8001 8015 8029 8044 8058 8073 8087 8101 8116 8130
8144 8159 8173 8187 8202 8216 8230 8244 8259 8273
8287 8302 8316 8330- 8344 8359 8373 8387 8401 8416
8430 8444 8458 8473 8487 8501 8515 8530 8544 8558
8572 8586 8601 8615 8629 8643 8657 8671 8686 87QO
8714 8728 8742 8756 8770 8785 8799 8813 8827 8841
8855 8869 8883 8897 8911 8926 8940 8954 8968 8982
8996 9010 9024 9038 9052 9066 9080 9094 9108 9122
49136 49150 49164 49178 49192 49206 49220 49234 49248 49262
9276 9290 9304 9318 9332 9346 9360 9374 9388 9402
9415 9429 9443 9457 9471 9485 9499 9513 9527 9541
9554 9568 9582 9596 9610 9624 9638 9651 9665 9679
9693 9707 9721 9734 9748 9762 9776 9790 9803 9817
9831 9845 9859 9872 9886 9900 9914 9927 9941 9955
9969 9982 9996 50010 50024 50037 50051 50065 50079 50092
501065012050133 0147 0161 0174 0188 0202 0215 0229
0243 0256 0270 0284 0297 0311 0325 0338 0352 0365
0379 0393 0406 0420 0433 0447 0461 0474 0488 0501
50515 50529 50542 50556 50569 50583 50596 50610 50623 50637
0651 0664 0678 0691 0705 0718 0732 0745 0759 0772
0786 0799 0813 0826 0840 0853 0866 0880 0893 0907
0920 0934 0947 0961 0974 0987 1001 1014 1028 1041
1055 1068 1081 1095 1108 1121 1135 1148 1162 1175
1188 1202 1215 1228 1242 1255 1268 1282 1295 1308
1322 1335 1348 1362 1375 1388 1402 1415 1428 1441
1455 1468 1481 1495 1508 1521 1534 1548 1561 1574
1587 1601 1614 1627 1640 1654 1667 1680 1693 1706
1720 1733 1746 1759 1772 1786 1799 1812 1825 1838
51851 51865 51878 51891 51904 51917 51930 51943 51957 51970
1983 1996 2009 2022 2035 2048 2061 2075 2088 2101
2114 2127 2140 2153 2166 2179 2192 2205 2218 2231
2244 2257 2270 2284 2297' 2310 2323 2336 2349 2362
2375 2388 2401 2414 2427 2440 2453 2466 2479 2492
2504 2517 2530 2543 2556 2569 2582 2595 2608 2621
2634 2647 2660 2673 2686 2699 2711 2724 2737 2750
2763 2776 2789 2802 2815 2827 2840 2853 2866 2879
2892 2905 2917 2930 2943 2956 2969 2982 2994 3007
3020 3033 3046 3058 3071 3084 3097 3110 3122 3135
53148 53161 53173 53186 53199 53212 53224 53237 53250 53263
3275 3288 3301 3314 3326 3339 3352 3364 3377 3390
3403 3415 3428 3441 3453 3466 3479 3491 3504 3517
3529 3542 3555 3567 3580 3593 3606 3618 3631 3643
3656 3668 3681 3694 3706 3719 3732 3744 3757 3769
3782 3794 3807 3820 3832 3845 3857 3870 3882 3895
3908 3920 3933 3945 3958 3970 3983 3995 4008 4020
4033 4045 4058 4070 4083 4095 4108 4120 4133 4145
4158 4170 4183 4195 4208 4220 4233 4245 4258 4270
4283 4295 4307 4320 4832 4345 4357 4370 4382 4394
54407 54419 54432 54444 54456 54469 54481 54494 54506 54518
TABLE 7.— LOGARITHMS OF NUMBERS. 163
N 0123456789
350 1
2 3 4 5 6 7 8 9
360
1 2 3
4 5 6
7 8 9
370
1 2
3
4 5 6 7 8 9
380
1 2 3
4 5 6 7 8 9
390
1 2 3 4 5 6 7 8 9
54407 54419 54432 54444 54456 54469 54481 54494 54506 54518
4531 4543 4555 4568 4580 4593 4605 4617 4630 4642
4654 4667 4679 4691 4704 4716 4728 4741 4753 4765
4777 4790 4802 4814 4827 4839 4851 4864 4876 4888
4900 4913 4925 4937 4949 4962 4974 4986 4998 6011
5023 5035 5047 5060 5072 5084 5096 5108 5121 5133
5145 5157 5169 5182 5194 5206 5218 5230 5242 5255
5267 5279 5291 5303 5315 5328 6340 5352 6364 5376
5388 5400 5413 5425 5437 6449 5461 5473 5485 5497
5509 5522 5534 5546 5558 6570 5582 6594 5606 6618
55630 55642 55654 55666 55678 65691 55703 55715 55727 55739
5751 5763 5775 6787* 5799 5811 5823 5835 5847 5859
5871 5883 5895 5907 5919 5931 5943 5955 5967 5979
5991 6003 6015 6027 6038 6050 6062 6074 6086 6098
6110 6122 6134 6146 6158 6170 6182 6194 6205 6217
6229 6241 . 6253 6265 6277 6289 6301 6312 6324 6336
6348 6360 6372 6384 6396 6407 6419 6431 6443 6455
6467 6478 6490 6502 6514 6526 6538 6549 6561 6573
6585 6597 6608 6620 6632 6644 6656 6667 6679 6691
6703 6714 6726 6738 6750 6761 6773 6785 6797 6808
56820 56832 56844 56855 56867 56879 56891 56902 56914 56926
6937 6949 6961 6972 6984 6996 7008 7019 7031 7043
7054 7066 7078 7089 7101 7113 7124 7136 7148 7159
7171 7183 7194 7206 7217 7229 7241 7252 7264 7276
7287 7299 7310 7322 7334 7345 7357 7368 7380 7392
7403 7415 7426 7438 7449 7461 7473 7484 7496 7507
7519 7530 7542 7553 7565 7576 7588 7600 7611 7623
7634 7646 7657 7669 7680 7692 7703 7715 7726 7738
7749 7761 7772 7784 7795 7807 7818 7830 7841 7852
7864 7875 7887 7898 7910 7921 7933 7944 7955 7967
57978 57990 58001 58013 58024 58035 58047 58058 58070 58081
8092 8104 8115 8127 8138 8149 8161 8172 8184 8195
8206 8218 8229 8240 8252 8263 8274 8286 8297 8309
8320 8331 8343 8354 8365 8377 8388 8399 8410 8422
8433 8444 8456 8467 8478 8490 8501 8512 8524 8535
8546 8557 8569 8580 8591 8602 8614 8625 8636 8647
8659 8670 8681 8692 8704 8715 8726 8737 8749 8760
8771 8782 8794 8805 8816 8827 8838 8850 8861 8872
8883 8894 8906 8917 8928 8939 8950 8961 8973 8984
8995 9006 9017 9028 9040 9051 9062 9073 9084 9095
59106 59118 59129 59140 59161 59162 59173 59184 59195 59207
9218 9229 9240 9251 9262 9273 9284 9295 9306 9318
9329 9340 9351 9362 9373 9384 9395 9406 9417 9428
9439 9450 9461 9472 9483 9494 9506 9517 9528 9539
9550 9561 9572 9583 9594 9605 9616 9627 9638 9649
9660 9671 9682 9693 9704 9715 9726 9737 9748 9759
9770 9780 9791 9802 9813 9824 9835 9846 9857 9868
9879 9890 9901 9912 9923 9934 9945 9956 9966 9977
9988 9999 60010 60021 60032 60043 60054 60065 60076 60086
60097 60108 0119 0130 0141 0152 0163 0173 0184 0195
400 60206 60217 60228 60239 60249 60260 60271 60282 60293 60304
164 TABLE 7. —LOGARITHMS OF NUMBERS.
NO123456789
400
1 2 3
4 5 6 7 8 9
410
1 2 3
4 5 6 7 8 9
420
1 2 3
4 5 6 7 8 9
430 1 2 3
4 5 6 7 8 9
440 1
2 3
4 5 6 7 8 9
450
60206 60217 60228 60239 60249 60260 60271 60282 60293 60304
0314 0325 0336 0347 0358 0369 0379 0390 0401 0412
0423 0433 0444 0455 0466 0477 0487 0498 0509 0520
0531 0541 0552 0563 0574 0584 0595 0606 0617 0627
0638 0649 0660 0670 0681 0692 0703 0713 0724 0735
0746 0756 0767 0778 0788 0799 0810 0821 0831 0842
0853 0863 0874 0885 0895 0906 0917 0927 0938 0949
0959 0970 0981 0991 1002 1013 1023 1034 1045 1055
1066 1077 1087 1098 1109 1119 1130 1140 1151 1162
1172 1183 1194 1204 1215 1225 1236 1247 1257 1268
61278 61289 61300 61310 61321 61331 61342 61352 61363 61374
1384 1395 1405 1416 1426 1437 1448 1458 1469 1479
1490 1500 1511 1521 1532 1542 1553 1563 1574 1584
1595 1606 1616 1627 1637 1648 1658 1669 1679 1690
1700 1711 1721 1731 1742 1752 1763 1773 1784 1794
1805 1815 1826 1836 1847 1857 1868 1878 1888 1899
1909 1920 1930 1941 1951 1962 1972 1982 1993 2003
2014 2024 2034 2045 2055 2066 2076 2086 2097 2107
2118 2128 2138 2149 2159 2170 2180 2190 2201 2211
2221 2232 2242 2252 2263 2273 2284 2294 2304
62325 62335 62346 62356 62366 62377 62387 62397 62408 62418
2428 2439 2449 2459 2469 2480 2490 2500 2511 2521
2531 2542 2552 2562 2572 2583 2593 2603 2613 2624
2634 2644 2655 2665 2675 2685 2696 2706 2716 2726
2737 2747 2757 2767 2778 2788 2798 2808 2818 2829
2839 2849 2859 2870 2880 2890 2900 2910 2921 2931
2941 2951 2961 2972 2982 2992 3002 3012 3022 3033
3043 3053 3063 3073 3083 3094 3104 3114 3124 3134
3144 3155 3165 3175 3185 3195 3205 3215 3225 3236
3246 3256 3266 3276 3286 3296 3306 3317 3327 3337
63347 63357 63367 63377 63387 63397 63407 63417 63428 63438
3448 3458 3468 3478 3488 3498 3508 3518 3528 3538
3548 3558 3568 3579 3589 3599 3609 3619 3629 3639
3649 3659 3669 3679 3689 3699 3709 3719 3729 3739
3749 3759 3769 3779 3789 3799 3809 3819 3829 3839
3849 3859 3869 3879 3889 3899 3909 3919 3929 3939
3949 3959 3969 3979 3988 3998 4008 4018 4028 4038
4048 4058 4068 4078 4088 4098 4108 4118 4128 4137
4147 4157 4167 4177 4187 4197 4207 4217 4227 4237
4246 4256 4266 4276 4286 4296 4306 4316 4326 4335
64345 64355 64365 64375 64385 64395 64404 64414 64424 64434
4444 4454 4464 4473 4483 4493 4503 4513 4523 4532
4542 4552 4562 4572 4582 4591 4601 4611 4621 4631
4640 4650 4660 4fc70 4680 4689 4699 4709 4719 4729
4738 4748 4758 4768 4777 4787 4797 4807 4816 4826
4836 4846 4856 4865 4875 4885 4895 4904 4914 4924
4933 4943 4953 4963 4972 4982 4992 5002 5011 5021
5031 5040 5050 5060 5070 5079 5089 5099 5108 5118
5128 6137 5147 5157 5167 5176 5186 5196 5205 5215
5225 6234 5244 5254 5263 5273 5283 5292 5302 5312
65321 65331 65341 65350 65360 65369 65379 65389 65398 65408
TABLE 7. -LOGARITHMS OF NUMBERS. 165
0123456789
450
1 2 3
4 5 6
7 8 9
460 1 2 3 4 5 6 7 % 9
3
4 5 6 7 8 9
500
65321 65331 65341 65350 65360 65369 65379 65389 65398 65408
5418 5427 5437 5447 5456 5466 5475 5485 5495 5504
5514 5523 5533 5543 5552 5562 5571 5581 5591 5600
5610 5619 5629 5639 5648 5658 5667 5677 5686 5696
5706 5715 5725 5734 5744 5753 5763 6772 5782 5792
5801 5811 5820 5830 5839 5849 5858 5868 6877 6887
5896 5906 5916 5925 5935 5944 5954 5963 5973 5982
5992 6001 6011 6020 6030 6039 6049 6058 6068 6077
6087 6096 6106 6115 6124 6134 6143 6153 6162 6172
6181 6191 6200 6210 6219 6229 6238 6247 6257 6266
66276 66285 66295 66304 66314 66323 66332 66342 66351 66361
6370 6380 6389 6398 T6408 6417 6427 6436 6445 6455
6464 6474 6483 6492 6502 6511 6521 6530 6539 6549
6558 6567 6577 6586 6596 6605 6614 6624 6633 6642
6652 6661 6671 6680 6689 6699 6708 6717 6727 6736
6745 6755 6764 6773 6783 6792 6801 6811 6820 6829
6839 6848 6857 6867 6876 6885 6894 6904 6913 6922
6932 6941 6950 6960 6969 6978 6987 6997 7006 7015
7025 7034 7043 7052 7062 7071 7080 7089 7099 7108
7117 7127 7136 7145 7154 7164 7173 7182 7191 7201
67210 67219 67228 67237 67247 67256 67265 67274 67284 67293
7302 7311 7321 7330 7339 7348 7357 7367 7376 7385
7394 7403 7413 7422 7431 7440 7449 7459 7468 7477
7486 7495 7504 7514 7523 7532 7541 7550 7560 7569
7578 7587 7596 7605 7614 7624 7633 7642 7651 7660
7669 7679 7688 7697 7706 7715 7724 7733 7742 7752
7761 7770 7779 7788 7797 7806 7815 7825 7834 7843
7852 7861 7870 7879 7888 7897 7906 7916 7925 7934
7943 7952 7961 7970 7979 7988 7997 8006 8015 8024
8034 8043 8052 8061 8070 8079 8088 8097 8106 8115
68124 68133 68142 68151 68160 68169 68178 68187 68196 68205
8215 8224 8233 8242 8251 8260 8269 8278 8287 8296
8305 8314 8323 8332 8341 8350 8359 8368 8377 8386
8395 8404 8413 8422 8431 8440 8449 8458 8467 8476
8485 8494 8502 8511 8520 8529 8538 8547 8556 8565
8574 8583 8592 8601 8610 8619 8628 8637 8646 8655
8664 8673 8681 8690 8699 8708 8717 8726 8735 8744
8753 8762 8771 8780 8789 8797 8806 8815 8824 8833
8842 8851 8860 8869 8878 8886 8895 8904 8913 8922
8931 8940 8949 8958 8966 8975 8984 8993 9002 9011
69020 69028 69037 69046 69055 69064 69073 69082 69090 69099
9108 9117 9126 9135 9144 9152 9161 9170 9179 9188
9197 9205 9214 9223 9232 9241 9249 9258 9267 9276
9285 9294 9302 9311 9320 9329 9338 9346 9355 9364
9373 9381 9390 9399 9408 9417 9425 9434 9443 $452
9461 9469 9478 9487 9496 9504 9513 9522 9531 9539
9548 9557 9566 9574 9583 9592 9601 9609 9618 9627
9636 9644 9653 9662 9671- 9679 9688 9697 9705 9714
9723 9732 9740 9749 9758 9767 9775 9784 9793 9801
9810 9819 9827 9836 9845 9854 9862 9871 9880
69897 69906 69914 69923 69932 69940 69949 69958 69966 69975
166 TABLE 7.— LOGARITHMS OF NUMBERS.
0123456789
500
1 2 3 4 5 6 7 8 9
510
1 2 3
4 5 6 7 8 9
520
1 2 3
4 5 6 7 8 9
530
1
2 3 4 5 6 7 8 9
540
1
2 3
4 5 G 7 8 9
550
69897 69906 69914 69923 69932 69940 69949 69958 69966 69975
9984 9992 70001 70010 70018 70027 70036 70044 70053 70062
70070 70079 0088 0096 0105 0114 0122 0131 0140 0148
0157 0165 0174 0183 0191 0200 0209 0217 0226 0234
0243 0252 0260 0269 0278 0286 0295 0303 0312 0321
0329 0338 0346 0355 0364 0372 0381 0389 0398 0406
0415 0424 0432 0441 0449 0458 0467 0475 0484 0492
0501 0509 0518 0526 0535 0544 0552 0561 0569 0578
0586 0595 0603 0612 0621 0629 0638 0646 065£ 0663
0672 0680 0689 0697 0706 0714 0723 0731 0740 0749
70757 70766 70774 70783 70791 70800 70808 70817 70825 70834
0842 0851 0859 0868 0876 0885 0893 0902 0910 0919
0927 0935 0944 0952 0961 0969 0978 0986 0995 1003
1012 1020 1029 1037 1046 1054 1063 1071 1079 1088
1096 1105 1113 1122 1130 1139 1147 1155 1164 1172
1181 1189 1198 1206 1214 1223 1231 1240 1248 1257
1273 1282 1290 1299 1307 1315 1324 1332 1341
1349 1357 1366 1374 1383 1391 1399 1408 1416 1425
1433 1441 1450 1458 1466 1475 1483 1492 1500 1508
1517 1525 1533 1542 1550 1559 1567 1575 1584 1592
71600 71609 71617 71625 71634 71642 71650 71659 71667 71675
1684 1692 1700 1709 1717 1725 1734 1742 1750 1759
1767 1775 1784 1792 1800 1809 1817 1825 1834 1842
1850 1858 1867 1875 1883 1892 1900 1908 1917 1925
1933 1941 1950 1958 1966 1975 1983 1991 1999 2008
2016 2024 2032 2041 2049 2057 2066 2074 2082 2090
2099 2107 2115 2123 2132 2140 2148 2156 2165 2173
2181 2189 2198 2206 2214 2222 2230 2239 2247 2255
2263 2272 2280 2288 2296 2304 2313 2321 2329 2337
2346 2354 2362 2370 2378 2387 2395 2403 2411 2419
72428 72436 72444 72452 72460 72469 72477 72485 72493 72501
2509 2518 2526 2534 2542 2550 2558 2567 2575 2583
2591 2599 2607 2616 2624 2632 2640 2648 2656 2665
2673 2681 2689 2697 2705 2713 2722 2730 2738 2746
2754 2762 2770 2779 2787 2795 2803 2811 2819 2827
2835 2843 2852 2860 2868 2876 2884 2892 2900 2908
2916 2925 2933 2941 2949 2957 2965 2973 2981 2989
2997 3006 3014 3022 3030 3038 3046 3054 3062 3070
3078 3086 3094 3102 3111 3119 3127 313^ 3143 3151
3159 3167 3175 3183 3191 3199 3207 3215 3223 3231
73239 73247 73255 73263 73272 73280 73288 73296 73304 73312
3320 3328 3336 3344 3352 3360 3368 3376 3384 3392
3400 3408 3416 3424 3432 3440 3448 3456 3464 3472
3480 3488 3496 3504 3512 3520 3528 3536 3544 3552
3560 3568 3576 3584 3592 3600 3608 3616 3624 3632
3640 3648 3656 3664 3672 3679 3687 3695 3703 3711
3719 3727 3735 3743 3751 3759 3767 377£ 3783 3791
3799 3807 3815 3823 3830 3838 3846 3854 3862 3870
3878 3886 3894 3902 3910 3918 3926 3933 3941 3949
3957 3965 3973 3981 3989 3997 400£ 4013 4020 4028
74036 74044 74052 74060 74068 74076 74084 74092 74099 74107
TABLE 7.— LOGARITHMS OF NUMBERS 167
NO1234:56789
550
1 2
3
4 5 6 7 8 9
560
1 2 3 4 5 6 7 8 9
570
1 2 3 4 5 6 7 8 9
580
1 2 3
4 5 6 7 8 9
590
1 2 3 4 5 6 7 8 9
74036 74044 74052 74060 74068 74076 74084 74092 74099 74107
4115 4123 4131 4139 4147 4155 4162 4170 4178 4186
4194 4202 4210 4218 4225 4233 4241 4249 4257 4265
4273 4280 4288 4296 4304 4312 4320 4327 4335 4343
4351 4359 4367 4374 4382 4390 4398 4406 4414 4421
4429 4437 4445 4453 4461 4468 4476 4484 4492 4500
4507 4515 4523 4531 4539 4547 4554 4562 4570 4578
4586 4593 4601 4609 4617 4624 4632 4640 4648 4656
4663 4671 4679 4687 4695 4702 4710 4718 4726 4733
4741 4749 4757 4764 4772 4780 4788 4796 4803 4811
74819 74827 74834 74842 74$50 74858 74865 74873 74881 74889
4896 4904 4912 4920 4927 4935 4943 4950 4958 4966
4974 4981 4989 4997 5005 5012 5020 5028 6035 5043
5051 5059 5066 5074 5082 5089 5097 5105 5113 5120
5128 5136 5143 5151 5159 5166 5174 5182 5189 5197
5205 5213 5220 5228 5236 5243 5251 5259 5266 5274
5282 5289 5297 5305 5312 5320 5328 5335 5343 5351
5358 5366 5374 5381 5389 5397 5404 5412 6420 5427
5435 5442 5450 5458 5465 5473 5481 5488 5496 5504
5511 5519 5526 5534 5542 5549 5557 556$ 5572 5580
75587 75595 75603 75610 75618 75626 75633 75641 75648 75656
5664 5671 5679 5686 5694 5702 5709 5717 5724 5732
5740 5747 5755 5762 5770 5778 5785 5793 5800 5808
5815 5823 5831 5838 5846 5853 5861 5868 5876 5884
5891 5899 5906 5914 5921 5929 5937 5944 5952 5959
5967 5974 5982 5989 5997 6005 6012 6020 6027 6035
6042 6050 6057 6065 6072 6080 6087 6095 6103 6110
6118 6125 6133 6140 6148 6155 6163 6170 6178 6185
6193 6200 6208 6215 6223 6230 6238 6245 6253 6260
6268 6275 6283 6290 6298 6305 6313 6320 6328 6335
76343 76350 76358 76365 76373 76380 76388 76395 76403 76410
6418 6425 6433 6440 6448 6455 6462 6470 6477 6485
6492 6500 6507 6515 6522 6530 6537 6545 6552 6559
6567 6574 6582 6589 6597 6604 6612 6619 6626 6634
6641 6649 6656 6664 6671 6678 6686 6693 6701 6708
6716 6723 6730 6738 6745 6753 6760 6768 677$ 6782
6790 6797 6805 6812 6819 6827 6834 6842 6849 6856
6864 6871 6879 6886 6893 6901 6908 6916 6923 6930
6938 6945 6953 6960 6967 6975 6982 6989 6997 7004
7012 7019 7026 7034 7041 7048 7056 7063 7070 7078
77085 77093 77100 77107 77115 77122 77129 77137 77144 77151
7159 7166 7173 7181 7188 7195 7203 7210 7217 722$
7232 7240 7247 7254 7262 7269 7276 7283 7291 7298
7305 7313 7320 7327 7335 7342 7349 7357 7364 7371
7379 7386 7393 7401 7408 7415 7422 7430 7437 7444
7452 7459 7466 7474 7481 7488 7495 7503 7510 7517
7525 7532 7539 7546 7554 7561 7568 7576 7583 7590
7597 7605 7612 7619 7627 7634 7641 7648 7656 7663
7670 7677 7685 7692 7699 7706 7714 7721 7728 7735
7743 7750 7757 7764 7772 7779 7786 7793 7801 7808
77815 77822 77830 77837 77844 77851 77859 77866 77873 77880
168 TABLE 7. —LOGARITHMS OP NUMBERS.
O123456789
600 1 2 3
4 5 6 7 8 9
610 1 2 3
4 5 6
7 8
620 1 2 3
4 5 6 7 8 9
1 2 3
4 5 6 7 8 9
640 1 2 3
4 5 8 7 8
650
77815 77822 77830 77837 77844 77851 77859 77866 77873 77880
7887 7895 7902 7909 7916 7924 7931 7938 7945 7952
7960 7967 7974 7981 7988 7996 8003 8010 8017 802$
8032 8039 8046 8053 8061- 8068 8075 8082 8089 8097
8104 8111 8118 8125 8132 8140 8147 8154 8161 8168
8176 8183 8190 8197 8204 8211 8219 8226 8233 8240
8247 8254 8262 8269 8276 8283 8290 8297 830$ 8312
8319 8326 8333 8340 8347 8355 8362 8369 8376 8383
8390 8398 8405 8412 8419 8426 8433 8440 8447 845$
8462 8469 8476 8483 8490 8497 8504 8512 8519 8526
78533 78540 78547 78554 78561 78569 78576 78583 78590 78597
8604 8611 8618 8625 8633 8640 8647 8654 8661 8668
8675 8682 8689 8606 8704 8711 8718 8725 8732 8739
8746 8753 8760 8767 8774 8781 8789 8796 8803 8810
8817 8824 8831 8838 8845 8852 8859 8866 8873 8880
8888 8895 8902 8909 8916 8923 8930 8937 8944 8951
8958 8965 8972 8979 8986 8993 9000 9007 9014 9021
9029 9036 9043 9050 9057 9064 9071 9078 9085 9092
9099 9106 9113 9120 9127 9134 9141 9148 9155 9162
9169 9176 9183 9190 9197 9204 9211 9218 9225 9232
79239 79246 79253 79260 79267 79274 79281 79288 79295 79302
9309 9316 9323 9335 9337 934 i 9351 9358 9365 9372
9379 9386 9393 9400 9407 9414 9421 9428 9435 9442
9449 9456 9463 9470 9477 9484 9491 9498 9505 9511
9518 9525 9532 9539 9546 9553 9500 9567 9574 9581
9588 9595 9602 9609 9616 9623 9630 9637 9644 9650
9657 9664 9671 9678 9685 9692 9699 9706 9713 9720
9727 9734 9741 9748 9754 9761 9768 9775 9782 9789
9796 9803 9810 9817 9824 9831 9837 9844 9851 9858
9865 9872 9879 9886 9893 9900 9906 9913 9920 9927
79934 79941 79948 79955 79962 79969 79975 79982 79989 79996
80003 80010 80017 80024 80030 80037 80044 80051 80058 80065
0072 0079 0085 0092 0099 0106 0113 0120 0127 0134
0140 0147 0154 0161 0168 0175 0182 0188 0195 0202
0209 0216 0223 0229 0236 0243 0250 0257 0264 0271
0277 0284 0291 0298 0305 0312 0318 0325 0332 0339
0346 0353 0359 0366 0373 0380 0387 0393 0400 0407
0414 0421 0428 0434 0441 0448 0455 0462 0468 0475
0482 0489 0496 0502 0509 0516 0523 0530 0536 0543
0550 0557 0564 0570 0577 0584 0591 0598 0604 0611
80618 80625 80632 8063P 80645 80652 80659 80665 80672 80679
0686 0693 0699 0706 0713 0720 0726 0733 0740 0747
0754 0760 0767 0774 0781 0787 0794 0801 0808 0814
0821 0828 0835 0841 0848 085$ 0862 0868 0875 0882
0889 0895 0902 0909 0916 0922 0929 0936 0943 0949
0956 0963 0969 0976 0983 0990 0996 1003 1010 1017
1023 1030 1037 1043 1050 1057 1064 1070 1077 1084
1090 1097 1104 1111 1117 1124 1131 1137 1144 1151
1158 1164 1171 1178 1184 1191 1198 1204 1211 1218
1224 1231 1238 124$ 1251 1258 126$ 1271 1278 128$
81291 81298 8130$ 81311 81318 8132$ 81331 81338 8134$ 81351
TABLE 7 — LOGARITHMS OF NUMBERS. 169
0123456789
650
1 2 3 4 5 6 7 8 9
660
1 2 3 4 5 6 7 8 9
3
4 5 6 7 8 9
690
1 2 3 4 5 6 7 8 9
700
81291 81298 81305 81311 81318 81325 81331 81338 81345 81351
1358 1365 1371 1378 1385 1391 1398 1405 1411 1418
1425 1431 1438 1445 1451 1458 1465 1471 1478 1485
1491 1498 1505 1511 1518 1525 1531 1538 1544 1551
1558 1564 1571 1578 1584 1591 1598 1604 1611 1617
1624 1631 1637 1644 1651 1657 1664 1671 1677 1684
1690 1697 1704 1710 1717 1723 1730 1737 1743 1750
1757 1763 1770 1776 1783 1790 1796 1803 1809 1816
1823 1829 1836 1842 1849 1856 1862 1869 1875 1882
1889 1895 1902 1908 1915 1921 1928 1935 1941 1948
81954 81961 81968 81974 81981 81987 81994 82000 82007 82014
2020 2027 2033 2040 2046 2053 2060 2066 2073 2079
2086 2092 2099 2105 2112 2119 2125 2132 2138 2145
2151 2158 2164 2171 2178 2184 2191 2197 2204 2210
2217 2223 2230 2236 2243 2249 2256 2263 2269 2276
2282 2289 2295 2302 2308 2315 2321 2328 2334 2341
2347 2354 2360 2367 2373 2380 2387 2393 2400 2406
2413 2419 2426 2432 2439 2445 2452 2458 2465 2471
2478 2484 2491 2497 2504 2510 2517 2523 2530 2536
2543 2549 2556 2562 2569 2575 2582 2588 2595 2601
82607 82614 82620 82627 82633 82640 82646 82653 82659 82666
2672 2679 2685 2692 2698 2705 2711 2718 2724 2730
2737 2743 2750 2750 2763 2769 2776 2782 2789 2795
2802 2808 2814 2821 2827 2834 2840 2847 2853 2860
2866 2872 2879 2885 2892 2898 2905 2911 2918 2924
2930 2937 2943 2950 2956 2963 2969 2975 2982 2988
2995 3001 3008 3014 3020 3027 3033 3040 3046 3052
3059 3065 3072 3078 3085 3091 3097 3104 3110 3117
3123 3129 3136 3142 3149 3155 3161 3168 3174 3181
3187 3193 3200 3206 3213 3219 3225 3232 3238 3245
83251 83257 83264 83270 83276 83283 83289 83296 83302 83308
3315 3321 3327 3334 3340 3347 3353 3359 3366 3372
3378 3385 3391 3398 3404 3410 3417 3423 3429 3436
3442 3448 3455 3461 3467 3474 3480 3487 3493 3499
3506 3512 3518 3525 3531 3537 3544 3550 3556 3563
3569 3575 3582 3588 3S94 3601 3607 3613 3620 3626
3632 3639 3645 3651 3658 3664 3670 3677 3683 3689
3696 3702 3708 3715 3721 3727 3734 3740 3746 3753
3759 3765 3771 3778 3784 3790 3797 3803 3809 3816
3822 3828 3835 3841 3847 3853 3860 3866 3872 3879
83885 83891 83897 83904 83910 83916 83923 83929 83935 83942
3948 3954 3960 3967 3973 3979 3985 3992 3998 4004
4011 4017 4023 4029 4036 4042 4048 4055 4061 4067
4073 4080 4086 4092 4098 4105 4111 4117 4123 4130
4136 4142 4148 4155 4161 4167 4173 4180 4186 4192
4198 4205 4211 4217 4223 4230 4236 4242 4248 4255
4261 4267 4273 4280 4286 4292 4298 4305 4311 4317
4323 4330 4336 4342 4348 4354 4361 4367 4373 4379
4386 4392 4398 4404 4410 4417 4423 4429 4435 4442
4448 4454 4460 4466 4473 4479 448£ 4491 4497 4504
84510 84516 84522 84528 84535 84541 84547 84553 84559 84566
170 TABLE 7.— LOGARITHMS OF NUMBERS.
N0123456789
700 1 2 3
4 5 6
7 8 9
710
1
2 3 4 5 6 7 8 9
720
1
2 3
4 5 6 7 8 9
730 1 2
3 4 5 6 7 8 9
740
1 2 3
4 5 6 7 8 9
750
84510 84516 84522 84528 84535 84541 84547 84553 84559 84560
4572 4578 4584 4590 4597 4603 4609 4615 4621 4628
4634 4640 4646 4652 4658 4665 4671 4677 4683 4689
4696 4702 4708 4714 4720 4726 4733 4739 4745 4751
4757 4763 4770 4776 4782 4788 4794 4800 4807 4813
4819 4825 4831 4837 4844 4850 4856 4862 4868 4874
4880 4887 4893 4899 4905 4911 4917 4924 4930 4936
4942 4948 4954 4960 4967 4973 4979 4985 4991 4997
5003 5009 5016 5022 5028 5034 5040 5046 5052 5058
5065 5071 5077 5083 5089 5095 5101 5107 5114 5120
85126 85132 85138 85144 85150 85156 85163 85169 85175 85181
5187 5193 5199 5205 5211 5217 5224 5230 5236 5242
5248 5254 5260 5266 5272 5278 . 5285 5291 5297 5303
5309 5315 5321 5327 5333 5339 5345 5352 5358 5364
5370 5376 5382 5388 5394 5400 5406 5412 5418 5425
5431 5437 5443 5449 5455 5461 *467 5473 5479 5485
5491 5497 5503 5509 5516 5522 5528 5534 5540 5546
5552 5558 5564 5570 5576 55C2 5588 5594 5600 5606
5612 5618 5625 5631 5637 5643 5649 5655 5661 5667
5673 5679 6685 5691 5697 6703 5709 5715 5721 5727
85733 85739 85745 85751 85757 85763 85769 85775 85781 85788
5794 5800 5806 5812 5818 5824 5830 5836 5842 5848
5854 5860 5866 5872 5878 5884 5890 5896 5902 5908
5914 5920 5926 5932 5938 5944 5950 5956 5962 5968
5974 5980 5986 5992 5998 6004 6010 6016 6022 6028
6034 6040 6046 6052 6058 6064 6070 6076 6082 6088
6094 6100 6106 6112 6118 6124 6130 6136 6141 6147
6153 6159 6165 6171 6177 6183 6189 6195 6201 6207
6213 6219 6225 6231 6237 6243 6249 6255 6261 6267
6273 6279 6285 6291 6297 6303 6308 6314 6320 6326
86332 86338 86344 86350 86356 86362 86368 86374 86380 86386
6392 6398 6404 6410 6415 6421 6427 6433 6439 6445
6451 6457 6463 6469 6475 6481 6487 6493 6499 6504
6510 6516 6522 6528 6534 6540 6546 6552 6558 6564
6570 6576 6581 6587 6593 6599 6605 6611 6617 6623
6629 6635 6641 6646 6652 6658 6664 6670 6676 6682
6688 6694 6700 6705 6711 6717 6723 6729 6735 6741
6747 6753 6759 6764 6770 6776 6782 6788 6794 6800
6806 6812 6817 6823 6829 6835 6841 6847 6853 6859
6864 6870 6876 6882 6888 6894 6900 6906 6911 6917
86923 86929 86935 86941 86947 86953 86958 86964 86970 86976
6982 6988 6994 6999 7005 7011 7017 7023 7029 7035
7040 7046 7052 7058 7064 7070 7075 7081 7087 7093
7099 7105 7111 7116 7122 7128 7134 7140 7146 7151
7157 7163 7169 7175 7181 7186 7192 7198 7204 7210
7216 7221 7227 7233 7239 7245 7251 7256 7262 7268
7274 7280 7286 7291 7297 7303 7309 7315 7320 7326
7332 7338 7344 7349 7355 7361 7367 7373 7379 7384
7390 7396 7402 7408 7413 7419 7425 7431 7437 7442
7448 7454 7460 7466 7471 7477 7483 7489 7493 7500
87506 87512 87518 87523 87529 87535 87541 87547 87552 87558
TABLE 7.— LOGARITHMS OF NUMBERS. 171
N0123456789
750 1
2 3
4 5 6 7 8 9
760 1
2 3
4 5 6
7 8 9
3 4 5 6 7 8 9
780 1 2 3 4 5 6 7 8 9
790
1 2 3 4 5 6 7 8 9
800
87506 87512 87518 87523 87529 87535 87541 87547 87552 87558
7564 7570 7576 7581 7587 7593 7599 7604 7610 7616
7622 7628 7633 7639 7645 7651 7656 7662 7668 7674
7679 7685 7691 7697 7703 .7708 7714 7720 7726 7731
7737 7743 7749 7754 7760 7766 7772 7777 7783 7789
7795 7800 7806 7812 7818 7823 7829 7835 7841 7846
7852 7858 7864 7869 7875 7881 7887 7892 7898 7904
7910 7915 7921 7927 7933 7938 7944 7950 7955 7961
7967 7973 7978 7984 7990 7996 8001 8007 8013 8018
8024 8030 8036 8041 8047. 8053 8058 8064 8070 8076
88081 88087 88093 88098 88104 88110 88116 88121 88127 88133
8138 8144 8150 8156 8161 8167 8173 8178 8184 8190
8195 8201 8207 8213 8218 8224 8230 8235 8241 8247
8252 8258 8264 8270 8275 8281 8287 8292 8298 8304
8309 8315 8321 8326 8332 8338 8343 8349 8355 8360
8366 8372 8377 8383 8389 8395 8400 8406 8412 8417
8423 8429 8434 8440 8446 8451 8457 8463 8468 8474
8480 8485 8491 8497 8502 8508 8513 8519 8525 8530
8536 8542 8547 8553 8559 8564 8570 8576 8581 8587
8593 8598 8604 8610 8615 8621 8627 8632 8638 8643
88649 88655 88660 88666 88672 88677 88683 88689 88694 88700
8705 8711 8717 8722 8728 8734 8739 8745 8750 8756
8762 8767 8773 8779 8784 8790 8795 8801 8807 8812
8818 8824 8829 8835 8840 8846 8852 8857 8863 8868
8874 8880 8885 8891 8897 8902 8908 8913 8919 8925
8930 8936 8941 8947 8953 S958 8964 8969 8975 8981
8986 8992 8997 9003 9009 9014 9020 9025 9031 9037
9042 9048 9053 9059 9064 9070 9076 9081 9087 9092
9098 9104 9109 9115 9120 9126 9131 9137 9143 9148
9154 9159 9165 9170 9176 9182 9187 9193 9198 9204
89209 89215 89221 89226 89232 89237 89243 89248 89254 89260
9265 9271 9276 9282 9287 9293 9298 9304 9310 9315
9321 9326 9332 9337 9343 9348 9354 9360 9365 9371
9376 9382 9387 9393 9398 1)404 9409 9415 9421 9426
9432 9437 9443 9448 9454 9459 9465 9470 9476 9481
9487 9492 9498 9504 9509 9515 9520 9526 9531 9537
9542 9548 9553 9559 9564 9570 9575 9581 9586 9592
9597 9603 9509 9614 9620 9625 9631 9636 9642 9647
9853 9653 9664 9669 9675 9680 9686 9691 9697 9702
9708 9713 9719 9724 9730 9735 9741 9746 9752 9757
89763 89768 89774 89779 89785 89790 89796 89801 89807 89812
9818 9323 9829 9834 9840 9845 9851 9856 9862 9867
9873 9878 9883 9889 9894 9900 9905 9911 9916 9922
9927 9933 9938 9944 9949 9955 9960 9966 9971 9977
9982 9988 9993 9998900049000990015900209002690031
90037 90042 90048 90053 0059 0064 0069 0073 0080 0086
0091 0097 0102 0108 0113 0119 0124 0129 013$ 0140
0146 0151 0157 0162 0168 0173 0179 0184 0189 0195
0200 0206 0211 0217 02'22 0227 0233 0238 0244 0249
0255 0260 0266 0271 0276 0282 0287 0293 0298 0304
90309 90314 90320 90325 90331 90336 90342 90347 90352 90358
172 TABLE 7.— LOGARITHMS OF NUMBERS.
N0123456789
800
1
4 5 6 7 8 9
810
1 2 3
4 5 6 7 8 9
820
1 2 3
4 5 6 7 8 9
830
1 2 3
4 5 6 7 8 9
840 1
2 3
4 5 6
7
850
90309 90314 90320 90325 90331 90336 90342 90347 90352 90358
0363 0369 0374 0380 0385 0390 0396 0401 0407 0412
0417 0423 0428 0434 0439 0445 0450 0455 0461 0466
0472 0477 0482 0488 0493 0499 0504 0509 0515 0520
0526 0531 0536 0542 0547 0553 0558 0563 0569 0574
0580 0585 0590 0596 0601 0607 0612 0617 0623 0628
0634 0639 0644 0650 0655 0660 0666 0671 0677 0682
0687 0693 0698 0703 0709 0714 0720 0725 0730 0736
0741 0747 0752 0757 0763 0768 0773 0779 0784 0789
0795 0800 0806 0811 0816 0822 0827 0832 0838 0843
90849 90854 90859 90865 90870 90875 90881 90886 90891 90897
0902 0907 0913 0918 0924 0929 0934 0940 0945 0950
0956 0961 0966 0972 0977 0982 0988 0993 0998 1004
1009 1014 1020 1025 1030 1036 1041 1046 1052 1057
1062 1068 1073 1078 1084 1089 1094 1100 1105 1110
1116 1121 1126 1132 1137 1142 1148 1153 1158 1164
1169 1174 1180 1185 1190 1196 1201 1206 1212 1217
1222 1228 1233 1238 1243 1249 1254 1259 1265 1270
1275 1281 1286 1291 1297 1302 1307 1312 1318 1323
1328 1334 1339 1344 1350 1355 1360 1365 1371 1376
91381 91387 91392 91397 91403 91408 91413 91418 91424 91429
1434 1440 1445 1450 1455 1461 1466 1471 1477 1482
1487 1492 1498 1503 1508 1514 1519 1524 1529 1535
1540 1545 1551 1556 1561 1566 1572 1577 1582 1587
1593 1598 1603 1609 1614 1619 1624 1630 1635 1640
1645 1651 1656 1661 1666 1672 1677 1682 1687 1693
1698 1703 1709 1714 1719 1724 1730 1735 1740 1745
1751 1756 1761 1766 1772 1777 1782 1787 1793 1798
1803 1808 1814 1819 1824 1829 1834 1840 1845 1850
1855 1861 1866 1871 1876 1882 1887 1892 1897 1903
91908 91913 91918 91924 91929 91934 91939 91944 91950 91955
1960 1965 1971 1976 1981 1986 1991 1997 2002 2007
2012 2018 2023 2028 2033 2038 2044 2049 2054 2059
2065 2070 2075 2080 2085 2091 2096 2101 2106 2111
2117 2122 2127 2132 2137 2143 2148 2153 2158 2163
2169 2174 2179 2184 2189 2195 2200 2205 2210 2215
2221 2226 2231 2236 2241 2247 2252 2257 2262 2267
2273 2278 2283 2288 2293 2298 2304 2309 2314 2319
2324 2330 2335 2340 2345 2350 2355 2361 2366 2371
2376 2381 2387 2392 2397 2402 2407 2412 2418 2423
92428 92433 92438 92443 92449 92454 92459 92464 92469 92474
2480 2485 2490 2495 2500 2505 2511 2516 2521 2526
2531 2536 2542 2547 2552 2557 2562 2567 2572 2578
2583 2588 2593 2598 2603 2609 2614 2619 2624 2629
2634 2639 2645 2650 2655 2660 2665 2670 2675 2681
2686 2691 2696 2701 2706 2711 2716 2722 2727 2732
2737 2742 2747 2752 2758 2763 2768 2773 2778 2783
2788 2793 2799 2804 2809 2814 2819 2824 2829 2834
2840 2845 2850 2855 2860 2865 2870 2875 2881 2886
2891 2896 2901 2906 2911 2916 2921 2927 2932 2937
92942 92947 92952 92957 92962 92967 92973 92978 92983 92988
TABLE 7.— LOGARITHMS OF NUMBERS. 173
NO123456789
850
1 2 3
4 5 6 7 8 9
860
1 2 3 4 5 6 7 8 9
870
1
2 3 4 5 6 7 8 9
880 1 2 3 4 5 6 7 8 9
890
1 2 3 4 5 6 7 8 9
900
92942 92947 92952 92957 92962 92967 92973 92978 92983 92988
2993 2998 3003 3008 3013 3018 3024 3029 3034 3039
3044 3049 3054 3059 3064 3069 3075 3080 3085 3090
3095 3100 3105 3110 3115 3120 3125 3131 3136 3141
3146 3151 3156 3161 3166 3171 3176 3181 3186 3192
3197 3202 3207 3212 3217 3222 3227 3232 3237 3242
3247 3252 3258 3263 3268 3273 3278 3283 3288 3293
3298 3303 3308 3313 3318 3323 3328 3334 3339 3344
3349 3354 3359 3364 3369 3374 3379 3384 3389 3394
3399 3404 3409 3414 3420 3425 3430 3435 3440 3445
93450 93455 93460 93465 93470*93475 93480 93485 93490 93495
3500 3505 3510 3515 3520 3526 3531 3536 3541 3546
3551 3556 3561 3566 3571 3576 3581 3586 3591 3596
3601 3606 3611 3616 3621 3626 3631 3636 3641 3646
3651 3656 3661 3666 3671 3676 3682 3687 3692 3697
3702 3707 3712 3717 3722 3727 3732 3737 3742 3747
3752 3757 3762 3767 3772 3777 3782 3787 3792 3797
3802 3807 3812 3817 3822 3827 3832 3837 3842 3847
3852 3857 3862 3867 3872 3877 3882 3887 3892 3897
3902 3907 3912 3917 3922 3927 3932 3937 3942 3947
93952 93957 93962 93967 93972 93977 93982 93987 93992 93997
4002 4007 4012 4017 4022 4027 4032 4037 4042 4047
4052 4057 4062 4067 4072 4077 4082 4086 4091 4096
4101 4106 4111 4116 4121 4126 4131 4136 4141 4146
4151 4156 4161 4166 4171 4176 4181 4186 4191 4196
4201 4206 4211 4216 4221 4226 4231 4236 4240 4245
4250 4255 4260 4265 4270 4275 4280 4285 4290 4295
4300 4305 4310 4315 4320 4325 4330 4335 4340 434£
4349 4354 4359 4364 4369 4374 4379 4384 4389 4394
4399 4404 4409 4414 4419 4424 4429 4433 4438 4443
94448 94453 94458 94463 94468 94473 94478 94483 94488 94493
4498 4503 4507 4512 4517 4522 4527 4532 4537 4542
4547 4552 4557 4562 4567 4571 4576 4581 4586 4591
4596 4601 4606 4611 4616 4621 4626 4630 4635 4640
4645 4650 4655 4660 4665 4670 4675 4680 4685 4689
4694 4699 4704 4709 4714 4719 4724 4729 4734 4738
4743 4748 4753 4758 4763 4768 4773 4778 4783 4787
4792 4797 4802 4807 4812 4817 4822 4827 4832 4836
4841 4846 4851 4856 4861 4866 4871 4876 4880 4885
4890 4895 4900 4905 4910 4915 4919 4924 4929 4934
94939 94944 94949 94954 94959 94963 94968 94973 94978 94983
4988 4993 4998 5002 5007 5012 5017 5022 5027 5032
5036 5041 5046 5051 5056 5061 5066 5071 5075 5080
5085 5090 5095 5100 5105 5109 5114 5119 5124 5129
5134 5139 5143 5148 5153 5158 5163 5168 5173 5177
5182 5187 5192 5197 5202 5207 5211 5216 5221 5226
5231 5236 5240 5245 5250 5255 5260 5265 5270 5274
5279 5284 5289 5294 5299 5303 5308 5313 5318 5323
5328 5332 5337 5342 5347 5352 5357 5361 5366 5371
5376 5381 5386 5390 5395 5400 5405 5410 5415 5419
95424 95429 95434 95439 95444 95448 95453 95458 95463 95468
174 TABLE 7.— LOGARITHMS OF NUMBERS.
0123456789
I
900
1 2 3 4 5 6 7 8 9
910
1 2 3 4 5 6 7 8 9
920 1 2 3
4 5 6
7 8 9
930
1
2 3
4 5 6 7 8 9
940
1
4 5 6 7 8 9
950
95424 95429 95434 95439 95444 95448 95453 95458 95463 95468
5472 5477 6482 5487 5492 5497 5501 5506 5511 5516
5521 5525 5530 5535 5540 5545 5550 5554 5559 5564
5569 5574 5578 5583 5588 ' 5593 5598 5602 5607 5612
5617 5622 5626 5631 6636 5641 5646 5650 5655 5660
5665 6670 5674 6679 6684 5689 5694 6698 5703 5708
5713 5718 5722 5727 5732 5737 5742 5746 5751 5756
5761 5766 5770 5775 5780 5785 5789 5794 5799 5804
5809 5813 5818 5823 5828 5832 5837 5842 5847 6852
5856 5861 6866 5871 5875 5880 5885 5890 5895 5899
95904 95909 95914 95918 95923 95928 95933 95938 95942 95947
5952 5957 5961 5966 5971 5976 5980 5985 5990 5995
5999 6004 6009 6014 6019 6023 6028 6033 6038 6042
6047 6052 6057 6061 6066 6071 6076 6080 6085 6090
609^ 6099 6104 6109 6114 6118 6123 6128 6133 6137
6142 6147 6152 6156 6161 6166 6171 6175 6180 6185
6190 6194 6199 6204 6209 6213 6218 6223 6227 6232
6237 6242 6246 6251 6256 6261 6265 6270 6275 6280
6284 6289 6294 6298 6303 6308 6313 6317 6322 6327
6332 6336 6341 6346 6350 6355 6360 6365 6369 6374
96379 96384 96388 96393 96398 96402 96407 96412 96417 96421
6426 6431 6435 6440 6445 6450 6454 6459 6464 6468
6473 6478 6483 6487 6492 6497 6501 6506 6511 6515
6520 6525 6530 6534 6539 6544 6548 6553 6558 6562
6567 6572 6577 6581 6586 6591 6595 6600 6605 6609
6614 6619 6624 6628 6633 6638 6642 6647 6652 6656
6661 6666 6670 6675 6680 6685 6689 6694 6699 6703
6708 6713 6717 6722 6727 6731 6736 6741 6745 6750
6755 6759 6764 6769 6774 6778 6783 6788 6792 6797
6802 6806 6811 6816 6820 6825 6830 6834 6839 6844
96848 96853 96858 96862 96867 96872 96876 96881 96886 96890
6895 6900 6904 6909 6914 6918 6923 6928 6932 6937
6942 6946 6951 6956 6960 6965 6970 6974 6979 6984
6988 6993 6997 7002 7007 7011 7016 7021 7025 7030
7035 7039 7044 7049 7053 7058 7063 7067 7072 7077
7081 7086 7090 7095 7100 7104 7109 7114 7118 7123
7128 7132 7137 7142 7146 7151 7155 7,160 7165 7169
7174 7179 7183 7188 7192 7197 7202 7206 7211 7216
7220 7225 7230 7234 7239 7243 7248 7253 7257 7262
7267 7271 7276 7280 7285 7290 7294 7299 7304 7308
97313 97317 97322 97327 97331 97336 97340 97345 97350 97354
7359 7364 7368 7373 7377 7382 7387 7391 7396 7400
7405 7410 7414 7419 7424 7428 7433 7437 7442 7447
7451 7456 7460 7465 7470 7474 7479 7483 7488 7493
7497 7502 7506 7511 7516 7520 7525 7529 7534 7539
7543 7548 7552 7557 7562 7566 7571 7575 7580 7585
7589 7594 7598 7603 7607 7612 7617 7621 7626 7630
7635 7640 7644 7649 7653 7658 7663 7667 7672 7676
7681 7685 -7690 7695 7699 7704 7708 7713 7717 7722
7727 7731 7736 7740 7745 7749 7754 7759 7763 7768
97772 97777 97782 97786 97791 97795 97800 97804 97809 97813
TABLE 7.— LOGARITHMS OF NUMBERS. 175
0123456789
950 97772 97777 97782 97786 97791 97795 97800 97804 97809 97813
1 7818 7823 7827 7832 7836 7841 7845 7850 7855 7859
2 7864 7868 7873 7877 7882 7886 7891 7896 7900 7905
3 7909 7914 7918 7923 7928 7932 7937 7941 7946 7950
4 7955 7959 7964 7968 7973 7978 7982 7987 7991 7996
5 8000 8005 8009 8014 8019 8023 8028 8032 8037 8041
6 8046 8050 8055 8059 8064 8068 8073 8078 8082 8087
7 8091 8096 8100 8105 8109 8114 8118 8123 8127 8132
8 8137 8141 8146 8150 8155 8159 8164 8168 8173 8177
9 8182 8186 8191 8195 8200. 8204 8209 8214 8218 8223
960 98227 98232 98236 98241 98245 98250 98254 98259 98263 98268
1 8272 8277 8281 8286 8290 8295 8299 8304 8308 8313
2 8318 8322 8327 8331 8336 8340 8345 8349 8354 8358
3 8363 8367 8372 8376 8381 8385 8390 8394 8399 8403
4 8408 8412 8417 8421 8426 8430 8435 8439 8444 8448
5 8453 8457 8462 8466 8471 8475 8480 8484 8489 8493
6 8498 8502 8507 8511 8516 8520 8525 8529 8534 8538
7 8543 8547 8552 8556 8561 8565 8570 8574 8579 8583
8 8588 8592 8597 8601 8605 8610 8614 8619 8623 8628
9 8632 8637 8641 8646 8650 8655 8659 8664 8668 8673
970 98677 98682 98686 98691 98695 98700 98704 98709 98713 98717
1 8722 8726 8731 8735 8740 8744 8749 8753 8758 8762
2 8767 8771 8776 8780 8784 8789 8793 8798 8802 8807
3 8811 8816 8820 8825 8829 8834 8838 8843 8847 8851
4 8856 8860 8865 8869 8874 8878 8883 8887 8892 8896
5 8900 8905 8909 8914 8918 8923 8927 8932 8936 8941
6 8945 8949 8954 8958 8963 B967 8972 8976 8981 8985
7 8989 8994 8998 9003 9007 9012 9016 9021 9025 9029
8 9034 9038 9043 9047 9052 9056 9061 9065 9069 9074
9 9078 9083 9087 9092 9096 9100 9105 9109 9114 9118
980 99123 99127 99131 99136 99140 99145 99149 99154 99158 99162
1 9167 9171 9176 9180 9185 9189 9193 9198 9202 9207
2 9211 9216 9220 9224 9229 9233 9238 9242 9247 9251
3 9255 9260 9264 9269 9273 9277 9282 9286 9291 9295
4 9300 9304 9308 9313 9317 9322 9326 9330 9335 9339
5 9344 9348 9352 9357 9361 9366 9370 9374 9379 9383
6 9388 9392 9396 9401 9405 9410 9414 9419 9423 9427
7 9432 9436 9441 9445 9449 9454 9458 9463 9467 9471
8 9476 9480 9484 9489 9493 9498 9502 9506 9511 9516
9 9520 9524 9528 9533 9537 9542 9546 9550 9555 9559
990 99564 99568 99572 99577 99581 99585 99590 99594 99599 99603
1 9607 9612 9616 9621 9625 9629 9634 9638 9642 9647
2 9651 9656 9660 9664 9669 9673 9677 9682 9686 9691
3 9695 9699 9704 9708 9712 9717 9721 9726 9730 9734
4 9739 9743 9747 9752 9756' 9760 9765 9769 9774 9778
5 9782 9787 9791 9795 9800 9804 9808 9813 9817 9822 i 9826 9830 9835 9839 9843 9848 9852 9856 9861 9865
7 9870 9874 9878 9883 9887 9891 9896 9900 9904 9909
8 9913 9917 9922 9926 9930 9935 9939 9944 9948 9952
9 9957 9961 9965 9970 9974 9978 9983 9987 9991 9996
1000 00000 00004 00009 00013 00017 00022 00026 00030 00035 00039
176 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
t |
0° |
1° |
2° |
||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
—00 |
10.00000 |
8.24186 |
9.99993 |
8.54282 |
9 99974 |
60 |
|
1 |
6.46373 |
00000 |
24903 |
99993 |
54642 |
99973 |
59 |
|
2 |
76476 |
00000 |
25609 |
' 99993 |
54999 |
99973 |
58 |
|
3 |
94085 |
00000 |
26304 |
99993 |
55354 |
99972 |
57 |
|
4 |
7.0G579 |
00000 |
26988 |
99992 |
55705 |
99972 |
56 |
|
5 |
16270 |
00000 |
27661 |
99992 |
56054 |
69971 |
55 |
|
6 |
24188 |
00000 |
28324 |
99992 |
56400 |
99971 |
54 |
|
7 |
30882 |
00000 |
28977 |
99992 |
56743 |
99970 |
51 |
|
8 |
36682 |
00000 |
29621 |
99992 |
57084 |
99970 |
52 |
|
9 |
41797 |
00000 |
30255 |
99991 |
57421 |
99969 |
51 |
|
10 |
7.46373 |
10.00000 |
8.30879 |
9.99991 |
8.57757 |
9.99969 |
50 |
|
11 |
50512 |
00000 |
31495 |
99991 |
58089 |
99968 |
49 |
|
12 |
54291 |
00000 |
32103 |
99990 |
58419 |
99968 |
48 |
|
13 |
57767 |
00000 |
32702 |
99990 |
58747 |
99967 |
47 |
|
14 |
60985 |
00000 |
33292 |
99990 |
59072 |
99967 |
46 |
|
15 |
63982 |
00000 |
33875 |
99990 |
59395 |
99967 |
45 |
|
16 |
66784 |
00000 |
34450 |
99989 |
59715 |
99960 |
44 |
|
17 |
69417 |
9.99999 |
35018 |
99989 |
60033 |
99966 |
43 |
|
18 |
71900 |
99999 |
35578 |
99989 |
60349 |
99965 |
42 |
|
19 |
74248 |
99999 |
36131 |
99989 |
60662 |
99964 |
41 |
|
20 |
7.76475 |
9.99999 |
8.36678 |
9.99988 |
8.60973 |
9.99964 |
40 |
|
21 |
78594 |
99999 |
37217 |
99988 |
61282 |
99963 |
39 |
|
22 |
80615 |
99999 |
37750 |
99988 |
61589 |
99963 |
38 |
|
23 |
82545 |
99999 |
38276 |
99987 |
61894 |
99962 |
37 |
|
24 |
84393 |
99999 |
38796 |
99987 |
62196 |
99962 |
36 |
|
25 |
86166 |
99999 |
39310 |
99987 |
62497 |
99961 |
35 |
|
26 |
87870 |
99999 |
39818 |
99986 |
62795 |
99961 |
34 |
|
27 |
89509 |
99999 |
40320 |
99986 |
63091 |
99960 |
33 |
|
28 |
91088 |
99999 |
40816 |
99986 |
63385 |
99960 |
32 |
|
29 |
92612 |
99998 |
41307 |
99985 |
63678 |
99959 |
31 |
|
30 |
7.94084 |
9.99998 |
8.41792 |
9.99985 |
8.63968 |
9.99959 |
30 |
|
31 |
95508 |
99998 |
42272 |
99982 |
64256 |
99958 |
29 |
|
32 |
96887 |
99998 |
42746 |
99984 |
64543 |
99958 |
28 |
|
33 |
98223 |
99998 |
43216 |
99984 |
64827 |
99957 |
27 |
|
34 |
99520 |
99998 |
43680 |
99984 |
65110 |
99956 |
26 |
|
35 |
8.00779 |
99998 |
44139 |
99983 |
65391 |
99956 |
25 |
|
36 |
02002 |
99998 |
44594 |
99983 |
65670 |
99955 |
24 |
|
37 |
03192 |
99997 |
45044 |
99983 |
65947 |
99955 |
23 |
|
38 |
04350 |
99997 |
45489 |
99982 |
66223 |
99954 |
22 |
|
39 |
05478 |
99997 |
45930 |
99982 |
66497 |
99954 |
21 |
|
40 |
8.06578 |
9.99997 |
8.46366 |
9.99982 |
8.66769 |
9.99953 |
20 |
|
41 |
07650 |
99997 |
46799 |
99981 |
67039 |
99952 |
19 |
|
42 |
08696 |
99997 |
47226 |
99981 |
67308 |
99952 |
18 |
|
43 |
09718 |
99997 |
47650 |
99981 |
67575 |
99951 |
17 |
|
44 |
10717 |
99996 |
48069 |
99980 |
67841 |
99951 |
16 |
|
45 |
11693 |
99996 |
48485 |
99980 |
68104 |
99950 |
15 |
|
46 |
12647 |
99996 |
48896 |
99979 |
68367 |
99949 |
14 |
|
47 |
13581 |
99996 |
49304 |
99979 |
68627 |
99949 |
13 |
|
48 |
14495 |
99996 |
49708 |
99979 |
68886 |
99948 |
12 |
|
49 |
15391 |
99996 |
50108 |
99978 |
69144 |
99948 |
11 |
|
50 |
8.16268 |
9.99995 |
8.50504 |
9.99978 |
8.69400 |
9.99947 |
10 |
|
51 |
17128 |
99995 |
50897 |
99977 |
69654 |
99946 |
9 |
|
52 |
17971 |
99995 |
51287 |
99977 |
69907 |
99946 |
8 |
|
53 |
18798 |
99995 |
51673 |
99977 |
70159 |
99945 |
7 |
|
54 |
19610 |
99995 |
52055 |
99976 |
70409 |
99944 |
6 |
|
55 |
20407 |
99994 |
52434 |
99976 |
70658 |
99944 |
5 |
|
56 |
21189 |
99994 |
52810 |
99975 |
70905 |
99943 |
4 |
|
57 |
21958 |
99994 |
53183 |
99975 |
71151 |
99942 |
3 |
|
58 |
22713 |
99994 |
53552 |
99974 |
71395 |
99942 |
2 |
|
59 |
23456 |
99994 |
53919 |
99974 |
71638 |
99941 |
1 |
|
60 |
24186 |
99993 |
54282 |
99974 |
71880 |
99940 |
0 |
|
/ |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
89° |
88 |
0 |
87° |
TABLE 8.— LOGARITHMIC SINES AND COSINES. 177
|
/ |
3° 4° 6° |
||||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
8.71880 |
9.99940 |
8.84358 |
9.99894 |
8.94030 |
9.99834 |
60 |
|
1 |
72120 |
99940 |
84539 |
99893 |
94174 |
99833 |
59 |
|
2 |
72359 |
99939 |
84718 |
99892 |
94317 |
99832 |
58 |
|
3 |
72597 |
99938 |
84897 |
99891 |
944C1 |
99831 |
57 |
|
4 |
72834 |
99938 |
85075 |
99891 |
94603 |
99830 |
66 |
|
5 |
73069 |
99937 |
85252 |
99890 |
94746 |
99829 |
55 |
|
6 |
73303 |
99936 |
85429 |
99889 |
94887 |
998*8 |
54 |
|
7 |
73535 |
99936 |
85605 |
99888 |
95029 |
99827 |
53 |
|
8 |
73767 |
99935 |
85780 |
99887 |
95170 |
99825 |
52 |
|
9 |
73997 |
99934 |
85955 |
99886 |
95310 |
99824 |
51 |
|
10 |
8.74226 |
9.99934 |
8.86128 |
9.99885 |
8.95450 |
9.99823 |
50 |
|
11 |
74454 |
99933 |
86301 |
99.884 |
95589 |
99822 |
49 |
|
12 |
74680 |
99932 |
86474 |
99*883 |
95728 |
99821 |
48 |
|
13 |
74906 |
99932 |
86645 |
99882 |
95867 |
99820 |
47 |
|
14 |
75130 |
99931 |
86816 |
99881 |
96005 |
99819 |
46 |
|
15 |
75853 |
99930 |
86987 |
99880 |
96143 |
99817 |
45 |
|
16 |
75575 |
99929 |
87156 |
99879 |
96280 |
99816 |
44 |
|
17 |
75795 |
99929 |
87325 |
99879 |
96417 |
99815 |
43 |
|
18 |
76015 |
99928 |
87494 |
99878 |
96553 |
99814 |
42 |
|
19 |
76234 |
99927 |
87661 |
99877 |
96689 |
99813 |
41 |
|
20 |
8.76451 |
9.99926 |
8.87829 |
9.99876 |
8.96825 |
9.99812 |
40 |
|
21 |
76667 |
99926 |
87995 |
99875 |
96960 |
99810 |
39 |
|
22 |
76883 |
99925 |
88161 |
99874 |
97095 |
99809 |
38 |
|
23 |
77097 |
99924 |
88326 |
99873 |
97229 |
99808 |
37 |
|
24 |
77310 |
99923 |
88490 |
99872 |
97363 |
99807 |
36 |
|
25 |
77522 |
99923 |
88654 |
99871 |
97496 |
99806 |
35 |
|
26 |
77733 |
99922 |
88817 |
99870 |
97629 |
99804 |
34 |
|
27 , |
77943 |
99921 |
88980 |
99869 |
97762 |
99803 |
33 |
|
28 |
78152 |
99920 |
89142 |
99868 |
97894 |
99802 |
33 |
|
29 |
78360 |
99920 |
89304 |
99867 |
98026 |
99801 |
31 |
|
30 |
8.78568 |
9.99919 |
8.89464 |
9.99866 |
8.98157 |
9.99800 |
30 |
|
31 |
78774 |
99918 |
89625 |
99805 |
98288 |
99798 |
29 |
|
32 |
78979 |
99917 |
89784 |
99864 |
98419 |
99797 |
28 |
|
33 |
79183 |
99917 |
89943 |
99863 |
98549 |
99796 |
27 |
|
34 |
79386 |
99916 |
P0102 |
9986'* |
98679 |
99795 |
26 |
|
35 |
79588 |
99915 |
90260 |
99861 |
98808 |
99793 |
25 |
|
36 |
79789 |
99914 |
90417 |
99860 |
98937 |
99792 |
24 |
|
37 |
79990 |
99913 |
90574 |
99859 |
99066 |
99791 |
23 |
|
38 |
80189 |
99913 |
90730 |
99858 |
99194 |
99790 |
22 |
|
39 |
80388 |
99912 |
90885 |
99857 |
99322 |
99788 |
21 |
|
40 |
8.80585 |
9.99911 |
8.91040 |
9.99856 |
8.99450 |
9.99787 |
20 |
|
41 |
8078-2 |
99910 |
91195 |
99855 |
99577 |
99786 |
19 |
|
42 |
80978 |
99909 |
91349 |
99854 |
99704 |
99785 |
18 |
|
43 |
81173 |
99909 |
91502 |
99853 |
99830 |
99783 |
17 |
|
44 |
81367 |
99908 |
91655 |
99852 |
99956 |
99782 |
16 |
|
45 |
81560 |
99907 |
91807 |
99851 |
9.00082 |
99781 |
15 |
|
46 |
81752 |
99906 |
91959 |
99850 |
00207 |
99780 |
14 |
|
47 |
81944 |
99905 |
92110 |
99848 |
00332 |
99778 |
13 |
|
48 |
82134 |
99904 |
92261 |
99847 |
00456 |
99777 |
12 |
|
49 |
82324 |
99904 |
92411 |
99846 |
00581 |
99776 |
11 |
|
50 |
8.82513 |
9.99903 |
8.92561 |
9.99845 |
9.00704 |
9.99775 |
10 |
|
51 |
82701 |
99902 |
92710 |
99844 |
00828 |
99773 |
9 |
|
52 |
82888 |
99901 |
92859 |
99843 |
00951 |
99772 |
8 |
|
53 |
83075 |
99900 |
93007 |
99842 |
01074 |
99771 |
7 |
|
54 |
83261 |
99899 |
93154 |
99841 |
01196 |
99769 |
6 |
|
55 |
83446 |
99898 |
93301 |
99840 |
01318 |
99768 |
5 |
|
56 |
83630 |
99898 |
93448 |
99839 |
01440 |
99767 |
4 |
|
57 |
83813 |
99897 |
93594 |
99838 |
01561 |
99765 |
3 |
|
58 |
83996 |
99896 |
93740 |
99837 |
01682 |
99764 |
2 |
|
59 |
84177 |
99895 |
93885 |
99836 |
01803 |
99763 |
1 |
|
60 |
84358 |
99894 |
94030 |
99834 |
01923 |
99761 |
0 |
|
/ |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
i |
86° |
85° |
84° |
178 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
/ |
6° |
7° |
8» |
/ |
|||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.01923 |
9.99761 |
9.08589 |
9.99675 |
9.14356 |
9.99575 |
60 |
|
1 |
02043 |
99760 |
08692 |
99674 |
14445 |
99574 |
59 |
|
2 |
02163 |
99759 |
08795 |
99672 |
14535 |
99572 • |
58 |
|
3 |
02283 |
99757 |
08897' |
99670 |
14624 |
99570 |
57 |
|
4 |
03402 |
99756 |
08999 |
99669 |
14714 |
99568 |
56 |
|
5 |
02520 |
99755 |
09101 |
99667 |
14803 |
99566 |
55 |
|
6 |
02639 |
99753 |
09202 |
99666 |
14891 |
99565 |
54 |
|
7 |
02757 |
99752 |
09304 |
99664 |
14980 |
99563 |
53 |
|
8 |
02874 |
99751 |
09405 |
99663 |
15069 |
99561 |
52 |
|
9 |
02992 |
99749 |
09506 |
99661 |
15157 |
99559 |
51 |
|
10 |
9.03109 |
9.99748 |
9.09606 |
9.99659 |
9.15245 |
9.99557 |
50 |
|
11 |
03226 |
99747 |
09707 |
99658 |
15333 |
99556 |
49 |
|
12 |
03342 |
99745 |
09807 |
99656 |
15421 |
99554 |
48 |
|
13 |
03458 |
99744 |
09907 |
99655 |
15508 |
99552 |
47 |
|
14 |
03574 |
99742 |
10006 |
99653 |
15596 |
99550 |
46 |
|
15 |
03690 |
99741 |
10106 |
99651 |
15683 |
99548 |
45 |
|
16 |
03805 |
99740 |
10205 |
99650 |
15770 |
99546 |
44 |
|
17 |
03920 |
99738 |
10304 |
99648 |
15857 |
99545 |
43 |
|
18 |
04034 |
99737 |
10402 |
99647 |
15944 |
99543 |
42 |
|
19 |
04149 |
99736 |
10501 |
99645 |
1C030 |
99541 |
41 |
|
20 |
9.04262 |
9.99734 |
9.10599 |
9.99643 |
9.16116 |
9.99539 |
40 |
|
21 |
04376 |
99733 |
10697 |
99642 |
16203 |
99537 |
39 |
|
22 |
04490 |
99731 |
10795 |
99640 |
16289 |
99535 |
38 |
|
23 |
04603 |
99730 |
10893 |
99638 |
16374 |
89533 |
37 |
|
24 |
04715 |
99728 |
10990 |
99637 |
16460 |
99532 |
86 |
|
25 |
04828 |
99727 |
11087 |
99635 |
16545 |
99530 |
35 |
|
26 |
04940 |
99726 |
11184 |
99633 |
16631 |
99528 |
34 |
|
27 |
05052 |
99724 |
11281 |
99632 |
16716 |
99526 |
33 |
|
28 |
05164 |
99723 |
11377 |
99630 |
16801 |
99524 |
32 |
|
29 |
05275 |
99721 |
11474 |
99629 |
16886 |
99522 |
31 |
|
30 |
9.05386 |
9.99720 |
9.11570 |
9.99627 |
9.16970 |
9.99520 |
30 |
|
31 |
05497 |
99718 |
11666 |
99625 |
17055 |
99518 |
29 |
|
32 |
05607 |
99717 |
11761 |
99624 |
17139 |
99517 |
28 |
|
33 |
05717 |
99716 |
11857 |
99622 |
17223 |
99515 |
27 |
|
34 |
05827 |
99714 |
11952 |
99620 |
J7807 |
99513 |
26 |
|
35 |
05937 |
99713 |
12047 |
99618 |
17391 |
99511 |
25 |
|
36 |
06046 |
99711 |
12142 |
99617 |
17474 |
99509 |
24 |
|
37 |
06155 |
99710 |
12236 |
99615 |
17558 |
99507 |
23 |
|
38 |
06264 |
99708 |
1233i |
99613 |
17641 |
99505 |
22 |
|
39 |
06372 |
99707 |
12425 |
99612 |
17724 |
99503 |
21 |
|
40 |
9.06481 |
9.99705 |
9.12519 |
&. 99610 |
9.17807 |
9.99501 |
20 |
|
41 |
06589 |
99704 |
12612 |
99608 |
17890 |
99499 |
19 |
|
42 |
06696 |
99702 |
12706 |
99607 |
17973 |
99497 |
18 |
|
43 |
06804 |
99701 |
12799 |
99605 |
18055 |
99495 |
17 |
|
44 |
06911 |
99699 |
12892 |
99603 |
18137 |
99494 |
16 |
|
45 |
07018 |
99698 |
12985 |
99601 |
18220 |
99492 |
15 |
|
46 |
07124 |
99696 |
13078 |
99600 |
18302 |
99490 |
14 |
|
47 |
07231 |
99695 |
13171 |
99598 |
18383 |
99488 |
13 |
|
48 |
07337 |
99G93 |
13263 |
99596 |
18465 |
99486 |
19 |
|
49 |
07442 |
99692 |
13355 |
99595 |
18547 |
99484 |
11 |
|
50 |
9.07548 |
9.99690 |
9.13447 |
9.99593 |
9.18628 |
9.99482 |
30 |
|
51 |
07653 |
99689 |
13539 |
99591 |
18709 |
99480 |
9 |
|
52 |
07758 |
99687 |
13630 |
99589 |
18790 |
99478 |
8 |
|
53 |
07863 |
99686 |
13722 |
99588 |
18871 |
99476 |
7 |
|
54 |
07968 |
99684 |
13813 |
99586 |
18952 |
99474 |
6 |
|
55 |
08072 |
99683 |
18904 |
99584 |
19033 |
99472 |
5 |
|
56 |
08176 |
99681 |
13994 |
99582 |
19113 |
99470 |
4 |
|
57 |
08280 |
99680 |
14085 |
99581 |
19193 |
99468 |
3 |
|
58 |
08383 |
99678 |
14175 |
99579 |
19273 |
99466 |
2 |
|
59 |
08486 |
99677 |
14266 |
99577 |
19353 |
99464 |
1 |
|
60 |
08589 |
99675 |
14356 |
99575 |
19433 |
99462 |
0 |
|
I » |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
I |
|
88° |
82° |
81* |
TABLE 8. —LOGARITHMIC SINES AND COSINES, 179
|
/ |
9 |
10° |
11 |
» |
/ |
||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.19433 |
S. 99482 |
9.23967 |
9.99335 |
9.28060 |
9.99195 |
60 |
|
1 |
19513 |
99460 |
24039 |
99333 |
28125 |
99192 |
59 |
|
2 |
19592 |
99458 |
24110 |
99331 |
28190 |
99190 |
58 |
|
3 |
19672 |
99456 |
24181 |
99328 |
28254 |
99187 |
57 |
|
4 |
19751 |
99454 |
24253 |
99326 |
28319 |
99185 |
56 |
|
5 |
19830 |
9945* |
24324 |
99324 |
28384 |
99182 |
55 |
|
6 |
19909 |
99450 |
24395 |
99322 |
28448 |
99180 |
54 |
|
7 |
19988 |
99448 |
24466 |
99319 |
28512 |
99177 |
53 |
|
8 |
20067 |
99446 |
24536 |
99317 |
28577 |
99175 |
52 |
|
9 |
20145 |
99444 |
24607 |
99315 |
28641 |
99172 |
61 |
|
10 |
9.20223 |
9.99442 |
9.24677 |
9.99313 |
9.28705 |
9.99170 |
50 |
|
11 |
20302 |
99440 |
24748 |
99310 |
2876» |
99167 |
49 |
|
12 |
20380 |
99438 |
24818 |
99308 |
28833 |
99165 |
48 |
|
13 |
20458 |
99436 |
24888 |
99306 |
28896 |
99162 |
47 |
|
14 |
20535 |
99434 |
24958 |
99304 |
28960 |
99160 |
46 |
|
15 |
20613 |
99432 |
25028 |
99301 |
29024 |
99157 |
45 |
|
16 |
20691 |
99429 |
25098 |
99299 |
29087 |
99155 |
44 |
|
17 |
207G8 |
99427 |
25168 |
99297 |
29150 |
99152 |
43 |
|
18 |
20845 |
99425 |
25237 |
99294 |
29214 |
99150 |
42 |
|
19 |
20922 |
99423 |
25307 |
99292 |
29277 |
99147 |
41 |
|
20 |
9.20999 |
9.99421 |
9.25376 |
9.99290 |
9.29340 |
9.99145 |
40 |
|
21 |
21076 |
99419 |
25445 |
99288 |
29403 |
99142 |
39 |
|
22 |
21153 |
99417 |
-25514 |
99285 |
29466 |
99140 |
38 |
|
23 |
21229 |
99415 |
25583 |
99283 |
29529 |
99137 |
37 |
|
24 21306 |
99413 |
25652 |
99281 |
29591 |
99135 |
36 |
|
|
25 |
21382 |
99411 |
25721 |
99278 |
29654 |
99132 |
35 |
|
2o |
21458 |
99409 |
25790 |
99276 |
29716 |
99130 |
34 |
|
27 |
21534 |
99407 |
25858 |
99274 |
29779 |
99127 |
33 |
|
28 |
21610 |
99404 |
25927 |
99271 |
29841 |
99124 |
32 |
|
29 |
21685 |
99402 |
25995 |
99269 |
29903 |
99122 |
31 |
|
30 |
9.21761 |
9.99400 |
9.26063 |
9.99267 |
9.29966 |
9.99119 |
30 |
|
31 |
21836 |
99398 |
26131 |
99264 |
30028 |
99117 |
29 |
|
32 |
21912 |
99396 |
26199 |
99262 |
30090 |
99114 |
28 |
|
33 |
21987 |
99394 |
26267 |
99260 |
30151 |
99112 |
27 |
|
34 |
22062 |
99392 |
26335 |
99257 |
30213 |
99109 |
26 |
|
35 |
22137 |
99390 |
26403 |
99255 |
30275 |
99106 |
25 |
|
36 |
22211 |
99388 |
26470 |
99252 |
30336 |
99104 |
24 |
|
37 |
22286 |
99385 |
26538 |
99250 |
30398 |
99001 |
23 |
|
38 |
22361 |
99383 |
26605 |
99248 |
30459 |
99099 |
22 |
|
39 |
22435 |
99381 |
26672 |
99245 |
30521 |
99096 |
21 |
|
40 |
9.22509 |
9.99379 |
9.26739 |
9.99243 |
9.30582 |
9.99093 |
20 |
|
41 |
22583 |
99377 |
26806 |
99241 |
30643 |
99091 |
19 |
|
42 |
22657 |
99375 |
26873 |
99238 |
30704 |
99088 |
18 |
|
43 |
22731 |
99372 |
26940 |
99236 |
30765 |
99086 |
17 |
|
44 |
22805 |
99370 |
27007 |
99233 |
30826 |
99083 |
16 |
|
45 |
22878 |
99368 |
27073 |
99231 |
30887 |
99080 |
15 |
|
46 |
22952 |
99366 |
27140 |
99229 |
30947 |
99078 |
14 |
|
47 |
23025 |
99364 |
27206 |
99226 |
31008 |
99075 |
13 |
|
48 |
23098 |
99362 |
27273 |
99224 |
31068 |
99072 |
12 |
|
49 |
23171 |
99359 |
27339 |
99221 |
81129 |
99070 |
11 |
|
50 |
9.23244 |
9.99357 |
9.27405 |
9.99219 |
9.31189 |
9.99067 |
10 |
|
51 |
23317 |
99355 |
27471 |
99217 |
31250 |
99064 |
9 |
|
52 |
23390 |
99353 |
27537 |
99214 |
31310 |
99062 |
8 |
|
53 |
23462 |
99351 |
27602 |
99212 |
31370 |
99059 |
7 |
|
54 |
23535 |
99348 |
27668 |
99209 |
31430 |
99056 |
6 |
|
55 |
23607 |
99346 |
27734 |
99207 |
31490 |
99054 |
5 |
|
56 |
23679 |
99344 |
27799 |
99204 |
. 31549 |
99051 |
4 |
|
57 |
23752 |
9934? |
27864 |
99202 |
31609 |
99048 |
3 |
|
58 |
23823 |
99340 |
27930 |
99200 |
31669 |
99046 |
2 |
|
59 |
23895 |
99337 |
27995 |
99197 |
31728 |
99043 |
1 |
|
60 |
23967 |
99335 |
28060 |
99195 |
31788 |
99040 |
0 |
|
t |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
80° |
79° |
78° |
180 TABLE 8. —LOGARITHMIC SINES AND COSINES.
|
I |
2° |
13° |
14° |
||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.31788 |
9.99040 |
9.35209 |
9.98872 |
9.38368 |
9.98690 |
60 |
|
1 |
31847 |
99038 |
35263 |
98869 |
38418 |
98687 |
59 |
|
2 |
31907 |
99035 |
35318 |
98867 |
38469 |
98684 |
58 |
|
3 |
31966 |
99032 |
35373 |
98864 |
38519 |
98681 |
57 |
|
4 |
32025 |
99030 |
35427 |
98861 |
38570 |
98678 |
56 |
|
5 |
32084 |
99027 |
35481 |
98858 |
38620 |
98675 |
55 |
|
6 |
32143 |
99024 |
35536 |
98855 |
38670 |
98671 |
54 |
|
7 |
32202 |
99022 |
35590 |
98852 |
38721 |
98668 |
53 |
|
8 |
32261 |
99019 |
35644 |
98849 |
38771 |
98665 |
52 |
|
9 |
32319 |
99016 |
35698 |
98846 |
38821 |
98662 |
51 |
|
10 |
9.32378 |
9.99013 |
9.35752 |
9.98843 |
9.38871 |
9.98659 |
50 |
|
11 |
32437 |
99011 |
35806 |
98840 |
38921 |
98656 |
49 |
|
12 |
32495 |
99008 |
35860 |
98837 |
38971 |
98652 |
48 |
|
13 |
32553 |
99005 |
35914 |
98834 |
39021 |
98649 |
47 |
|
14 |
32612 |
99002 |
35968 |
98831 |
39071 |
98646 |
46 |
|
15 |
32670 |
99000 |
36022 |
98828 |
39121 |
98643 |
45 |
|
16 |
32728 |
98997 |
36075 |
98825 |
39170 |
98640 |
44 |
|
17 |
32786 |
98994 |
' 36129 |
98822 |
39220 |
98636 |
43 |
|
18 |
32844 |
98991 |
36182 |
98819 |
39270 |
98633 |
42 |
|
19 |
32902 |
98989 |
36236 |
98816 |
39319 |
98030 |
41 |
|
20 |
9.32960 |
9.98986 |
9.36289 |
9.98813 |
9.39369 |
9.98627 |
40 |
|
21 |
33018 |
98983 |
36342 |
98810 |
39418 |
98623 |
39 |
|
22 |
33075 |
98980 |
36395 |
98807 |
39467 |
98620 |
38 |
|
23 |
33133 |
98978 |
36449 |
98804 |
39517 |
98617 |
37 |
|
24 |
33190 |
98975 |
36502 |
98801 |
39566 |
98614 |
36 |
|
25 |
33248 |
98972 |
36555 |
98798 |
39615 |
98610 |
35 |
|
26 |
33305 |
98969 |
36608 |
98795 |
39664 |
98607 |
34 |
|
27 |
33362 |
98967 |
36660 |
98792 |
39713 |
98604 |
33 |
|
28 |
33420 |
98964 |
36713 |
98789 |
39762 |
98601 |
32 |
|
29 |
33477 |
98961 |
36766 |
98786 |
39811 |
98597 |
31 |
|
30 |
9.33534 |
9.98958 |
9.36819 |
9.98783 |
9.39860 |
9.98594 |
30 |
|
31 |
33591 |
98955 |
36871 |
98780 |
39909 |
98591 |
29 |
|
32 |
33647 |
98953 |
36924 |
98777 |
39958 |
98588 |
28 |
|
33 |
33704 |
98950 |
36976 |
98774 |
40006 |
98584 |
27 |
|
34 |
33761 |
98947 |
37028 |
98771 |
40055 |
98581 |
26 |
|
35 |
33818 |
98944 |
37081 |
98768 |
40103 |
98578 |
25 |
|
36 |
33874 |
98941 |
37133 |
98765 |
40152 |
98574 |
24 |
|
37 |
83931 |
98938 |
37185 |
98762 |
40200 |
98571 |
23 |
|
38 |
33987 |
98936 |
37237 |
98759 |
40249 |
98568 |
22 |
|
39 |
34043 |
98933 |
37289 |
98756 |
40297 |
98565 |
21 |
|
40 |
9.34100 |
9.98930 |
9.37341 |
9.98753 |
9.40346 |
9.98561 |
20 |
|
41 |
34156 |
98927 |
37393 |
98750 |
40394 |
98558 |
19 |
|
42 |
34212 |
98924 |
37445 |
98746 |
40442 |
98555 |
18 |
|
43 |
34268 |
98921 |
37497 |
98743 |
40490 |
98551 |
17 |
|
44 |
34324 |
98919 |
37549 |
98740 |
40538 |
98548 |
16 |
|
45 |
34380 |
98916 |
37600 |
98737 |
4058G |
98545 |
15 |
|
46 |
34436 |
98913 |
37652 |
98734 |
40634 |
98541 |
14 |
|
47 |
34491 |
98910 |
37703 |
98731 |
40682 |
98538 |
13 |
|
48 |
34547 |
98907 |
37755 |
98728 |
40730 |
98535 |
12 |
|
49 |
34602 |
98904 |
37806 |
98725 |
40778 |
98531 |
11 |
|
50 |
9.34658 |
9.98901 |
9.37858 |
9.98722 |
9.40825 |
9.98528 |
10 |
|
51 |
34713 |
98898 |
37909 |
98719 |
40873 |
98525 |
9 |
|
52 |
34769 |
98896 |
37960 |
' 98715 |
40921 |
98521 |
8 |
|
53 |
34824 |
98893 |
38011 |
98712 |
40968 |
98518 |
7 |
|
54 |
34879 |
98890 |
38062 |
98709 |
41016 |
98515 |
6 |
|
55 |
34934 |
98887 |
38113 |
98706 |
41063 |
98511 |
5 |
|
56 |
34989 |
98884 |
38164 |
98703 |
41111 |
98508 |
4 |
|
57 |
35044 |
98881 |
38215 |
98700 |
41158 |
98505 |
3 |
|
58 |
35099 |
98878 |
38266 |
98697 |
41205 |
98501 |
2 |
|
59 |
35154 |
98875 |
38317 |
98694 |
41252 |
98498 |
1 |
|
00 |
35209 |
98872 |
38368 |
98690 |
41300 |
98494 |
0 |
|
t |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
t |
|
77o |
76° |
75° |
TABLE 8.— LOGARITHMIC SINES AND COSINES. 181
|
t |
15° |
16° |
17° |
/ |
|||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.41300 |
9.98494 |
9.44034 |
9.98284 |
9.46594 |
9.98060 |
60 |
|
I |
41347 |
98491 |
44078 |
98281 |
46635 |
98056 |
59 |
|
2 |
41394 |
98488 |
44122 |
98277 |
46676 |
98052 |
58 |
|
3 |
41441 |
98484 |
44166 |
98273 |
46717 |
98048 |
57 |
|
4 |
41488 |
98481 |
44210 |
98270 |
46758 |
98044 |
56 |
|
5 |
41535 |
98477 |
44253 |
98266 |
46800 |
98040 |
55 |
|
6 |
41582 |
98474 |
44297 |
98262 |
46841 |
98036 |
54 |
|
7 |
416-,>8 |
98471 |
44341 |
98259 |
46882 |
98032 |
53 |
|
8 |
41675 |
98467 |
44385 |
98255 |
46923 |
98029 |
52 |
|
9 |
41722 |
98464 |
44428 |
98251 |
46964 |
98025 |
51 |
|
10 |
9.41768 |
9.98460 |
9.44472 |
9.98248 |
9.47005 |
9.98021 |
50 |
|
11 |
41815 |
98457 |
44516 |
98244 |
47045 |
98017 |
49 |
|
12 |
41861 |
98453 |
44559 |
96240 |
47086 |
98013 |
48 |
|
18 |
41908 |
98450 |
44602 |
98237 |
47127 |
98009 |
47 |
|
14 |
41954 |
98447 |
44646 |
98233 |
47168 |
98005 |
46 |
|
15 |
42001 |
98443 |
44689 |
98229 |
47209 |
98001 |
45 |
|
16 |
42047 |
98440 |
44733 |
98226 |
47249 |
97997 |
44 |
|
17 |
42093 |
98436 |
44776 |
98222 |
47290 |
97993 |
43 |
|
18 |
42140 |
98433 |
44819 |
98218 |
47330 |
97989 |
42 |
|
19 |
42186 |
98429 |
44862 |
98215 |
47371 |
97986 |
41 |
|
20 |
9.42232 |
9.98426 |
9.44905 |
9.98211 |
9.47411 |
9.97982 |
40 |
|
21 |
42278 |
98422 |
44948 |
98207 |
47452 |
97978 |
39 |
|
22 |
42324 |
98419 |
44992 |
98204 |
47492 |
97974 |
38 |
|
23 |
42370 |
98415 |
45035 |
98200 |
47533 |
97970 |
37 |
|
24 |
42416 |
98412 |
45077 |
98196 |
47573 |
97966 |
36 |
|
25 |
42461 |
98409 |
45120 |
98192 |
47613 |
97962 |
35 |
|
26 |
42507 |
98405 |
45163 |
98189 |
41654 |
97958 |
34 |
|
27 |
42553 |
98402 |
45206 |
98185 |
47694 |
97954 |
33 |
|
28 |
42599 |
98398 |
45249 |
98181 |
47734 |
97950 |
32 |
|
29 |
42(344 |
98395 |
45292 |
98177 |
47774 |
97946 |
31 |
|
30 |
9.42690 |
9.98391 |
9.45334 |
9.98174 |
9.47814 |
9.97942 |
30 |
|
31 |
42735 |
98388 |
45377 |
98170 |
47854 |
97938 |
29 |
|
32 |
42781 |
98384 |
45419 |
98166 |
47894 |
97934 |
28 |
|
33 |
42826 |
98381 |
45462 |
98162 |
47934 |
97930 |
27 |
|
34 |
42872 |
98377 |
45504 |
98159 |
47974 |
97926 |
26 |
|
35 |
42917 |
98373 |
45547 |
98155 |
4h014 |
97922 |
25 |
|
36 |
42962 |
98370 |
45589 |
98151 |
48054 |
97918 |
24 |
|
37 |
4:3008 |
98366 |
45632 |
98147 |
48094 |
97914 |
23 |
|
38 |
43053 |
98363 |
45674 |
98144 |
48133 |
97910 |
22 |
|
39 |
43098 |
98359 |
45716 |
98140 |
48173 |
97906 |
21 |
|
40 |
9.43143 |
9.98356 |
9.45758 |
9.98136 |
9.48213 |
9.97902 |
20 |
|
41 |
43188 |
98352 |
45801 |
98132 |
48252 |
97898 |
19 |
|
42 |
43233 |
98349 |
45843 |
98129 |
48292 |
97894 |
18 |
|
43 |
43278 |
98345 |
4.1885 |
98125 |
48332 |
97890 |
17 |
|
44 |
43323 |
98342 |
45927 |
98121 |
48371 |
97886 |
16 |
|
45 |
43367 |
98338 |
45969 |
98117 |
48411 |
97882 |
15 |
|
46 |
43412 |
98334 |
46011 |
98113 |
48450 |
97878 |
14 |
|
47 |
43457 |
98331 |
46053 |
98110 |
48490 |
97874 |
18 |
|
48 |
43502 |
98327 |
46095 |
98106 |
48529 |
97870 |
12 |
|
49 |
43546 |
98324 |
46136 |
98102 |
48568 |
97866 |
|1 |
|
50 |
9.43591 |
9.98320 |
9.46178 |
9.98098 |
9.48607 |
9.97861 |
10 |
|
51 |
43635 |
98317 |
46220 |
98094 |
48647 |
97857 |
9 |
|
52 |
43680 |
98313 |
46-^62 |
98090 |
48686 |
97853 |
8 |
|
53 |
43724 |
98309 |
46303 |
9H087 |
48725 |
97849 |
7 |
|
54 |
43769 |
98306 |
46345 |
98083 |
48764 |
97845 |
6 |
|
55 |
43813 |
98302 |
46386 |
98079 |
48803 |
97841 |
5 |
|
56 |
43857 |
98299 |
46428 |
98075 |
48842 |
97837 |
4 |
|
57 |
43901 |
98295 |
46469 |
98071 |
48881 |
97833 |
3 |
|
58 |
43946 |
98291 |
46511 |
98067 |
4S920 |
97829 |
2 |
|
59 |
43990 |
98288 |
46552 |
98063 |
48959 |
97825 |
1 |
|
60 |
44034 |
98284 |
36594 |
98060 |
48998 |
97821 |
0 |
|
f |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
74° |
73° |
72° |
182 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
18° |
19° |
20° |
|||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine Cosine |
|||
|
0 |
9.48998 |
9.97821 |
9.51264 |
9.97567 |
9.53405 9 |
97299 |
60 1 |
|
1 |
49037 |
97817 |
51301 |
97563 |
53440 |
97294 |
59 ) |
|
2 |
49076 |
97812 |
51338 |
97558 |
53475 |
97289 |
58 |
|
3 |
49115 |
97808 |
51374 |
97554 |
53509 |
97285 |
57 |
|
4 |
49153 |
97804 |
51411 |
97550 |
53544 |
97280 |
50 |
|
5 |
49192 |
97800 |
51447 |
97545 |
53578 |
97276 |
55 |
|
6 |
49231 |
97796 |
51484 |
97541 |
53613 |
97271 |
54 |
|
7 |
49269 |
97792 |
51520 |
97536 |
53647 |
97266 |
53 |
|
8 |
49308 |
97788 |
51557 |
97532 |
53682 |
97262 |
52 |
|
9 |
49347 |
97784 |
51593 |
97528 |
53716 |
97257 |
51 |
|
10 |
9.49385 |
9.97779 |
9.51629 |
9.97523 |
9.53751 9 |
97252 |
50 |
|
11 |
49424 |
97775 |
51666 |
97519 |
53785 |
97248 |
49 |
|
12 |
49462 |
97771 |
51702 |
97515 |
53819 |
97243 |
48 |
|
18 |
49500 |
97767 |
51738 |
97510 |
53854 |
97238 |
47 |
|
14 |
49539 |
97763 |
51774 |
97506 |
53888 |
97234 |
46 |
|
15 |
49577 |
97759 |
51811 |
97501 |
53922 |
97229 ; |
45 |
|
16 |
49615 |
97754 |
51847 |
97497 |
53957 |
97224 |
44 |
|
17 |
49654 |
97750 |
51883 |
97492 |
53991 |
97220 |
43 |
|
18 |
49692 |
97746 |
51919 |
97488 |
54025 |
97215 |
42 |
|
19 |
49730 |
97742 |
51955 |
97484 |
54059 |
97210 |
41 |
|
20 |
9.49768 |
9.97738 |
9.51991 |
9.97479 |
9.54093 9 |
97206 |
40 |
|
21 |
49806 |
97734 |
52027 |
97475 |
54127 |
97201 |
39 |
|
22 |
49844 |
97729 |
52063 |
97470 |
54161 |
97196 |
38 |
|
23 |
49882 |
97725 |
52099 |
97466 |
54195 |
97192 |
37 |
|
24 |
49920 |
97721 |
52135 |
97461 |
54229 |
97187 |
36 |
|
25 |
49958 |
97717 |
52171 |
97457 |
54263 |
97182 |
35 |
|
26 |
49996 |
97713 |
52207 |
97453 |
54297 |
97178 |
34 |
|
27 |
50034 |
97708 |
52242 |
97448 |
54331 |
97173 |
33 |
|
28 |
50072 |
97704 |
52278 |
97444 |
54365 |
97168 |
32 |
|
29 |
50110 |
97700 |
52314 |
97439 |
54399 |
97163 |
31 |
|
30 |
9.50148 |
9.97696 |
9.52350 |
9.97435 |
9.54433 9 |
97159 |
30 |
|
31 |
50185 |
97691 |
52385 |
97430 |
54466 |
97154 |
29 |
|
32 |
50223 |
97687 |
52421 |
97426 |
54500 |
97149 |
28 |
|
33 |
50261 |
97683 |
52456 |
97421 |
54534 |
97145 |
27 |
|
34 |
50298 |
97679 |
52492 |
97417 |
54567 |
97140 |
26 |
|
35 |
50336 |
97674 |
52527 |
97412 |
54601 |
97135 |
25 |
|
36 |
50374 |
97670 |
52563 |
97408 |
54635 |
97130 |
24 |
|
37 |
50411 |
97666 |
52598 |
97403 |
54668 |
97126 |
23 |
|
38 |
50449 |
97662 |
52634 |
97399 |
54702 |
97121 |
22 |
|
39 |
50486 |
97657 |
52669 |
97394 |
54735 |
97116 |
21 |
|
40 |
9.50523 |
9.97653 |
9.52705 |
9.97390 |
9.54769 9 |
97111 |
20 |
|
41 |
50561 |
97649 |
52740 |
97385 |
54802 . |
97107 |
19 |
|
42 |
50593 |
97645 |
52775 |
97381 |
54836 |
97102 |
18 |
|
43 |
50635 |
97640 |
52811 |
97376 |
54869 |
97097 |
17 |
|
44 |
50673 |
97636 |
52846 |
97372 |
54903 |
97092 |
16 |
|
45 |
50710 |
97632 |
52881 |
97367 |
54936 |
97087 |
15 |
|
46 |
50747 |
97628 |
52916 |
97363 |
54969 |
97083 |
14 |
|
47 |
50784 |
97623 |
52951 |
97358 |
55003 |
97078 |
13 |
|
48 |
50821 |
97619 |
52986 |
97353 |
55036 |
97073 |
12 |
|
49 |
50858 |
97615 |
53021 |
97349 |
55069 |
97068 |
11 |
|
50 |
9.50896 |
9.97610 |
9.53056 |
9.97344 |
9.55102 9 |
.97063 |
10 |
|
51 |
50933 |
97606 |
53092 |
97340 |
55136 |
97059 |
9 |
|
52 |
50970 |
97602 |
53126 |
97335 |
55169 |
97054 |
8 |
|
53 |
51007 |
97597 |
53161 |
97331 |
55202 |
97049 |
7 |
|
54 |
51043 |
97593 |
53196 |
97326 |
55235 |
97044 |
6 |
|
55 |
51080 |
97589 |
53231 |
97322 |
55068 |
97039 |
5 |
|
56 |
51117 |
97584 |
53266 |
97317 |
55301 |
97035 |
4 |
|
57 |
51154 |
97580 |
53301 |
97312 |
55334 |
97030 |
3 |
|
58 |
51191 |
97576 |
53336 |
97308 |
55367 |
97025 |
2 |
|
59 |
51227 |
97571 |
53370 |
97303 |
55400 |
97020 |
1 |
|
60 |
51264 |
97567 |
53405 |
9729!) |
55433 |
97015 |
0 |
|
t |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
71° |
70° |
69° |
TABLE 8.— LOGARITHMIC SINES AND COSINES. 183
|
/ |
21° |
22° |
23 |
o |
t |
||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.55433 |
9.97015 |
9.57358 |
9.96717 |
9.59188 |
9.96403 |
60 |
|
1 |
55466 |
97010 |
57389 |
96711 |
59218 |
96397 |
59 |
|
2 |
55499 |
97005 |
57420 |
96706 |
59247 |
96392 |
58 |
|
3 |
5553vJ |
97001 |
57451 |
96701 |
59277 |
963^7 |
57 |
|
4 |
55564 |
96996 |
57482 |
96696 |
59307 |
96381 |
56 |
|
5 |
55597 |
96991 |
57514 |
96691 |
59336 |
96376 |
55 |
|
6 |
55630 |
96986 |
57545 |
96686 |
59366 |
96370 |
54 |
|
7 |
55663 |
96981 |
57576 |
96681 |
59396 |
96365 |
53 |
|
8 |
55695 |
96976 |
57607 |
96676 |
59425 |
96360 |
52 |
|
9 |
55728 |
96971 |
57638 |
96670 |
59455 |
96354 |
51 |
|
10 |
9.55761 |
9.96966 |
9.57669 |
9.96665 |
9.59484 |
9.96349 |
50 |
|
11 |
55793 |
969(52 |
57700 |
96C60 |
59514 |
96343 |
49 |
|
12 |
55S26 |
96957 |
57731 |
96655 |
59543 |
96338 |
48 |
|
13 |
55858 |
96952 |
57762 |
96650 |
59573 |
96333 |
47 |
|
14 |
55891 |
96947 |
57793 |
96645 |
59602 |
96327 |
46 |
|
15 |
55923 |
96942 |
57824 |
96640 |
59632 |
96322 |
45 |
|
16 |
55956 |
96937 |
57855 |
96634 |
59661 |
96316 |
44 |
|
17 |
55988 |
96932 |
57885 |
96629 |
59690 |
96311 |
43 |
|
18 |
56021 |
96927 |
57916 |
96624 |
59720 |
96305 |
42 |
|
19 |
56053 |
90922 |
57947 |
96619 |
59749 |
96300 |
41 |
|
20 |
9.56085 |
9.96917 |
9.57978 |
9.96614 |
9.59778 |
9.96294 |
40 |
|
21 |
56118 |
96912 |
5800.8 |
96608 |
59808 |
96289 |
39 |
|
22 |
56150 |
96907 |
58039 |
96603 |
59837 |
96284 |
38 |
|
23 |
56182 |
96903 |
58070 |
96598 |
59866 |
96278 |
37 |
|
24 |
56215 |
96898 |
58101 |
96593 |
59895 |
96273 |
36 |
|
25 |
56-J47 |
96893 |
58131 |
96588 |
59924 |
96267 |
35 |
|
26 |
56279 |
96888 |
58162 |
96582 |
59954 |
96262 |
34 |
|
27 |
56311 |
96883 |
58192 |
96577 |
59983 |
96256 |
33 |
|
28 |
56343 |
96878 |
58223 |
96572 |
60012 |
96251 |
32 |
|
29 |
56375 |
96873 |
58253 |
96567 |
60041 |
96245 |
31 |
|
30 |
9.56408 |
9.96868 |
9.58284 |
9.96562 |
9.60070 |
9.96240 |
30 |
|
31 |
56440 |
96863 |
58314 |
96556 |
60099 |
96234 |
29 |
|
32 |
56472 |
96858 |
58345 |
96551 |
60128 |
96229 |
28 |
|
33 |
56504 |
96853 |
58375 |
96546 |
60157 |
962^3 |
27 |
|
34 |
56536 |
96848 |
58406 |
96541 |
60186 |
90218 |
26 |
|
35 |
56568 |
96843 |
58436 |
96535 |
60215 |
96212 |
25 |
|
36 |
56599 |
96838 |
58467 |
96530 |
60244 |
96207 |
24 |
|
37 |
56631 |
96833 |
58497 |
965^5 |
60273 |
96201 |
23 |
|
38 |
56663 |
96828 |
58527 |
96520 |
60302 |
96196 |
22 |
|
39 |
56695 |
96823 |
58557 |
96514 |
60331 |
96190 |
21 |
|
40 |
9.56727 |
9.96818 |
9.58588 |
9.96509 |
9.60359 |
9.96185 |
20 |
|
41 |
56759 |
90813 |
58618 |
96504 |
60^88 |
96179 |
19 |
|
42 |
56790 |
96808 |
58648 |
96498 |
60417 |
96174 |
18 |
|
43 |
668*2 |
96803 |
58678 |
96493 |
60446 |
96168 |
17 |
|
44 |
56854 |
96798 |
58709 |
96488 |
60474 |
96162 |
16 |
|
45 |
56886 |
96793 |
58739 |
96483 |
60503 |
i!6157 |
15 |
|
46 |
56917 |
96788 |
58769 |
96477 |
60532 |
96151 |
14 |
|
47 |
56949 |
96783 |
58799 |
96472 |
60561 |
96146 |
13 |
|
48 |
56980 |
96778 |
58829 |
96467 |
60589 |
96140 |
12 |
|
49 |
57012 |
90772 |
58859 |
96461 |
60618 |
96135 |
11 |
|
50 |
9.57044 |
9.96767 |
9.58889 |
9.96456 |
9.60646 |
9.96129 |
10 |
|
51 |
57075 |
96702 |
58919 |
96451 |
60675 |
96123 |
9 |
|
52 |
57107 |
96757 |
58949 |
96445 |
60704 |
96118 |
8 |
|
53 |
57138 |
96752 |
58979 |
96440 |
60732 |
96112 |
7 |
|
54 |
57169 |
90747 |
59009 |
96435 |
60761 |
96107 |
6 |
|
55 |
57201 |
96742 |
59039 |
96429 |
60789 |
96101 |
5 |
|
56 |
96737 |
59069 |
96424 |
60818 |
96095 |
4 |
|
|
57 |
57264 |
96732 |
59098 |
96419 |
60846 |
96090 |
8 |
|
58 |
57295 |
96727 |
59128 |
96413 |
60875 |
96084 |
2 |
|
59 |
57326 |
96722 |
59158 |
96408 |
60903 |
96079 |
1 |
|
60 |
57358 |
96717 |
59188 |
96403 |
60931 |
96073 |
0 |
|
t |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
i |
|
68° |
67° |
66° |
184 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
24° |
25° |
\ |
6° |
||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
o |
9.60931 |
9.96073 |
9.62595 |
9.95728 |
9.64184 |
9.95366 |
60 |
|
1 |
60960 |
96067 |
62622 |
95722 |
64210 |
95360 |
59 |
|
2 |
60988 |
96062 |
62649 |
95716 |
64236 |
95354 |
58 |
|
3 |
61016 |
96056 |
62676 |
95710 |
64262 |
95348 |
57 |
|
4 |
61045 |
96050 |
62703 |
95704 |
64288 |
95341 |
56 |
|
5 |
61073 |
96045 |
62730 |
95698 |
64313 |
95335 |
55 |
|
6 |
61101 |
96039 |
62757 |
95692 |
64339 |
95329 |
54 |
|
7 |
61129 |
96034 |
62784 |
95686 |
64365 |
95323 |
53 |
|
8 |
61158 |
96028 |
62811 |
95680 |
64391 |
95317 |
52 |
|
9 |
61186 |
96022 |
62838 |
95674 |
64417 |
95310 |
51 |
|
10 |
9.61214 |
9.96017 |
9.62865 |
9.95668 |
9.64442 |
9.95304 |
50 |
|
11 |
61242 |
96011 |
62892 |
95663 |
64468 |
95298 |
49 |
|
12 |
61270 |
96005 |
62918 |
95657 |
64494 |
95292 |
48 |
|
13 |
61298 |
96000 |
62945 |
95651 |
64519 |
95286 |
47 |
|
14 |
61326 |
95994 |
62972 |
95645 |
64545 |
95279 |
46 |
|
15 |
61354 |
95988 |
62999 |
95639 |
64571 |
95273 |
45 |
|
16 |
61382 |
95982 |
63026 |
95633 |
64596 |
95267 |
44 |
|
17 |
61411 |
95977 |
63052 |
95627 |
64622 |
95261 |
43 |
|
18 |
61438 |
95971 |
63079 |
95621 |
64647 |
95254 |
42 |
|
19 |
61466 |
95965 |
63106 |
95615 |
64673 |
95248 |
41 |
|
20 |
9.61494 |
9.95960 |
9.63133 |
9.95609 |
9.64698 |
9.95242 |
40 |
|
21 |
61522 |
95954 |
63159 |
95603 |
64724 |
95236 |
39 |
|
22 |
61550 |
95948 |
63186 |
95597 |
64749 |
95229 |
38 |
|
23 |
61578 |
95942 |
63213 |
95591 |
64775 |
95223 |
37 |
|
24 |
61606 |
95937 |
63239 |
95585 |
64800 |
95217 |
36 |
|
25 |
61634 |
95931 |
632G6 |
95579 |
64826 |
95211 |
35 |
|
26 |
61662 |
95925 |
63292 |
95573 |
64851 |
95204 |
34 |
|
27 |
61689 |
95920 |
63319 |
95567 |
64877 |
95198 |
33 |
|
28 |
61717 |
95914 |
63345 |
95561 |
64902 |
95192 |
32 |
|
29 |
61745 |
95908 |
63372 |
95555 |
64927 |
95185 |
31 |
|
30 |
9.61773 |
9.95902 |
9.63398 |
9.95549 |
9.64953 |
9.95179 |
30 |
|
31 |
61800 |
95897 |
63425 |
95543 |
64978 |
95173 |
29 |
|
32 |
618-28 |
95891 |
63451 |
95537 |
65003 |
95167 |
28 |
|
33 |
61856 |
95885 |
63478 |
95531 |
65029 |
95160 |
27 |
|
34 |
61883 |
95879 |
C3504 |
95525 |
65054 |
95154 |
26 |
|
35 |
61911 |
95873 |
63531 |
95519 |
65079 |
95148 |
25 |
|
86 |
61939 |
95868 |
63557 |
95513 |
65104 |
95141 |
24 |
|
37 |
61966 |
95862 |
63583 |
95507 |
65130 |
95135 |
23 |
|
38 |
61994 |
95856 |
63610 |
95500 |
65155 |
95129 |
22 |
|
39 |
62021 |
95850 |
63636 |
95494 |
65180 |
95122 |
21 |
|
40 |
9.62049 |
9.95844 |
9.63662 |
9.95488 |
9.65205 |
9.95116 |
20 |
|
41 |
62076 |
95839 |
63689 |
95482 |
65230 |
95110 |
19 |
|
42 |
62104 |
95833 |
63715 |
95476 |
65255 |
95103 |
18 |
|
43 |
62131 |
95827 |
63741 |
95470 |
65281 |
95097 |
17 |
|
44 |
62159 |
95821 |
63767 |
95464 |
65306 |
95090 |
16 |
|
45 |
62186 |
95815 |
63794 |
95458 |
65331 |
95084 |
15 |
|
46 |
62214 |
95810 |
63820 |
95452 |
65356 |
95078 |
14 |
|
47 |
62241 |
95804 |
63846 |
95446 |
65381 |
95071 |
13 |
|
48 |
62268 |
95798 |
63872 |
95440 |
65406 |
95065 |
12 |
|
49 |
62296 |
95792 |
63898 |
95431 |
65431 |
95059 |
11 |
|
50 |
9.62323 |
9.95786 |
9.63924 |
9.95427 |
9.65456 |
9.95052 |
10 |
|
51 |
62350 |
95780 |
63950 |
95421 |
65481 |
95046 |
9 |
|
52 |
62377 |
95775 |
63976 |
95415 |
65506 |
95039 |
8 |
|
53 |
62405 |
95769 |
64002 |
95409 |
65531 |
95033 |
7 |
|
54 |
62432 |
95763 |
64028 |
95403 |
65565 |
95027 |
6 |
|
55 |
62459 |
95757 |
64054 |
95397 |
65580 |
95020 |
5 |
|
56 |
62486 |
95751 |
64080 |
95391 |
65605 |
95014 |
4 |
|
57 |
62513 |
95745 |
64106 |
95384 |
65630 |
95007 |
3 |
|
58 |
62541 |
95739 |
64132 |
95378 |
65655 |
95001 |
2 |
|
59 |
62568 |
95733 |
64158 |
95372 |
65680 |
94995 |
1 |
|
60 |
62595 |
95728 |
64184 |
95366 |
65705 |
94988 |
0 |
|
/ |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
66° |
64° |
63° |
TABLE 8.— LOGARITHMIC SINES AND COSINES. 185
|
/ |
27° |
28° |
29° |
t |
|||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.65705 |
9.94988 |
9.67161 |
9.94593 |
9.68557 |
9.94182 |
60 |
|
1 |
65729 |
94982 |
67185 |
94587 |
68580 |
94175 |
59 |
|
2 |
65754 |
94975 |
67208 |
94580 |
68603 |
94168 |
58 |
|
3 |
65779 |
94969 |
67232 |
94573 |
68625 |
94161 |
57 |
|
4 |
65804 |
94962 |
67256 |
94567 |
68648 |
94154 |
56 |
|
5 |
65828 |
94956 |
07280 |
94560 |
68671 |
94147 |
55 |
|
6 |
65853 |
94949 |
67303 |
94553 |
68694 |
94140 |
54 |
|
7 |
65878 |
94943 |
67327 |
94546 |
68716 |
94133 |
53 |
|
8 |
65902 |
94936 |
67350 |
94540 |
68739 |
94126 |
52 |
|
9 |
65927 |
94930 |
67374 |
94533 |
68762 |
94119 |
51 |
|
10 |
9.65952 |
9.94923 |
9.67398 |
9.94526 |
9.68784 |
9.94112 |
50 |
|
11 |
65976 |
94917 |
67421 |
94519 |
68807 |
94105 |
49 |
|
12 |
66001 |
94911 |
67445 |
94513 |
68829 |
94098 |
48 |
|
18 |
66025 |
94904 |
67468 |
94506 |
68852 |
94090 |
47 |
|
14 |
66050 |
94898 |
67492 |
94499 |
68875 |
94083 |
46 |
|
15 |
66075 |
94891 |
67515 |
94492 |
68897 |
94076 |
45 |
|
16 |
66099 |
94885 |
67539 |
94485 |
68920 |
94069 |
44 |
|
17 |
66124 |
94878 |
67562 |
94479 |
68942 |
94062 |
43 |
|
18 |
66148 |
94871 |
67586 |
94472 |
68965 |
94055 |
42 |
|
19 |
66173 |
94805 |
67609 |
94465 |
68987 |
94048 |
41 |
|
20 |
9.66197 |
9.94858 |
9.67633 |
9.94458 |
9.69010 |
9.94041 |
40 |
|
21 |
66221 |
94852 |
67656 |
94451 |
69032 |
94034 |
39 |
|
22 |
66246 |
94845 |
67680 |
94445 |
69055 |
94027 |
38 |
|
23 |
66270 |
94839 |
67703 |
94438 |
69077 |
94020 |
37 |
|
24 |
66295 |
9J832 |
67726 |
94431 |
69100 |
94012 |
36 |
|
25 |
66319 |
94826 |
67750 |
94424 |
69122 |
94005 |
35 |
|
26 |
66343 |
94819 |
67773 |
91417 |
69144 |
93998 |
34 |
|
27 |
66368 |
94813 |
67796 |
94410 |
69167 |
93991 |
33 |
|
28 |
66392 |
94806 |
67820 |
94404 |
69189 |
S3984 |
82 |
|
29 |
66416 |
94799 |
67843 |
94397 |
69212 |
93977 |
31 |
|
30 |
9.66441 |
9.94793 |
9.67866 |
9.94390 |
9.69234 |
9.93970 |
30 |
|
31 |
66465 |
94786 |
67890 |
94883 |
69256 |
93963 |
29 |
|
32 |
66489 |
94780 |
67913 |
94376 |
69279 |
93955 |
28 |
|
33 |
66513 |
94773 |
67936 |
94369 |
69301 |
93948 |
27 |
|
34 |
66537 |
94767 |
67959 |
94362 |
69323 |
93941 |
26 |
|
* 35 |
66562 |
94760 |
67982 |
94355 |
69345 |
93934 |
25 |
|
36 |
665^6 |
94753 |
68006 |
94349 |
69368 |
93927 |
24 |
|
37 |
66610 |
94747 |
68029 |
94342 |
69390 |
93920 |
23 |
|
38 |
66634 |
94740 |
68052 |
94335 |
69412 |
93912 |
22 |
|
39 |
66G58 |
94734 |
68075 |
94328 |
69434 |
93905 |
21 |
|
40 |
9.66682 |
9.94727 |
9.68098 |
9.94321 |
9.69456 |
9.93898 |
20 |
|
41 |
66706 |
94720 |
68121 |
94314 |
69479 |
93891 |
19 |
|
42 |
66731 |
94714 |
68144 |
94307 |
69501 |
93884 |
18 |
|
43 |
66755 |
94707 |
68167 |
94300 |
69523 |
93876 |
17 |
|
44 |
66779 |
94700 |
68190 |
94293 |
69545 |
93869 |
16 |
|
45 |
66803 |
94694 |
68213 |
94286 |
69567 |
93862 |
15 |
|
46 |
66827 |
9468? |
68237 |
94279 |
69589 |
93855 |
14 |
|
47 |
66851 |
94680 |
68260 |
94273 |
69611 |
93847 |
13 |
|
48 |
66875 |
94674 |
68283 |
94266 |
69638 |
93840 |
12 |
|
49 |
66899 |
94667 |
68305 |
94259 |
69655 |
93833 |
11 |
|
50 |
9.66922 |
9.94660 |
9.68328 |
9.94252 |
9.69677 |
9.93826 |
10 |
|
51 |
66946 |
94654 |
68351 |
94245 |
69699 |
93819 |
9 |
|
52 |
66970 |
94647 |
68374 |
94238 |
93811 |
8 |
|
|
53 |
66994 |
94640 |
68397 |
94231 |
69743 |
93804 |
7 |
|
54 |
67018 |
94634 |
68420 |
94224 |
69765 |
93797 |
6 |
|
55 |
67042 |
94627 |
68443 |
94217 |
69787 |
93789 |
5 |
|
66 |
67066 |
94620 |
68466 |
94210 |
69809 |
93782 |
4 |
|
57 |
67090 |
94614 |
68489 |
94203 |
69831 |
93775 |
3 |
|
58 |
67113 |
94607 |
68512 |
94196 |
69853 |
93768 |
2 |
|
59 |
67137 |
94GOO |
68534 |
94189 |
69875 |
93760 |
1 |
|
60 |
67161 |
94593 |
68557 |
94182 |
69897 |
93753 |
0 |
|
/ |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
62° |
61 |
o |
60° |
186 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
$ |
80° |
81° |
8 |
!2° |
|||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.69897 |
9.93753 |
9.71184 |
9.93307 |
9.72421 |
9.92842 |
60 |
|
1 |
69919 |
93746 |
71205 |
93299 |
72441 |
92834 |
59 |
|
2 |
69941 |
93738 |
71226 |
93291 |
72461 |
92826 |
58 |
|
3 |
69963 |
93731 |
71247 |
93284 |
72482 |
92818 |
57 |
|
4 |
69984 |
93724 |
71268 |
93276 |
72502 |
92810 |
50 |
|
5 |
70006 |
93717 |
71289 |
93269 |
72528 |
92803 |
55 |
|
6 |
70028 |
93709 |
71310 |
93261 |
72542 |
92795 |
54 |
|
7 |
70050 |
93702 |
71331 |
93253 |
7256-3 |
92787 |
53 |
|
8 |
70072 |
93595 |
71352 |
93246 |
72582 |
92779 |
52 |
|
9 |
70093 |
93687 |
71373 |
93238 |
72602 |
92771 |
51 |
|
10 |
9.70115 |
9.93680 |
9.71393 |
9.93230 |
9 726°2 |
9.92703 |
50 |
|
11 |
70137 |
93673 |
71414 |
932,3 |
72048 |
92755 |
49 |
|
12 |
70159 |
93665 |
71435 |
93215 |
72063 |
92747 |
48 |
|
13 |
70180 |
93658 |
71456 |
93207 |
7208 J |
92739 |
47 |
|
14 |
70202 |
93650 |
71477 |
93200 |
72703 |
92731 |
46 |
|
15 |
70224 |
93643 |
71498 |
93192 |
72723 |
92723 |
45 |
|
16 |
70245 |
93636 |
71519 |
93184 |
72743 |
92715 |
44 |
|
17 |
70267 |
93628 |
71539 |
93177 |
72763 |
92707 |
43 |
|
18 |
70288 |
936'>1 |
71560 |
93169 |
72783 |
92099 |
42 |
|
19 |
70310 |
93614 |
71581 |
93161 |
72803 |
92691 |
41 |
|
20 |
9.70332 |
9.93606 |
9.71602 |
9.93154 |
9.72828 |
9.92683 |
40 |
|
21 |
70353 |
93599 |
71622 |
93146 |
72843 |
92675 |
39 |
|
22 |
70375 |
93591 |
71643 |
93138 |
72863 |
92667 |
38 |
|
23 |
70396 |
93584 |
71664 |
93131 |
72883 |
92659 |
37 |
|
24 |
70418 |
93577 |
71685 |
93123 |
72902 |
92051 |
36 |
|
25 |
70439 |
93569 |
71705 |
93115 |
72922 |
92043 |
35 |
|
26 |
70461 |
93562 |
71726 |
93108 |
72942 |
92635 |
34 |
|
27 |
70482 |
93554 |
71747 |
93100 |
72962 |
92027 |
33 |
|
28 |
70504 |
93547 |
71767 |
93092 |
72982 |
92019 |
32 |
|
29 |
70525 |
93539 |
71788 |
93084 |
73002 |
92011 |
31 |
|
80 |
9.70547 |
9.93532 |
9.71809 |
9.93077 |
9.73022 |
9.92603 |
30 |
|
81 |
70508 |
93525 |
71829 |
93069 |
73041 |
92595 |
29 |
|
32 |
70590 |
93517 |
71850 |
93061 |
73061 |
92587 |
28 |
|
33 |
70611 |
93510 |
71870 |
93053 |
73081 |
92579 |
27 |
|
34 |
70633 |
93502 |
71891 |
93046 |
73101 |
92571 |
26 |
|
35 |
70654 |
93495 |
71911 |
93038 |
73121 |
92563 |
25 |
|
36 |
70675 |
93487 |
71932 |
93030 |
73140 |
92555 |
24 |
|
37 |
70697 |
93480 |
7195-J |
93022 |
73160 |
92546 |
23 |
|
38 |
70718 |
93472 |
71973 |
93014 |
73180 |
92538 |
22 |
|
39 |
70739 |
93465 |
71994 |
93007 |
73200 |
92530 |
21 |
|
40 |
9.70761 |
9.93457 |
9.72014 |
9.92999 |
9.73219 |
9.92522 |
20 |
|
41 |
70782 |
93450 |
72034 |
92991 |
73239 |
92514 |
19 |
|
42 |
70803 |
93442 |
72055 |
92983 |
73259 |
92500 |
18 |
|
43 |
70824 |
934:35 |
72075 |
92976 |
73278 |
92498 |
17 |
|
44 |
70846 |
93427 |
72096 |
92968 |
73298 |
92490 |
16 |
|
45 |
70867 |
93420 |
72116 |
92960 |
73318 |
92482 |
15 |
|
46 |
70888 |
93412 |
72137 |
92952 |
73337 |
92473 |
14 |
|
47 |
70909 |
93405 |
72157 |
92944 |
73357 |
92465 |
13 |
|
48 |
70931 |
93397 |
72177 |
92936 |
73377 |
92457 |
12 |
|
49 |
70952 |
93390 |
72198 |
92929 |
73396 |
92449 |
11 |
|
50 |
9.70973 |
9.93382 |
9.72218 |
9.92921 |
9.73416 |
9.92441 |
10 |
|
51 |
70994 |
93375 |
72238 |
92913 |
73435 |
92433 |
9 |
|
62 |
71015 |
93367 |
72259 |
92905 |
73455 |
92425 |
8 |
|
53 |
71036 |
93360 |
72279 |
92897 |
73474 |
92416 |
7 |
|
54 |
71058 |
93352 |
72299 |
92889 |
73494 |
92408 |
6 |
|
55 |
71079 |
93344 |
72320 |
92881 |
73513 |
92400 |
5 |
|
56 |
71100 |
93337 |
72340 |
92874 |
73533 |
92392 |
4 |
|
57 |
71121 |
93329 |
72360 |
92866 |
73552 |
92384 |
3 |
|
58 |
71142 |
93322 |
72881 |
92858 |
73572 |
92376 |
2 |
|
59 |
71163 |
93314 |
72401 |
92850 |
73591 |
92367 |
1 |
|
60 |
71184 |
93307 |
72421 |
92842 |
73611 |
92359 |
0 |
|
/ |
Cosine |
Sine |
Cosine Sine |
Cosine |
Sine |
/ |
|
|
69° |
58° |
67° |
TABLE 8.— LOGARITHMIC SINES AND COSINES. 187
|
88 |
84° |
35 |
0 |
||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.73611 |
9.92359 |
9.74756 |
9.91857 |
9.75859 |
9.91336 |
60 |
|
1 |
73630 |
92351 |
74775 |
91849 |
75877 |
91328 |
59 |
|
2 |
73650 |
92343 |
74794 |
91840 |
75895 |
91319 |
58 |
|
3 |
73669 |
92335 |
74812 |
91832 |
75913 |
91310 |
57 |
|
4 |
73689 |
92326 |
74&31 |
91823 |
75931 |
91301 |
56 |
|
5 |
73708 |
92318 |
74850 |
91815 |
75949 |
91292 |
55 |
|
6 |
73727 |
92310 |
74868 |
91806 |
75967 |
91288 |
54 |
|
7 |
73747 |
92302 |
74887 |
91798 |
75985 |
91274 |
53 |
|
8 |
73766 |
92293 |
74906 |
91789 |
76003 |
91266 |
52 |
|
9 |
73785 |
92285 |
74924 |
91781 |
76021 |
91257 |
51 |
|
10 |
9.73805 |
9.92277 |
9.74943 |
9.91772 |
9.76039 |
9.91248 |
50 |
|
11 |
73824 |
92269 |
74961 |
91763 . |
. 76057 |
91239 |
49 |
|
12 |
73843 |
922GO |
74980 |
91755 |
76075 |
91230 |
48 |
|
13 |
73863 |
92252 |
74999 |
91746 |
76093 |
91221 |
47 |
|
14 |
73SS2 |
92244 |
75017 |
91738 |
76111 |
91212 |
46 |
|
15 |
73901 |
92235 |
75036 |
91729 |
76129 |
91203 |
45 |
|
16 |
73921 |
92227 |
75054 |
91720 |
76146 |
91194 |
44 |
|
17 |
73940 |
92219 |
75073 |
91712 |
76164 |
91185 |
43 |
|
18 |
73959 |
92211 |
75091 |
91703 |
76182 |
91176 |
42 |
|
19 |
73978 |
92202 |
75110 |
91695 |
76200 |
91167 |
41 |
|
20 |
9.73997 |
9.92194 |
9.75128 |
9. 91 f 86 |
9.76218 |
9.91158 |
40 |
|
21 |
74017 |
92186 |
75147 |
91677 |
76236 |
91149 |
39 |
|
22 |
74036 |
92177 |
75165 |
91669 |
76253 |
91141 |
38 |
|
28 |
74055 |
92169 |
75184 |
91660 |
76271 |
91132 |
37 |
|
24 |
74074 |
92161 |
75202 |
91651 |
76289 |
91123 |
36 |
|
25 |
74093 |
92152 |
75221 |
91643 |
76307 |
91114 |
35 |
|
26 |
74113 |
92144 |
75239 |
916^4 |
76324 |
91105 |
34 |
|
27 |
74132 |
92136 |
75258 |
91625 |
76342 |
91096 |
33 |
|
28 |
74151 |
92127 |
75276 |
91617 |
76360 |
91087 |
32 |
|
29 |
74170 |
92119 |
75294 |
91608 |
76378 |
91078 |
31 |
|
30 |
9.74189 |
9.92111 |
9.75313 |
9.91599 |
9.76395 |
9.91069 |
30 |
|
31 |
74208 |
92102 |
75331 |
91591 |
76413 |
91060 |
29 |
|
32 |
74227 |
92094 |
75350 |
91582 |
76431 |
91051 |
28 |
|
33 |
74246 |
92086 |
75368 |
91573 |
76448 |
91042 |
27 |
|
34, |
r,4265 |
92077 |
75386 |
91565 |
76466 |
91033 |
26 |
|
35 |
74284 |
92069 |
75405 |
91556 |
76484 |
91023 |
25 |
|
36 |
74303 |
92060 |
75423 |
91547 |
76501 |
91014 |
24 |
|
sr |
74322 |
92052 |
75441 |
91538 |
76519 |
91005 |
23 |
|
38 |
74341 |
92044 |
75459 |
91530 |
76537 |
90996 |
22 |
|
39 |
74360 |
92035 |
75478 |
91521 |
76554 |
90987 |
21 |
|
40 |
9.74379 |
9.92027 |
9.75496 |
9.91512 |
9.76572 |
9.90978 |
20 |
|
41 |
74398 |
92018 |
75514 |
91504 |
76590 |
90969 |
19 |
|
42 |
74417 |
92010 |
75533 |
91495 |
76607 |
90960 |
18 |
|
43 |
74436 |
92002 |
75551 |
91486 |
76625 |
90951 |
17 |
|
44 |
74455 |
91993 |
75569 |
91477 |
76642 |
90942 |
16 |
|
45 |
74474 |
91985 |
75587 |
91469 |
76660 |
90933 |
15 |
|
46 |
74493 |
91976 |
75605 |
91460 |
76677 |
90924 |
14 |
|
47 |
74512 |
91968 |
75624 |
91451 |
76695 |
90915 |
13 |
|
48 |
74531 |
91959 |
75642 |
91442 |
76712 |
90906 |
12 |
|
49 |
74549 |
91951 |
75660 |
91433 |
76730 |
90696 |
11 |
|
50 |
9.74568 |
9.91942 |
9.75678 |
9.91425 |
9.76747 |
9.90887 |
10 |
|
51 |
74587 |
91934 |
75696 |
91416 |
76765 |
90878 |
9 |
|
52 |
74606 |
91925 |
75714 |
91407 |
76782 |
90869 |
8 |
|
53 |
74625 |
91917 |
75733 |
91398 |
76800 |
90860 |
7 |
|
54 |
74644 |
91908 |
75751 |
91389 |
76817 |
90851 |
6 |
|
55 |
74662 |
91900 |
75769 |
91381 |
76835 |
90842 |
5 |
|
56 |
74681 |
91891 |
75787 |
91372 |
76852 |
90832 |
4 |
|
57 |
74700 |
91883 |
75805 |
91363 |
76870 |
90823 |
3 |
|
58 |
74719 |
91874 |
75823 |
91354 |
76887 |
90814 |
2 |
|
59 |
74737 |
91866 |
75841 |
91345 |
76904 |
90805 |
1 |
|
60 |
74756 |
91857 |
75859 |
91336 |
76922 |
90796 |
0 |
|
t |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
f |
|
66° |
66° |
64° |
188 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
t |
86° |
37° |
38° |
||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.76922 |
9.90796 |
9.77946 |
9.90235 |
9.78934 |
9.89653 |
60 |
|
1 |
76939 |
90787 |
77963 |
90225 |
78950 |
89643 |
59 |
|
2 |
76957 |
90777 |
77980 |
90216 |
78967 |
89633 |
58 |
|
3 |
76974 |
90768 |
77997 |
90206 |
78983 |
89624 |
57 |
|
4 |
76991 |
90759 |
78013 |
90197 |
78999 |
89614 |
56 |
|
5 |
77009 |
90750 |
78030 |
90187 |
79015 |
89604 |
55 |
|
6 |
77026 |
90741 |
78047 |
90178 |
79031 |
89594 |
54 |
|
7 |
77043 |
90731 |
78063 |
90168 |
79047 |
89584 |
53 |
|
8 |
77061 |
90722 |
78080 |
90159 |
79063 |
89574 |
52 |
|
9 |
77078 |
90713 |
78097 |
90149 |
79079 |
89564 |
51 |
|
10 |
9.77095 |
9.90704 |
9.78113 |
9.90139 |
9.79095 |
9.89554 |
50 |
|
11 |
77112 |
90694 |
78130 |
90130 |
79111 |
89544 |
49 |
|
12 |
77130 |
90685 |
78147 |
90120 |
79128 |
89534 |
48 |
|
13 |
77147 |
90676 |
78163 |
90111 |
79144 |
89524 |
47 |
|
14 |
77164 |
90667 |
78180 |
90101 |
79160 |
89514 |
46 |
|
15 |
77181 |
90657 |
78197 |
90091 |
79176 |
89504 |
45 |
|
16 |
77199 |
90648 |
78213 |
90082 |
79192 |
89495 |
44 |
|
17 |
77216 |
90639 |
78230 |
90072 |
79208 |
89485 |
43 |
|
18 |
77233 |
90630 |
78246 |
90063 |
79224 |
89475 |
42 |
|
19 |
77250 |
90620 |
78263 |
90053 |
79240 |
89465 |
41 |
|
20 |
9.77268 |
9.90611 |
9.73280 |
9.90043 |
9.79256 |
9.89455 |
40 |
|
21 |
77285 |
90602 |
78296 |
90034 |
79272 |
89445 |
39 |
|
22 |
77302 |
90592 |
78313 |
, 90024 |
79288 |
89435 |
38 |
|
23 |
77319 |
90583 |
78329 |
90014 |
79304 |
89425 |
37 |
|
24 |
77336 |
90574 |
78346 |
90005 |
19319 |
89415 |
36 |
|
25 |
77353 |
90565 |
7836-2 |
89995 |
79335 |
89405 |
35 |
|
26 |
77370 |
90555 |
78379 |
89985 |
79351 |
89395 |
34 |
|
27 |
7738 r |
90546 |
78395 |
89976 |
79367 |
89385 |
33 |
|
28 |
77405 |
90537 |
78412 |
89966 |
79383 |
89375 |
32 |
|
29 |
77422 |
905:27 |
78428 |
89956 |
Y9399 |
89364 |
31 |
|
30 |
9.77439 |
9.90518 |
9.78445 |
9.89947 |
9.79415 |
9.89354 |
30 |
|
31 |
77456 |
90509 |
78461 |
89937 |
79431 |
89344 |
29 |
|
38 |
77473 |
90499 |
78478 |
89927 |
79447 |
89334 |
28 |
|
33 |
77490 |
90490 |
78494 |
89918 |
79463 |
89824 |
27 |
|
34 |
77507 |
90480 |
78510 |
89908 |
79478 |
89314 |
26 |
|
35 |
77524 |
90471 |
785-27 |
89898 |
79494 |
89304 |
25 |
|
36 |
77541 |
90462 |
78543 |
89888 |
79510 |
89294 |
24 |
|
37 |
77558 |
90452 |
78560 |
89879 |
79526 |
89284 |
23 |
|
38 |
77575 |
90443 |
78576 |
89869 |
79542 |
89274 |
22 |
|
39 |
77592 |
90434 |
7859;! |
89859 |
79558 |
89264 |
21 |
|
40 |
9.77609 |
9.90424 |
9.78609 |
9.89849 |
9.79573 |
9.89254 |
20 |
|
41 |
77626 |
90415 |
78625 |
89840 |
79589 |
89244 |
19 |
|
42 |
"7643 |
90405 |
7864-2 |
89830 |
79605 |
89233 |
18 |
|
48 |
"7060 |
90396 |
78658 |
89820 |
78621 |
89223 |
17 |
|
44 |
"7677 |
90386 |
78674 |
89810 |
79636 |
89213 |
16 |
|
45 |
"7694 |
90377 |
78691 |
89801 |
79652 |
89203 |
15 |
|
46 |
"7711 |
9036S |
78707 |
89791 |
79668 |
89193 |
14 |
|
47 |
""7728 |
90358 |
78723 |
89781 |
79684 |
89183 |
13 |
|
48 |
7744 |
90349 |
78739 |
89771 |
79699 |
89173 |
12 |
|
49 |
"7761 |
90339 |
78756 |
89761 |
79715 |
89162 |
11 |
|
50 |
9.77778 |
9.90330 |
9.78772 |
9.89752 |
9.79731 |
9.89152 |
10 |
|
51 |
77795 |
90320 |
78788 |
89742 |
79746 |
89142 |
9 |
|
52 |
77812 |
90311 |
78805 |
89732 |
79762 |
89132 |
8 |
|
53 |
77849 |
90301 |
78821 |
89722 |
79778 |
89122 |
7 |
|
54 |
77846 |
90292 |
78837 |
89712 |
79793 |
89112 |
6 |
|
55 |
77862 |
90282 |
78853 |
89702 |
79809 |
89101 |
5 |
|
f)6 |
77879 |
90273 |
78869 |
89693 |
79825 |
89091 |
4 |
|
57 |
77896 |
90263 |
78886 |
89683 |
79840 |
89081 |
3 |
|
58 |
77913 |
90254 |
78902 |
89673 |
79856 |
89071 |
2 |
|
59 |
77930 |
90244 |
78918 |
89663 |
79872 |
89060 |
1 |
|
GO |
77946 |
90235 |
78934 |
89653 |
79887 |
89050 |
0 |
|
* |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
, |
|
68° |
62° |
61° |
TABLE 8.— LOGARITHMIC SINES AND COSINES. 189
|
/ |
39° |
40° |
41° |
/ |
|||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.79887 |
9.89050 |
9.80807 |
9.88425 |
9.81694 |
9.87778 |
60 |
|
1 |
79903 |
89040 |
80822 |
88415 |
81709 |
87767 |
59 |
|
2 |
79918 |
89030 |
80837 |
88404 |
81723 |
87756 |
58 |
|
3 |
79934 |
89020 |
80852 |
88394 |
81738 |
87745 |
57 |
|
4 |
79950 |
89009 |
80867 |
88383 |
81752 |
87734 |
56 |
|
5 |
79965 |
88999 |
80882 |
88372 |
81767 |
87723 |
55 |
|
6 |
79981 |
88989 |
80897 |
88362 |
81781 |
87712 |
54 |
|
7 |
79996 |
88978 |
80912 |
88351 |
81796 |
87701 |
53 |
|
8 |
80012 |
88968 |
80927 |
88340 |
81810 |
87690 |
52 |
|
9 |
80027 |
88958 |
80942 |
88330 |
81825 |
87679 |
51 |
|
10 |
9.80043 |
9.88948 |
9.80957 |
9.88319 . |
9.81839 |
9.87668 |
50 |
|
11 |
80058 |
88937 |
80972 |
88308 |
81854 |
87657 |
49 |
|
12 |
80074 |
88927 |
80987 |
88298 |
81868 |
87646 |
48 |
|
13 |
80089 |
88917 |
81002 |
88287 |
81882 |
87635 |
47 |
|
14 |
80105 |
88906 |
81017 |
88276 |
81897 |
87624 |
46 |
|
15 |
80120 |
88896 |
81032 |
88266 |
81911 |
87613 |
45 |
|
16 |
80136 |
88886 |
81047 |
88255 |
81926 |
87601 |
44 |
|
17 |
80151 |
88875 |
81061 |
88244 |
81940 |
87590 |
43 |
|
18 |
80166 |
88865 |
81076 |
88234 |
81955 |
87579 |
42 |
|
19 |
80182 |
88855 |
81091 |
88223 |
61969 |
87568 |
41 |
|
20 |
9.80197 |
9.88844 |
9.81106 |
9.88212 |
9.81983 |
9.87557 |
40 |
|
21 |
80213 |
88834 |
81121 |
88201 |
81998 |
87546 |
39 |
|
22 |
80228 |
88824 |
81136 |
88191 |
82012 |
87535 |
38 |
|
23 |
80244 |
88813 |
81151 |
88180 |
8-J026 |
87524 |
37 |
|
24 |
80259 |
8S803 |
81166 |
88169 |
82041 |
87513 |
36 |
|
& |
80274 |
88793 |
81180 |
88158 |
82055 |
87501 |
35 |
|
26 |
80290 |
88782 |
81195 |
88148 |
82069 |
87490 |
34 |
|
27 |
80305 |
88772 |
81210 |
88137 |
82084 |
87479 |
33 |
|
28 |
80320 |
88761 |
81225 |
88*26 |
82098 |
87468 |
82 |
|
29 |
80336 |
88751 |
81240 |
88115 |
82112 |
87457 |
31 |
|
30 |
9.80351 |
9.88741 |
9.81254 |
9.88105 |
9.82126 |
9.87446 |
30 |
|
31 |
80366 |
88730 |
81269 |
88094 |
82141 |
87434 |
29 |
|
32 |
80382 |
88720 |
81284 |
88083 |
82155 |
87423 |
£8 |
|
m |
80397 |
88709 |
81299 |
88072 |
82169 |
87412 |
27 |
|
34 |
80412 |
88699 |
81314 |
88061 |
82184 |
87401 |
M |
|
35 |
80428 |
88688 |
81328 |
88051 |
82198 |
87390 |
25 |
|
36 |
80443 |
88678 |
81343 |
88040 |
82212 |
87378 |
24 |
|
37 |
80458 |
88668 |
81358 |
88029 |
82226 |
87367 |
23 |
|
38 |
80473 |
88657 |
81372 |
88018 |
82240 |
87356 |
22 |
|
39 |
80489 |
88647 |
81387 |
88007 |
82255 |
87345 |
21 |
|
40 |
9.80504 |
9.88636 |
9.81402 |
9.87996 |
9.82269 |
9.87334 |
20 |
|
41 |
80519 |
88626 |
81417 |
87985 |
82283 |
87322 |
19 |
|
42 |
80534 |
88615 |
81431 |
87975 |
82297 |
87311 |
18 |
|
43 |
80550 |
88605 |
81446 |
87964 |
82311 |
87300 |
17 |
|
44 |
80565 |
88594 |
81461 |
87953 |
82326 |
87288 |
16 |
|
45 |
80580 |
88584 |
81475 |
87942 |
82340 |
87277 |
15 |
|
46 |
80595 |
8*573 |
81490 |
87931 |
82354 |
87266 |
14 |
|
47 |
80610 |
88563 |
81505 |
87920 |
82368 |
87255 |
13 |
|
48 |
80625 |
88552 |
81519 |
87909 |
82382 |
87243 |
12 |
|
49 |
80641 |
88542 |
81534 |
87898 |
82396 |
87232 |
11 |
|
50 |
9.80656 |
9.88531 |
9.81549 |
9.87887 |
9.82410 |
9.87221 |
10 |
|
51 |
80671 |
88521 |
81563 |
87877 |
82424 |
87209 |
9 |
|
52 |
80686 |
88510 |
81578 |
87866 |
82439 |
87198 |
8 |
|
53 |
80701 |
88499 |
81592 |
87855 |
824f3 |
87187 |
7 |
|
54 |
80716 |
88489 |
81607 |
87844 |
82467 |
87175 |
6 |
|
55 |
80731 |
88478 |
81622 |
87833 |
82481 |
87164 |
5 |
|
56 |
80746 |
88468 |
81636 |
•87822 |
62495 |
87153 |
4 |
|
57 |
80762 |
88457 |
81651 |
87811 |
82509 |
87141 |
3 |
|
58 |
80777 |
88447 |
81665 |
87800 |
82523 |
87130 |
2 |
|
59 |
80792 |
88436 |
81680 |
87789 |
82537 |
87119 |
1 |
|
60 |
80807 |
88425 |
81694 |
87778 |
82551 |
87107 |
0 |
|
t |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
50° |
49 |
o |
48° |
190 TABLE 8.— LOGARITHMIC SINES AND COSINES.
|
42° |
48° |
44° |
|||||
|
Sine |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
||
|
0 |
9.82551 |
9.8710? |
9.83378 |
9.86413 |
9.84177 |
9.85693 |
60 |
|
1 |
82565 |
87096 |
83392 |
86401 |
84190 |
85681 |
59 |
|
2 |
82579 |
87085 |
83405 |
86889 |
84203 |
85669 |
58 |
|
3 |
82593 |
87073 |
83419 |
86377 |
84216 |
85657 |
57 |
|
4 |
82607 |
87062 |
83432 |
86366 |
84229 |
85645 |
56 |
|
5 |
82621 |
87050 |
83446 |
86354 |
84242 |
85C32 |
55 |
|
6 |
82635 |
87039 |
83459 |
86342 |
84255 |
85620 |
54 |
|
7 |
82649 |
87028 |
83473 |
80330 |
84269 |
85608 |
53 |
|
8 |
82663 |
87016 |
83486 |
86318 |
84282 |
85596 |
52 |
|
9 |
82677 |
87005 |
83500 |
86306 |
84295 |
85583 |
51 |
|
10 |
9.82691 |
9.86993 |
9.83513 |
9.86295 |
9.84308 |
9.85571 |
50 |
|
11 |
82705 |
86982 |
83527 |
86283 |
84321 |
85559 |
49 |
|
12 |
82719 |
86970 |
83540 |
86271 |
84334 |
85547 |
48 |
|
13 |
82733 |
86959 |
83554 |
86259 |
84347 |
85534 |
47 |
|
14 |
82747 |
86947 |
83567 |
86247 |
84360 |
85522 |
46 |
|
15 |
sarei |
86936 |
83581 |
86235 |
84373 |
85510 |
45 |
|
16 |
82775 |
86924 |
83594 |
86223 |
84385 |
85497 |
44 |
|
17 |
82788 |
86913 |
83608 |
86211 |
84398 |
85485 |
43 |
|
18 |
82802 |
86902 |
83621 |
86200 |
84411 |
85473 |
42 |
|
19 |
82816 |
86890 |
83634 |
86188 |
84424 |
85460 |
41 |
|
20 |
9.82830 |
9.86879 |
9.83648 |
9.86176 |
9.84437 |
9.85448 |
40 |
|
21 |
82844 |
86867 |
83661 |
86164 |
84450 |
85436 |
39 |
|
22 |
82858 |
86855 |
83674 |
86152 |
84463 |
85423 |
38 |
|
23 |
82872 |
86844 |
83688 |
86140 |
84476 |
85411 |
37 |
|
24 |
82885 |
86832 |
83701 |
86128 |
84489 |
85399 |
36 |
|
25 |
82899 |
86821 |
83715 |
86116 |
84502 |
85386 |
35 |
|
26 |
82913 |
86809 |
83728 |
86104 |
84515 |
85874 |
34 |
|
27 |
82927 |
86798 |
83741 |
86092 |
84528 |
85361 |
33 |
|
28 |
82941 |
86786 |
83755 |
86080 |
84540 |
85349 |
32 |
|
29 |
82955 |
86775 |
83768 |
86068 |
84553 |
85337 |
31 |
|
30 |
9.82968 |
9.86763 |
9.83781 |
9.86056 |
9.84566 |
9.85324 |
30 |
|
31 |
82982 |
86752 |
83795 |
86044 |
84579 |
85312 |
29 ' |
|
32 |
82996 |
86740 |
83808 |
86032 |
84592 |
85299 |
28 |
|
33 |
83010 |
86728 |
83821 |
86020 |
84605 |
85287 |
27 |
|
34 |
83023 |
86717 |
83834 |
86008 |
84618 |
85274 |
26 |
|
a5 |
83037 |
86705 |
83848 |
85996 |
84630 |
85262 |
25 |
|
36 |
83051 |
86694 |
83861 |
85984 |
84643 |
85250 |
24 |
|
37 |
83065 |
86682 |
83874 |
85972 |
84656 |
85237 |
23 |
|
38 |
83078 |
86670 |
83887 |
85960 |
84669 |
85225 |
22 |
|
39 |
83092 |
86659 |
83901 |
85948 |
84682 |
85212 |
21 |
|
40 |
9.83106 |
9.86647 |
9.83914 |
9.85936 |
9.84694 |
9.85200 |
20 |
|
41 |
83120 |
86635 |
83927 |
85924 |
84707 |
85187 |
19 |
|
42 |
83133 |
86624 ' |
83940 |
85912 |
84720 |
85175 . |
18 |
|
43 |
83147 |
86612 |
83954 |
85900 |
84733 |
85162 |
17 |
|
44 |
83161 |
86600 |
83967 |
85888 |
84745 |
85150 |
16 |
|
45 |
83174 |
86589 |
83980 |
85876 |
84758 |
85137 |
15 |
|
46 |
88188 |
86577 |
83993 |
85864 |
84771 |
85125 |
14 |
|
47 |
83202 |
86565 |
84006 |
85851 |
84784 |
85112 |
13 |
|
48 |
83215 |
86554 |
84020 |
85839 |
84796 |
85100 |
12 |
|
49 |
832v!9 |
86542 |
84033 |
85827 |
84809 |
85087 |
11 |
|
50 |
9.83242 |
9.86530 |
9.84046 |
9.85815 |
9.84822 |
9.85074 |
10 |
|
51 |
83256 |
86518 |
84059 |
85803 |
84835 |
85062 |
9 |
|
52 |
a3270 |
86507 |
84072 |
85791 |
84847 |
85049 |
8 |
|
53 |
83283 |
86495 |
84085 |
85779 |
84860 |
85037 |
7 |
|
54 |
83297 |
86483 |
84098 |
85766 |
84873 |
85024 |
6 |
|
55 |
83310 |
86472 |
84112 |
85754 |
84885 |
85012 |
5 |
|
56 |
83324 |
86460 |
84125 |
85742 |
84898 |
84999 |
4 |
|
57 |
83338 |
86448 |
84138 |
85730 |
84911 |
84986 |
3 |
|
58 |
83351 |
86436 |
84151 |
85718 |
84923 |
84974 |
2 |
|
59 |
83365 |
86425 |
84164 |
85706 |
84936 |
84961 |
1 |
|
60 |
83378 |
86413 |
84177 |
85693 |
84949 |
84949 |
0 |
|
/ |
Cosine |
Sine |
Cosine |
Sine |
Cosine |
Sine |
/ |
|
47° |
46* |
46° |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 191
|
0° |
1° |
2° |
/ |
||||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
o |
— 00 |
00 |
8.24192 |
11.75808 |
8.54308 |
11.45692 |
60 |
|
1 |
6.46373 |
13.53627 |
24910 |
75090 |
54669 |
45331 |
59 |
|
2 |
76476 |
23524 |
25616 |
74884 |
55027 |
44973 |
58 |
|
3 |
94085 |
05915 |
26312 |
73688 |
55382 |
44618 |
57 |
|
4 |
7.06579 |
12.93421 |
26996 |
73004 |
55734 |
44266 |
56 |
|
5 |
16270 |
83730 |
27669 |
72331 |
56083 |
43917 |
55 |
|
6 |
24188 |
75812 |
28332 |
71668 |
56429 |
43571 |
54 |
|
7 |
80882 |
69118 |
28986 |
71014 |
56773 |
43227 |
53 |
|
8 |
36682 |
63318 |
29629 |
70371 |
57114 |
4tt86 |
62 |
|
9 |
41797 |
58203 |
30263 |
69737 |
57452 |
42548 |
51 |
|
10 |
7.46373 |
12.53627 |
8.30888 |
11.69112 |
8. 57788 |
11.42212 |
no |
|
11 |
50512 |
49488 |
31505 |
68495 |
58121 |
41879 I 49 |
|
|
12 |
54291 |
45709 |
32112 |
67888 |
58451 |
41549 |
48 |
|
13 |
57767 |
42233 |
32711 |
67289 |
58779 |
41221 |
47 |
|
14 |
60986 |
39014 |
33302 |
66698 |
59105 |
40895 |
46 |
|
15 |
63982 |
36018 |
33886 |
66114 |
59428 |
40572 |
45 |
|
16 |
66785 |
33215 |
34461 |
65539 |
59749 |
40251 |
44 |
|
1? |
69418 |
30582 |
35029 |
64971 |
60068 |
39932 |
43 |
|
18 |
71900 |
28100 |
35590 |
64410 |
60384 |
39616 |
42 |
|
19 |
74248 |
25752 |
36143 |
63857 |
60698 |
89302 |
41 |
|
20 |
7.76476 |
12.23524 |
8.36689 |
11.63311 |
8.610T9 |
11.38991 |
40 |
|
21 |
78595 |
21405 |
37229 |
62771 |
61319 |
38681 |
80 |
|
22 |
80615 |
19385 |
37762 |
62238 |
61626 |
38374 |
38 |
|
23 |
82546 |
17454 |
38289 |
61711 |
61931 |
38069 |
37 |
|
24 |
84394 |
15606 |
38809 |
61191 |
62234 |
37766 |
36 |
|
25 |
86167 |
13833 |
39323 |
60677 |
62535 |
37465 |
35 |
|
26 |
87871 |
12129 |
39832 |
60168 |
62834 |
87166 |
34 |
|
27 |
89510 |
10490 |
40334 |
59666 |
63131 |
36869 |
33 |
|
28 |
91089 |
08911 |
40830 |
59170 |
63426 |
36574 |
32 |
|
29 |
92613 |
07387 |
41321 |
58679 |
63718 |
36282 |
31 |
|
30 |
7.94086 |
12.05914 |
8.41807 |
11.58193 |
8.64009 |
11.35991 |
30 |
|
31 |
95510 |
04490 |
42287 |
57713 |
64298 |
35702 |
29 |
|
32 |
* 96889 |
03111 |
42762 |
57238 |
64585 |
35415 |
28 |
|
33 |
98225 |
01775 |
43232 |
56768 |
64870 |
35130 |
27 |
|
34 |
99522 |
00478 |
43696 |
56304 |
65154 |
34846 |
26 |
|
35 |
8.00781 |
11.99219 |
44156 |
55844 |
65435 |
34565 |
25 |
|
36 |
02004 |
97996 |
44611 |
55389 |
65715 |
34285 |
24 |
|
37 |
03194 |
96806 |
45061 |
54939 |
65993 |
34007 |
23 |
|
38 |
04353 |
95647 |
45507 |
54493 |
66269 |
33731 |
22 |
|
39 |
05481 |
94519 |
45948 |
54052 |
66543 |
33457 |
21 |
|
40 |
6.06581 |
11.93419 |
8.46385 |
11.53615 |
8.66816 |
11.38184 |
20 |
|
41 |
07653 |
92347 |
46817 |
53183 |
67087 |
82913 |
19 |
|
42 |
08700 |
91300 |
47245 |
52755 |
67356 |
32644 |
18 |
|
43 |
09722 |
90278 |
47669 |
52331 |
67624 |
32376 |
17 |
|
44 |
10720 |
89280 |
48089 |
51911 |
67890 |
32110 |
16 |
|
45 |
11696 |
88304 |
48505 |
51495 |
68154 |
31846 |
15 |
|
46 |
12651 |
87349 |
48917 |
51083 |
68417 |
31583 |
14 |
|
47 |
13585 |
86415 |
49325 |
50675 |
68678 |
31322 |
13 |
|
48 |
14500 |
85500 |
49729 |
50271 |
68938 |
31062 |
12 |
|
49 |
15395 |
84605 |
50130 |
49870 |
69196 |
30804 |
11 |
|
50 |
8.16273 |
11.83727 |
8.50527 |
11.49473 |
8.69453 |
11.30547 |
10 |
|
51 |
17133 |
82867 |
50920 |
49080 |
69708 |
20292 |
9 |
|
52 |
17976 |
82024 |
51310 |
48690 |
69962 |
30038 |
8 |
|
53 |
18804 |
81196 |
51696 |
48304 |
70214 |
29786 |
7 |
|
54 |
19616 |
80384 |
52079 |
47921 |
70465 |
29535 |
6 |
|
55 |
20413 |
79587 |
52459 |
47541 |
70714 |
29286 |
5 |
|
56 |
21195 |
78805 |
52835 |
47165 |
70962 |
29038 |
4 |
|
57 |
21964 |
78036 |
53208 |
46792 |
71208 |
28792 |
8 |
|
58 |
22720 |
77280 |
53578 |
46422 |
71453 |
2F547 |
2 |
|
59 |
23462 |
76538 |
53945 |
46055 |
71697 |
28303 |
1 |
|
60 |
24192 |
75808 |
54308 |
45692 |
71940 |
28060 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
/ |
|
89° |
88° |
87° |
192 TABLE 9.— LOG. TANGENTS AND COTANGENTS
|
8° |
4° |
5° |
|||||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
8.71940 |
11.28060 |
8.84464 |
11.15536 |
8.94195 |
11.05805 |
60 |
|
1 |
72181 |
27819 |
84646 |
15354 |
94340 |
05660 |
59 |
|
2 |
72420 |
27580 |
84826 |
15174 |
94485 |
05515 |
58 |
|
3 |
72659 |
27341 |
85006 |
14994 |
94630 |
05370 |
57 |
|
4 |
72896 |
27104 |
85185 |
14815 |
94773 |
05227 |
56 |
|
5 |
73132 |
26868 |
85363 |
14637 |
94917 |
05083 |
55 |
|
6 |
73366 |
26634 |
85540 |
14460 |
95060 |
04940 |
54 |
|
73600 |
26400 |
85717 |
14283 |
95202 |
04798 |
53 |
|
|
8 |
73832 |
2616S |
85893 |
14107 |
95344 |
04656 |
52 |
|
9 |
74063 |
25937 |
86069 |
13931 |
95486 |
04514 |
51 |
|
10 |
8.74292 |
11.25708 |
8.86243 |
11.13757 |
8.95627 |
11.04373 |
50 |
|
11 |
74521 |
25479 |
86417 |
13583 |
95767 |
04233 |
49 |
|
12 |
74748 |
25252 |
86591 |
13409 |
95908 |
04092 |
48 |
|
18 |
74974 |
25028 |
86763 |
13237 |
96047 |
03953 |
47 |
|
14 |
75199 |
24801 |
86935 |
13065 |
96187 |
03813 |
46 |
|
15 |
75423 |
24577 |
87106 |
12894 |
96325 |
03675 |
45 |
|
16 |
75645 |
24355 |
87277 |
12723 |
96464 |
03536 |
44 |
|
17 |
75867 |
24133 |
87447 |
12553 |
96602 |
03398 |
43 |
|
18 |
76087 |
JJ3913 |
87616 |
12384 |
96739 |
03261 |
42 |
|
19 |
76306 |
23694 |
87785 |
12215 |
96877 |
02123 |
41 |
|
20 |
8.76525 |
11.23475 |
8.87953 |
11.12047 |
8.97013 |
11.02987 |
40 |
|
21 |
76742 |
23258 |
88120 |
11880 |
97150 |
02850 |
39 |
|
22 |
76958 |
23042 |
88287 |
11713 |
97285 |
02715 |
38 |
|
23 |
77173 |
22827 |
88453 |
11547 |
97421 |
02579 |
37 |
|
24 |
77387 |
22613 |
88618 |
11382 |
97556 |
02444 |
36 |
|
25 |
77600 |
22400 |
88783 |
11217 |
97691 |
02309 |
35 |
|
26 |
77811 |
22189 |
88948 |
11052 |
97825 |
02175 |
34 |
|
27 |
78022 |
21978 |
89111 |
10889 |
97959 |
02041 |
33 |
|
28 |
78232 |
21768 |
89274 |
10726 |
98092 |
01908 |
3* |
|
29 |
78441 |
21559 |
89437 |
10563 |
98225 |
01775 |
31 |
|
30 |
8.78649 |
11.21351 |
8.89598 |
11.10402 |
8.98358 |
11.01642 |
30 |
|
31 |
78855 |
21145 |
89760 |
10240 |
98490 |
01510 |
29 |
|
32 |
79061 |
20939 |
89920 |
10080 |
98622 |
01378 |
28 |
|
83 |
79266 |
20734 |
90080 |
09920 |
98753 |
01247 |
27 |
|
34 |
79470 |
20530 |
90240 |
09760 |
98884 |
01116 |
26 |
|
35 |
79673 |
20327 |
90399 |
09601 |
99015 |
00985 |
25 |
|
36 |
79875 |
20125 |
90557 |
09443 |
99145 |
00855 |
24 |
|
37 |
80076 |
19924 |
90715 |
09285 |
99275 |
00725 |
23 |
|
38 |
80277 |
19723 |
90872 |
09128 |
99405 |
00595 |
22 |
|
39 |
80476 |
19524 |
91029 |
08971 |
99534 |
00466 |
21 |
|
40 |
8.80674 |
11.19326 |
8.91185 |
11.08815 |
8.99662 |
11.00338 |
20 |
|
41 |
80872 |
19128 |
91340 |
08660 |
99791 |
00209 |
19 |
|
42 |
81068 |
18932 |
91495 |
08505 |
99919 |
00081 |
18 |
|
43 |
81264 |
18736 |
91650 |
08350 |
9.00046 |
10.99954 |
17 |
|
44 |
81459 |
18541 |
91803 |
08197 |
00174 |
99826 |
16 |
|
45 |
81653 |
18347 |
91957 |
08043 |
00301 |
99699 |
15 |
|
46 |
81846 |
18154 |
92110 |
07890 |
00427 |
99573 |
14 |
|
47 |
82038 |
17962 |
92262 |
07738 |
00553 |
99447 |
13 |
|
48 |
82230 |
17770 |
92414 |
07586 |
00679 |
99821 |
12 |
|
49 |
82420 |
17580 |
92565 |
07435 |
00805 |
99195 |
11 |
|
50 |
8.82610 |
11.17390 |
8.92716 |
11.07284 |
9.00930 |
10.99070 |
10 |
|
51 |
82799 |
17201 |
92866 |
07134 |
01055 |
98945 |
9 |
|
52 |
82987 |
17013 |
93016 |
06984 |
01179 |
98821 |
8 |
|
53 |
83175 |
16825 |
93165 |
068&5 |
01303 |
98697 |
7 |
|
54 |
83361 |
16639 |
93313 |
06687 |
01427 |
98573 |
6 |
|
55 |
83547 |
16453 |
93462 |
06538 |
01550 |
98450 |
5 |
|
56 |
83732 |
16268 |
93609 |
06391 |
01673 |
98327 |
4 |
|
57 |
83916 |
16084 |
93756 |
06244 |
01796 |
98204 |
3 |
|
58 |
84100 |
15900 |
93903 |
06097 |
01918 |
98082 |
2 |
|
59 |
84282 |
15718 |
94049 |
05951 |
02040 |
97960 |
1 |
|
60 |
84464 |
15536 |
94195 |
05805 |
02162 |
97838 |
0 |
|
, |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
t |
|
86' |
85° |
84« |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 193
|
/ |
6 |
0 |
7° |
8° |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.02162 |
10.97838 |
9.08914 |
10.91086 |
9.14780 |
10.86220 |
60 |
|
1 |
02283 |
97717 |
09019 |
90981 |
14872 |
85128 |
59 |
|
2 |
02404 |
97596 |
09123 |
90877 |
14963 |
85037 |
58 |
|
3 |
02525 |
97475 |
09227 |
90773 |
15054 |
84946 |
57 |
|
4 |
02645 |
97355 |
09330 |
90670 |
15145 |
84855 |
56 |
|
5 |
02766 |
97234 |
09434 |
90566 |
15236 |
84764 |
55 |
|
6 |
02885 |
97115 |
09537 |
90463 |
15327 |
84673 |
54 |
|
7 |
C3005 |
96995 |
09640 |
90360 |
15417 |
84583 |
53 |
|
8 |
03124 |
96876 |
09742 |
90258 |
15508 |
84492 |
52 |
|
9 |
03242 |
96758 |
09845 |
90155 |
15598 |
84402 |
51 |
|
10 |
9.03361 |
10.96639 |
9.09947 |
10.90053 |
9.15688 |
10.84312 |
50 |
|
11 |
03479 |
96521 |
10049 |
89951 |
15777 |
84228 |
49 |
|
12 |
03597 |
96403 |
10150 |
89850 |
15867 |
84133 |
48 |
|
13 |
03714 |
96286 |
10252 |
89748 |
15956 |
84044 |
47 |
|
14 |
03832 |
96168 |
10353 |
89647 |
16046 |
83954 |
46 |
|
15 |
03948 |
96052 |
10454 |
89546 |
16135 |
83865 |
45 |
|
16 |
04065 |
95935 |
10555 |
89445 |
16224 |
83776 |
44 |
|
17 |
04181 |
95819 |
10656 |
89344 |
16312 |
83688 |
43 |
|
18 |
04297 |
95703 |
10756 |
89244 |
16401 |
83599 |
42 |
|
19 |
04413 |
95587 |
10856 |
89144 |
16489 |
83511 |
41 |
|
20 |
9.045C8 |
10.95472 |
9.10956 |
10.89044 |
9.16577 |
10.83423 |
40 |
|
21 |
04643 |
95357 |
11056 |
88944 |
16665 |
83335 |
39 |
|
22 |
04758 |
95242 |
11155 |
88845 |
16753 |
83247 |
38 |
|
23 |
04873 |
95127 |
11254 |
88746 |
16841 |
83159 |
87 |
|
24 |
04987 |
95018 |
11353 |
88647 |
16928 |
83072 |
86 |
|
25 |
05101 |
94899 |
11452 |
88548 |
17016 |
P2984 |
35 |
|
26 |
05214 |
94786 |
11551 |
88449 |
17103 |
82897 |
34 |
|
27 |
05378 |
94672 |
11649 |
88351 |
17190 |
82810 |
33 |
|
28 |
05441 |
94559 |
11747 |
882f.3 |
17277 |
82723 |
82 |
|
29 |
^ 05553 |
94447 |
11845 |
88155 |
17363 |
82637 |
31 |
|
30 |
9.05666 |
10.94334 |
9.11943 |
10.88057 |
9.17450 |
10.82550 |
30 |
|
31 |
05778 |
94222 |
12040 |
87960 |
17536 |
82464 |
29 |
|
32 |
05890 |
94110 |
12138 |
87862 |
17622 |
82378 |
28 |
|
33 |
06002 |
93998 |
12235 |
87765 |
17708 |
82292 |
27 |
|
34 |
06113 |
93887 |
12332 |
87668 |
17794 |
82206 |
26 |
|
35 |
06224 |
93776 |
12428 |
87572 |
17880 |
82120 |
25 |
|
36 |
06335 |
93665 |
12525 |
87475 |
17965 |
82035 |
24 |
|
37 |
06445 |
93555 |
12621 |
87379 |
18051 |
81949 |
23 |
|
38 |
06556 |
93444 |
12717 |
87283 |
18136 |
81864 |
22 |
|
39 |
06666 |
93334 |
12813 |
87187 |
18221 |
81779 |
21 |
|
40 |
9.06775 |
10.93225 |
9.12909 |
10.87091 |
9.18306 |
10.81694 |
20 |
|
41 |
06885 |
93115 |
13004 |
86996 |
18391 |
81609 |
19 |
|
42 |
06994 |
93006 |
13099 |
86901 |
18475 |
81525 |
18 |
|
43 |
07103 |
92897 |
13194 |
86806 |
18560 |
81440 |
17 |
|
44 |
07211 |
92789 |
13289 |
86711 |
18644 |
81856 |
16 |
|
45 |
07820 |
92680 |
13384 |
86616 |
18728 |
81272 |
15 |
|
46 |
07428 |
92572 |
13478 |
86522 |
18812 |
81188 |
14 |
|
47 |
\536 |
92464 |
13573 |
86427 |
18896 |
81104 |
13 |
|
48 |
07643 |
92357 |
13667 |
86338 |
18979 |
81021 |
K |
|
49 |
07751 |
92249 |
13761 |
86239 |
19063 |
80937 |
11 |
|
50 |
9.07858 |
10.92142 |
9.13854 |
10.86146 |
9.19146 |
10.80854 |
10 |
|
51 |
07964 |
92036 |
13948 |
86052 |
19229 |
80771 |
9 |
|
52 |
08071 |
91929 |
14041 |
85959 |
19312 |
80688 |
8 |
|
53 |
08177 |
91823 |
14134 |
85866 |
19395 |
80605 |
1 |
|
54 |
08288 |
91717 |
14227 |
85773 |
19478 |
80522 |
6 |
|
55 |
08389 |
91611 |
14320 |
85680 |
19561 |
80439 |
5 |
|
56 |
08495 |
91505 |
14412 |
85588 |
1964:3 |
80357 |
4 |
|
57 |
08600 |
91400 |
14504 |
85496 |
19725 |
80275 |
3 |
|
58 |
08705 |
91295 |
14597 |
85403 |
19807 |
80193 |
2 |
|
59 |
08810 |
91190 |
14688 |
85312 |
19889 |
80111 |
1 |
|
60 08914 |
91086 |
14780 |
85220 |
19971 |
800-^9 |
0 |
|
|
, |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
i |
|
83° |
82» |
81° |
194 TABLE 9.— LOG. TANGENTS AND COTANGENTS.
|
t |
9° |
10° |
11° |
/ 1 |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.19971 |
10.800-29 |
9.24632 |
10.75368 |
9.28865 |
10.71135 |
60 |
|
1 |
20053 |
79947 |
24706 |
75294 |
28933 |
71067 |
59 |
|
2 |
20134 |
79S66 |
24779 |
75221 |
29000 |
71000 |
58 |
|
3 |
20-216 |
79784 |
24853 |
75147 |
29067 |
70933 |
57 |
|
4 |
20297 |
79703 |
24926 |
75074 |
29134 |
70866 |
56 |
|
5 |
20378 |
79622 |
25000 |
75000 |
29201 |
70799 |
55 |
|
6 |
20459 |
79541 |
25073 |
74927 |
29268 |
70732 |
54 |
|
7 |
20540 |
79460 |
25146 |
74854 |
29335 |
70605 |
53 |
|
8 |
20621 |
79379 |
25219 |
74781 |
29402 |
70598 |
52 |
|
9 |
20701 |
79299 |
25292 |
74708 |
29468 |
70532 |
51 |
|
10 |
9.20782 |
10.79218 |
9.25365 |
10.74635 |
9.29535 |
10.70465 |
50 |
|
11 |
20862 |
79138 |
25437 |
74563 |
29601 |
70399 |
49 |
|
If |
20942 |
79058 |
25510 |
74490 |
29668 |
70332 |
48 |
|
13 |
21022 |
78978 |
25582 |
74418 |
29734 |
70266 |
47 |
|
14 |
21102 |
78898 |
25655 |
74345 |
29800 |
70200 |
46 |
|
15 |
21182 |
78818 |
25727 |
74273 |
29866 |
70134 |
45 |
|
16 |
21261 |
78739 |
25799 |
74201 |
29932 |
70068 |
44 |
|
17 |
21341 |
78659 |
25871 |
74129 |
29998 |
70002 |
43 |
|
18 |
21420 |
78580 |
25943 |
74057 |
30064 |
69936 |
42 |
|
19 |
21499 |
78501 |
26015 |
73985 |
30130 |
69870 |
41 |
|
20 |
9.21578 |
10.78422 |
9.26086 |
10.73914 |
9.30195 |
10.69805 |
40 |
|
21 |
21657 |
78343 |
26158 |
73842 |
30261 |
69739 |
39 |
|
22 |
21736 |
78264 |
26229 |
73771 |
30326 |
69674 |
38 |
|
*3 |
21814 |
78186 |
26301 |
73699 |
30391 |
69609 |
37 |
|
24 |
21893 |
78107 |
26372 |
73628 |
30457 |
69543 |
36 |
|
25 |
21971 |
78029 |
26443 |
73557 |
30522 |
69478 |
35 |
|
26 |
22049 |
77951 |
26514 |
73486 |
30587 |
69413 |
34 |
|
27 |
22127 |
77873 |
26585 |
30652 |
69348 |
33 |
|
|
28 |
22205 |
77795 |
26655 |
30717 |
69283 |
32 |
|
|
29 |
22283 |
77717 |
26726 |
30782 |
69218 |
31 |
|
|
30 |
9.22361 |
10.77639 |
9.26797 |
10.73203 |
9.30846 |
10.69154 |
30 |
|
31 |
22438 |
7756C |
26867 |
73133 |
30911 |
69089 |
29 |
|
33 |
22516 |
77484 |
26937 |
73063 |
30975 |
69025 |
28 |
|
33 |
225,98 |
77407 |
27008 |
72992 |
31040 |
68960 |
27 |
|
34 |
22670 |
77330 |
27078 |
72922 |
31104 |
68896 |
26 |
|
35 |
22747 |
77253 |
27148 |
72852 |
31168 |
68832 |
25 |
|
36 |
22824 |
77176 |
27218 |
72782 |
31233 |
68767 |
24 |
|
37 |
22901 |
77099 |
27288 |
72712 |
31297 |
68703 |
23 |
|
38 |
22977 |
77023 |
27357 |
72648 |
31361 |
68639 |
22 |
|
39 |
23054 |
76946 |
27427 |
72573 |
31425 |
68575 |
21 |
|
40 |
9.23130 |
10.76870 |
9.27496 |
10.72504 |
9.31489 |
10.68511 |
20 |
|
41 |
28206 |
76794 |
27566 |
72434 |
31552 |
68448 |
19 |
|
42 |
23283 |
76717 |
27635 |
72365 |
31616 |
68384 |
18 |
|
43 |
23359 |
76641 |
27704 |
72296 |
31679 |
68321 |
17 |
|
44 |
23435 |
76565 |
27773 |
72227 |
31743 |
68257 |
16 |
|
45 |
23510 |
76490 |
27842 |
72158 |
31806 |
68194 |
15 |
|
46 |
23586 |
76414 |
27911 |
72089 |
31870 |
68130 |
14 |
|
47 |
23661 |
76339 |
27980 |
72020 |
31933 |
68067 |
13 |
|
48 |
23787 |
76263 |
28049 |
71951 |
31996 |
68004 |
12 |
|
49 |
23812 |
76188 |
28117 |
71883 |
32059 |
67941 |
11 |
|
50 |
9.23887 |
10.76113 |
9.28186 |
10.71814 |
9.32122 |
10.67878 |
10 |
|
51 |
23962 |
76038 |
28254 |
71746 |
32185 |
67815 |
9 |
|
52 |
24037 |
75963 |
28323 |
71677 |
32248 |
67752 |
8 |
|
53 |
24112 |
75888 |
28391 |
71609 |
32311 |
67689 |
7 |
|
54 |
24186 |
75814 |
28459 |
71541 |
32373 |
67627 |
6 |
|
55 |
24261 |
75739 |
28527 |
71473 |
3243G |
67564 |
5 |
|
56 |
24335 |
75665 |
28595 |
71405 |
32498 |
67502 |
4 |
|
57 |
24410 |
75590 |
28662 |
71338 |
32561 |
67439 |
3 |
|
58 |
24484 |
75516 |
28730 |
71270 |
32623 |
67377 |
2 |
|
59 |
24558 |
75442 |
28798 |
71202 |
32685 |
67315 |
1 |
|
60 |
24632 |
75368 |
28865 |
71135 |
32747 |
67253 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
|
|
80* |
79° |
78° |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 195
|
12° |
18° |
14° |
/ |
||||
|
Tan |
Cotan |
Tan |
Co fan |
Tan |
Cotan |
||
|
o |
9.32747 |
10.67253 |
9.36336 |
10.63664 |
9.39677 |
10.60323 |
60 |
|
1 |
32810 |
67190 |
36394 |
63606 |
39731 |
60269 |
59 |
|
2 |
32872 |
67128 |
36452 |
63548 |
39785 |
60?15 |
68 |
|
3 |
32933 |
67067 |
36509 |
63491 |
39838 |
60162 |
57 |
|
4 |
32995 |
67005 |
36566 |
63434 |
89892 |
60108 |
66 |
|
5 |
33057 |
66943 |
36624 |
68376 |
89945 |
60055 |
65 |
|
6 |
33119 |
66881 |
36681 |
63319 |
39999 |
60001 |
54 |
|
7 |
83180 |
66820 |
36738 |
63262 |
40052 |
59948 |
53 |
|
8 |
83->42 |
66758 |
36795 |
63205 |
40106 |
59894 |
62 |
|
9 |
83303 |
66697 |
36852 |
63148 |
40159 |
59841 |
61 |
|
10 |
9.33365 |
10.66635 |
9.36909 |
10.63091 |
9.40212 |
10.59788 |
50 |
|
n |
33426 |
66574 |
36966 |
63034 |
40266 |
59734 |
49 |
|
12 |
33487 |
66513 |
37023 |
62977 |
40319 |
59681 |
48 |
|
13 |
33548 |
66452 |
37080 |
62920 |
40372 |
59628 |
47 |
|
14 |
33609 |
66391 |
37137 |
628C3 |
40425 |
59575 |
46 |
|
15 |
336^0 |
66330 |
37193 |
62807 |
40478 |
59522 |
45 |
|
16 |
33731 |
66269 |
37250 |
62750 |
40531 |
59469 |
44 |
|
17 |
33792 |
66208 |
37306 |
62694 |
40584 |
59416 |
43 |
|
18 |
33853 |
66147 |
37363 |
62637 |
40636 |
59364 |
42 |
|
19 |
83913 |
66087 |
37419 |
62581 |
40689 |
59311 |
41 |
|
20 |
9.33974 |
10.66026 |
9.37476 |
10.62524 |
9.40742 |
10.59258 |
40 |
|
21 |
34034 |
65966 |
37532 |
62468 |
40795 |
69205 |
39 |
|
22 |
34095 |
65905 |
37588 |
62412 |
40847 |
59153 |
38 |
|
23 |
84155 |
65845 |
37644 |
62356 |
40900 |
59100 |
37 |
|
24 |
34215 |
65785 |
37700 |
62300 |
40952 |
59048 |
36 |
|
25 |
34276 |
66724 |
377'56 |
62244 |
41005 |
58995 |
35 |
|
26 |
34336 |
65664 |
37812 |
62188 |
41057 |
58943 |
34 |
|
27 |
34396 |
65604 |
37868 |
62132 |
41109 |
58891 |
33 |
|
28 |
|I456 |
65544 |
87924 |
62076 |
41161 |
58839 |
3d |
|
29 |
34516 |
65484 |
87980 |
62020 |
41214 |
58786 |
31 |
|
30 |
9.34576 |
10.65424 |
9.38035 |
10.61965 |
9.41266 |
10.58734 |
30 |
|
31 |
34635 |
65365 |
38091 |
61909 |
41318 |
58682 |
29 |
|
32 |
34695 |
65305 |
38147 |
61853 |
41370 |
58630 |
28 |
|
33 |
34755 |
65245 |
38202 |
61798 |
41422 |
58578 |
27 |
|
34 |
34814 |
65186 |
38257 |
61743 |
41474 |
58526 |
26 |
|
35 |
34874 |
65126 |
38313 |
61687 |
41526 |
68474 |
25 |
|
86 |
34933 |
65067 |
38368 |
61632 |
41578 |
58422 |
24 |
|
37 |
34992 |
65008 |
38423 |
61577 |
41629 |
58371 |
23 |
|
38 |
35051 |
64949 |
38479 |
61521 |
41681 |
58319 |
22 |
|
39 |
35111 |
64889 |
38534 |
61466 |
41733 |
58267 |
21 |
|
40 |
9.35170 |
10.64830 |
9.38589 |
10.61411 |
9.41784 |
10.58216 |
20 |
|
41 |
35229 |
64771 |
38644 |
61356 |
41836 |
58164 |
19 |
|
42 |
35288 |
64712 |
38699 |
61301 |
41887 |
58113 |
18 |
|
43 |
35347 |
64653 |
38754 |
61246 |
41939 |
58061 |
17 |
|
44 |
35405 |
64595 |
38808 |
61192 |
41990 |
58010 |
16 |
|
45 |
35464 |
64536 |
38863 |
61137 |
42041 |
57959 |
15 |
|
46 |
35523 |
64477 |
38918 |
61082 |
42093 |
57907 |
14 |
|
47 |
35581 |
64419 |
38972 |
61028 |
42144 |
57856 |
13 |
|
48 |
35640 |
64360 |
39027 |
60973 |
42195 |
57805 |
12 |
|
49 |
35698 |
64302 |
39082 |
60918 |
42246 |
57754 |
11 |
|
50 |
9.35757 |
10.64243 |
9.39136 |
10.60864 |
9.42297 |
10.57703 |
10 |
|
51 |
35815 |
64185 |
39190 |
60810 |
42348 |
57652 |
9 |
|
52 |
35873 |
64127 |
39245 |
60755 |
42399 |
57601 |
8 |
|
53 |
35931 |
64069 |
39299 |
60701 |
42450 |
57550 |
7 |
|
54 |
35989 |
64011 |
39353 |
60647 |
42501 |
57499 |
6 |
|
55 |
36047 |
63953 |
39407 |
60593 |
42552 |
57448 |
5 |
|
56 |
36105 |
63895 |
39461 |
60539 |
42603 |
57397 |
4 |
|
57 |
36163 |
63837 |
39515 |
60485 |
42653 |
57347 |
8 |
|
58 |
36221 |
63779 |
39569 |
60431 |
42704 |
57296 |
2 |
|
59 |
36279 |
63721 |
39623 |
60377 |
42755 |
57245 |
1 |
|
60 |
36336 |
63664 |
39677 |
60323 |
42805 |
57195 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
i |
|
77° |
76° |
76* - |
196 TABLE 9.— LOG. TANGENTS AND COTANGENTS.
|
0 |
15° |
16° |
17° |
/ |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
o |
9.42805 |
10.57195 |
9.45750 |
10.54250 |
9.48534 |
10.51466 |
60 |
|
1 |
42856 |
57144 |
45797 |
54203 |
48579 |
51421 |
59 |
|
2 |
42906 |
57094 |
45845 |
54155 |
48624 |
51376 |
58 |
|
3 |
42957 |
57043 |
45892 |
54108 |
48669 |
51331 |
57 |
|
4 |
43007 |
56993 |
45940 |
54060 |
48714 |
51286 |
56 |
|
5 |
43057 |
56943 |
45987 |
54013 |
48759 |
51241 |
55 |
|
6 |
43108 |
56892 |
46035 |
53965 |
48804 |
51196 |
54 |
|
7 |
43158 |
56842 |
46082 |
53918 |
48849 |
51151 |
53 |
|
8 |
43208 |
56792 |
46130 |
53870 |
48894 |
51106 |
52 |
|
9 |
43258 |
56742 |
46177 |
53823 |
48939 |
51061 |
51 |
|
10 |
9.43308 |
10.56692 |
9.46224 |
10.53776 |
9.48984 |
10.51016 |
50 |
|
11 |
43358 |
56642 |
46271 |
53729 |
49029 |
50971 |
49 |
|
12 |
43408 |
56592 |
46319 |
53681 |
49073 |
50927 |
48 |
|
18 |
43458 |
56542 |
46366 |
53634 |
49118 |
50882 |
47 |
|
14 |
43508 |
56492 |
46413 |
53587 |
49163 |
50837 |
46 |
|
15 |
43558 |
56442 |
46460 |
53540 |
49207 |
50793 |
45 |
|
16 |
43607 |
56393 |
46507 |
53493 |
49252 |
50748 |
44 |
|
17 |
43657 |
56343 |
46554 |
53446 |
49296 |
50704 |
43 |
|
18 |
43707 |
56293 |
46601 |
53399 |
49341 |
50659 |
42 |
|
19 |
43756 |
56244 |
46648 |
53352 |
49385 |
50615 |
41 |
|
20 |
9.43806 |
10.56194 |
9.46694 |
10.53306 |
9.49430 |
10.50570 |
40 |
|
21 |
43855 |
56145 |
46741 |
53259 |
49474 |
50526 |
39 |
|
22 |
43905 |
56095 |
46788 |
53212 |
49519 |
50481 |
38 |
|
23 |
43954 |
56046 |
46835 |
53165 |
49563 |
50437 |
37 |
|
24 |
44004 |
55996 |
46881 |
53119 |
49607 |
50393 |
36 |
|
25 |
44053 |
55947 |
46928 |
53072 |
49652 |
50348 |
85 |
|
26 |
44102 |
55898 |
46975 |
53025 |
49696 |
50304 |
34 |
|
27 |
44151 |
55849 |
47021 |
52979 |
49740 |
50260 |
33 |
|
28 |
44201 |
55799 |
47068 |
52932 |
49784 |
50216 |
32 |
|
29 |
44250 |
55750 |
47114 |
52886 |
49828 |
50172 |
31 |
|
30 |
9.44299 |
10.55701 |
9.47160 |
10.52840 |
9.49872 |
10.50128 |
30 |
|
31 |
44348 |
55652 |
47207 |
52793 |
49916 |
50084 |
29 |
|
32 |
44397 |
55603 |
47253 |
52747 |
49960 |
50040 |
28 |
|
33 |
44446 |
55554 |
47299 |
52701 |
50004 |
49996 |
27 |
|
34 |
44495 |
55505 |
47346 |
52654 |
50048 |
49952 |
26 |
|
35 |
44544 |
55456 |
47392 |
52608 |
50092 |
49908 |
25 |
|
36 |
44592 |
55408 |
47438 |
52562 |
50136 |
49864 |
24 |
|
37 |
44641 |
55359 |
47484 |
52516 |
50180 |
49820 |
23 |
|
38 |
44690 |
55310 |
47530 |
52470 |
50223 |
49777 |
22 |
|
39 |
44738 |
55262 |
47576 |
52424 |
50267 |
49733 |
21 |
|
40 |
9.44787 |
10.55213 |
9.47622 |
10.52378 |
9.50311 |
10.49689 |
20 |
|
41 |
44836 |
55164 |
47668 |
52332 |
50355 |
49645 |
19 |
|
42 |
44884 |
55116 |
47714 |
52286 |
50398 |
49602 |
18 |
|
43 |
44933 |
55067 |
47760 |
52240 |
50442 |
49558 |
17 |
|
44 |
44981 |
55019 |
47806 |
52194 |
50485 |
49515 |
16 |
|
45 |
45029 |
54971 |
47852 |
52148 |
50529 |
49471 |
15 |
|
46 |
45078 |
54922 |
47897 |
52103 |
50572 |
49428 |
14 |
|
47 |
45126 |
54874 |
47943 |
52057 |
50616 |
49384 |
13 |
|
48 |
45174 |
54826 |
47989 |
52011 |
50659 |
49341 |
12 |
|
49 |
45222 |
54778 |
48035 |
51965 |
50703 |
49297 |
11 |
|
50 |
9.45271 |
10.54729 |
9.48080 |
10.51920 |
9.50746 |
10.49254 |
10 |
|
51 |
45319 |
54681 |
48126 |
51874 |
50789 |
49211 |
9 |
|
52 |
45367 |
54633 |
48171 |
51829 |
50833 |
49167 |
8 |
|
53 |
45415 |
54585 |
48217 |
51783 |
50876 |
49124 |
7 |
|
54 |
45463 |
54537 |
48262 |
51738 |
50919 |
49081 |
6 |
|
55 |
45511 |
54489 |
48307 |
51693 |
50962 |
49038 |
5 |
|
56 |
45559 |
54441 |
48353 |
51647 |
51005 |
48995 |
4 |
|
57 |
45606 |
54394 |
48398 |
51602 |
51048 |
48952 |
3 |
|
58 |
45654 |
54346 |
48443 |
51557 |
51092 |
48908 |
2 |
|
59 |
457C2 |
54298 |
48489 |
51511 |
51135 |
48865 |
1 |
|
60 |
45750 |
54250 |
48534 |
51466 |
51178 |
48822 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
/ |
|
74° |
73° |
72° |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 197
|
18° |
19° |
20° |
/ |
||||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.51178 |
10.48822 |
9.53697 |
10.46303 |
9.56107 |
10.43893 |
60 |
|
1 |
51221 |
48779 |
53738 |
46262 |
56146 |
43854 |
59 |
|
2 |
51264 |
48736 |
53779 |
46221 |
56185 |
43815 |
58 |
|
3 |
51306 |
48694 |
53820 |
46180 |
56224 |
43776 |
57 |
|
4 |
51349 |
48651 |
53861 |
46139 |
56264 |
43736 |
56 |
|
5 |
51392 |
48608 |
53902 |
46098 |
56303 |
43697 |
55 |
|
6 |
51435 |
48565 |
53943 |
46057 |
56342 |
43658 |
54 |
|
7 |
51478 |
48522 |
53984 |
46016 |
56381 |
43619 |
53 |
|
8 |
51520 |
48480 |
54025 |
45975 |
56420 |
48580 |
52 |
|
9 |
51563 |
48437 |
54065 |
45935 |
56459 |
43541 |
51 |
|
10 |
9.51606 |
10.48394 |
9.54106 |
10.45894 |
9.56498 |
10.43502 |
50 |
|
11 |
51648 |
48352 |
54147 |
45853 |
" 56537 |
43463 |
49 |
|
12 |
51691 |
48309 |
54187 |
45813 |
56576 |
43424 |
48 |
|
13 |
51734 |
48266 |
54228 |
45772 |
56815 |
43385 |
47 |
|
14 |
51776 |
48224 |
54269 |
45731 |
56654 |
445346 |
46 |
|
15 |
51819 |
48181 |
54309 |
45691 |
56693 |
43307 |
45 |
|
16 |
51861 |
48139 |
54350 |
45650 |
56738 |
43268 |
44 |
|
17 |
51903 |
48097 |
54390 |
45610 |
56771 |
43229 |
43 |
|
18 |
51946 |
48054 |
54431 |
45569 |
56810 |
43190 |
42 |
|
19 |
51988 |
48012 |
54471 |
45529 |
56849 |
43151 |
41 |
|
20 |
9.52031 |
10.47969 |
9.54512 |
10.45488 |
9.56887 |
10.43113 |
40 |
|
21 |
52073 |
47927 |
54552 |
45448 |
56926 |
43074 |
39 |
|
22 |
52115 |
47885 |
54593 |
45407 |
56965 |
43035 |
38 |
|
23 |
52157 |
47843 |
54633 |
45367 |
57004 |
42996 |
37 |
|
24 |
52200 |
47800 |
54673 |
45327 |
57042 |
42958 |
36 |
|
25 |
52242 |
47758 |
54714 |
45286 |
57081 |
42919 |
35 |
|
26 |
52284 |
47716 |
54754 |
45246 |
57120 |
42880 |
34 |
|
27 |
52326 |
47674 |
54794 |
45206 |
57158 |
42842 |
33 |
|
28 |
52368 |
47632 |
54835 |
45165 |
57197 |
42803 |
82 |
|
29 |
5241JJ |
47590 |
54875 |
45125 |
57235 |
42765 |
31 |
|
30 |
9.52452 |
10.47548 |
9.54915 |
10.45085 |
9.57274 |
10.42726 |
30 |
|
31 |
52494 |
47506 |
54955 |
45045 |
57312 |
42688 |
29 |
|
32 |
52536 |
47464 |
54995 |
45005 |
57351 |
42649 |
88 |
|
33 |
52578 |
47422 |
55035 |
44965 |
57389 |
42611 |
27 |
|
34 |
52620 |
47380 |
55075 |
44925 |
57428 |
42572 |
26 |
|
35 |
52661 |
47339 |
55115 |
44885 |
57466 |
42534 |
25 |
|
36 |
52703 |
47297 |
55155 |
44845 |
57504 |
42496 |
24 |
|
37 |
52745 |
47255 |
55195 |
44805 |
57543 |
42457 |
23 |
|
38 |
52787 |
47213 |
55235 |
44765 |
57581 |
42419 |
22 |
|
39 |
52829 |
47171 |
55275 |
44725 |
57619 |
42381 |
21 |
|
40 |
9.52870 |
10.47130 |
9.55315 |
10.44685 |
9.57658 |
10.42342 |
20 |
|
41 |
52912 |
47088 |
55355 |
44645 |
57696 |
42304 |
19 |
|
42 |
52953 |
47047 |
55395 |
44605 |
57734 |
42266 |
18 |
|
43 |
52995 |
47005 |
55434 |
44566 |
57772 |
42228 |
17 |
|
44 |
53037 |
46963 |
55474 |
44526 |
57810 |
42190 |
16 |
|
45 |
53078 |
46922 |
55514 |
44486 |
57849 |
42151 |
15 |
|
46 |
53120 |
46880 |
55554 |
44446 |
57887 |
42113 |
14 |
|
47 |
53161 |
46839 |
55593 |
44407 |
57925 |
42075 |
13 |
|
48 |
53202 |
46798 |
55633 |
44367 |
57963 |
42037 |
12 |
|
49 |
53244 |
46756 |
55673 |
44327 |
56001 |
41999 |
11 |
|
50 |
9.53285 |
10.46715 |
9.55712 |
10.44288 |
9.58039 |
10.41961 |
10 |
|
51 |
53327 |
46673 |
55752 |
44248 |
58077 |
41923 |
9 |
|
52 |
53368 |
46632 |
55791 |
44209 |
58115 |
41885 |
8 |
|
53 |
53409 |
46591 |
55831 |
44169 |
58153 |
41847 |
7 |
|
54 |
53450 |
46550 |
55870 |
44130 |
58191 |
41809 |
6 |
|
55 |
53492 |
46508 |
55910 |
44090 |
58229 |
41771 |
5 |
|
56 |
53533 |
46467 |
55949 |
44051 |
58267 |
41733 |
4 |
|
57 |
53574 |
46426 |
55989 |
44011 |
58304 |
41696 |
3 |
|
58 |
53615 |
46385 |
56028 |
43972 |
58342 |
41658 |
2 |
|
59 |
53656 |
• 46344 |
56067 |
43933 |
58380 |
41620 |
1 |
|
60 |
53697 |
46303 |
56107 |
43893 |
58418 |
41582 |
0 |
|
> |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
/ |
|
71° |
70° |
69° |
198 TABLE 9.— LOG. TANGENTS AND COTANGENTS,
|
1 |
21° |
22° |
23° |
/ |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.58418 |
10.41582 |
9.60641 |
10.39359 |
9.62785 |
10.37215 |
60 |
|
1 |
58455 |
41545 |
60677 |
39323 |
62820 |
37180 |
59 |
|
2 |
58493 |
41507 |
60714 |
39-386 |
62855 |
37145 |
58 |
|
3 |
58531 |
41469 |
60750 |
39250 |
62890 |
37110 |
57 |
|
4 |
58569 |
41431 |
60786 |
39214 |
62926 |
37074 |
56 |
|
5 |
58606 |
41394 |
60823 |
39177 |
62961 |
37039 |
55 |
|
6 |
58644 |
41356 |
60859 |
39141 |
62996 |
37004 |
54 |
|
7 |
58681 |
41319 |
60895 |
39105 |
63031 |
36.969 |
53 |
|
8 |
58719 |
41281 |
60931 |
39069 |
68066 |
36934 |
52 |
|
9 |
58757 |
41243 |
60967 |
39033 |
63101 |
36899 |
51 |
|
10 |
9.58794 |
10.41206 |
9.61004 |
10.38996 |
9.63135 |
10.36865 |
50 |
|
11 |
58832 |
41168 |
61040 |
38960 |
63170 |
36830 |
49 |
|
12 |
58869 |
41131 |
61076 |
38924 |
63205 |
36795 |
• 48 |
|
13 |
58907 |
41093 |
61112 |
38888 |
63240 |
36760 |
47 |
|
14 |
58944 |
41056 |
61148 |
38852 |
63275 |
36725 |
46 |
|
15 |
58981 |
41019 |
61184 |
38816 |
63310 |
36690 |
45 |
|
16 |
59019 |
40981 |
61220 |
38780 |
68345 |
36655 |
44 |
|
17 |
59056 |
40944 |
61256 |
38744 |
63379 |
36621 |
43 |
|
18 |
59094 |
40906 |
61292 |
38708 |
63414 |
36586 |
42 |
|
19 |
59131 |
40869 |
61328 |
38672 |
63449 |
36551 |
41 |
|
20 |
9.59168 |
10.40882 |
9.61304 |
10.38636 |
9.63484 |
10.36516 |
40 |
|
21 |
69205 |
40795 |
61400 |
3860C |
63519 |
36481 |
39 |
|
22 |
59243 |
40757 |
61436 |
3856* |
63553 |
36447 |
88 |
|
23 |
59280 |
40720 |
61472 |
38528 |
63588 |
36412 |
37 |
|
24 |
59317 |
40688 |
61508 |
38492 |
63623 |
36377 |
36 |
|
25 |
59854 |
40646 |
61544 |
38456 |
63657 |
36343 |
85 |
|
26 |
59391 |
40609 |
61579 |
38421 |
63692 |
36308 |
34 |
|
27 |
59429 |
40571 |
61615 |
38385 |
G3726 |
36274 |
33 |
|
28 |
59466 |
40534 |
61651 |
38349 |
63761 |
36239 |
32 |
|
29 |
59503 |
40497 |
61687 |
38313 |
63796 |
36204 |
31 |
|
80 |
9.59540 |
10.40460 |
9.61722 |
10.38278 |
9.63830 |
10.36170 |
30 |
|
31 |
59577 |
40423 |
61758 |
38242 |
63865 |
36135 |
29 |
|
32 |
59614 |
40386 |
61794 |
38206 |
63899 |
36101 |
28 |
|
33 |
59651 |
40349 |
61830 |
38170 |
63934 |
36066 |
27 |
|
34 |
69688 |
40312 |
61865 |
38135 |
63968 |
36032 |
26 |
|
35 |
59725 |
40275 |
61901 |
38099 |
64003 |
35997 |
25 |
|
36 |
69762 |
40238 |
61936 |
38064 |
64037 |
35963 |
24 |
|
87 |
59799 |
40201 |
61972 |
38028 |
64072 |
35928 |
23 |
|
38 |
59835 |
40165 |
62008 |
37992 |
64106 |
35894 |
22 |
|
39 |
59872 |
40128 |
62043 |
37957 |
64140 |
35860 |
21 |
|
40 |
9.59909 |
10.40091 |
9.62079 |
10.37921 |
9.64175 |
10.35825 |
20 |
|
41 |
59946 |
40054 |
62114 |
87886 |
64209 |
35791 |
19 |
|
42 |
59983 |
40017 |
62150 |
37850 |
64243 |
35757 |
18 |
|
43 |
60019 |
89981 |
62185 |
37815 |
64278 |
35722 |
17 |
|
44 |
60056 |
39944 |
62221 |
37779 |
64312 |
35688 |
16 |
|
45 |
60093 |
39907 |
62256 |
37744 |
64346 |
35654 |
15 |
|
46 |
60130 |
39870 |
62292 |
37708 |
64381 |
35619 |
14 |
|
47 |
60166 |
39834 |
62327 |
37673 |
64415 |
35585 |
13 |
|
48 |
60203 |
39797 |
62362 |
37638 |
64449 |
35551 |
12 |
|
49 |
60240 |
39760 |
62398 |
37602 |
64483 |
35517 |
11 |
|
50 |
9.60276 |
10.39724 |
9.62433 |
10.37567 |
9.64517 |
10.85483 |
10 |
|
51 |
60313 |
39687 |
62468 |
37532 |
64552 |
35448 |
9 |
|
52 |
60349 |
39651 |
62504 |
37496 |
64586 |
35414 |
8 |
|
53 |
60386 |
39614 |
62539 |
37461 |
64620 |
35380 |
IJr |
|
54 |
60422 |
39578 |
62574 |
37426 |
64654 |
35346 |
6 |
|
55 |
60459 |
39541 |
62609 |
37391 |
64688 |
35312 |
5 |
|
56 |
60495 |
39505 |
62645 |
37855 |
64722 |
35278 |
4 |
|
57 |
60532 |
39468 |
62680 |
37320 |
64756 |
35244 |
8 |
|
58 |
605(58 |
39432 |
62715 |
37285 |
64790 |
35210 |
|
|
59 |
60605 |
89395 |
62750 |
37250 |
64824 |
35176 |
1 1 |
|
60 |
60641 |
39359 |
62785 |
87215 |
64858 |
85142 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
f |
|
68» |
67° |
66° |
TA!BLE 9.— LOG. TANGENTS AND COTANGENTS. 199
|
/ |
24° |
25° |
26° |
/ |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.64858 |
10.35142 |
9.66867 |
10.33133 |
9.68818 |
10.31182 |
60 |
|
1 |
64892 |
35108 |
66900 |
33100 |
68850 |
31150 |
59 |
|
2 |
64926 |
35074 |
66933 |
33067 |
68882 |
31118 |
58 |
|
3 |
64960 |
35040 |
66966 |
33034 |
68914 |
31086 |
57 |
|
4 |
64994 |
35006 |
66999 |
33001 |
68946 |
31054 |
56 |
|
5 |
65028 |
84972 |
67032 |
32968 |
68978 |
31022 |
55 |
|
6 |
65062 |
34938 |
67065 |
32935 |
69010 |
90990 |
54 |
|
7 |
65096 |
34904 |
67098 |
32902 |
69042 |
30958 |
53 |
|
8 |
65130 |
34870 |
67131 |
32869 |
69074 |
30926 |
52 |
|
9 |
65164 |
34836 |
67163 |
32837 |
69106 |
30894 |
51 |
|
10 |
9.65197 |
10.34803 |
9.67196 |
10.32804 |
9-. 69138 |
10.30862 |
50 |
|
11 |
65231 |
34769 |
67229 |
32771 |
69170 |
30830 i 49 |
|
|
12 |
65265 |
34735 |
67262 |
32738 |
69202 |
80798 |
48 |
|
13 |
65299 |
34701 |
67295 |
32705 |
69234 |
30766 |
47 |
|
14 |
65333 |
34667 |
67327 |
32673 |
69266 |
80734 |
46 |
|
15 |
65366 |
34634 |
67360 |
32640 |
69298 |
30702 |
45 |
|
16 |
65400 |
34600 |
67393 |
32607 |
69329 |
30671 |
44 |
|
17 |
65434 |
34566 |
67426 |
82574 |
69361 |
30689 |
43 |
|
18 |
65467 |
34533 |
67458 |
32542 |
69393 |
30607 |
42 |
|
19 |
65501 |
34499 |
67491 |
32509 |
69425 |
30575 |
41 |
|
20 |
9.65535 |
10.34465 |
9.67524 |
10.32476 |
9.69457 |
10.30543 |
40 |
|
21 |
65568 |
34432 |
67556 |
32444 |
69488 |
30512 |
39 |
|
22 |
65602 |
34398 |
67589 |
32411 |
69520 |
30480 |
38 |
|
23 |
65636 |
34364 |
67622 |
32378 |
69552 |
30448 |
37 |
|
24 |
656(59 |
34331 |
67654 |
32346 |
69584 |
30416 |
36 |
|
25 |
65703 |
34297 |
67687 |
32313 |
69615 |
30385 |
35 |
|
26 |
65736 |
34264 |
67719 |
32281 |
69647 |
30353 |
34 |
|
27 |
65770 |
34230 |
67752 |
32248 |
69679 |
30321 |
33 |
|
28 |
65803 |
^ 34197 |
67785 |
32215 |
69710 |
30290 |
32 |
|
29 |
65837 |
34163 |
67817 |
32183 |
69742 |
30258 |
31 |
|
30 |
9.65870 |
10.34130 |
9.67850 |
10.32150 |
9.69774 |
10.30226 |
30 |
|
31 |
65904 |
34096 |
67882 |
32118 |
69805 |
30195 |
29 |
|
32 |
65937 |
34063 |
67915 |
32085 |
69837 |
30163 |
28 |
|
33 |
65971 |
34029 |
67947 |
32053 |
69868 |
30132 |
27 |
|
34 |
66004 |
33996 |
67980 |
32020 |
69900 |
30100 |
26 |
|
35 |
66038 |
33962 |
68012 |
31988 |
69932 |
80068 |
25 |
|
M |
66071 |
83929 |
68044 |
31956 |
69963 |
30037 |
24 |
|
37 |
66104 |
33896 |
68077 |
31923 |
69995 |
30005 |
23 |
|
38 |
66138 |
33862 |
68109 |
31891 |
70026 |
29974 |
22 |
|
39 |
66171 |
33829 |
68142 |
31858 |
70058 |
29942 |
21 |
|
40 |
9.66204 |
10.38796 |
9.68174 |
10.31826 |
9.70089 |
10.29911 |
20 |
|
41 |
66238 |
33762 |
68206 |
31794 |
70121 |
29879 |
19 |
|
42 |
66271 |
33729 |
68239 |
31761 |
70152 |
29848 |
18 |
|
43 |
66304 |
33696 |
68271 |
31729 |
70184 |
29816 |
17 |
|
44 |
66337 |
33663 |
68303 |
31697 |
70215 |
29785 |
16 |
|
45 |
66371 |
33629 |
68336 |
31664 |
70247 |
29753 |
15 |
|
46 |
66404 |
33506 |
68368 |
31632 |
70278 |
29722 |
14 |
|
47 |
66437 |
33563 |
68400 |
31600 |
70309 |
29691 |
13 |
|
48 |
66470 |
33530 |
68432 |
31568 |
70341 |
29659 |
12 |
|
49 |
06503 |
33497 |
68465 |
31585 |
70372 |
29628 |
11 |
|
50 |
0.0(5537 |
10.33463 |
9.68497 |
10.31503 |
9.70404 |
10.29596 |
10 |
|
51 |
66570 |
33430 |
6a529 |
31471 |
70435 |
29565 |
9 |
|
52 |
66603 |
33397 |
68561 |
31439 |
70466 |
29534 |
8 |
|
f>3 |
66636 |
33364 |
68593 |
31407 |
70498 |
29502 |
7 |
|
54 |
66669 |
33331 |
68626 |
31374 |
70529 |
29471 |
6 |
|
55 |
66702 |
33298 |
68658 |
31342 |
70560 |
29440 |
5 |
|
56 |
6673") |
33265 |
68690 |
31310 |
70592 |
29408 |
4 |
|
57 |
66768 |
33232 |
68722 |
31278 |
70623 |
29377 |
8 |
|
58 |
66801 |
33199 |
68754 |
31246 |
70654 |
29346 2 |
|
|
59 |
66834 |
33166 |
68786 |
31214 |
70685 |
29315 ! 1 |
|
|
fiO 66867 |
33133 |
68818 |
31182 |
70717 |
29283 i 0 |
||
|
/ |
Otan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
/ |
|
65° |
64° |
63° |
200 TABLE 9.— LOG. TANGENTS AND COTANGENTS.
|
/ |
27° |
28° |
29° |
/ |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
o |
9.70717 |
10.29283 |
9.72567 |
10.27433 |
9.74375 |
10.25625 |
60 |
|
1 |
70748 |
29252 |
72598 |
27402 |
74405 |
25595 |
59 |
|
2 |
70779 |
29221 |
72628 |
27372 |
74435 |
25565 |
58 |
|
3 |
70810 |
29190 |
72659 |
27341 |
74465 |
25535 |
57 |
|
4 |
70841 |
29159 |
72689 |
27311 |
74494 |
25506 |
56 |
|
5 |
70873 |
29127 |
72720 |
27280 |
74524 |
25476 |
55 |
|
6 |
70904 |
29096 |
72750 |
27250 |
74554 |
25446 |
54 |
|
7 |
70935 |
29065 |
72780 |
27220 |
74583 |
25417 |
53 |
|
8 |
70966 |
29034 |
72811 |
27189 |
74613 |
25387 |
52 |
|
9 |
70997 |
29003 |
72841 |
27159 |
74643 |
25357 |
51 |
|
10 |
9.71028 |
10.28978 |
9.72872 |
10.27128 |
9.74673 |
10.25327 |
50 |
|
11 |
71059 |
28941 |
72902 |
27098 |
74702 |
25298 |
49 |
|
12 |
71090 |
28910 |
72932 |
27068 |
74732 |
25268 |
48 |
|
13 |
71121 |
28879 |
72963 |
27037 |
74762 |
25238 |
47 |
|
14 |
71153 |
28847 |
72993 |
27007 |
74791 |
25209 |
46 |
|
15 |
71184 |
28816 |
73023 |
26977 |
74821 |
25179 |
45 |
|
16 |
71215 |
28785 |
73054 |
26946 |
74851 |
25149 |
44 |
|
17 |
71246 |
28754 |
73084 |
26916 |
74880 |
25120 |
43 |
|
18 |
71277 |
28723 |
73114 |
26886 |
74910 |
25090 |
42 |
|
19 |
71308 |
28692 |
73144 |
26856 |
74939 |
25061 |
41 |
|
20 |
9.71339 |
10.28661 |
9.73175 |
10.26825 |
9.74969 |
10.25031 |
40 |
|
21 |
71370 |
28630 |
73205 |
26795 |
74998 |
25002 |
39 |
|
22 |
71401 |
28599 |
73235 |
26765 |
75028 |
24972 |
38 |
|
23 |
71431 |
28569 |
73265 |
26735 |
75058 |
24942 |
37 |
|
24 |
71462 |
28538 |
73295 |
26705 |
75087 |
24913 |
36 |
|
25 |
71493 |
28507 |
73326 |
26674 |
75117 |
24883 |
35 |
|
26 |
71524 |
28476 |
73356 |
26644 |
75146 |
24854 |
34 |
|
27 |
71555 |
28445 |
73386 |
26614 |
75176 |
24824 |
33 |
|
28 |
71586 |
28414 |
73416 |
26584 |
75205 |
24795 |
32 |
|
29 |
71617 |
28383 |
73446 |
26554 |
75235 |
24765 |
31 |
|
30 |
9.71648 |
10.28352 |
9.73476 |
10.26524 |
9.75264 |
10.24736 |
30 |
|
31 |
71679 |
28321 |
73507 |
26493 |
75294 |
24706 |
29 |
|
32 |
71709 |
28291 |
73537 |
26463 |
75323 |
24677 |
28 |
|
33 |
71740 |
28260 |
73567 |
26433 |
75353 |
24647 |
27 |
|
34 |
71771 |
28229 |
73597 |
26403 |
75382 |
24618 |
26 |
|
35 |
- 71802 |
28198 |
73627 |
26373 |
75411 |
24589 |
25 |
|
36 |
71833 |
28167 |
73657 |
26343 |
75441 |
24559 |
24 |
|
87 |
71863 |
28137 |
73687 |
26313 |
75470 |
24530 |
23 |
|
38 |
71894 |
28108 |
73717 |
26283 |
75500 |
24500 |
22 |
|
39 |
71925 |
28075 |
73747 |
26253 |
75529 |
24471 |
21 |
|
40 |
9.71955 |
10.28045 |
9.73777 |
10.26223 |
9.75558 |
10.24442 |
20 |
|
41 |
71986 |
28014 |
73807 |
26193 |
75588 |
24412 |
19 |
|
42 |
72017 |
27983 |
73837 |
26163 |
75617 |
24383 |
18 |
|
43 |
72048 |
27952 |
73867 |
26133 |
75647 |
24353 |
17 |
|
44 |
72078 |
27922 |
73897 |
26103 |
75676 |
24324 |
16 |
|
45 |
72109 |
27891 |
78927 |
26073 |
75705 |
24295 |
15 |
|
46 |
72140 |
27860 |
73957 |
26043 |
75735 |
24265 |
14 |
|
47 |
72170 |
27830 |
73987 |
26013 |
75764 |
24236 |
13 |
|
48 |
72201 |
27799 |
74017 |
25983 |
75793 |
24207 |
12 |
|
49 |
72231 |
27769 |
74047 |
25953 |
75822 |
24178 |
11 |
|
50 |
9.72262 |
10.27738 |
9.74077 |
10.25923 |
9.75852 |
10.24148 |
10 |
|
51 |
72293 |
27707 |
74107 |
25893 |
75881 |
24119 |
9 |
|
52 |
72323 |
27677 |
74137 |
25863 |
75910 |
24080 |
8 |
|
53 |
72354 |
27646 |
74166 |
25834 |
75939 |
24061 |
7 |
|
54 |
72384 |
27616 |
74196 |
25804 |
75969 |
24031 |
6 |
|
55 |
72415 |
27585 |
74226 |
25774 |
75998 |
24002 |
5 |
|
56 |
72445 |
27555 |
74256 |
25744 |
76027 |
23973 |
4 |
|
57 |
72476 |
27524 |
74286 |
25714 |
76056 |
23944 |
3 |
|
58 |
72506 |
27494 |
74316 |
25684 |
76086 |
28914 |
2 |
|
59 |
72537 |
27463 |
74345 |
25655 |
76115 |
23885 |
1 |
|
60 |
72567 |
27433 |
74375 |
25625 |
76144 |
23856 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
, |
|
62 • |
, |
61' |
60° |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 201
|
f |
30° |
31° |
32° |
t |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.76144 |
10.23856 |
9.77877 |
10.22123 |
9.79579 |
10.20421 |
60 |
|
1 |
76173 |
23827 |
77906 |
22094 |
79607 |
20393 |
59 |
|
2 |
76202 |
23798 |
77935 |
22065 |
79635 |
20365 |
58 |
|
3 |
76231 |
23769 |
77963 |
22037 |
79663 |
20337 |
57 |
|
4 |
76261 |
23739 |
77992 |
22008 |
79691 |
20309 |
56 |
|
5 |
76290 |
23710 |
78020 |
21980 |
797J 9 |
20281 |
55 |
|
6 |
76319 |
23681 |
78049 |
21951 |
79747 |
20253 |
64 |
|
7 |
76348 |
23C52 |
78077 |
21923 |
79776 |
20224 |
53 |
|
8 |
76377 |
23623 |
78106 |
21894 |
79804 |
20196 |
52 |
|
9 |
76406 |
23594 |
78135 |
.21865 |
. 79832 |
20168 |
51 |
|
10 |
9.76435 |
10.23565 |
9.78163 |
10.21837 |
9.79860 |
10.20140 |
50 |
|
11 |
76464 |
23536 |
78192 |
21808 |
79888 |
20112 |
49 |
|
12 |
76493 |
23507 |
78220 |
21780 |
79916 |
20084 |
48 |
|
13 |
76522 |
23478 |
78249 |
21751 |
79944 |
20056 |
47 |
|
14 |
76551 |
23449 |
78277 |
21723 |
79972 |
20028 |
46 |
|
15 |
76580 |
23420 |
78306 |
21694 |
80000 |
20000 |
45 |
|
16 |
76609 |
23391 |
78334 |
21666 |
80028 |
19972 |
44 |
|
17 |
76639 |
23361 |
78363 |
21637 |
80056 |
19944 |
43 |
|
18 |
76668 |
23332 |
78391 |
21609 |
80084 |
19916 |
42 |
|
13 |
76697 |
23303 |
78419 |
21581 |
80112 |
19888 |
41 |
|
20 |
9.76725 |
10.23275 |
9.78448 |
10.21552 |
9.80140 |
10.19860 |
40 |
|
21 |
76754 |
23246 |
78476 |
21524 |
80168 |
19832 |
39 |
|
22 |
76783 |
23217 |
78505 |
21495 |
80195 |
19805 |
38 |
|
23 |
76812 |
23188 |
78533 |
21467 |
80223 |
19777 |
87 |
|
24 |
76841 |
2M59 |
78562 |
21438 |
80251 |
19749 |
86 |
|
25 |
76870 |
23180 |
78590 |
21410 |
80279 |
19721 |
35 |
|
26 |
76899 |
23101 |
78618 |
21382 |
80307 |
19693 |
34 |
|
27 |
76928 |
23072 |
78647 |
21353 |
80335 |
19665 |
33 |
|
28 |
76957 |
23043 |
78675 |
21325 |
80363 |
19637 |
82 |
|
29 |
76986 |
23014 |
78704 |
21296 |
80391 |
19609 |
31 |
|
30 |
9.77015 |
10.22985 |
9.78732 |
10.21268 |
9.80419 |
10.19581 |
30 |
|
31 |
77044 |
22956 |
78760 |
21240 |
80447 |
19553 |
29 |
|
32 |
77073 |
22927 |
78789 |
21211 |
80474 |
19526 |
28 |
|
33 |
77101 |
22899 |
78817 |
21183 |
80502 |
19498 |
27 |
|
31 |
77130 |
22870 |
78845 |
21155 |
80530 |
19470 |
26 |
|
35 |
77159 |
22841 |
78874 |
21126 |
80558 |
19442 |
25 |
|
36 |
77188 |
22812 |
78902 |
21098 |
80586 |
19414 |
24 |
|
37 |
77217 |
22783 |
78930 |
21070 |
80614 |
19386 |
23 |
|
38 |
77246 |
22754 |
78959 |
21041 |
80642 |
19358 |
22 |
|
39 |
77274 |
22726 |
78987 |
21013 |
80669 |
19331 |
21 |
|
40 |
9.77303 |
10.22697 |
9.79015 |
10.20985 |
9.80697 |
10.19303 |
20 |
|
41 |
77332 |
22668 |
79043 |
20957 |
80725 |
19275 |
19 |
|
42 |
77361 |
22639 |
79072 |
20928 |
80753 |
19247 |
18 |
|
43 |
77390 |
22610 |
79100 |
20900 |
80781 |
19219 |
17 |
|
44 |
77418 |
22582 |
79128 |
20872 |
80808 |
19192 |
16 |
|
45 |
77447 |
22553 |
79156 |
20844 |
80836 |
19164 |
15 |
|
46 |
77476 |
22524 |
79185 |
20815 |
80864 |
19136 |
14 |
|
47 |
77505 |
22495 |
79213 |
20787 |
80892 |
19108 |
13 |
|
48 |
77533 |
22467 |
79241 |
20759 |
80919 |
19081 |
12 |
|
49 |
77562 |
22438 |
79269 |
20731 |
80947 |
19053 |
11 |
|
50 |
9.77591 |
10.22409 |
9.79297 |
10.20703 |
9.80975 |
10.19025 |
10 |
|
51 |
77619 |
22381 |
79326 |
20674 |
81003 |
18997 |
9 |
|
52 |
77648 |
22352 |
79354 |
20646 |
81030 |
18970 |
8 |
|
53 |
77677 |
22323 |
79382 |
20618 |
81058 |
18942 |
7 |
|
54 |
77706 |
22294 |
79410 |
20590 |
81086 |
18914 |
6 |
|
55 |
77734 |
22266 |
79438 |
20562 |
81113 |
18887 |
5 |
|
50 |
77763 |
22237 |
79466 |
20534 |
81141 |
18859 |
4 |
|
57 |
77791 |
22209 |
79495 |
20505 |
81169 |
18831 |
3 |
|
58 |
77820 |
22180 |
79523 |
20477 |
81196 |
18804 |
2 |
|
59 |
77849 |
22151 |
79551 |
20449 |
81224 |
18776 |
1 |
|
60 |
77877 |
22123 |
79579 |
20421 |
81252 |
18748 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
/ |
|
59° |
68° |
67° |
202 TABLE 9.— LOG. TANGENTS AND COTANGENTS.
|
/ |
83° |
84° |
85° |
||||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
o |
9.81252 |
10.18748 |
9.82899 |
. 10.17101 |
9.84523 |
10.15477 |
60 |
|
1 |
81279 |
18721 |
82926 |
17074 |
81550 |
15450 |
59 |
|
2 |
81307 |
18693 |
82953 |
17047 |
84576 |
15424 |
58 |
|
3 |
81335 |
18665 |
82980 |
17020 |
84603 |
15397 |
57 |
|
4 |
81362 |
18638 |
83008 |
16992 |
84630 |
15870 |
56 |
|
5 |
81390 |
18610 |
83035 |
16965 |
84657 |
15343 |
55 |
|
6 |
81418 |
18582 |
83063 |
16938 |
84684 |
15316 |
54 |
|
7 |
81445 |
18555 |
83089 |
16911 |
84711 |
15289 |
53 |
|
8 |
81473 |
18527 |
83117 |
16883 |
84738 |
15262 |
52 |
|
9 |
81500 |
18500 |
83144 |
16856 |
84764 |
15236 |
51 |
|
10 |
9.81528 |
10.18472 |
9.83171 |
10.168-29 |
9.84791 |
10.15209 |
50 |
|
11 |
81556 |
18444 |
83198 |
16802 |
84818 |
15182 |
49 |
|
12 |
81583 |
18417 |
83-225 |
16775 |
84845 |
15155 |
48 |
|
18 |
81611 |
18389 |
83252 |
16748 |
84872 |
15128 |
47 |
|
14 |
81638 |
18362 |
83280 |
16720 |
84899 |
15101 |
46 |
|
15 |
81666 |
18334 |
83307 |
16693 |
84925 |
15075 |
45 |
|
16 |
81693 |
18307 |
83334 |
16666 |
84952 |
15048 |
44 |
|
17 |
81721 |
18279 |
83361 |
16639 |
84979 |
15021 |
43 |
|
18 |
81748 |
18252 |
83388 |
16612 |
85006 |
14994 |
43 |
|
19 |
81776 |
18224 |
83415 |
16585 |
85033 |
14967 |
41 |
|
20 |
9.81803 |
10.18197 |
9.83142 |
10.16558 |
9.85059 |
10.14941 |
40 |
|
21 |
81831 |
18169 |
83470 |
16530 |
85086 |
14914 |
39 |
|
22 |
81858 |
18142 |
83497 |
16503 |
85113 |
14887 |
38 |
|
23 |
81886 |
18114 |
83524 |
16476 |
85140 |
14860 |
37 |
|
24 |
81913 |
18087 |
83551 |
16449 |
85166 |
14834 |
36 |
|
25 |
81941 |
18059 |
83578 |
16423 |
85193 |
14807 |
35 |
|
26 |
81968 |
18032 |
83605 |
16395 |
85220 |
14780 |
34 |
|
27 |
81996 |
18004 |
83632 |
16368 |
85247 |
14753 |
33 |
|
28 |
82023 |
17'977 |
83659 |
16341 |
85273 |
14737 |
3.' |
|
29 |
82051 |
17949 |
83686 |
16314 |
85300 |
14700 |
81 |
|
30 |
9.82078 |
10.17922 |
9.83713 |
10.16287 |
9.85327 |
10.14673 |
30 |
|
31 |
82106 |
17894 |
83740 |
16260 |
85354 |
14046 |
29 |
|
32 |
82133 |
178«7 |
83768 |
16232 |
85380 |
14620 |
*8 |
|
83 |
82161 |
17839 |
83795 |
16205 |
85407 |
14593 |
|
|
34 |
82188 |
17812 |
83822 |
16178 |
85434 |
145G6 |
2(j |
|
35 |
82215 |
17785 |
83849 |
16151 |
85460 |
14540 |
25 |
|
36 |
82243 |
17757 |
83876 |
16124 |
85487 |
14513 |
24 |
|
37 |
82270 |
17730 |
83903 |
16097 |
85514 |
14486 |
23 |
|
38 |
82298 |
17702 |
83930 |
16070 |
85540 |
14460 |
22 |
|
39 |
82325 |
17675 |
83957 |
16043 |
£5567 |
14433 |
21 |
|
40 |
9.82352 |
10.17648 |
9.83984 |
10.16016 |
9.85594 |
10.14406 |
20 |
|
41 |
82380 |
17620 |
84011 |
15989 |
85620 |
14380 |
19 |
|
42 |
82407 |
17593 |
84038 |
15962 |
85647 |
14353 |
18 |
|
43 |
82435 |
17565 |
84065 |
15935 |
85674 |
14326 |
17 |
|
44 |
82462 |
17538 |
8409-2 |
15908 |
85700 |
14300 |
16 |
|
45 |
82489 |
17511 |
84119 |
15881 |
85727 |
14273 |
15 |
|
46 |
82517 |
17483 |
84146 |
15854 |
85754 |
14246 |
14 |
|
47 |
82544 |
17456 |
84173 |
15827 |
85780 |
14220 |
18 |
|
48 |
82571 |
17429 |
84200 |
15800 |
85807 |
14193 |
13 |
|
49 |
82599 |
17401 |
84227 |
15773 |
85834 |
141C6 |
11 |
|
50 |
9.82626 |
10.17374 |
9.84254 |
10.15746 |
9.85860 |
10.14140 |
10 |
|
51 |
82653 |
17347 |
84280 |
15720 |
85887 |
14113 |
9 |
|
52 |
82681 |
17319 |
84307 |
15693 |
85913 |
14087 |
8 |
|
53 |
82708 |
17292 |
84334 |
15666 |
85940 |
14060 |
7 |
|
54 |
82735 |
. 17265 |
84361 |
15639 |
85967 |
14033 |
6 |
|
55 |
82762 |
17238 |
84388 |
15612 |
85993 |
14007 |
5 |
|
56 |
82790 |
17210 |
84415 |
15585 |
86020 |
13980 |
4 |
|
57 |
82817 |
17183 |
84443 |
15558 |
86046 |
13954 |
3 |
|
58 |
83844 |
17156 |
84469 |
15531 |
86073 |
13927 |
2 |
|
59 |
82871 |
17129 |
84496 |
15504 |
86100 |
13900 |
1 |
|
60 |
82899 |
17101 |
84523 |
15477 |
86126 |
13874 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
/ |
|
56° |
65° |
64° |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 203
|
/ |
80° |
87° |
88° |
/ |
|||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.86126 |
10.13874 |
9.87711 |
10.12289 |
9.89281 |
10.10-719 |
60 |
|
1 |
86153 |
13847 |
87738 |
12262 |
89307 |
10693 |
59 |
|
2 |
86179 |
13821 |
87764 |
12236 |
89333 |
10667 |
58 |
|
3 |
86206 |
13794 |
87790 |
12210 |
89359 |
10641 |
57 |
|
4 |
86232 |
13768 |
87817 |
12183 |
89385 |
10615 |
56 |
|
5 |
86259 |
13741 |
87843 |
12157 |
89411 |
10589 |
55 |
|
6 |
86285 |
13715 |
87869 |
12131 |
89437 |
10563 |
54 |
|
7 |
86312 |
13688 |
87895 |
12105 |
89463 |
10537 |
53 |
|
8 |
8633S |
13662 |
87922 |
12078 |
89489 |
10511 |
52 |
|
9 |
86365 |
13635 |
87948 |
12052 |
• 89515 |
10485 |
61 |
|
10 |
9.86392 |
10.13608 |
9.87974 |
10.12026 |
9.89541 |
10.10459 |
50 |
|
11 |
86418 |
13582 |
88000 |
12000 |
89567 |
10433 I 49 |
|
|
12 |
86445 |
13555 |
88027 |
11973 |
89593 |
10407 48 |
|
|
13 |
86471 |
13529 |
88053 |
11947 |
89619 |
10381 47 |
|
|
14 |
86498 |
13502 |
88079 |
11921 |
89645 |
10355 46 |
|
|
15 |
86524 |
13476 |
88105 |
11895 |
89671 |
10329 |
45 |
|
16 |
86551 |
13449 |
88J31 |
11869 |
89697 |
10303 |
44 |
|
17 |
86577 |
13423 |
88158 |
11842 |
89723 |
10277 |
43 |
|
18 |
86603 |
13397 |
88184 |
11816 |
89749 |
10251 |
42 |
|
19 |
86630 |
13370 |
88210 |
11790 |
89775 |
10225 |
41 |
|
20 |
9.86656 |
10.13344 |
9.88236 |
10.11764 |
9.89801 |
10.10199 |
40 |
|
21 |
. 86683 |
13317 |
88262 |
11738 |
89827 |
10173 |
39 |
|
22 |
86709 |
13291 |
88289 |
11711 |
89853 |
10147 |
38 |
|
23 |
86736 |
133£4 |
88315 |
11685 |
89879 |
10121 |
37 |
|
24 |
86762 |
13238 |
88341 |
11659 |
89905 |
10095 |
36 |
|
25 |
86789 |
13211 |
88367 |
11633 |
89931 |
10069 |
35 |
|
26 |
86815 |
13185 |
88393 |
11607 |
89957 |
10043 |
34 |
|
27 |
86842 |
13158 |
88420 |
11580 |
89983 |
10017 |
33 |
|
28 |
86868 |
13132 |
88446 |
11554 |
90009 |
09991 |
32 |
|
29 |
86894 |
13106 |
88472 |
11528 |
90035 |
09965 |
31 |
|
30 |
9.86921 |
10.13079 |
9.88498 |
10.11502 |
9.90061 |
10.09939 |
30 |
|
31 |
86947 |
13053 |
88524 |
11476 |
90086 |
09914 |
29 |
|
32 |
86974 |
13026 |
88550 |
11450 |
90112 |
09888 |
28 |
|
33 |
87000 |
13000 |
88577 |
11423 |
90138 |
09862 |
27 |
|
34 |
87027 |
12973 |
88603 |
11397 |
90164 |
09836 |
26 |
|
35 |
87053 |
12947 |
88629 |
11371 |
90190 |
09810 |
25 |
|
36 |
87079 |
12921 |
88655 |
11345 |
90216 |
09784 |
24 |
|
37 |
87106 |
12894 |
88681 |
11319 |
90242 |
09758 |
23 |
|
38 |
87132 |
12868 |
88707 |
11293 |
90268 |
09732 |
22 |
|
39 |
87158 |
12842 |
88733 |
11267 |
90294 |
09706 |
21 |
|
40 |
9.87185 |
10.12815 |
9.88759 |
10.11241 |
9.90320 |
10.09680 |
20 |
|
41 |
87211 |
12789 |
88786 |
11214 |
90346 |
09654 |
19 |
|
42 |
87238 |
12762 |
88812 |
11188 |
90371 |
09629 |
18 |
|
43 |
87264 |
12736 |
88838 |
11162 |
90397 |
09603 |
17 |
|
44 |
87290 |
12710 |
88864 |
11136 |
90423 |
09577 |
16 |
|
45 |
87317 |
12683 |
88890 |
11110 |
90449 |
09551 |
15 |
|
46 |
87343 |
12657 |
88916 |
11084 |
90475 |
09525 |
14 |
|
47 |
87369 |
12631 |
88942 |
11058 |
90501 |
09499 |
13 |
|
48 |
87396 |
12604 |
88968 |
11032 |
90527 |
09473 |
12 |
|
49 |
87422 |
12578 |
88994 |
11006 |
90553 |
09447 |
11 |
|
50 |
9.87448 |
10.12552 |
9.89020 |
10.10980 |
9.90578 |
10.09422 |
10 |
|
51 |
87475 |
12525 |
89046 |
10954 |
90604 |
09396 |
9 |
|
52 |
87501 |
12499 |
89073 |
10927 |
90630 |
09370 |
8 |
|
53 |
87527 |
12473 |
89099 |
10901 |
90656 |
09344 |
7 |
|
54 |
87554 |
12446 |
89125 |
10875 |
90682 |
09818 |
6 |
|
55 |
87580 |
12420 |
89151 |
10849 |
90708 |
09292 |
5 |
|
56 |
87606 |
12394 |
89177 |
10823 |
90734 |
09266 |
4 |
|
57 |
87633 |
12367 |
89203 |
10797 |
90759 |
09241 |
3 |
|
58 |
87659 |
12341 |
89229 |
10771 |
90785 |
09215 |
2 |
|
59 |
87685 |
12315 |
89255 |
10745 |
90811 |
09189 |
1 |
|
60 |
87711 |
12289 |
89281 |
10719 |
90837 |
09163 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
, |
|
63° |
62° |
61' |
204 TABLE 9.— LOG. TANGENTS AND COTANGENTS-
|
89° |
40° |
41° |
|||||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
o |
9.90837 |
10.09163 |
9.92381 |
10.07619 |
9.93916 |
10.06084 |
60 |
|
1 |
90863 |
09137 |
92407 |
07593 |
93942 |
06058 |
59 |
|
2 |
90889 |
09111 |
92433 |
07567 |
93967 |
06033 |
58 |
|
3 |
90914 |
09086 |
92458 |
07542 |
93993 |
06007 |
57 |
|
4 |
90940 |
09060 |
92484 |
07516 |
94018 |
05982 |
56 |
|
5 |
90966 |
09034 |
92510 |
07490 |
94044 |
05956 |
55 |
|
6 |
90992 |
09008 |
92535 |
07465 |
94069 |
05931 |
54 |
|
7 |
91018 |
08982 |
92561 |
07439 |
94095 |
05905 |
53 |
|
8 |
91043 |
08957 |
92587 |
07413 |
94120 |
05880 |
52 |
|
9 |
91069 |
08931 |
92612 |
07388 |
94146 |
05854 |
51 |
|
10 |
9.91095 |
10.08905 |
9.92638 |
10.07362 |
9.94171 |
10.05829 |
50 |
|
11 |
91121 |
08879 |
92663 |
07337 |
94197 |
05803 |
49 |
|
12 |
91147 |
08853 |
92689 |
07311 |
94222 |
05778 |
48 |
|
13 |
91172 |
08828 |
92715 |
07285 |
94248 |
05752 |
47 |
|
14 |
91198 |
08802 |
92740 |
07260 |
94273 |
05727 |
46 |
|
15 |
9J224 |
08776 |
92766 |
07234 |
94299 |
05701 |
45 |
|
16 |
91250 |
08750 |
92792 |
07208 |
94324 |
05676 |
44 |
|
17 |
91276 |
08724 |
92817 |
07183 |
94350 |
05650 |
43 |
|
18 |
91301 |
08699 |
92843 |
07157 |
94375 |
05625 |
42 |
|
19 |
91327 |
08673 |
92868 |
07132 |
94401 |
05599 |
41 |
|
20 |
9.91353 |
10.08647 |
9.92894 |
10.07106 |
9.94426 |
10.05574 |
40 |
|
21 |
91379 |
08621 |
92920 |
07080 |
94452 |
05548 |
39 |
|
22 |
91404 |
08596 |
92945 |
07055 |
94477 |
05523 |
38 |
|
23 |
91430 |
08570 |
92971 |
07029 |
94503 |
05497 |
37 |
|
24 |
91456 |
08544 |
92996 |
07004 |
94528 |
05472 |
36 |
|
25 |
9148,! |
08518 |
93022 |
06978 |
94554 |
05446 |
35 |
|
26 |
91507 |
08493 |
93048 |
06952 |
94579 |
05421 |
34 |
|
27 |
91533 |
08467 |
93073 |
06927 |
94604 |
05396 |
33 |
|
28 |
91559 |
08441 |
93099 |
06901 |
94G30 |
05370 |
32 |
|
29 |
91585 |
08415 |
93124 |
06876 |
94655 |
05345 |
3! |
|
30 |
9.91610 |
10.08390 |
9.93150 |
10.06850 |
9.94681 |
10.05319 |
30 |
|
31 |
91636 |
08364 |
93175 |
06825 |
94706 |
05294 |
29 |
|
33 |
91662 |
08338 |
93201 |
06799 |
94732 |
05268 |
28 |
|
33 |
91683 |
08312 |
93227 |
06773 |
94757 |
05243 |
27 |
|
34 |
91713 |
08287 |
93252 |
06748 |
94783 |
05217 |
26 |
|
35 |
91739 |
08261 |
93278 |
06722 |
94808 |
05192 |
25 |
|
36 |
91765 |
08235 |
93303 |
06697 |
94834 |
05166 |
24 |
|
37 |
91791 |
08209 |
93329 |
06671 |
94859 |
05141 |
23 |
|
38 |
91816 |
08184 |
93354 |
06646 |
94884 |
05116 |
22 |
|
39 |
91842 |
08158 |
93380 |
06620 |
94910 |
05090 |
21 |
|
40 |
9.91868 |
10.08132 |
9.93406 |
10.06594 |
9.94935 |
10.05065 |
20 |
|
41 |
91893 |
08107 |
93431 |
06569 |
94961 |
05039 |
19 |
|
4-4 |
91919 |
08081 |
93457 |
06543 |
94986 |
05014 |
18 |
|
43 |
91945 |
08055 |
93482 |
06518 |
95012 |
04988 |
17 |
|
44 |
91971 |
08029 |
93508 |
06492 |
95037 |
04963 |
16 |
|
45 |
91996 |
08004 |
93533 |
06467 |
95062 |
04938 |
15 |
|
46 |
92022 |
07978 |
93559 |
06441 |
95088 |
04912 |
14 |
|
47 |
92048 |
07952 |
93584 |
06416 |
95113 |
04887 |
13 |
|
48 |
92073 |
07927 |
93610 |
06390 |
95139 |
04861 |
12 |
|
49 |
92099 |
07901 |
93636 |
06364 |
95164 |
04836 |
11 |
|
50 |
9.92125 |
10.07875 |
9.93661 |
10.06339 |
9.95190 |
10.04810 |
10 |
|
51 |
92150 |
07850 |
93687 |
06318 |
95215 |
04785 |
9 |
|
52 |
92176 |
07824 |
93712 |
06288 |
95240 |
04760 |
8 |
|
53 |
92202 |
07798 |
93738 |
06262 |
95266 |
04734 |
7 |
|
54 |
92227 |
07773 |
93763 |
06237 |
95291 |
04709 |
6 |
|
55 |
92253 |
07747 |
93789 |
06211 |
95317 |
04683 |
5 |
|
56 |
92279 |
07721 |
93814 |
06186 |
95342 |
04658 |
4 |
|
57 |
92304 |
07696 |
93840 |
06160 |
95368 |
04632 |
3 |
|
58 |
92330 |
07670 |
93865 |
06135 |
95393 |
04607 |
0 |
|
59 |
92356 |
07644 |
93891 |
06109 |
95418 |
04582 |
1 |
|
60 |
92381 |
07619 |
93916 |
06084 |
95444 |
04556 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
, |
|
60* |
49° |
48° |
TABLE 9.— LOG. TANGENTS AND COTANGENTS. 205
|
42° |
43° |
440 |
|||||
|
Tan |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
||
|
0 |
9.95444 |
10.04556 |
9.96966 |
10.03034 |
9.98484 |
10.01516 |
60 |
|
1 |
95469 |
04531 |
96991 |
03009 |
98509 |
01491 |
59 |
|
2 |
95495 |
04505 |
97016 |
02984 |
98534 |
01466 |
58 |
|
3 |
95520 |
04480 |
97042 |
0-^958 |
98560 |
01440 |
57 |
|
4 |
95545 |
04455 |
97067 |
02933 |
98585 |
01415 |
56 |
|
5 |
95571 |
04429 |
97092 |
02908 |
98610 |
01390 |
55 |
|
6 |
95596 |
04404 |
97118 |
02882 |
98635 |
01365 |
54 |
|
95622 |
04378 |
97143 |
02857 |
98661 |
01339 |
53 |
|
|
8 |
95647 |
04353 |
97168 |
02832 |
98686 |
01314 |
52 |
|
9 |
95672 |
04328 |
97193 |
02807 |
98711 |
01289 |
51 |
|
10 |
9.95698 |
10.04302 |
9.97219 |
10.02781 |
9.98737 |
10.01263 |
50 |
|
11 |
95723 |
04277 |
97244 |
02756 |
98762 |
01238 |
49 |
|
12 |
95748 |
04252 |
97269 |
02731 |
98787 |
01213 |
48 |
|
13 |
95774 |
04226 |
97295 |
02705 |
98812 |
01188 |
47 |
|
14 |
95799 |
04201 |
97320 |
02680 |
98838 |
01162 |
46 |
|
15 |
95825 |
04175 |
97345 |
02655 |
98863 |
01137 |
45 |
|
16 |
95850 |
04150 |
97371 |
02629 |
98888 |
01112 |
44 |
|
1? |
95875 |
04125 |
97396 |
02604 |
98913 |
01087 |
43 |
|
18 |
95901 |
04099 |
97421 |
02579 |
98939 |
01061 |
42 |
|
19 |
95926 |
04074 |
97447 |
02553 |
98964 |
01086 |
41 |
|
20 |
9.95952 |
10.04048 |
9.97472 |
10.02508 |
9.98989 |
10.01011 |
40 |
|
21 |
95977 |
04023 |
97497 |
02503 |
99015 |
00985 |
39 |
|
22 |
96002 |
03998 |
97523 |
02477 |
99040 |
00960 |
38 |
|
28 |
96028 |
03972 |
97548 |
02452 |
99065 |
00935 |
37 |
|
24 |
96053 |
03947 |
97573 |
02427 |
99090 |
00910 |
36 |
|
25 |
96078 |
03922 |
97598 |
0^402 |
99116 |
008S4 |
35 |
|
26 |
96104 |
03896 |
97624 |
02376 |
99141 |
00859 |
34 |
|
27 |
96129 |
03871 |
97649 |
02351 |
99166 |
00834 |
33 |
|
28 |
96155 |
03845 |
97674 |
02326 |
99191 |
00809 |
82 |
|
29 |
96180 |
03820 |
97700 |
02300 |
99217 |
00783 |
31 |
|
30 |
9.96205 |
10.03795 |
9.97725 |
10.02275 |
9.99242 |
10.00758 |
30 |
|
31 |
96231 |
03769 |
97750 |
02250 |
99267 |
00733 |
29 |
|
32 |
96256 |
03744 |
97776 |
02224 |
99293 |
00707 |
28 |
|
33 |
96281 |
03719 |
97801 |
02199 |
99318 |
00682 |
27 |
|
34 |
96307 |
03693 |
97826 |
02174 |
99343 |
00657 |
26 |
|
35 |
96332 |
03668 |
97851 |
02149 |
99368 |
00632 |
25 |
|
36 |
96357 |
03643 |
97877 |
02123 |
59394 |
00606 |
24 |
|
37 |
96383 |
03617 |
97902 |
02098 |
99419 |
00581 |
23 |
|
38 |
96408 |
0359-2 |
97927 |
02073 |
99444 |
00556 |
22 |
|
39 |
96433 |
03567 |
97953 |
0^047 |
99469 |
00531 |
21 |
|
40 |
9.96459 |
10.03541 |
9.97978 |
10.02022 |
9.99495 |
10.00505 |
20 |
|
41 |
96484 |
03516 |
9b003 |
01997 |
99520 |
00480 |
19 |
|
42 |
96510 |
03490 |
98029 |
01971 |
99545 |
00455 |
18 |
|
43 |
96535 |
03465 |
98054 |
C1946 |
99570 |
00430 |
17 |
|
44 |
96560 |
03440 |
98079 |
01921 |
99596 |
00404 |
16 |
|
45 |
965S6 |
03414 |
98104 |
01896 |
99621 |
00379 |
15 |
|
46 |
96611 |
03389 |
98130 |
01870 |
99646 |
00354 |
14 |
|
47 |
96636 |
03364 |
98155 |
01845 |
99672 |
00328 |
13 |
|
48 |
96662 |
03338 |
98180 |
01880 |
99697 |
00303 |
12 |
|
49 |
96687 |
03313 |
98206 |
01794 |
99722 |
00278 |
11 |
|
50 |
9.96712 |
10.03288 |
9.98231 |
10.01769 |
9.99747 |
10.00253 |
10 |
|
51 |
96738 |
03262 |
98256 |
01744 |
99773 |
00227 |
9 |
|
52 |
96763 |
03237 |
98281 |
01719 |
99798 |
00202 |
8 |
|
53 |
96788 |
03212 |
98307 |
01693 |
99823 |
00177 |
7 |
|
54 |
96814 |
03186 |
98332 |
01668 |
99848 |
00152 |
6 |
|
55 |
96839 |
03161 |
98357 |
01643 |
99874 |
00126 |
5 |
|
W |
96864 |
03136 |
98383 |
01617 |
99899 |
00101 |
4 |
|
57 |
96890 |
03110 |
98408 |
01592 |
99924 |
00076 |
3 |
|
58 |
06915 |
03085 |
98433 |
01567 |
99949 |
00051 |
2 |
|
59 |
96940 |
03060 |
98458 |
01542 |
99975 |
00025 |
1 |
|
60 |
96966 |
03034 |
98484 |
01516 |
10.00000 |
00000 |
0 |
|
/ |
Cotan |
Tan |
Cotan |
Tan |
Cotan |
Tan |
, |
|
47° |
*«° |
45<> I |
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS.
|
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t |
|
|
o 2 3 4 |
.00000 .00029 .00058 .00087 .00116 |
One One One One One |
.00000 .00029 .00058 .00087 .00116 |
Infinite 3437-75 1718.87 1145.92 809.436 |
.01745 .01774 .01803 .01832 .01862 |
.99985 -99984 .99984 .99983 .99983 |
.01746 .01775 .01804 .01833 .01862 |
57.2900 56.3506 55-4415 54-5613 53-7086 |
60 59 58 57 56 |
|
5 6 8 g |
.00145 .00175 .00204 .00233 .00262 |
One One One One One |
.00145 .00175 .00204 .00233 .00262 |
687-549 572-957 491.106 429.718 381.971 |
.01891 .01920 .01949 .01978 .02007 |
.99982 .99982 .99981 .99980 .99980 |
.01891 .01920 .01949 .01978 .02007 |
52.8821 52-0807 51-3032 50.5485 49.8157 |
55 54 53 52 51 |
|
_£ — 10 11 12 13 14 |
.00291 .00320 .00349 .00378 .00407 |
One .99999 .99999 .99999 .99999 |
.00291 .00320 .00349 .00378 .00407 |
343-774 312-521 286.478 264.441 245.552 |
.02036 .02065 .02094 .02123 .02152 |
.99979 .99979 .99978 .99977 .99977 |
.02036 .02066 .02095 .02124 .02153 |
49*1039 48-4121 47.7395 47.0853 46.4489 |
5O 49 48 47 46 |
|
15 16 17 18 19 |
.00436 .00465 .00495 .00524 .00553 |
.99999 .99999 .99999 .99999 .99998 |
.00436 .00465 .00495 .00524 .00553 |
229-182 214.858 202-219 190-984 180-932 |
.02131 .02211 .02240 .02269 .02298 |
.99976 -99976 .99975 -99974 -99974 |
.02182 .02211 .02240 .02269 .02298 |
45-8294 45-2261 44-6386 44-0661 43-5081 |
45 44 43 42 41 |
|
20 21 22 23 24 |
.00582 .00611 .00640 .00669 .00698 |
.99998 .99998 .99998 .99998 .99998 |
.00582 .00611 .00640 .00669 .00698 |
171-885 163-700 156-259 149-465 143-237 |
.02327 .02356 .02385 .02414 .02443 |
.99973 .99972 .99972 .99971 .99970 |
.02328 .02357 .02386 .02415 .02444 |
42-9641 42-4335 41.9158 41.4106 40.9174 |
4O 39 38 37 36 |
|
25 26 27 28 29 |
.00727 .00756 $0785 .00814 .00844 |
.99997 .99997 .99997 .99997 .99996 |
.00727 .00756 .00785 .00815 .00844 |
137.507 132-219 127-321 122.774 118.540 |
.02472 .02501 .02530 .02560 .02589 |
.99969 .99969 .99968 .99967 .99966 |
.02473 .02502 .02531 .02560 .02589 |
40.4358 39-9655 39.5059 39.0568 38-6177 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.00873 .00902 .00931 .00960 .00989 |
.99998 .99996 .99996 .99995 .99995 |
.00873 .00902 .00931 .00960 .00989 |
114-589 110.892 107.426 104.171 101.107 |
.02618 .02647 .02676 .02705 .02734 |
.99966 .99965 .99964 .99963 -99963 |
.02619 .02648 .02677 .02706 .02735 |
38-1885 37-7686 37.3579 36.9560 36.5627 |
30 29 28 27 26 |
|
35 36 87 38 39 |
.01018 .01047 .01076 .01105 .01134 |
.99995 .99995 .99994 .99994 .99994 |
.01018 .01047 .01076 .01105 .01135 |
98-2179 95.4895 92-9085 90.4633 88-1436 |
.02763 .02792 .02821 .02850 .02879 |
.99962 .99961 .99960 .99959 .99959 |
.02764 -02793 .02822 .02851 .02881 |
36.1776 35-8006 35.4313 35-C695 34-7151 |
25 24 23 22 -21 |
|
40 41 42 43 44 |
.01164 .01193 .01222- .01251 .01280 |
.99993 .99993 .99993 .99992 .99992 |
.01164 .01193 .01222 .01251 .01280 |
85-9398 83-8435 8L8470 79.9434 78.1263 |
•02908 •02938 •02967 •02996 .03025 |
-99958 -99957 -99956 .99955 .99954 |
•02910 -02939 .02968 .02997 .03026 |
34-3678 34.0273 33-6935 33-3662 33-0452 |
20 19 18 17 .18 |
|
45 46 47 48 49 |
.01309 .01338 .01367 .01396 •01425 |
.99991 .99991 .99991 .99990 .99990 |
•01309 .01338 .01367 .01396 .01425 |
76-3900 74.7292 73-1390 71-6151 70-1533 |
•03054 .03083 •03112 -03141 .03170 |
.99953 .99952 .99952 .99951 .99950 |
.03055 -03084 .03114 -03143 .03172 |
32-7303 32-4213 32-1181 31-8205 31-5234 |
15 14 13 12 .11 |
|
50 51 52 53 54 |
.01454 •01483 •01513 .01542 .01571 |
.99989 .99989 .99989 .99988 .99988 |
.01455 .01484 .01513 .01542 .01571 |
68.7501 67.4019 66.1055 64-8580 63.6567 |
.03199 -03228 .03257 .03286 .03316 |
.99949 .99948 .99947 .99946 .99945 |
.03201 .03230 -03259 .03288 .03317 |
31.2416 30-9599 30-6833 30.4116 30-1446 |
10 9 8 7 6 |
|
55 56 57 58 59 |
.01600 •01629 .01658 •01687 .01716 |
.99987 .99987 .99986 .99986 .99985 |
.01600 .01629 .01658 .01687 .01716 |
62.4992 61.3829 60-3058 59.2659 58.2612 |
.03345 -03374 .03403 .03432 -03461 |
.99944 .99943 .99942 .99941 .99940 |
-03346 .03376 .03405 .03434 -03463 |
29.8823 29.6245 29.3711 29-1220 28.8771 |
5 4 3 2 1 |
|
60 |
.01745 |
.99985 |
.01746 |
57-2900 |
-03490 |
.99939 |
.03492 |
28-6363 |
-° |
|
/ |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
|
|
1 |
19° |
2( |
)6 |
€ |
18° |
Inserted by permission from Webb's Railroad Construction.
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 2° 3°
|
1 |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t |
|
0 2 3 |
03490 03519 03548 03577 03606 |
99939 .99938 .99937 .99936 .99935 |
03492 03521 03550 03579 03609 |
28-6363 28-3994 28.1664 27-9372 27-7117 |
05234 05263 05292 05321 05350 |
99863 99861 99860 99858 99857 |
05241 05270 05299 05328 05357 |
19-0511 18-9755 18-8711 18-7678 18.6656 |
60 59 58 57 58 |
|
~5~ 6 7 8 g |
03635 03664 03693 03723 03752 |
.99934 .99933 .99932 .99931 .99930 |
03638 03667 03696 03725 03754 |
27-4899 27-2715 27-0566 26.8450 26-6367 |
05379 05408 05437 05466 05495 |
99855 99854 99852 99851 99849 |
.05387 .05416 .05445 .05474 .05503 |
18-5645 18-4645 18.3655 18-2677 18-1708 |
55 54 53 52 _51 |
|
10 11 12 13 14 |
03781 03810 03839 03868 03897 |
.99929 .99927 99926 99925 99924 |
03783 03812 03842 03871 03900 |
26.4316 26-2296 26-0307 25.8348 25-6418 |
05524 05553 05582 05611 05640 |
99847 99846 99844 99842 99841 |
.05533 .05562 .05591 .05620 .05649 |
18-0750 17-9802 17.8863 17-7934 17-7015 |
50 49 48 47 48 |
|
15~ 16 17 18 19 |
03926 03955 03984 04013 04042 |
99923 99922 99921 99919 99918 |
03929 03958 03987 04016 04046 |
25.4517 25-2644 25.0798 24-8978 24-7185 |
05669 05698 .05727 .05756 .05785 |
99839 99838 99836 99834 99ff33 |
.05678 .05708 .05737 .05766 .05795 |
17.6108 17.5205 17-4314 17-3432 17-2558 |
45 44 43 42 -M |
|
20 21 22 23 24 |
04071 .04100 .04129 .04159 .04188 |
99917 99916 99915 99913 99912 |
04075 04104 04133 04162 04191 |
24-5418 24.3675 24.1957 24-0263 23-8593 |
.05814 .05844 .05873 .05902 .05931 |
99831 99829 99827 .99826 .99824 |
.05824 .05854 .05883 .05912 -05941 |
17-1693 17-0837 16-9990 16-9150 16-8319 |
40 39 38 37 _38 |
|
25~ 28 27 28 29 |
.04217 .04246 .04275 .04304 .04333 |
99911 99910 .99909 .99907 .99906 |
04220 04250 04279 04308 04337 |
23.6945 23-5321 23-3718 23-2137 23-0577 |
.05960 .05989 .06018 .06047 .06076 |
.99822 .99821 .99819 .99817 .99815 |
.05970 .05999 .06029 .06058 .06087 |
16.7498 16-6681 16-5874 16-5075 16-4283 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.04362 .04391 .04420 .04449 .04478 |
.99905 .99904 .99902 .99901 .99900 |
04366 .04395 .04424 .04454 .04483 |
22-9038 22.7519 22-6020 22-4541 22-3081 |
.06105 .06134 .06163 .06192 .06221 |
.99813 .99812 .99810 .99808 .99806 |
.06116 .06145 -06175 -06204 .06233 |
16-3499 16-2722 16-1952 18.1190 16-0435 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.04507 .04536 .04565 .04594 .04623 |
.99898 .99897 .99896 .99894 .99893 |
.04512 .04541 .04570 .04599 .04628 |
22-1640 22-0217 21-8813 21-7426 21-6056 |
.06250 .06279 .06308 .06337 .06366 |
.99804 .99803 .99801 .99799 .99797 |
-06262 .06291 .06321 .06350 .06379 |
15-9687 15-8945 15-8211 15-7483 15-6762 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.04653 .04682 .04711 .04740 .04769 |
.99892 .99890 .99889 .99888 ,99886 |
.04658 .04687 .04716 .04745 •04774 |
21-4704 21-3369 21-2049 21-0747 20-9460 |
.06395 .06424 .06453 .06482 .06511 |
.99795 .99793 .99792 .99790 .99788 |
.06408 .06437 .06467 .06496 .06525 |
15-6048 15-5340 15-4638 15-3943 15-3254 |
20 19 18 17 18 |
|
45 46 47 48 49 |
.04798 •04827 .04856 .04885 .04914 |
.99885 .99883 .99882 •99881 .99879 |
.04803 .04833 04862 •04891 .04920 |
20-8188 20-6932 20-5691 20-4465 20-3253 |
.06540 .06569 .06598 .06627 •06656 |
.99786 .99784 .99782 .99780 .99778 |
.06554 .06584 .06613 .06642 .06671 |
15-2571 15-1893 15-1222 15-0557 14-9898 |
Ib 14 13 12 11 |
|
50 51 52 53 54 |
.04943 .04972 .05001 .05030 .05059 |
.99878 .99876 .99875 .99873 .99872 |
.04949 .04978 .05007 .05037 .05066 |
20-2056 20-0872 19-9702 19-8546 19-7403 |
.06685 -06714 -06743 .06773 .06802 |
.99776 .99774 .99772 .99770 .99768 |
.06700 .06730 .06759 .06788 .06817 |
14-9244 14-8596 14-7954 14.7317 14-6685 |
1O 9 8 7 8 |
|
55 56 67 68 59 |
.05088 .05117 .05146 .05175 .05205 |
.99870 .99869 .99867 .99866 .99864 |
.05095 .05124 .05153 .05182 .05212 |
19-6273 19-5156 19-4051 19-2959 19-1879 |
.06831 .06860 .06889 .06918 .06947 |
.99766 .99764 .99762 .99760 .99758 |
.06847 .06876 .06905 .06934 .06963_ |
14.6059 14-5438 14-4823 14-4212 14-3607 |
5 3 2 |
|
60 |
.05234 |
.99863 |
.05241 |
19-0811 |
.06976 |
.99756 |
.06993 |
14-3007 |
0 |
|
/ |
Cos. |
Sin. |
Cot. |
an. |
Cos. |
Sin. |
Cot. |
Tan. |
|
|
* |
>7° |
207 |
86° |
TABLE 10.— NATURAL SINES, COSINES, TANGENTS. AND COTANGENT&
4° 5°
|
1 |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
' |
|
0 2 3 4 |
.06976 .07005 .07034 .07063 .07092 |
.99756 .99754 .99752 .99750 .99748 |
.06993 .07022 .07051 .07080 .07110 |
14.3007 14.2411 14-1821 14.1235 14.0655 |
.08716 .08745 .08774 .08803 .08831 |
99619 .99617 .99614 -99612 -99609 |
08749 08778 08807 .08837 .08866 |
11.4301 11.3919 11.3540 11.3163 11.2789 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.07121 .07150 .07179 .07208 .07237 |
.99746 .99744 .99742 .99740 .99738 |
.07139 .07168 .07197 .07227 .07256 |
14-0079 13.9507 13.8940 13-8378 13.7821 |
.08860 .08889 .08918 .08947 .08976 |
-99607 -99604 .99602 .99599 -99596 |
.08895 -08925 -08954 .08983 .09013 |
11.2417 11.2048 11.1681 11.1316 11.0954 |
55 54 53 52 51 |
|
10 11 12 13 ,14 |
.07266 .07295 .07324 .07353 .07382 |
.99736 .99734 .99731 .99729 .99727 |
.07285 .07314 .07344 .07373 .07402 |
13.7267 13-6719 13.6174 13.5634 13.5098 |
.09005 .09034 .09063 .09092 .09121 |
.99594 .99591 .99588 -99586 .99583 |
-09042 .09071 -09101 .09130 .09159 |
11.0594 11.0237 10-9882 10-9529 10.9178 |
50 49 48 47 4B |
|
15 16 17 18 19 |
.07411 .07440 .07469 .07498 .07527 |
.99725 .99723 .99721 .99719 .99716 |
.07431 .07461 .07490 .07519 .07548 |
13-4566 13.4039 13.3515 13-2996 13-2480 |
-09150 .09179 .09208 .09237 .09266 |
.99580 .99578 .9C575 .9&S72 .99570 |
.09189 .09218 .09247 .09277 .09306 |
10-8829 10-8483 10-8139 10-7797 10-7457 |
45 44 43 42 41 |
|
20 21 22 23 24 |
.07556 .07585 .07614 .07643 .07672 |
.99714 .99712 .99710 .99708 .99705 |
.07578 .07607 .07636 .07665 .07695 |
13.1969 13-1461 13-0958 13.0458 12-9962 |
.09295 .09324 .09353 .09382 .09411 |
.99567 .99564 .99562 .99559 .99556 |
.09335 .09365 .09394 -09423 -09453 |
10-7119 10.6783 10.6450 10-6118 10-5789 |
40 39 38 37 36 |
|
25 26 27 28 29 |
•07701 .07730 .07759 .07788 .07817 |
.99703 .99701 .99699 .99696 .99694 |
.07724 .07753 .07782 .07812 .07841 |
12-9469 12-8981 12.8496 12.8014 12.7536 |
.09440 -09469 -09498 .09527 .09556 |
.99553 .99551 .99548 .99545 .99542 |
.09482 .09511 .09541 .09570 .09600 |
10-5462 10-5136 10.4813 10-4491 10-4172 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.07846 .07875 .07904 .07933 .07962 |
.99692 .99689 .99687 .99685 .99683 |
.07870 .07899 .07929 .07958 .07987 |
12.7062 12.6591 12-6124 12.5660 12.5199 |
•09585 .09614 .09642 .09671 .09700 |
.99540 -99537 -99534 -99531 -99528 |
-09629 .09658 .09688 .09717 .09746 |
10-3854 10-3538 10-3224 10.2913 10.2602 |
30 29 28 27 26 |
|
35 36 87 38 89 |
.07991 .08020 .08049 .08078 .08107 |
.99680 .99678 .99676 .99673 .99671 |
.08017 .08046 .08075 .08104 .08134 |
12.4742 12.4288 12-3838 12.3390 12-2946 |
.09729 -09758 .09787 .09816 .09845 |
-99526 .99523 .99520 .99517 .99514 |
-09776 .09805 •09834 .09864 .09893 |
10.2294 10-1988 10.1683 i0.1381 10.1080 |
25 24 23 22 ,.21 |
|
40 41 42 43 44 |
.08136 .08165 .08194 .08223 .08252 |
.99668 .99666 .99664 .99661 .99659 |
•08163 .08192 .08221 .08251 .08280 |
12-2505 12.2067 12.1632 12.1201 12.0772 |
.09874 .09903 .09932 •09961 .09990 |
•99511 •99508 .99506 .99503 .99500 |
.09923 .09952 .09981 .10011 .10040 |
10-0780 10-0483 10-0187 9-98931 9.96007 |
20 19 18 17 16 |
|
45 46 47 48 49 |
•08281 .08310 .08339 .08368 .08397 |
.99657 .99654 .99652 .99649 .99647 |
.08309 .08339 .08368 .08397 .08427 |
12.0346 11.9923 11.9504 11-9087 11-8673 |
-10019 .10048 -10077 .10106 .10135 |
.99497 .99494 .99491 .99488 .99485 |
.10069 .10099 .10128 .10158 -10187 |
9-93101 9-90211 9-87338 9 • 84482 9.81641 |
15 14 13 12 _!! |
|
50 51 52 53 54 |
.08426 .08455 .08484 .08513 .08542 |
.99644 .99642 .99639 .99637 .99635 |
.08456 .08485 .08514 .08544 .08573 |
11.8262 11.7853 11.7448 11.7045 11.6645 |
-10164 -10192 -10221 .10250 .10279 |
-99482 -99479 .99476 .99473 .99470 |
.10216 -10246 -10275 .10305 .10334 |
9-78817 9-76009 9-73217 9.70441 9-67680 |
10 9 8 7 6 |
|
55 56 57 58 59 |
.08571 .08600 .08629 .08658 .08687 |
.99632 .99630 .99627 .99625 .99622 |
.08602 .08632 .08661 .08690 .08720 |
11.6248 11.5853 11.5461 11.5072 11.4685 |
.10308 .10337 .10366 .10395 .10424 |
.99467 -99464 .99461 -99458 -99455 |
.10363 .10393 .10422 •10452 .10481 |
9.64935 9-62205 9.59490 9-56791 9-54106 |
5 4 3 2 |
|
60 |
.08716 |
.99619 |
.08749 |
11-4301 |
.10453 |
•99452 |
.10510 |
9.51436 |
O |
|
1 / |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
86°
208
84°
TABLE 10 —NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 6° 7°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t |
|
o 1 2 3 |
10453 10482 10511 10540 10569 |
.99452 .99449 .99446 .99443 .99440 |
10510 10540 10569 10599 10628 |
9.51436 9.48781 9.46141 9.43515 9.40904 |
12187 12216 12245 12274 12302 |
99255 99251 99248 99244 99240 |
12278 12308 .12338 .12367 .12397 |
8.14435 8.12481 8.10536 8.08600 8.06674 |
60 59 58 57 56 |
|
5 6 7 8 9 |
10597 10626 10655 .10684 .10713 |
.99437 .99434 .99431 .99428 .99424 |
10657 .10687 .10716 .10746 .10775 |
9.38307 9.35724 9.33155 9.30599 9.28058 |
.12331 .12360 •12389 .12418 .12447 |
99237 .99233 .99230 .99226 •99222 |
•12426 •12456 .12485 .12515 .12544 |
8-04756 8.02848 8.00948 7.99058 7-97176 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.10742 .10771 .10800 .10829 .10858 |
.99421 .99418 .99415 .99412 .99409 |
.10805 .10834 .10863 .10893 .10922 |
9-25530 9.23016 9-20516 9.18028 9-15554 |
.12476 .12504 .12533 .12562 .12591 |
.99219 •99215 .99211 .99208 .99204 |
.12574 .12603 .12633 .12662 .12692 |
7.95302 7-93438 7-91582 7-89734 7-87895 |
50 49 48 47 46 |
|
15 16 17 18 19 |
.10887 .10916 .10945 .10973 .11002 |
.99406 .99402 .99399 .99396 .99393 |
.10952 .10981 .11011 .11040 .11070 |
9.13093 9-10646 9.08211 9.05789 9-03379 |
.12620 .12649 .12678 .12706 .12735 |
.99200 .99197 .99193 .99189 .99186 |
.12722 .12751 .12781 .12810 .12840 |
7-86064 7-84242 7-82428 7-80622 7.78825 |
45 44 43 42 -il |
|
2O 21 22 23 24 |
.11031 .11060 .11089 -11118 .11147 |
.99390 .99386 .99383 .99380 .99377 |
.11099 .11128 .11158 .11187 .11217 |
9.00983 8-98598 8-96227 8.93867 8.91520 |
.12764 .12793 .12822 .12851 .12880 |
.99182 .99178 •99175 .99171 .99167 |
.12869 .12899 .12929 .12958 .12988 |
7-77035 7-75254 7-73480 7.71715 7.69957 |
40 39 38 37 36 |
|
25 26 £7 28 29 |
.11176 •11205 11234 .11263 .11291 |
.99374 .99370 .99367 .99364 .99360 |
-11246 •11276 .11305 .11335 .11364 |
8-89185 8-86862 8.84551 8-82252 8-79964 |
.12908 .12937 .12966 .12995 .13024 |
•99163 -99160 •99156 .99152 .99148 |
.13017 .13047 .13076 .13106 .13136 |
7.68208 7.66466 7.64732 7.63005 7.61287 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.11320 •11349 .11378 •11407 .11436 |
.99357 .99354 .99351 -99347 .99344 |
.11394 .11423 .11452 .11482 .11511 |
8-77689 8-75425 8-73172 8-70931 8.68701 |
.13053 .13081 .13110 .13139 .13168 |
.99144 .99141 .99137 .99133 .99129 |
.13165 .13195 .13224 .13254 .13284 |
7-59575 7-57872 7-56176 7-54487 7-52806 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.11465 .11494 .11523 .11552 •11580 |
.99341 .99337 .99334 .99331 .99327 |
.11541 .11570 .11600 .11629 .11659 |
8.66482 8-64275 8.- 62078 8.59893 8.57718 |
•13197 .13226 .13254 .13283 .13312 |
.99125 .99122 .99118 .99114 •99110 |
.13313 .13343 .13372 .13402 .13432 |
7.51132 7-49465 7-47806 7-46154 7-44509 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.11609 •11638 11667 .11698 .11725 |
.99324 .99320 .99317 .99314 .99310 |
.11688 .11718 .11747 .11777 .11806 |
8-55555 8-53402 8.51259 8-49128 8-47007 |
•13341 .13370 .13399 .13427 .13456 |
.99106 .90102 .99098 .99094 .99091 |
.13461 .13491 .13521 .13550 .13580 |
7-42871 7-41240 7-39616 7-37999 7-36389 |
20 19 18 17 18 |
|
45 46 47 48 49 |
.11754 .11783 .11812 •11840 .11869 |
.99307 .99303 .99300 •99297 .99293 |
.11836 .11865 .11895 .11924 •11954 |
8-44896 8-42795 8-40705 8-38625 8-36555 |
.13485 •13514 .13543 .13572 .13600 |
.99087 .99083 .99079 .99075 .99071 |
.13609 .13639 .13669 .13698 .13728 |
7-34786 7-33190 7-31600 7-30018 7-28442 |
15 14 13 12 11 |
|
50 51 52 53 54 |
.11898 .11927 .11956 .11985 .12014 |
.99290 .99286 .99283 •99279 .99276 |
.11983 =12013 .12042 •12072 .12101 |
8.34496 8.32446 8-30406 8-28376 8.26355 |
.13629 .13658 •13687 .13716 .13744 |
.99067 .99063 .99059 .99055 .99051 |
.13758 •13787 .13817 .13846 .13876 |
7-26873 7-25310 7-23754 7-22204 7-20661 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•12043 •12071 .12100 .12129 .12158 |
.99272 .99269 .99265 •99262 .99258 |
.12131 .12160 .12190 •12219 •12249 |
8.24345 8-22344 8.20352 8.18370 8.16398 |
.13773 .13802 .13831 .13860 .13889 |
.99047 .99043 .99039 •99035 .99031 |
.13906 .13935 .13965 .13995 .14024 |
7-19125 7-17594 7-16071 7-14553 7-13042 |
5 3 2 |
|
60 |
.12187 |
.99255 |
.12278 |
8.14435 |
.13917 |
.99027 |
.14054 |
7-11537 |
0 |
|
1 |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
/ |
S3?
209
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 8° 9°
|
t |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t 60 59 58 57 56 55 54 53 52 51 |
|
0 2 3 4 5 6 7 8 9 10 11 12 13 LL 15 16 17 18 !2_ 20 21 22 23 24 25 26 27 28 29 |
.13917 •13946 •13975 •14004 .14033 |
•99027 .99023 .99019 .99015 .99011 |
.14054 .14084 .14113 .14143 .14173 |
7.11537 7-10038 7-08546 7-07059 7-05579 |
.15643 .15672 .15701 .15730 .15758 |
.98769 .98764 .98760 .98755 .98751 |
.15838 .15868 .15898 .15928 .15958 |
6.31375 6.30189 6-29007 6.27829 6.26655 |
|
|
.14061 .14090 .14119 .14148 .14177 |
.99006 .99002 .98998 .98994 .98990 |
.14202 .14232 .14262 .14291 .14321 |
7-04105 7-02637 7.01174 6-99718 6-98268 |
-15787 •15816 .15845 •15873 •15902 |
.98746 •98741 .98737 •98732 .98728 |
.15988 .16017 .16047 .16077 .16107 |
6-25488 6.24321 6-23160 6-22003 6-20851 |
||
|
.14205 .14234 .14263 .14292 .14320 |
.98986 .98982 .98978 .98973 .98969 |
.14351 .14381 .14410 . 14440 .14470 |
6-96823 6-95385 6-93952 6-92525 6-91104 |
-15931 .15959 .15988 .16017 -16046 |
•98723 .98718 .98714 .98709 .98704 |
.16137 .16167 .16196 .16226 .16256 |
6.19703 6-18559 6.17419 6.16283 6-15151 |
5O 49 48 47 _46 45 44 43 42 -il 40 39 38 37 36 35 34 33 32 31 |
|
|
.14349 .14378 .14407 .14436 . 14464 |
.98965 .98961 .98957 .98953 .98948 |
.14499 .14529 .14559 .14588 .14618 |
6.89688 6-88278 6-86874 6-85475 6-84082 |
.16074 .16103 .16132 .16160 .16189 |
.98700 •98695 -98690 -98686 .98681 |
.16286 -16316 .16346 -16376 -16405 |
6.14023 6.12899 6.11779 6.10664 6-09552 |
||
|
.14493 •14522 .14551 .14580 .14608 |
.98944 .98940 .98936 .98931 .98927 |
.14648 .14678 .14707 .14737 .14767 |
6.82694 6-81312 6-79936 6-78564 6-77199 |
.16218 .16246 .16275 .16304 .16333 |
.98676 .98671 .98667 .98662 .98657 |
.16435 .16465 .16495 .16525 .16555 |
6.08444 6.07340 6-06240 6.05143 6-04051 |
||
|
.14637 .14666 .14695 .14723 .14752 |
.98923 .98919 .98914 .98910 .98906 |
.14796 .14826 .14856 .14886 .14915 |
6.75838 6-74483 6-73133 6-71789 6-70450 |
.16361 .16390 .16419 .16447 .16476 |
.98652 .98648 -98643 .98638 -98633 |
.16585 .16615 .16645 .16674 .16704 |
6.02962 6.01878 6-00797 5.99720 5.98646 |
||
|
30 31 32 33 34_ 35 36 37 38 39_ 40 41 42 43 44 |
.14781 .14810 .14838 .14867 .14896 |
.98902 .98897 .98893 .98889 .98884 |
.14945 .14975 .15005 .15034 .15064 |
6.69116 6-67787 6-66463 6-65144 6.63831 |
.16505 .16533 .16562 .16591 .16620 |
-98629 .98624 .98619 .98614 .98609 |
.16734 -16764 .16794 -16824 .16854 |
5-97576 5-96510 5.95448 5.94390 5-93335 |
30 29 28 27 26 25 24 23 22 21 |
|
.14925 .14954 .14982 .15011 .15040 |
.98880 .98876 .98871 .98867 .98863 |
.15094 •15124 .15153 .15183 .15213 |
6-62523 6.61219 6-59921 6-58627 6.57339 |
.16648 .16677 .16706 -16734 -16763 |
.98604 .98600 .98595 .98590 .98585 |
.16884 .16914 .16944 .16974 .17004 |
5.92283 5.91236 5.90191 5.89151 5.88114 |
||
|
.15069 •15097 .15126 .15155 .15184 |
.98858 .98854 .98849 .98845 .98841 |
•15243 .15272 .15302 .15332 .15362 |
6.56055 6.54777 6.53503 6.52234 6.50970 |
.16792 .16820 .16849 .16878 -16906 |
.98580 .98575 .98570 .98565 -98561 |
.17033 .17063 .17093 -17123 .17153 |
5.87080 5-86051 5-85024 5-84001 5.82982 |
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 3 2 -0 |
|
|
45 46 47 48 49 |
.15212 .15241 .15270 .15299 •15327 |
.98836 .98832 .98827 .98823 .98818 |
.15391 .15421 .15451 .15481 .15511 |
6.49710 6.48456 6-47206 6.45961 6.44720 |
.16935 -16964 •16992 •17021 .17050 |
.98556 -98551 -98548 -98541 .98536 |
.17183 .17213 .17243 .17273 .17303 |
5.81966 5.80953 5.79944 5-78938 5-77936 |
|
|
50 51 52 53 54 55 56 57 58 59 |
•15356 .15385 .15414 .15442 .15471 |
•98814 .98809 .98905 •98800 •98796 |
•15540 .15570 .15600 .15630 .15660 |
6-43484 6.42253 6.41026 6.39804 6-38587 |
•17078 .17107 .17136 .17164 •17193 |
.98531 -98526 -98521 .98516 .98511 |
.17333 .17363 .17393 .17423 .17453 |
5-76937 5.75941 5.74949 5-73960 5.72974 |
|
|
•15500 -15529 •15557 •15586 .15615 |
•98791 .98787 .98782 .98778 .98773 |
•15689 .15719 .15749 .15779 .15809 |
6-37374 6-36165 6-34961 6.33761 6.32566 |
.17222 •17250 •17279 •17308 -17336 |
-98506 .98501 .98496 .98491 .98486 |
-17483 •17513 -17543 .17573 .17603 |
5-71992 5-71013 5-70037 5-69064 5-68094 |
||
|
60. |
•15643 |
-98769 |
.15838 |
6.31375 |
.17365 |
.98481 |
.17633 |
5-67128 |
|
|
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
81°
210
80°
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 10° 11°
|
t |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
0 2 3 ~5~ 8 7 8 JL_ 10 11 12 13 14 15 16 17 18 12- 20 21 22 23 24^ 25 26 27 28 29_ 30 31 32 33 3JL 35 36 37 38 82- 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 |
.17365 •17393 -17422 •17451 .17479 |
.98481 .98476 .98471 .98466 .98461 |
•17633 -17663 •17693 .17723 -17753 |
5-67128 5-66165 5-65205 5-64248 5-63295 |
-19081 -19109 -19138 •19167 •19195 |
.'98163 -98157 -98152 -98146 -98140 |
-19438 -19468 .19498 •19529 .19559 |
5.14455 5-13658 5-12862 5-12069 5-11279 |
60 59 58 57 56 |
|
•17508 •17537 .17565 .17594 -17623 |
.98455 .98450 .98445 .98440 .98435 |
.17783 .17813 .17843 .17873 •17903 |
5-62344 5-61397 5 . 60452 5-59511 5.58573 |
•19224 • 19.252 -19281 -19309 -19338 |
•98135 -98i29 -98124 -98118 98112 |
•19589 •19619 •19649 .19680 .19710 |
5-10490 5.09704 5.08921 5-08139 5-07360 |
55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 |
|
|
.17651 •17680 .17708 .17737 •17766 |
.98430 .98425 •98420 .98414 .98409 |
17933 .17963 .17993 •18023 .18053 |
5-57638 5.56706 5-65777 5.54851 5-53927 |
.19366 -19395 .19423 •19452 -19481 |
-98UD7 -98101 -98096 -98090 -98084 |
.19740 •19770 .19801 -19831 .19861 |
5-06584 5-05809 5-05037 5-04267 5-03495 |
||
|
.17794 .17823 .17852 .17880 .17909 |
.98404 .98399 .98394 .98389 .98383 |
•18083 .18113 . 18143 •18173 .18203 |
5-53007 5-52090 5-51176 5-50264 5-49356 |
.19509 •19538 -19566 -19595 -19623 |
•98079 .98073 .98067 .98061 .98056 |
•19891 •19921 •19852 .19982 -20012 |
5.02734 5-01971 5-01210 5-00451 4-99695 |
||
|
17937 .17966 .17995 .18023 .18052 |
.98378 .98373 .98368 .98362 .98357 |
.18233 .18263 .18293 .18323 .18353 •18384 .18414 .18444 .18474 .18504 |
5-48451 5-47548 5-46648 5-45751 5-44857 |
.19652 -19680 •19709 •19737 -19766 |
.98050 .98044 .98039 .98033 .98027 |
. 20042 -20073 -20103 -20133 -20164 |
4-98940 4-98188 4-97438 4.96690 4-95945 |
||
|
.18081 .18109 -18138 .18166 .18195 |
.98352 .98347 .98341 .98336 .98331 |
5-43966 5-43077 5-42192 5-41309 5-40429 |
.19794 -19823 -19851 .19880 -19908 |
.98021 .98016 .98010 •98004 -97998 |
•20194 .20224 •20254 •20285 -20315 |
4-95201 4.94460 4-93721 4-92984 4-92249 |
|||
|
•18224 .18252 .18281 .18309 .18338 |
.98325 .98320 .98315 .98310 .98304 |
•18534 .18564 .18594 •18624 .18654 |
5-39552 5-38677 5.37805 5-36936 5-36070 |
-19937 -19965 -19994 -20022 -20051 |
.97992 -97987 -97981 .97975 -97969 |
- 20345 -20376 -20406 -20436 •20466 |
4-91516 4-90785 4-90056 4-89330 4-88605 |
3O 29 28 27 26 25 24 23 22 21 |
|
|
.18367 .18395 .18424 •18452 .18481 |
.98299 .98294 •98288 .982b3 .98277 |
.18634 •18714 .18745 .18775 .18805 |
5-35206 5.34345 5-33487 5-32631 5 31778 |
.20079 -20108 -20136 -20165 •20193 |
-97963 -97958 .97952 .97946 .97940 |
.20497 .20527 •20557 -20588 -20618 |
4-87882 4-87162 4-86444 4-85727 4 85013 |
||
|
•18509 •18538 .18567 .18595 .18624 |
.98272 .98267 .98261 •98256 •98250 |
.18835 .18865 .18895 .18925 .18955 |
5-30928 5-30080 5-29235 5-28393 5.27553 |
-20222 •20250 -20279 -20307 -20336 |
•97934 .97928 -97922 .97916 -97910 |
-20648 -20679 -20709 -20739 -20770 |
4-84300 4-83590 4-82882 4-82175 4-81471 |
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 3 2 ~~0 |
|
|
.18652 •18681 •18710 •18738 .18767 |
.98245 •98240 •98234 •98229 .98223 |
.18986 -19016 .19046 .19076 .19106 |
5-26715 5-25880 5.25C48 5-24218 5.23391 |
-20364 •20393 -20421 •20450 •20478 |
-97905 .97899 .97893 -97887 -97881 |
.20800 -20830 -20861 -20891 -20921 |
4-80769 4-80068 4-79370 4-78673 4-77978 |
||
|
-18795 .18824 .18852 .18881 •18910 |
.98218 •98212 .98207 •98201 .98196 |
.19136 -19166 •19197 .19227 .19257 |
5-22566 5.21744 5-20925 5.20107 5-19293 |
-20507 -20535 -20563 -20592 -20620 |
-97875 -97869 -97863 -97857 .97851 |
•20952 -20982 -21013 -21043 -21073 |
4.77286 4-76595 4-75906 4-75219 4-74534 |
||
|
55 56 57 58 59 60_ |
.18938 .18967 •18995 .19024 .19052 |
.98190 .98185 .98179 .98174 •98168 |
.19287 •19317 .19347 •19378 .19408 |
5-18480 5.17671 5-16863 5-16058 5-15256 |
-20649 -206.77 -20706 -20734 •20763 |
-97845 -97839 .97833 -97827 .97821 |
-21104 -21134 -21164 -21195 .21225 |
4.73851 4-73170 4-72490 4-71813 4-71137 |
|
|
-19081 |
.98163 |
•19438 |
5-14455 |
-20791 |
-97815 |
-21256 |
4-70463 |
||
|
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
79°
211
78°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 12° 13°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
0 1 2 3 4 |
.20791 .20820 •20848 .20877 . 20905 |
.97815 .97809 •97803 .97797 •97791 |
-21256 -21286 -21316 .21347 •21377 |
4.70463 4-69791 4.69121 4.68452 4-67786 |
-22495 -22523 -22552 -22580 -22608 |
•97437 -97430 -97424 -97417 -97411 |
-23087 -23117 -23148 -23179 •23209 |
4-33148 4-32573 4-32001 4-31430 4-30860 |
60 59 58 57 5B |
|
5 6 7 8 9 |
•20933 .20962 . 2099-0 .21019 .21047 |
.97784 •97778 .97772 .97766 .97760 |
•21408 •21438 •21469 -21499 .21529 |
4-67121 4.66458 4-65797 4-65138 4-64480 |
-22637 -22665 -22693 -22722 .22750 |
-97404 .97398 •97391 •97384 -97378 |
-23240 -23271 -23301 •23332 •23363 |
4-30291 4-29724 4-29159 4-28595 4-28032 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.21076 .21104 -2U32 .21161 .21189 |
.97754 •97748 .97742 •97735 .97729 |
-21560 •21590 -21621 •21651 -21682 |
4-63825 4-63171 4-62518 4-61868 4-61219 |
.22778 .22807 -22835 -22863 -22892 |
•97371 •97365 .97358 .97351 -97345 |
.23393 -23424 -23455 -23485 •23516 |
4-27471 4-26911 4-26352 4-25795 4-25239 |
50 49 48 47 4B |
|
15 16 17 18 19 |
.21218 •2124S -21275 •21303 -21331 |
.97723 •97717 .97711 •97705 •97698 |
.21712 .21743 .21773 -21804 -21834 |
4-60572 4-59927 4-59283 4-58641 4-58001 |
•22920 -22948 -22977 -23005 .23033 |
.97338 .97331 •97325 .97318 -97311 |
-23547 -23578 .23608 -23639 -23670 |
4-24685 4.24132 4-23580 4.23030 4-22481 |
45 44 43 42 41 |
|
20 21 22 23 24 |
.21360 .21388 .21417 . 21445 •21474 |
.97692 .97686 .97680 -97673 •97667 |
.21864 -21895 -21925 -21956 •21986 |
4-57363 4-56726 4.56091 4.55458 4-54826 |
-23062 -23090 -23118 -23146 .23175 |
•97304 -97298 -97291 -97284 .97278 |
.23700 -23731 -23762 -23793 -23823 |
4-21933 4-21387 4-20842 4.20298 4-19756 |
40 39 38 37 36 |
|
25 26 27 28 29 |
•21502 •21530 •21559 •21587 .21616 |
.97661 .97655 •97648 •97642 -97636 |
.22017 •22047 •22078 •22108 .22139 |
4.54196 4.53568 4.52941 4-52316 4-51693 |
.23203 .23231 -23260 •23288 •23316 |
•97271 •97264 -97257 .97251 •97244 |
.23854 -23885 -23916 .23946 -23977 |
4-19215 4.18675 4.18137 4.17600 4-17064 |
35 34 33 32 31 |
|
30 31 32 33 34 |
•21644 •21672 •21701 .21729 .21758 |
•97630 •97623 •97617 .97611 .97604 |
.22169 -22200 -22231 •22261 •22292 |
4-51071 4-50451 4.49832 4-49215 4-48600 |
•23345 -23373 •23401 •23429 •23458 |
•97237 •97230 .97223 .97217 •97210 |
. 24008 •24039 .24069 .24100 .24131 |
4.16530 4-15997 4-15465 4-14934 4-14405 |
30 29 28 27 26 |
|
35 36 37 38 39 |
•21786 .21814 •21843 •21871 •21899 |
.97598 .97592 .97585 .97579 -97573 |
.22322 •22353 -22383 •22414 . 22444 |
4-47986 4.47374 4-46764 4-46155 4-45548 |
23486 •23514 •23542 •23571 •23599 |
•97203 .97196 .97189 •97182 -97176 |
•24162 •24193 •24223 •24254 .24285 |
4-13877 4-13350 4-12825 4-12301 4-11778 |
25 24 23 22 21 |
|
40 41 42 48 44 |
.21928 .21956 •21985 •22013 . 22041 |
•97566 .97560 .97553 .97547 •97541 |
.22475 •22505 •22536 •22567 •22597 |
4-44942 4-44338 4-43735 4-43134 4-42534 |
•23627 .23656 •23684 •23712 .23740 |
-97169 •97162 -97155 -97148 -97141 |
.24316 •24347 •24377 . 24408 . 24439 |
4-11256 4-10736 4-10216 4-09699 4-09182 |
20 19 18 17 16 |
|
45 46 47 48 49 |
•22070 •22098 •22126 •22155 .22183 |
•97534 .97528 .97521 .97515 .97508 |
.22628 •22658 •22689 .22719 -22750 |
4.41936 4-41340 4.40745 4-40152 4-39560 |
.23769 •23797 •23825 •23853 .23882 |
-97134 -97127 -97120 .97113 -97106 |
. 24470 .24501 .24532 •24562 •24593 |
4.08666 4-08152 4-07639 4-07127 4-06616 |
15 14 13 12 11 |
|
50 51 52 53 54 |
•22212 •22240 •22268 .22297 •22325 |
.97502 .97496 .97489 •97483 •97476 |
•22781 .22811 .22842 •22872 •22903 |
4-38969 4-38381 4.37793 4-37207 4-36623 |
.23910 •23938 •23966 .23995 .24023 |
.97100 .97093 -97086 .97079 -97072 |
.24624 .24655 -24686 .24717 .24747 |
4-06107 4-05599 4-05092 4-04586 4-04081 |
10 9 8 7 6 |
|
55 56 57 58 59 |
.22353 .22382 •22410 .22438 .22467 |
•97470 -97463 •97457 •97450 -97444 |
.22934 .22964 •22995 .23026 •23056 |
4-36040 4-35459 4-34879 4-34300 4-33723 |
•24051 •24079 •24108 •24136 .24164 |
-97065 -97058 -97051 -97044 -97037 |
.24778 -24809 -24840 •24871 - 24902 |
4-03578 4.03076 4.02574 4-02074 4-01576 |
5 4 3 2 1 |
|
60 |
•22495 |
•97437 |
.23087 |
4-33148 |
.24192 |
-97030 |
-24933 |
4-01078 |
0 |
|
' |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
/ |
77°
212
76°
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 14° 15°
|
t |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
o 1 2 3 4 |
.24192 .24220 . 24249 -24277 .24305 |
•97030 •97023 •97015 -97008 .97001 |
•24933 •24964 .24995 •25026 •25056 |
4-01078 4-00582 4-00086 3-99592 3-99099 |
-25882 -25910 -25938 .25966 -25994 |
•96593 .96585 -96578 -96570 -96562 |
-26795 -26826 -26857 -26888 -26920 |
3-73205 3-72771 3-72338 3-71907 3-71476 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.24333 .24362 .24390 .24418 . 24446 |
-96994 .96987 -96980 -96973 .96966 |
•25087 .25118 .25149 .25180 .25211 |
3-98607 3-98117 3.97627 3-97139 3-96651 |
-26022 .26050 -26079 -26107 -26135 |
-96555 -96547 •96540 •96532 -96524 |
-26951 -26982 -27013 -27044 -27076 |
3-71046 3-70616 3-70188 3-69761 3-69335 |
55 54 53 52 51 |
|
10 11 12 13 14 |
. 24474 .24503 .24531 .24559 .24587 |
.96959 .96952 .96945 -96937 -96930 |
.25242 •25273 .25304 •25335 .25366 |
3-96165 3-95680 3-95196 3-94713 3-94232 |
-26163 -26191 -26219 -26247 -26275 |
-965,17 •96509 .96502 .96494 .96486 |
-27107 -27138 -27169 -27201 •27232 |
3-68909 3-68485 3-68061 3-67638 3-67217 |
50 49 48 47 46 |
|
15 16 17 18 19 |
•24615 •24644 .24672 .24700 .24728 |
.96923 -96916 -96909 -96902 .96894 |
•25397 .25428 •25459 •25490 .25521 |
3-93751 3-93271 3-92793 3-92316 3-91839 |
-26303 -26331 .26359 -26387 -26415 |
-96479 -96471 -96463 -96456 -96448 |
-27263 -27294 -27326 -27357 .27388 |
3-66796 3-66376 3-65957 3-65538 3-65121 |
45 44 43 42 -ii |
|
20 21 22 23 24 |
.24756 .24784 •24813 . 24841 .24869 |
•96887 •96880 -96873 .96866 -96858 |
•25552 •25583 •25614 •25645 •25676 |
3-91384 3.90890 3-90417 3-89945 3-89474 |
-26443 -26471 -26500 -26528 -26556 |
-96440 -96433 .96425 -96417 .96410 |
.27419 •27451 .27482 -27513 -27545 |
3-64705 3-64289 3-63874 3-63461 3 • 63048 |
4O 39 38 37 36 |
|
25 26 27 28 29 |
24897 24925 24954 24982 25010 |
-96851 -96844 -96837 -96829 -96822 |
•25707 •25738 •25769 •25800 .25831 |
3-89004 3-88536 3-88068 3-87601 3-87136 |
-26584 -26612 -26640 -26668 -266P8 |
-96402 -96394 -96386 -96379 -96371 |
-27576 -27607 -27638 -27670 -27701 |
3-62636 3-62224 3-61814 3-61405 3.60996 |
35 34 33 32 31 |
|
30 31 32 33 34 |
25038 25066 25094 25122 25151 |
-96815 -96807 -96800 -96793 -96786 |
•25862 •25893 •25924 •25955 •25983 |
3-86671 3-86208 3-85745 3-85284 3-84824 |
.26724 26752 26780 26808 26836 |
-96363 •96355 -96347 .96340 -96332 |
-27732 .27764 -27795 .27826 -27858 |
3-60588 3-60181 3-59775 3-59370 3-58966 |
30 29 28 27 28 |
|
35 36 37 38 39 |
25179 25207 25235 25263 25291 |
•96778 •96771 -96764 .96756 •96749 |
•26017 •26048 •26079 .26110 -26141 |
3-84364 3-83908 3-83449 3-82992 3-82537 |
26864 26892 26920 26948 26976 |
-96324 -96316 •96308 -96301 -96293 |
-27889 •27921 -27952 .27983 -28015 |
3-58562 3-58160 3-57758 3-57357 3-56957 |
25 24 23 22 21 |
|
40 41 42 43 44 |
25320 25348 25376 25404 25432 |
•96742 •96734 •96727 •96719 •96712 |
•26172 •26203 •26235 •26268 •28297 |
3-82083 3-81630 3-81177 3-80726 3-80278 |
27004 27032 27060 27088 -27116 |
-96285 •96277 •96269 •96261 •96253 |
-28046 •28077 -28109 -28140 -28172 |
3-56557 3-56159 3-55761 3-55364 3-54968 |
20 19 18 17 18 |
|
45 46 47 48 49 |
25460 25488 25516 25545 25573 |
•96705 .96697 •96690 •96682 •96675 |
•26328 .26359 .26390 .26421 .26452 |
3-79827 3.79378 3-78931 3-78485 3 - 78040 |
-27144 .27172 -27200 -27228 -27256 |
.96246 •96238 •96230 -96222 -96214 |
-28203 •28234 -28266 -28297 -28329 |
3-54573 3-54179 3-53785 3-53393 3-53001 |
15 14 13 12 11 |
|
50 51 52 53 54 |
25601 25829 25657 25685 25713 |
•96667 •96660 •96653 •96645 •96638 |
.26483 •26515 •26546 •26577 •26608 |
3-77595 3.77152 3.76709 3-76268 3-75828 |
-27284 -27312 -27340 27368 -27396 |
-96206 -96198 -96190 .96182 96174 |
-28360 .28391 .28423 .28454 -28486 |
3-52609 3-52219 3-518?9 3-51441 3-51053 |
10 9 8 7 6 |
|
55 56 57 58 59 |
25741 25769 25798 25826 25854 |
•96630 .96623 .96615 •96608 •96600 |
.26639 .26670 •26701 •26733 •26764 |
3.75388 3.74950 3.74512 3.74075 3-73640 |
. 27424 27452 27480 27508 27536 |
96166 96158 96150 96142 96134 |
-28517 .28549 .28580 •28612 .28643 |
3-50666 3-50279 3-49894 3-49509 3-49125 |
5 4 3 2 1 |
|
GO |
25882 |
•96593 |
.26795 |
3-73205 |
27564 |
96126 |
-28675 |
3-48741 |
0 |
|
' |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
75°
213
74°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 16° 17°
|
• |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
' |
|
o 1 2 3 |
• 27564 .27592 .27620 .27648 .27676 |
.96126 .96118 .96110 .96102 .96094 |
.28675 .28706 .28738 .28769 .28800 |
3-48741 3-48359 3-47977 3-47596 3-47216 |
.29237 -29265 .29293 .29321 .29348 |
.95630 -95622 -95613 -95605 .95596 |
•30573 -30605 •30637 .30669 .30700 |
3-27085 3-26745 3-26406 3-26067 3-25729 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.27704 .27731 .27759 .27787 .27815 |
.96086 .96078 .96070 .96062 .96054 |
.28832 .28864 .28895 .28927 .28958 |
3-46837 3-46458 3-46080 3-45703 3.45327 |
•29376 .29404 .29432 .29460 .29487 |
.95588 -95579 -95571 -95562 -95554 |
•30732 .30764 -30796 .30828 .30860 |
3-25392 3-25055 3-24719 3-24383 3 • 24049 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.27843 .27871 .27899 .27927 .27955 |
.96046 •96037 .96029 .96021 -96013 |
.28990 .29021 .29053 .29084 .29116 |
3-44951 3-44576 3-44202 3-43829 3-43456 |
.29515 .29543 .29571 .29599 •29626 |
.95545 •95536 -95528 -95519 -95511 |
.30891 .30923 .30955 .30987 -31019 |
3-23714 3-23381 3-23048 3-22715 3-22384 |
5O 49 48 47 46 |
|
15 16 17 18 19 |
.27983 .28011 .28039 .28067 -28095 |
.96005 .95997 .95989 .95981 .95972 |
•29147 •29179 •29210 .29242 .29274 |
3-43084 3-42713 3.42343 3-41973 3-41604 |
.29654 .29682 .29710 .29737 .29765 |
•95502 •95493 •95485 -95476 -95467 |
.31051 .31083 -31115 -31147 .31178 |
3-22053 3 21722 3-21392 3-21063 3-20734 |
45 44 43 42 41 |
|
20 21 22 23 24 |
.28123 .28150 -28178 .28206 .28234 |
.95964 .95956 .95948 .95940 .95931 |
.29305 .29337 .29368 .29400 .29432 |
3-41236 3.40869 3-40502 3-40136 3-39771 |
.29793 .29821 .29849 .29876 .29904 |
-95459 -95450 -95441 •95433 •95424 |
.31210 -31242 -31274 -31306 .31338 |
3-20406 3-20079 3-19752 3-19426 3-19100 |
40 39 38 37 36 |
|
25 26 27 28 29 |
.28262 -28290 .28318 .28346 .28374 |
.95923 .95915 .95907 .95898 .95890 |
.29463 •29495 .29526 .29558 .29590 |
3.39406 3-39042 3-38679 3-38317 3-37955 |
.29932 .29960 .29987 .30015 .30043 |
.95415 .95407 -95398 -95389 -95380 |
.31370 -31402 .31434 .31466 .31498 |
3-18775 3-18451 3-18127 3-17804 3-1748] |
35 34 33 32 31 |
|
30 31 32 33 34 |
.28402 .28429 .28457 .28485 .28513 |
.95882 .95874 .95865 .95857 .95849 |
.29621 .29653 .29685 .29716 .29748 |
3.37594 3-37234 3-36875 3-36516 3-36158 |
.30071 -30098 -30126 -30154 .30182 |
.95372 -95363 •95354 .95345 .95337 |
.31530 .31562 -31594 .31626 -31658 |
3-17159 3-16838 3-16517 3-16197 3-15877 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.28541 28569 -28597 .28625 .28652 |
.95841 95832 .95824 .95816 .95807 |
.29780 .29811 .29843 .29875 .29906 |
3-35800 3-35443 3-35087 3-34732 3-34377 |
.30209 -30237 -30265 .30292 .30320 |
.95328 .95319 .95310 .95301 -95293 |
-31690 -31722 •31754 •31786 •31818 |
3-15558 3-15240 3-14922 3-14605 3-14288 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.28680 28708 .28736 .28764 .28792 |
.95799 .95791 .95782 •95774 .95766 |
.29938 .29970 .30001 .30033 .30065 |
3-34023 3-33670 3-33317 3-32965 3-32614 |
.30348 •30376 •30403 -30431 -30459 |
.95284 •95275 •95266 •95257 .95248 |
•31850 .31882 .31914 .31946 .31978 |
3-13972 3-13656 3-13341 3-13027 3-12713 |
2O 19 18 17 18 |
|
45 46 47 48 49 |
.28820 28847 28875 28903 28931 |
•95757 •95749 .95740 •95732 .95724 |
.30097 .30128 •30160 .30192 •30224 |
3-32264 3-31914 3-31565 3-31216 3-30868 |
•30486 •30514 -30542 -30570 .30597 |
•95240 •95231 •95222 -95213 •95204 |
.32010 .32042 -32074 •32106 -32139 |
3-12400 3-12087 3-11775 3-11464 3-11153 |
15 14 13 12 11 |
|
50 51 52 53 54 |
28959 28987 29015 29042 29070 |
.95715 .95707 •95698 .95690 .95681 |
•30255 •30287 30319 30351 30382 |
3-30521 3-30174 3-29829 3-29483 3-29139 |
•30625 .30653 .30680 .30708 -30736 |
•95195 -95186 .95177 .95168 •95159 |
-32171 .32203 •32235 .32267 32299 |
3-10842 3-10532 3-10223 3-09914 3-09606 |
10 9 8 7 6 |
|
55 56 57 58 59 |
29098 29126 29154 29182 29209 |
.95673 •95664 .95656 •95647 .95639 |
30414 30446 30478 30509 30541 |
3-28795 3-28452 3-28109 3-27767 3-27426 |
.30763 30791 30819 30846 30874 |
.95150 •95142 .95133 •95124 •95115 |
32331 32363 32396 32428 32460 |
3-09298 3-08991 3-08685 3-08379 3-08073 |
5 3 2 1 |
|
£0_ |
29237 |
-95630 |
30573 |
3-27085 |
30902 |
.95106 |
32492 |
3-07768 |
O |
|
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
* |
73°
214
73°
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 18° 19°
|
' |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
o 1 2 3 4 |
.30902 .30929 .30957 .30985 .31012 |
.95106 .95097 .95088 .95079 .95070 |
•32492 .32524 •32556 .32588 .32621 |
3-07768 3-07464 3-07160 3-06857 3-06554 |
-32557 •32584 -32612 •32639 -32667 |
•94552 •94542 •94533 •94523 •94514 |
•34433 -34465 -34498 -34530 .34563 |
2-90421 2-90147 2-89873 2-89600 2-89327 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.31040 .31068 .31095 .31123 .31151 |
.95061 .95052 .95043 .95033 .95024 |
.32653 .32685 .32717 •32749 .32782 |
3-06252 3-05950 3.05649 3-05349 3-05049 |
-32694 -32722 •32749 •32777 •32804 |
-94504 •94495 -94485 •94476 • 94466 |
.34596 .34628 .34661 -34693 •34726 |
2-89055 2-88783 2-88511 2-88240 2-87970 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.31178 .31206 .31233 .31261 .31289 |
.95015 .95006 .94997 .94988 .94979 |
.32814 .32846 .32878 .32911 .32943 |
3 - 04749 3-04450 3-04152 3-03854 3-03556 |
-32832 .32859 -32887 •32914 .32942 |
-94457 • 94447 •94438 •94428 .94418 |
•34758 -34791 •34824 •34856 .34889 |
2-87700 2.87430 2.87161 2-86892 2.86624 |
5O 49 48 47 46 |
|
15 16 17 18 19 |
•31316 .31344 •31372 .31399 •31427_ |
.94970 .94961 .94952 .94943 .94933 |
•32975 .33007 .33040 .33072 .33104 |
3-03260 3-02963 3-02667 3-02372 3-02077 |
•32969 .32997 -33024 ,33051 .33079, |
.94409 •94399 •94390 •94380 .94370 |
.34922 .34954 •34987 .35020 .35052 |
2.86356 2-86089 2-85822 2-85555 2-85289 |
45 44 43 42 41 |
|
30 21 22 23 24 |
.31454 .31482 .31510 .31537 .31565 |
.94924 .94915 .94906 .94897 .94888 |
.33136 .33169 .33201 .33233 .33266 |
3-01783 3-01489 3-01196 3-00903 3-00611 |
•33106 •33134 -33161 .33189 .33216 |
-94361 .94351 .94342 .94332 .94322 |
.35085 .35118 .35150 .35183 .35216 |
2-85023 2-84758 2-84494 2-84229 2-83965 |
4O 39 38 37 36 |
|
25 26 27 28 29 |
•31593 .31620 •31648 •31675 .31703 |
.94878 .94869 •94860 .94851 .94842 |
.33298 .33330 .33363 .33395 .33427 |
3-00319 3-00028 2-99738 2-99447 2-99158 |
•33244 -33271 -33298 -33326 •33353 |
.94313 .94303 .94293 .94284 .94274 |
.35248 .35281 .35314 .35346 .35379 |
2-83702 2-83439 2-83176 2-82914 2-82653 |
35 34 33 32 31 |
|
30 31 32 33 34 |
•31730 •31758 •31786 •31813 .31841 |
.94832 .94823 .94814 .94805 .94795 |
•33460 .33492 •33524 •33557 .33589 |
2-98868 2-98580 2-98292 2-98004 2-97717 |
•33381 •33408 •33436 •33463 •33490 |
-94264 -94254 .94245 .94235 •94225 |
-35412 •35445 -35477 -35510 •35543 |
2-82391 2-82130 2-81870 2-81610 2-81350 |
30 29 28 27 36 |
|
35 36 37 38 39 |
.31868 .31896 .31923 •31951 .31979 |
.94786 .94777 .94768 .94758 .94749 |
•33621 •33654 •33686 -33718 •33751 |
2-97430 2-97144 2-96858 2-96573 2-9fi288 |
-33518 •33545 •33573 •33600 .33627 |
-94215 -94206 -94196 -94186 .94176 |
-35576 -35608 -35641 -35674 -35707 |
2-81091 2-80833 2-80574 2-80316 2-80059 |
25 24 23 22 -21 |
|
4O 41 42 43 44 |
.32006 .32034 .32061 .32089 .32116 |
.94740 •94730 •94721 •94712 .94702 |
•33783 •33818 .33848 •33881 .33913 |
2-96004 2-95721 2-95437 2-95155 2-94872 |
-33655 •33682 •33710 •33737 •33764 |
.94167 -94157 -94147 -94137 -94127 |
-35740 -35772 •35805 •35838 .35871 |
2-79802 2-79545 2-79289 2-79033 2-78778 |
20 19 18 17 16 |
|
45 46 47 48 49 |
.32144 .32171 .32199 .32227 •32254 |
.94693 .94684 •94674 •94665 .94656 |
•33945 •33978 •34010 . 34043 . 34075 |
2-94591 2-94309 2-94028 2-93748 2-93468 |
-33792 •33819 •33846 •33874 •33901 |
.94118 .94108 -94098 -94088 -94078 |
.35904 .35937 .35969 .36002 .36035 |
2-78523 2-78269 2-78014 2-77761 2-77507 |
15 14 13 12 11 |
|
50 51 52 53 54 |
•32282 .32309 .32337 .32364 .32392 |
.94646 .94637 •94627 •94618 .94609 |
•34108 •34140 •34173 •34205 -34238 |
2-93189 2.92910 2.92632 2.92354 2-92076 |
-33929 •33956 •33983 -34011 -34038 |
-94068 -94058 • 94049 •94039 •94029 |
-36068 .36101 -36134 •36167 -36199 |
2-77254 2-77002 2-76750 2-76498 2-76247 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•32419 •32447 •32474 •32502 .32529 |
.94599 .94590 .94580 .94571 .94561 |
•34270 •34303 -34335 •34368 . 34400 |
2.91799 2-91523 2-91246 2-90971 2-90696 |
-34065 •34093 -34120 •34147 •34175 |
-94019 -94009 .93999 .93989 •93979 |
-36232 •36265 .36298 .36331 •36364 |
2-75996 2-75746 2-75496 2.75246 2-74997 |
5 4 3 2 |
|
80 |
.32557 |
.94552 |
.34433 |
2-90421 |
.34202 |
-93969 |
.36397 |
2 - 74748 |
O |
|
Cos. |
Sin. |
Cot. |
Tan. |
COP. |
Sin. |
Cot. |
Tan. |
71°
215
70°
TABLE 10 —NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 30° 31°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t 60 59 58 57 56 55 54 53 52 51 |
|
o 1 2 3 4 |
-34202 .34229 .34257 .34284 •34311 |
•93969 •93959 •93949 •93939 .93929 |
•36397 •36430 •36463 •36496 .36529 |
2-74748 2.74499 2-74251 2-74004 2-73756 |
•35837 •35864 .35891 .35918 .35945 |
-93358 -93348 -93337 .93327 .93316 |
-38386 -38420 -38453 -38487 •38520 |
2-60509 2-60283 2-60057 2-59831 2-59606 |
|
|
5 6 7 8 9 10 12 13 14 15 16 17 18 19_ 30 21 22 23 24 |
.34339 .34366 .34393 .34421 .34448 |
•93919 .93909 .93899 .93889 .93879 |
•36562 •36595 .36628 •36661 .36694 |
2-73509 2-73263 2-73017 2-72771 2-72526 |
•35973 -36000 -36027 -36054 -36081 |
•93306 .93295 .93285 •93274 -93264 |
-38553 -385S7 -38620 -38654 •38687 |
2-59381 2-59156 2-58932 2.58708 2-58484 |
|
|
.34475 .34503 .34530 .34557 -34584 |
.93869 .93859 .93849 .93839 .93829 |
•36727 .36760 .36793 .36826 .36859 |
2-72281 2-72036 2-71792 2-71548 2.71305 |
•36108 •36135 .36162 •36190 •36217 |
-93253 •93243 .93232 -93222 -93211 |
•38721 •38754 -38787 -38821 .38854 |
2-58261 2-58038 2-57815 2.57593 2-57371 |
50 49 48 47 46 |
|
|
.34612 34639 -34666 .34694 .34721 |
.93819 .93809 •93799 .93789 .93779 |
.36892 .36925 .36958 •36991 .37024 |
2-71062 2-70819 2-70577 2-70335 2-70094 |
.36244 •36271 -36298 .36325 .36352 |
.93201 .93190 •93180 .93169 -93159 |
-38888 -38921 -38955 •38988 .39022 |
2-57150 2.56928 2-56707 2-56487 2-56266 |
45 44 43 42 41 |
|
|
•34748 .34775 .34803 .34830 .34857 |
.93769 .93759 .93748 .93738 .93728 |
-37057 •37090 •37123 .37157 .37190 |
2-69853 2-69612 2-69371 2-69131 2-68892 |
.36379 -36406 -36434 .36461 -36488 |
-93148 -93137 -93127 -93116 -93106 |
•39055 -39089 -39122 -39156 -39190 |
2-56046 2-55827 2-55608 2-55389 2-55170 |
40 39 38 37 36 |
|
|
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 |
•34884 •34912 .34939 .34966 .34993 |
.93718 .93708 .93698 .93688 .93677 |
.37223 .37256 .37289 .37322 .37355 |
2-68653 2-68414 2-68175 2-67937 2-67700 |
-36515 -36542 .36569 .36596 .36623 |
.93095 •93084 .93074 .93063 .93052 |
-39223 39257 .39290 -39324 -39357 |
2-54952 2.54734 2-54516 2.54299 2-54082 |
35 34 33 32 31 30 29 28 27 26 |
|
.35021 .35048 .35075 .35102 -35130 |
.93667 .93657 •93647 •93637 .93626 |
.37383 .37422 -37455 •37488 -37521 |
2.67462 2.67225 2.66989 2.66752 2-66516 |
.36650 .36677 -36704 -36731 -36758 |
.93042 .93031 •93020 •93010 -92999 |
39391 -39425 •39458 -39492 -39526 |
2-53865 2-53648 2-53432 2-53217 2-53001 |
||
|
•35157 •35184 •35211 •35239 .35266 |
.93616 •93606 •93596 •93585 .93575 |
•37554 •37588 •37621 •37654 .37687 |
2-66281 2-66046 2.65811 2.65576 2-65342 |
-36785 -36812 -36839 -36867 -36894 |
.92988 -92978 -92967 -92956 -92945 |
-39559 -39593 -39626 -39660 -39694 |
2-52786 2-52571 2-52357 2.52142 2-51929 |
25 24 23 22 21 |
|
|
40 41 42 43 44 |
•35293 .35320 •35347 •35375 •35402 |
.93565 .93555 .93544 .93534 .93524 |
.37720 •37754 -37787 -37820 -37853 |
2-65109 2-64875 2.64642 2-64410 2-64177 |
-36921 -36948 -36975 -37002 -37029 |
-92935 -92924 -92913 •92902 .92892 |
-39727 -39761 •39795 •39829 .39862 |
2.51715 2.51502 2-51289 2.51076 2-50864 |
30 19 18 17 16 15 14 13 12 11 1O 9 8 7 6 5 4 3 2 1 -£ |
|
45 46 47 48 49 |
•35429 •35456 .35484 •35511 35538 |
•93514 .93503 •93493 •93483 .93472 |
.37887 .37920 .37953 •37986 -38020 |
2.63945 2-63714 2.63483 2-63252 2-63021 |
-37056 -37083 .37110 .37137 .37164 |
-92881 -928VO -92859 -92849 -92838 |
-39896 •39930 -39963 •39997 .40031 |
2-50652 2 - 50440 2-50229 2-50018 2-49807 |
|
|
50 51 52 53 54 55 56 57 58 59 60. |
35565 35592 35619 35647 35674 |
•93462 •93452 •93441 -93431 .93420 |
.38053 •38086 .38120 .38153 38186 |
2.62791 2-62561 2-62332 2-62103 2-61874 |
.37191 .37218 .37245 .37272 -37299 |
•92827 .92816 .92805 .92794 .92784 |
-40065 .40098 -40132 -40166 - 40200 |
2-49597 2-49386 2-49177 2-48967 2-48758 |
|
|
35701 35728 35755 35782 35810 |
•93410 .93400 •93389 .93379 .93368 |
•38220 38253 38286 38320 -38353 |
2-61646 2.61418 2-61190 2-60963 2-60736 |
-37326 -37353 -37380 37407 37434 |
.92773 -92762 -92751 -92740 92729 |
-40234 40267 40301 40335 40369 |
2-48549 2-48340 2-48132 2-47924 2-47716 |
||
|
35837 |
•93358 |
-38386 |
2-60509 |
37461 |
92718 |
40403 |
2-47509 |
||
|
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
216
68°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS, 22° 23°
|
1 |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
, |
|
0 2 8 4 |
.37461 .37488 •37515 .37542 .37569 |
.92718 .92707 •92697 .92686 .92675 |
.40403 .40436 .40470 .40504 .40538 |
2-47509 2.47302 2.47095 2-46888 2-46682 |
.39073 .39100 -39127 -39153 .39180 |
•92050 .92039 .92028 -92016 -92005 |
•42447 .42482 .42516 .42551 .42585 |
2-35585 2.35395 2-35205 2-35015 2-34825 |
60 59 58 57 5ft |
|
5 6 7 8 9 |
•37595 .37622 •37649 .37676 .37703 |
.92664 .92653 .92642 .92631 92620 |
.40572 .40606 .40640 .40674 .40707 |
2-46476 2-46270 2-46065 2.45860 2.45655 |
•39207 -39234 .39260 •39287 .39314 |
•91994 .91982 .91971 .91959 •91948 |
.42619 .42654 •42688 -42722 •42757 |
2-34636 2-34447 2-34258 2-34069 2-33881 |
55 54 53 52 51 |
|
10 11 12 13 14 |
•37730 .37757 •37784 .37811 .37838 |
.92609 .92598 .92587 .92576 .92565 |
.40741 .40775 .40809 .40843 .40877 |
2-45451 2-45246 2-45043 2.44839 2.44636 |
•39341 .39367 •39394 -39421 .39448 |
.91936 -91925 .91914 .91902 .91891 |
-42791 •42826 .42860 •42894 .42929 |
2-33693 2-33505 2-33317 2-33130 2-32943 |
50 49 48 47 46 |
|
15 16 17 18 19 |
.37865 .37892 .37919 .37946 .37973 |
.92554 .92543 .92532 .92521 .92510 |
.40911 .40945 .40979 .41013 .41047 |
2-44433 2-44230 2-44027 2-43825 2-43623 |
.39474 .39501 .39528 .39555 .39581 |
.91879 .91868 .91856 .91845 .91833 |
•42963 .42998 .43032 .43067 .43101 |
2-32756 2-32570 2-32383 2-32197 2.32012 |
45 44 43 42 41 |
|
20 21 22 23 24 |
.37999 .38026 .38053 .38080 .38107 |
.92499 .92488 .92477 .92466 .92455 |
.41081 .41115 .41149 .41183 .41217 |
2-43422 2-43220 2-43019 2-42819 2-42618 |
•39608 •39635 •39661 .39688 .39715 |
-91822 .91810 .91799 .91787 .91775 |
.43136 .43170 .43205 -43239 -43274 |
2-31826 2.31641 2-31456 2-31271 2-31086 |
40 39 38 37 36 |
|
25 26 27 28 29 |
.38134 .38161 .38188 -38215 .38241 |
.92444 .92432 .92421 .92410 .92399 |
.41251 .41285 .41319 .41353 .41387 |
2-42418 2-42218 2-42019 2.41819 2-41620 |
-39741 .39768 .39795 .39822 .39848 |
.91764 .91752 .91741 .91729 .91718 |
-43308 .43343 •43378 -43412 -43447 |
2-30902 2-30718 2-30534 2-30351 2-30167 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.38268 .38295 .38322 .33349 .38376 |
.92388 .92377 •92366 .92355 .92343 |
.41421 .41455 .41490 .41524 .41558 |
2 41421 2-41223 2-41025 2-40827 2-40629 |
•39875 -39902 .39928 -39955 .39982 |
-91706 .91694 .91683 .91671 .91660 |
-43481 .43516 .43550 -43585 .43620 |
2.29984 2-29801 2.29619 2-29437 2-29254 |
30 29 28 27 26 |
|
35 36 37 38 39 |
-38403 .38430 .38456 .38483 .38510 |
.92332 .92321 .92310 .92299 .92287 |
-41592 .41626 .41660 .41694 .41728 |
2-40432 2-40235 2-40038 2-39841 2-39645 |
.40008 •40035 •40062 •40088 .40115 |
.91648 .91636 .91625 .91613 .91601 |
.43654 .43689 .43724 .43758 .43793 |
2-29073 2-28891 2-28710 2-28528 2.28348 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.38537 .38564 .38591 •38617 .38644 |
.92276 .92265 .92254 .92243 .92231 |
.41763 .41797 .41831 .41865 .41899 |
2-39449 2.39253 2-39058 2-38863 2.38668 |
.40141 •40168 •40195 -40221 .40248 |
.91590 .91578 .91566 .91555 .91543 |
.43828 .43862 •43897 -43932 .43966 |
2-28167 2-27987 2.27806 2-27626 2-27447 |
2O 19 18 17 16 |
|
45 46 47 48 49 |
-38671 .38698 .38725 .38752 -38778 |
.92220 .92209 .92198 .92186 .92175 |
.41933 .41968 .42002 .42036 .42070 |
2.38473 2-38279 2-38084 2-37891 2-37697 |
-40275 40301 -40328 .40355 .40381 |
.91531 .91519 .91508 .91496 .91484 |
-44001 .44036 -44071 .44105 .44140 |
2-27267 2-27088 2-26909 2-26730 2-26552 |
15 14 13 12 11 |
|
5O 51 52 53 54 |
.38805 .38832 .38859 .38886 .38912 |
.92164 .92152 .92141 .92130 .92119 |
.42105 .42139 .42173 .42207 .42242 |
2-37504 2-37311 2-37118 2-36925 2.36733 |
.40408 •40434 .40461 .40488 •40514 |
.91472 .91461 .91449 .91437 .91425 |
-44175 .44210 .44244 .44279 .44314 |
2-26374 2-26196 2-26018 2-25840 2-25663 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•38939 •38966 •38993 .39020 .39046 |
.92107 .92096 •92085 .92073 .92062 |
•42276 .42310 .42345 .42379 .42413 |
2-36541 2.36349 2.36158 2-35967 2-35776 |
.40541 •40567 .40594 .40621 .40347 |
.91414 .91402 .91390 .91378 .91366 |
.44349 .44384 .44418 .44453 .44488 |
2-25486 2-25309 2-25132 2-24956 2-24780 |
5 "4 3 2 |
|
60 |
.39073 |
.92050 |
•42447 |
2-35585 |
.40674 |
.91355 |
.44523 |
2-24604 |
O |
|
1 |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
67°
217
66°
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 34° 25°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
f |
|
0 1 2 3 4 |
.40674 .40700 .40727 .40753 .40780 |
.91355 .91343 .91331 .91319 .91307 |
•44523 •44558 •44593 •44627 .44662 |
2.24604 2-24428 2.24252 2.24077 2.23902 |
-42262 .42288 .42315 .42341 -42367 |
•90631 -90618 •90606 •90594 .90582 |
.46631 •46666 •46702 •46737 •46772 |
2-14451 2-14288 2.14125 2-13963 2-13801 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.40806 .40833 .40860 -40886 .40913 |
.91295 •91283 .91272 .91260 .91248 |
•44697 •44732 •44767 .44802 •44837 |
2-23727 2.23553 2.23378 2-23204 2-23030 |
.42394 •42420 .42446 •42473 -42499 |
-90569 •90557 .90545 -90532 .90520 |
.46808 -46843 .46879 •46914 .46950 |
2-13639 2.13477 2-13316 2.13154 2-12993 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.40939 .40966 •40992 .41019 .41045 |
.91236 .91224 .91212 .91200 .91188 |
•44872 .44907 .44942 .44977 .45012 |
2-22857 2.22683 2-22510 2.22337 2.22164 |
•42525 .42552 .42578 .42604 .42631 |
.90507 .90495 -90483 •90470 .90458 |
.46985 .47021 .47056 .47092 -47128 |
2-12832 2.12671 2-12511 2-12350 2-12190 |
50 49 48 47 46 |
|
15 16 17 18 19 |
•41072 .41098 .41125 .41151 .41178 |
.91176 .91164 .91152 .91140 .91128 |
.45047 .45082 .45117 •45152 .45187 |
2.21992 2.21819 2.21647 2.21475 2-21304 |
-42657 .42683 -42709 -42736 -42762 |
. 90446 •90433 •90421 .90408 -90396 |
.47163 .47199 .47234 -47270 .47305 |
2-12030 2-11871 2-11711 2-11552 2-11392 |
45 44 43 42 41 |
|
20 21 22 23 24 |
•41204 •41231 .41257 .41284 •41310 |
-91116 •91104 .91092 .91080 .91068 |
.45222 •45257 .45292 •45327 .45362 |
2-21132 2.20961 2-20790 2-20619 2-20449 |
•42788 -42815 .42841 -42867 .42894 |
.90383 •90371 .90358 .90346 .90334 |
-47341 -47377 .47412 .47448 .47483 |
2-11233 2-11075 2-10916 2-10758 2-10600 |
40 39 38 37 36 |
|
25 26 27 28 29 |
.41337 •41363 •41390 •41416 •41443 |
•91056 •91044 •91032 •91020 .91008 |
•45397 -45432 .45467 •45502 .45538 |
2-20278 2.20108 2-19938 2-19769 2-19599 |
-42920 -42946 •42972 -42999 .43025 |
-90321 .90309 .90296 -90284 .90271 |
-47519 -47555 .47590 .47626 -47662 |
2-10442 2-10284 2-10126 2-09969 2-09811 |
35 34 33 32 31 |
|
30 31 32 33 34 |
•41469 .41496 .41522 .41549 .41575 |
.90996 .90984 .90972 .90960 .90948 |
.45573 •45608 .45643 -45678 .45713 |
2.19430 2.19261 2-19092 2-18923 2-18755 |
.43051 .43077 •43104 .43130 -43156 |
-90259 .90246 .90233 .90221 •90208 |
.47698 .^7733 .47769 .47805 .47840 |
2-09654 2-09498 2-09341 2-09184 2-09028 |
30 29 28 27 26 |
|
35 36 37 38 39 |
•41602 •41628 .41655 •41681 •41707 |
90936 •90924 -90911 •90899 -90887 |
•45748 •45784 •45819 •45854 .45889 |
2-18587 2-18419 2-18251 2-18084 2-17916 |
•43182 .43209 •43235 •43261 -43287 |
-90196 -90183 -90171 •90158 .90146 |
.47876 .47912 .47948 .47984 .48019 |
2-08872 2-08716 2-08560 2-08405 2-08250 |
25 24 23 22 -21 |
|
40 41 42 43 44 |
•41734 •41760 •41787 •41813 •41840 |
•90875 .90863 -90851 -90839 -90826 |
•45924 .45960 •45995 •46030 .46065 |
2-17749 2-17582 2-17416 2-17249 2.17083 |
-43313 .43340 •43366 •43392 .43418 |
.90133 .90120 .90108 •90095 -90082 |
.48055 -48091 .48127 .48163 .48198 |
2-08094 2-07939 2-07785 2.07630 2-07476 |
20 19 18 17 16 |
|
45 46 47 48 49 |
•41866 .41892 .41919 •41945 .41972 |
•90814 •90802 .90790 •90778 .90766 |
.46101 •46136 .46171 •46206 •46242 |
2.16917 2-16751 2-16585 2-16420 2-16255 |
• 43445 •43471 •43497 •43523 .43549 |
•90070 •90057 .90045 -90032 -90019 |
.48234 .48270 -48306 -48342 .48378 |
2-07321 2-07167 2-07014 2-06860 2-06706 |
15 14 13 12 11 |
|
50 51 52 53 54 |
•41998 .42024 •42051 .42077 .42104 |
•90753 -90741 .90729 .90717 •90704 |
.46277 •46312 •46348 •46383 •46418 |
2-16090 2-15925 2-15760 2-15596 2-15432 |
•43575 •43602 •43628 •43654 .43680 |
.90007 •89994 •89981 -89968 .89956 |
.48414 .48450 .48486 .48521 .48557 |
2-06553 2.06400 2-06247 2-06094 2-05942 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•42130 •42156 .42183 .42209 .42235 |
•90692 •90680 •90668 .90655 .90643 |
.46454 .46489 •46525 •46560 .46595 |
2-15268 2- 15104* 2-14940 2-14777 2-14614 |
•43706 •43733 -43759 •43785 .43811 |
.89943 .89930 -89918 .89905 .89892 |
.48593 .48629 .48665 •48701 •48737 |
2-05790 2.05637 2-05485 2-05333 2-05182 |
5 4 3 2 1 |
|
60 |
.42262 |
.90631 |
-46631 |
2-14451 |
•43837 |
.89879 |
.48773 |
2-05030 |
_o |
|
/ |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
/ |
65°
218
64°
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 26° 27°
|
* |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t |
|
0 2 3 4 |
•43837 .43863 .43889 .43916 .43942 |
.89879 •89867 .89854 .89841 .89828 |
.48773 .48809 .48845 .48881 .48917 |
2.05030 2.04879 2.04728 2-04577 2-04426 |
.45399 •45425 .45451 .45477 .45503 |
-89101 -89087 -89074 -89061 .89048 |
-50953 -50989 -51026 -51063 -51099 |
1-96261 1-98120 1-95979 1.95838 1-95698 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.43968 .43994 .44020 . 44046 .44072 |
.89816 .89803 .89790 .89777 .89764 |
.48953 .48989 .49026 .49062 .49098 |
2-04276 2.04125 2.03975 2.03825 2-03675 |
.45529 .45554 .45580 .45606 .45632 |
-89035 -89021 .89008 .88995 .88981 |
.51136 .51173 .51209 .51246 •51283 |
1-95557 1-95417 1-95277 1-95137 1-94997 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.44098 .44124 .44151 .44177 .44203 |
.89752 .89739 .89726 .89713 .89700 |
.49134 .49170 .49206 .49242 .49278 |
2.03526 2.03376 2-03227 2-03078 2-02929 |
.45658 -45684 -45710 -45736 .45762 |
•88968 -88955 -88942 .88928 -88915 |
-51319 -51356 .51393 -51430 -51467 |
1-94858 1-94718 1-94579 1-94440 1-94301 |
5O 49 48 47 46 |
|
15 16 17 18 19 |
•44229 •44255 •44281 .44307 .44333 |
.89687 .89674 .89662 .89649 .89636 |
.49315 .49351 .49387 •49423 .49459 |
2.02780 2.02631 2-02483 2.02335 2-02187 |
.45787 .45813 .45839 .45865 .45891 |
.88902 .88888 .88875 -88862 .88848 |
-51503 -51540 -51577 -51614 .51651 |
1.94162 1.94023 1.93885 1.93746 1.93608 |
45 44 43 42 41 |
|
20 21 22 23 24 |
.44359 .44385 .44411 .44437 .44464 |
.89623 .89610 .89597 .89584 .89571 |
•49495 .49532 .49568 .49604 .49640 |
2-02039 2-01891 2.01743 2-01596 2-01449 |
-45917 .45942 .45968 •45994 .46020 |
-88835 •88822 .88808 •88795 .88782 |
•51688 •51724 •51761 .51798 .51835 |
1.93470 1-93332 1.93195 1.93057 1-9?920 |
40 39 38 37 36 |
|
25 2fi 27 28 29 |
•44490 •44516 .44542 •44568 .44594 |
.89558 .89545 .89532 .89519 .89506 |
•49677 .49713 .49749 .49786 -49822 |
2.01302 2-01155 2.01008 2.00862 2-00715 |
.46046 .46072 -46097 -46123 -46149 |
-88768 -88755 .88741 .88728 .88715 |
.51872 -51909 -51946 -51983 -52020 |
1.92782 1.92645 1.92508 1.92371 1.92235 |
35 34 33 32 31 |
|
30 81 82 33 34 |
.44620 .44646 .44672 .44698 44724 |
•89493 .89480 .89467 .89454 .89441 |
.49858 .49894 .49931 .49967 . 50004 |
2.00569 2-00423 2-00277 2-00131 1.99986 |
-46175 -46201 -46226 .46252 .46278 |
.88701 .88688 .88674 .88661 .88647 |
-52057 -52094 -52131 .52168 .52205 |
1.92098 1-91962 1.91826 1.91690 1.91554 |
30 29 28 27 26 |
|
35 36 37 38 39 |
44750 44776 44802 44828 44854 |
.89428 .89415 .89402 .89389 .89376 |
. 50040 .50076 •50113 .50149 .50185 |
1.99841 1.99695 1.99550 1.99406 1.99261 |
.46304 -46330 -46355 -46381 .46407 |
.88634 •88620 .88607 .88593 .88580 |
.52242 .52279 .52316 .52353 .52390 |
1.91418 1-91282 1.91147 1.91012 1-90876 |
25 24 23 22 -21 |
|
!i° 42 43 44 |
44880 44906 44932 44958 44984 |
.89363 .89350 .89337 .89324 .89311 |
.50222 .50258 .50295 .50331 .50368 |
1-99116 1.98972 1.98828 1.98684 1.98540 |
-46433 •46458 .46484 .46510 .46536 |
•88566 •88553 •88539 .88526 .88512 |
.52427 .52464 -52501 -•52538 -52575 |
1-90741 1-90607 1-90472 1-90637 1-90203 |
30 19 18 17 16 |
|
45 46 47 48 49 |
45010 45036 45062 45088 45114 |
.89298 .89285 .89272 .89259 .89245 |
. 50404 . 50441 •50477 .50514 .50550 |
1-98396 1.98253 1.98110 1-97966 1-97823 |
.46561 .46587 •46613 46639 .46664 |
-88499 .88485 .88472 .88458 .88445 |
-52613 •52650 52687 52724 .52761 |
1-90069 1-89935 1-89801 1-89667 1.89533 |
15 14 13 12 11 |
|
50 51 52 53 54 |
45140 45166 45192 45218 45243 |
.89232 .89219 .89206 .89193 .89180 |
.50587 .50623 50660 .50696 .50733 |
1.97681 1.97538 1.97395 1.97253 1.97111 |
-46690 46716 46742 46767 46793 |
-88431 .88417 .88404 .88390 -88377 |
52798 52836 52873 52910 52947 |
1-89400 1-99266 1-89133 1.89000 1.88867 |
10 9 8 7 6 |
|
55 56 57 58 59 |
45269 45295 45321 45347 45373 |
•89167 .89153 .89140 •89127 .89114 |
•50769 .50806 .50843 .50879 50916 |
1-96969 1-96827 1.96685 1.96544 1-96402 |
46819 46844 46870 46896 46921 |
88363 88349 88336 88322 88308 |
52985 53022 53059 53096 53134 |
1-88734 1-88602 1-88469 1-88337 1-88205 |
5 4 3 2 1 |
|
60 |
45399 |
.89101 |
.50953 |
1.96261 |
46947 |
88295 |
53171 |
1-88073 |
_2 |
|
"7~ |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
|
|
ft |
*° |
21 |
9 |
G |
J° |
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 28° 29° i
|
9 |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
0 1 3 |
.46947 .46973 .46999 .47024 .47050 |
.88295 .88281 .88267 .88254 .88240 |
•53171 .53208 53246 .53283 .53320 |
1-88073 1-87941 1-87809 1-87677 1.87546 |
•48481 .48506 .48532 .48557 .48583 |
87462 .87448 •87434 87420 .87406 |
.55431 •55469 -55507 -55545 .55583 |
i 80405 1-80281 1.80158 1-80034 1-79911 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.47076 .47101 •47127 .47153 .47178 |
.88226 88213 .88199 .88185 .88172 |
•53358 .53395 .53432 53470 .53507 |
1-87415 1-87283 1-87152 1-87021 1.86891 |
-48608 .48634 -48659 .48684 -48710 |
-87391 -87377 -87363 -87349 .87335 |
.55621 •55659 •55697 •55736 .55774 |
1 79788 1 79665 1.79542 1-79419 1-79296 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.47204 .47229 .47255 .47281 .47306 |
.88158 .88144 .88130 .88117 .88103 |
.53545 .53582 .53620 .53657 .53694 |
1.86760 1.86630 1.86499 1.86369 1.86239 |
.48735 •48761 .48786 -48811 •48837 |
.87321 .87306 .87292 .87278 .87264 |
•55812 •55850 .55888 .55926 •55964 |
1-79174 1.79053 1-78929 1-78807 1.78685 |
50 49 48 47 46 |
|
15 16 17 18 J9 |
.47332 •47358 .47383 .47409 .47434 |
.88089 .88075 .88062 .88048 .88034 |
•53732 .53769 .53807 .53844 .53882 |
1-86109 1.85979 1.85850 1-85720 1-85591 |
.48862 .48888 .48913 .48938 -48964 |
.87250 .87235 .87221 .87207 .87193 |
.56003 -56041 -56079 .56117 -56156 |
1-78563 1 - 78441 1-78319 1-78198 1.78077 |
45 44 43 42 -41 |
|
20 21 22 23 24 |
.47460 .47486 .47511 .47537 .47562 |
.88020 .88006 .87993 .87979 .87965 |
.53920 .53957 .53995 .54032 .54070 |
1-85462 1-85333 1-85204 1-85075 1-84946 |
.48989 .49014 •49040 •49065 .49090 |
-87178 .87164 .87150 .87136 .87121 |
.56194 -56232 -56270 .56309 .56347 |
1-77955 1-77834 1-77713 1-77592 1.77471 |
40 39 38 37 36 |
|
25 26 27 28 29 |
.47588 •47614 • 47639 .47665 .47690 |
.87951 •87937 •87923 .87909 .87896 |
.54107 .54145 •54183 . 54220 .54258 |
1.84818 1-84689 1-84561 1-84433 1-84305 |
-49116 .49141 .49166 -49192 .49217 |
-87107 87093 -87079 -87064 .87050 |
-56385 -56424 -56462 -56501 .56539 |
1-77351 1-77230 1.77110 1-76990 1.76869 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.47716 .47741 .47767 .47793 .47818 |
.87882 .87868 .87854 .87840 .87826 |
•54296 .54333 .54371 . 54409 . 54446 |
1-84177 1 . 84049 1.83922 1-83794 1.83667 |
.49242 -49268 .49293 .49318 .49344 |
.87036 .87021 .87007 .86993 .86978 |
.56577 -56616 .56654 .56693 -56731 |
1 - 76749 1-76629 1-76510 1-76390 1-76271 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.47844 .47869 .47895 .47920 .47946 |
.87812 .87798 .87784 .87770 .87756 |
. 54484 •54522 .54560 .54597 .54635 |
1.83540 1-83413 1-83286 1-83159 1.83033 |
.49369 .49394 .49419 .49445 .49470 |
-86964 -86949 -86935 -86921 -86906 |
-56769 -56808 -56846 -56885 .56923 |
1-76151 1-76032 1-75913 1-75794 1.75675 |
25 24 23 22 -21 |
|
40 41 42 43 44 |
.47971 .47997 .48022 .48048 .48073 |
•87743 •87729 .87715 .87701 .87687 |
. 54673 .54711 .54748 ..54786 .54824 |
1-82906 1-82780 1.82654 1.82528 1-82402 |
-49495 -49521 .49546 -49571 .49596 |
.86892 -86878 .86863 -86849 .86834 |
•56962 .57000 -57039 -57078 -57116 |
1.75556 1-75437 1-75319 1-75200 1-75082 |
20 19 18 17 16 |
|
45 46 47 48 49 |
.48099 .48124 .48150 .48175 .48201 |
.87673 .87659 .87645 .87631 .87617 |
•54862 .54900 .54938 .54975 .55013 |
1-82276 1-82150 1-82025 1-81899 1.81774 |
-49622 -49647 -49672 -49697 .49723 |
-86820 -86805 -86791 -86777 -86762 |
-57155 -57193 -57232 -57271 .57309 |
1-74964 1-74846 1-74728 1-74610 1 . 74492 |
15 14 13 12 11 |
|
50 51 52 53 54 |
.48226 .48252 48277 .48303 .48328 |
•87603 •87589 .87575 •87561 •87546 |
•55051 .55089 .55127 .55165 .55203 |
1-81649 1-81524 1-81399 1-81274 1.81150 |
-49748 -49773 -49798 .49824 .49849 |
.86748 .86733 .86719 .86704 .86690 |
-57348 -57386 -57425 .57464 .57503 |
1-74375 1-74257 1-74140 1 - 74022 1-73905 |
10 9 8 7 6 |
|
55 56 57 58 59 |
.48354 .48379 .48405 .48430 .48456 |
•87532 •87518 .87504 .87490 .87476 |
.55241 .55279 .55317 .55355 .55393 |
1-81025 1-80901 1-80777 1-80653 i-80529 |
-49874 .49899 .49924 .49950 .49975 |
.86675 -86661 -86646 -86632 .86617 |
-57541 -57580 -57619 -57657 .57696 |
1-73788 1-73671 1-73555 1-73438 1-73321 |
5 4 3 2 1 |
|
60 |
. 48481 |
•87462 |
•55431 |
1-80405 |
.50000 |
-86603 |
.57735 |
1-73205 |
O |
|
/ |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
' |
61°
220
60°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS 30° 31°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
f |
|
0 1 2 3 4 |
. 50000 .50025 .50050 .50076 .50101 |
86603 86588 86573 .86559 .86544 |
.57735 .57774 .57813 •57851 •57890 |
1.73205 1.73089 1.72973 1.72857 1-72741 |
•51504 •51529 .51554 .51579 .51604 |
.85717 .85702 .85687 .85672 .85657 |
-60086 -60126 .60165 .60205 •60245 |
1.66428 1-66318 1.66209 1-66099 1.65990 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.50126 .50151 .50176 .50201 .50227 |
.86530 .86515 .86501 .86486 .86471 |
.57929 .57968 •58007 .58046 .58085 |
1-72625 1-72509 1-72393 1-72278 1-72163 |
.51628 •51653 -51678 .51703 .51728 |
•85642 •85627 .85612 •85597 •85582 |
.60284 -60324 .60364 .60403 . 60443 |
1.65881 1-65772 1-65663 1-65554 1.65445 |
55 54 53 52 51 |
|
10 11 12 13 |
.50252 .50277 -50302 .50327 .50352 |
•86457 • 86442 •86427 .86413 •86398 |
•58124 .58162 .58201 .58240 -58279 |
1 . 72047 1-71932 1-71817 1-71702 1-71588 |
•51753 •51778 •51803 •51828 .51852 |
•85567 •85551 .85536 .85521 -85506 |
-60483 .60522 •60562 •60602 .60642 |
1-65337 1.65228 1-65120 1-65011 1 • 64903 |
5O 49 48 47 48 |
|
15 16 17 18 19 |
•50377 . 50403 .50428 .50453 .50478 |
•86384 •86369 •86354 •86340 -86325 |
.58318 .58357 .58396 .58435 •58474 |
1.71473 1.71358 1.71244 1.71129 1-71015 |
.51877 .51902 .51927 .51952 -51977 |
.85491 .85476 .85461 .85446 .85431 |
.60681 .60721 .60761 .60801 .60841 |
1.64795 1-64687 1-64579 1-64471 1.64363 |
45 44 43 42 41 |
|
20 21 22 23 24 |
•50503 .50528 .50553 .50578 .50603 |
•86310 •86295 .86281 •86266 •86251 |
.58513 -58552 -58591 -58631 .58670 |
1-70901 1-70787 1.70673 1-70560 1 - 70446 |
•52002 -52026 -52051 -52076 •52101 |
•85416 .85401 •85385 .85370 -85355 |
.60881 .60921 .60960 .61000 •61040 |
1-64256 1.64148 1-64041 1.63934 1.63826 |
40 39 38 37 36 |
|
25 23 27 28 39 |
•50628 •50654 .50679 .50704 -50729 |
.86237 .86222 .86207 .86392 .86178 |
58709 .58748 .58787 .58826 .58865 |
1-70332 1.70219 1.70106 1-69992 1-69879 |
•52126 .52151 .52175 .52200 .52225 |
-85340 -85325 -85310 •85294 .85279 |
-61080 -61120 .61160 -61200 -61240 |
1.63719 1-63612 1.63505 1-63398 1.63292 |
35 34 33 32 31 |
|
30 31 32 33 34_ |
.50754 .50779 .50804 •50829 •50854 |
.86163 •86148 .86133 .86119 .86104 |
.58905 .58944 .58983 .59022 .59061 |
1-69766 1.69653 1-69541 1.69428 1.69316 |
•52250 .52275 -52299 .52324 -52349 |
.85264 •85249 .85234 .85218 .85203 |
.61280 •61320 -61360 -61400 .61440 |
1-63185 1.63079 1.62972 1-62866 1.62760 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.50879 •50904 -50929 •50954 •50979 |
•86089 .86074 •86059 •86045 •86030 |
.59101 .59140 .59179 59218 .59258 |
1-69203 1-69091 1-68979 1.68866 1-68754 |
•52374 •52399 •52423 •52448 .52473 |
.85188 .85173 •85157 •85142 -85127 |
.61480 •61520 •61561 .61601 •61641 |
1.62654 1-62548 1.62442 1.62336 1-62230 |
25 24 23 22 21 |
|
40 41 42 43 44 |
•51004 .51029 .51054 •51079 •51104 |
•86015 .86000 85985 •85970 .85956 |
.59297 .59336 .59376 .59415 .59454 |
1.68643 1-68531 1.68419 1.68308 1.68196 |
•52498 •52522 •52547 •52572 -52597 |
.85112 .85096 •85081 .85066 •85051 |
.61681 .61721 .61761 .61801 •61842 |
1.62125 ]. 62019 1.61914 1.61808 1.61703 |
20 19 18 17 16 |
|
45 46 47 48 49 |
.51129 •51154 .51179 •51204 •51229 |
.85941 .85926 •85911 .85896 .85881 |
.59494 .59533 .59573 •59612 .59651 |
1-68085 1.67974 1-67863 1-67752 1-67641 |
•52621 •52646 •52671 .52696 •52720 |
•85035 •85020 .85005 .84989 .84974 |
.61882 •61922 -61962 •62003 -62043 |
1.61598 1.61493 1.61388 1.61283 1.61179 |
15 14 13 12 11 |
|
50 51 52 53 54 |
.51254 •51279 •51304 •51329 •51354 |
.85866 .85851 <85836 •85821 •8o806 |
•59691 •59730 •59770 .59809 •59849 |
1-67530 1.67419 1.67309 1-67198 1.67088 |
•52745 •52770 •52794 •52319 .52844 |
•84959 - 84943 .84928 .84913 .84897 |
•62083 •62124 .62164 .62204 •62245 |
1-61074 1.60970 1 60865 1-60761 1.60657 |
1O 9 8 7 6 |
|
55 56 57 58 59 |
•51379 51404 .51429 •51454 •51479 |
•85792 .85777 •85762 •85747 .85732 |
•59888 .59928 •59967 •60007 . 60046 |
1.66978 1.66867 1.66757 1.66647 1.66538 |
-52869 -52893 -52918 •52943 .52967 |
.84882 .84866 .84851 .84836 •84820 |
.62285 •62325 .62366 .62406 .62446 |
1.60553 1-60449 1-60345 1 • 60241 1-60137 |
5 4 3 2 1 |
|
?0 |
•51504 |
-85717 |
•60086 |
1-66428 |
•52992 |
.84805 |
•62487 |
1 - 60033 |
O |
|
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
59°
221
58°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS. AND COTANGENTS 33° 33°
|
t |
Sin. |
Cos |
Tan. |
Cot |
Sin. |
Cos. |
Tan. |
Cot. |
< |
|
0 2 3 |
.52992 .53017 .53041 .53066 .53091 |
•84805 .84789 .84774 .84759 . 84743 |
•62487 .62527 .62568 .62608 •62649 |
1-60033 1-59930 1.59826 1.59723 1-59620 |
-54464 •54488 •54513 •54537 .54561 |
.83867 •83851 .83835 •83819 •83804 |
•64941 •64982 •65024 •65065 •65106 |
1.53986 1.53888 1.53791 1-53693 1-53595 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.53115 .53140 .53164 .53189 .53214 |
•84728 .84712 •84697 .84681 .84666 |
.62689 .62730 .62770 •62811 .62852 |
1-59517 1.59414 1.59311 1-59208 1.59105 |
. 54585 -&4610 .54635 •54659 .54683 |
•83788 •83772 •83756 •83740 •83724 |
-65148 •65189 •65231 •65272 •65314 |
1.53497 1 • 53400 1-53302 1-53205 1.53107 |
55 54 53 52 51. |
|
10 11 12 13 !!_ |
.53238 53263 53288 » 53312 .53337 |
.84650 .84635 .84619 .84604 .84588 |
•62892 .62933 .62973 .63014 .63055 |
1.59002 1-58900 1.58797 1.58695 1.58593 |
•54708 •54732 •54756 •54781 •54805 |
.83708 •83692 •83676 .83660 .83645 |
•65355 •65397 .65438 •65480 -65521 |
1.53010 1.52913 1.52816 1.52719 1-52622 |
50 49 48 47 46 |
|
15 16 17 18 19 |
.53361 .53386 .53411 .53435 .53460 |
.84573 .84557 .84542 .84526 .84511 |
.63095 .63136 .63177 .63217 .63258 |
1.58490 1.58388 1-58286 1.58184 1.58083 |
-54829 .54854 •54878 .54902 .54927 |
.83629 .83613 .83597 .83581 .83565 |
-65563 -65604 -65646 •65688 .65729 |
1-52525 1.52429 1-52332 1.52235 1.52139 |
45 44 43 42 41 |
|
20 21 22 23 24 |
53484 .53509 •53534 .53558 .53583 |
.84495 .84480 .84464 . 84448 .84433 |
.63299 .63340 .63380 .63421 .63462 |
1.57981 1.57879 1.57778 1.57676 1.57575 |
54951 .54975 •54999 •55024 .55048 |
.83549 .83533 .83517 .83501 .83485 |
-65771 -65813 -65854 -65896 -65938 |
1.52043 1.51946 1.51850 1.51754 1-51658 |
40 39 38 37 36 |
|
25 26 27 28 29 |
.53607 .53632 .53656 -53681 .53705 |
.84417 .84402 •84386 .84370 .84355 |
•63503 •63544 .63584 •63625 .63666 |
1.57474 1.57372 1.57271 1.57170 1.57069 |
.55072 .55097 .55121 •55145 .55169 |
.83469 •83453 .83437 -83421 .83405 |
.65980 -66021 -66063 -66105 -66147 |
1-51562 1.51466 1.51370 1.51275 1.51179 |
35 34 33 32 31 |
|
30 81 82 33 34 |
.53730 .53754 •53779 .53804 .53828 |
•84339 .84324 .84308 .84292 .84277 |
.63707 .63748 .63789 .63830 .63871 |
1.56969 1.56868 1.56767 1.56667 1.56566 |
.55194 .55218 .55242 .55266 .55291 |
.83389 •83373 •83356 •83340 .83324 |
-66189 .66230 .66272 .66314 •66356 |
1.51084 1.50988 1.50893 1-50797 1 . 50702 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.53853 .53877 .53902 .53926 .53951 |
.84261 .84245 .84230 .84214 .84198 |
.63912 .63953 .63994 .64035 .64076 |
1.56466 1.56366 1.56265 1.56165 1.56065 |
•55315 .55339 .55363 .55388 .55412 |
.83308 .83292 .83276 .83260 •83244 |
•66398 •66440 .66482 .66524 •66566 |
1-50607 1.50512 1-50417 1.50322 1-50228 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.53975 .54000 . 54024 . 54049 .54073 |
.84182 .84167 .84151 •84135 .84120 |
.64117 .64158 •64199 . 64240 •64281 |
1.55966 1.55866 1.55766 1.55666 1.55567 |
.55436 .55460 •55484 .55509 .55533 |
•83228 .83212 .83195 .83179 -83163 |
.66608 .66650 .66692 .66734 .66776 |
1.50133 1.50038 1.49944 1.49849 1.49755 |
20 19 18 17 16 |
|
45 46 47 48 49 |
•54097 .54122 •54146 .54171 .54195 |
•84104 •84038 •84072 •84057 . 84041 |
.64322 •64363 . 64404 . 64446 .64487 |
1.55467 1.55368 .55269 .55170 .55071 |
•55557 .55581 •55605 •55630 -55654 |
-83147 -83131 -83115 •83098 •83082 |
.66818 .66860 .66902 .66944 .66986 |
1.49661 1.49566 1-49472 1-49378 1-49284 |
15 14 13 12 11 |
|
50 51 59, 53 54 |
.54220 . 54244 .54269 .54293 .54317 |
•84025 .84009 •83994 .83978 •83962 |
.64528 •64569 •64610 .64652 . 64693 |
•54972 .54873 .54774 1-54675 1-54676 |
.55678 .55702 .55726 •55750 .55775 |
•83066 .83050 .83034 •83017 .83001 |
.67028 .67071 .67113 .67155 .67197 |
1-49190 1-49097 1-49003 1-48909 1-48816 |
10 9 8 7 6 |
|
55 56 57 58 59 |
.54342 •54366 • 54391 .54415 . 54440 |
.83946 .83930 •83915 .83899 •83883 |
.64734 .64775 .64817 •64858 •64899 |
1-54478 1-54379 1.54281 1.54183 1 • 54085 |
•55799 .55823 .55847 •55871 .55895 |
•82985 82969 •82953 •82936 •82920 |
.67239 .67282 .67324 .67366 .67409 |
1-48722 1.48629 1-48536 1-48442 1.48349 |
5 4 3 2 |
|
60 |
• 54464 |
.83867 |
•64941 |
1-53986 |
55919 |
•82904 |
.67451 |
1.48256 |
O |
|
' |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
57°
222
66°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS, 34° 35°
|
Sin. |
Cos. |
Tan. |
Cot, |
Sin. |
Cos. |
Tan. |
Cot. |
9 |
|
|
0 2 8 |
55919 55943 55968 55992 56016 |
82904 82887 82871 82855 82839 |
67451 67493 67536 67578 67620 |
1.48256 1-48163 1.48070 1.47977 1.47885 |
57358 57381 57405 57429 57453 |
81915 81899 81882 81865 81848 |
70021 70064 .70107 •70151 •70194 |
1.42815 1.42726 1.42638 .42550 .42462 |
60 59 58 57 56 |
|
5 6 7 8 9 |
56040 56064 56088 56112 56136 |
82822 82806 82790 82773 82757 |
67663 67705 67748 67790 67832 |
1-47792 1-47699 1.47607 1.47514 1.47422 |
57477 57501 57524 57548 .57572 |
81832 81815 81798 .81782 •81765 |
•70238 •70281 •70325 •70368 -70412 |
.42374 .42286 •42198 .42110 1-42022 |
53 54 53 52 51 |
|
10 11 12 13 14 |
56160 56184 56208 56232 56256 |
82741 82724 82708 .82692 .82675 |
67875 67917 67960 68002 68045 |
1.47330 1.47238 1.47146 1-47053 1-46962 |
•57596 .57619 •57643 .57667 .57691 |
•81748 •81731 •81714 •81698 .81681 |
•70455 •70499 - 70542 -70586 -70629 |
1-41934 1.41847 1.41759 1.41672 1.41584 |
5O 49 48 47 46 |
|
15 16 17 18 19 |
56280 56305 56329 56353 56377 |
.82659 .82643 .82626 .82610 .82593 |
68088 68130 .68173 .68215 .68258 |
1.46870 1.46778 1.46686 1.46595 1.46503 |
-57715 .57738 -57762 •57786 .57810 |
-81664 .81647 .81631 .81614 •81597 |
-70673 -70717 -70760 -70804 - 70848 |
1.41497 1.41409 1-41322 1.41235 1.41148 |
45 44 43 42 41 |
|
20 21 22 23 24 |
56401 .56425 . 56449 . 56473 .56497 |
.82577 .82561 .82544 .82528 .82511 |
.68301 .68343 .68386 .68429 .68471 |
1.46411 1-46320 1-46229 1.4*6137 1.46046 |
.57833 •57857 •57881 •57904 .57928 |
-81580 .81563 .81546 .81530 -81513 |
•70891 •70935 -70979 •71023 •71066 |
1.41061 1.40974 1.40887 1.40800 1-40714 |
4O 39 38 37 36 |
|
25 26 27 28 29 |
.56521 56545 .56569 .56593 .56617 |
•82495 .82478 .82462 .82446 .82429 |
.68514 .68557 .68600 .68642 .68685 |
1.45955 1.45864 1.45773 1.45682 1.45592 |
.57952 -57976 .57999 -58023 .58047 |
-81496 •81479 .81462 .81445 .81428 |
.71110 •71154 -71198 .71242 -71285 |
•40627 .40540 .40454 .40367 .40281 |
35 34 33 32 31 |
|
30 31 32 33 34 |
.56641 .56665 .56689 .56713 •56736 |
.82413 .82396 .82380 .82363 .82347 |
.68728 .68771 .68814 .68857 .68900 |
1.45501 1.45410 1.45320 1.45229 1.45139 |
.58070 .58094 .58118 .58141 .58165 |
.81412 .81395 .81378 .81361 .81344 |
•71329 •71373 .71417 .71461 .71505 |
.40195 .40109 1-40022 1.39936 1-39850 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.56760 . 5678<c .56803 .56832 -568'i6_ |
.82330 .82314 .82297 .82281 .82264 |
.68942 68985 .69028 .69071 -69114 |
1-45049 1-44958 1.44868 1-44778 1-44688 |
.58189 .58212 .58236 .58260 -58283 |
•81327 .81310 .81293 .81276 .81259 |
.71549 .71593 .71637 .71681 •71725 |
1-39764 1.39679 1.39503 1-39507 1-39421 |
25 24 23 22 -21 |
|
40 41 42 43 44 |
.56880 .56904 .56928 •56952 .56976 |
.82248 •82231 .82214 .82198 .82181 |
.69157 .69200 .69243 .69286 -69329 |
1-44598 1.44508 1.44418 1-44329 1.44239 |
-58307 -58330 -58354 -58378 .58401 |
•81242 •81225 •81208 •81191 •81174 |
-71769 -71813 .71857 .71901 .71946 |
1-39336 1-39250 1-39165 1.39079 1-38994 |
20 19 18 17 16 |
|
45 46 47 48 49 |
.57000 .57024 •57047 .57071 .57095 |
.82165 .82148 •82132 .82115 .82098 |
•69372 .69416 •69459 .69502 .69545 |
1.44149 1.44060 1-43970 1.43881 1-43792 |
.58425 . 58449 .58472 .58496 .58519 |
.81157 •81140 .81123 •81106 .81089 |
-71990 -72034 .72078 .72122 •72167 |
1-38909 1-38824 1.38738 1-38653 1.38568 |
15 14 13 12 Ui |
|
50 51 52 53 54 |
.57119 .57143 .57167 •57191 .57215 |
•82082 •82065 •82048 .82032 .82015 |
•69588 •69631 •69675 •69718 •69761 |
1.43703 1-43614 1.43525 1-43436 1.43347 |
.58543 .58567 .58590 .58614 •58637 |
•81072 •81055 .81038 -81021 .81004 |
•72211 •72255 .72299 . 72344 •72388 |
1.38484 1.38399 1-38314 1-38229 1.38145 |
10 9 8 7 _6 |
|
55 56 57 58 59 |
•57238 •57262 •57286 •57310 •57334 |
.81999 •81982 •81965 81949 81932 |
•69804 •69847 •69891 •69934 •69977 |
1-43258 1.43169 1-43080 1.42992 1.42903 |
.58661 .58684 •58708 .58731 .58755 |
-80987 .80970 .80953 .80936 .80919 |
.72432 •72477 .72521 .72565 -72610 |
1.38060 1.37976 1.37891 1.37807 1-37722 |
9 3 2 |
|
60 |
.57358 |
81915 |
.70021 |
1-42815 |
.58779 |
-80902 |
-72654 |
1-37638 |
0. |
|
"^ |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
|
|
£ |
;s° |
2 |
23 |
fi |
4° |
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS 36° 37°
|
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
, |
|
|
0 2 3 |
•58779 •58802 58826 .58849 .58873 |
80902 80835 80867 80350 80833 |
.72654 .72699 .72743 .72788 .72832 |
1-37638 1.37554 1.37470 1.37386 1-37302 |
•60182 •60205 •60228 •60251 . 60274 |
-79864 - 79846 -79829 .79811 -79793 |
-75355 . 75401 •75447 -75492 -75538 |
1-32704 1-32624 1-32544 1-32464 1-32384 |
60 59 58 57 56 |
|
5 6 7 8 9 |
58896 58920 58943 58967 58990 |
80816 80799 80782 80765 80748 |
•72877 .72921 72966 .73010 73055 |
1.37218 1.37134 1.37050 1.36967 1.36883 |
. 60298 .60321 .60344 -60367 .60390 |
.79776 .79758 .79741 .79723 .79706 |
-75584 -75629 -75675 .75721 .75767 |
1-32304 1-32224 1-32144 1-32064 1.31984 |
55 54 53 52 SI |
|
10 11 12 13 14 |
59014 59037 59061 59084 59108 |
80730 80713 80696 80679 80662 |
73100 73144 73189 73234 73278 |
1.36800 1.36716 1.36633 1.36549 1.36466 |
. 60414 .60437 . 60460 .60483 -60506 |
.79688 .79671 .79653 .79635 .79618 |
.75812 .75858 -75904 •75950 .75996 |
1.31904 1.31825 1-31745 1.31666 1-31586 |
50 49 48 47 46 |
|
15 16 17 18 19 |
59131 59154 59178 59201 59225 |
80644 80627 80610 80593 80576 |
73323 73368 73413 73457 73502 |
1.36383 1.36300 1.36217 1.36134 1.36053 |
•60529 .60553 .60576 .60599 .60622 |
•79600 •79583 .79565 -79547 .79530 |
•76042 .76088 .76134 •76180 76226 |
1-31507 1.31427 1-31348 1-31269 1-31190 |
45 44 43 42 41 |
|
20 21 22 23 24 |
59248 59272 59295 59318 59342 |
80558 8054.1 80524 80507 80489 |
73547 73592 73637 73681 73726 |
1.35968 1.35885 1.35802 1.35719 1-35637 |
. 60645 .60668 •60691 -60714 •60738 |
79512 .79494 .79477 •79459 •79441 |
.76272 .76318 .76364 •76410 .76456 |
1-31110 1.31031 1.30952 1.30873 1-30795 |
4O 39 38 37 36 |
|
25 26 27 28 29 |
59365 59389 59412 59436 59459 |
80472 80455 80438 80420 80403 |
73771 73816 73861 73906 73951 |
1.35554 1-35472 1.35389 1.35307 1.35224 |
.60761 •6G784 •60807 •60830 •60853 |
.79424 •79406 •79388 •79371 •79353 |
.76502 .76548 .76594 -76640 -76686 |
1-30716 1.30637 1.30558 1 • 30480 1-30401 |
35 34 33 32 31 |
|
30 81 32 33 34 |
59482 59506 59529 59552 59576 |
80386 80368 80351 80334 80316 |
73996 .74041 74086 74131 74176 |
1.35142 1.35060 1.34978 1.34896 1.34814 |
•60876 •60899 •60922 •60945 .60968 |
.79335 •79318 .79300 .79282 .79264 |
.76733 .76779 -76825 -76871 .76918 |
1-30323 1.30244 1-30166 1-30087 1-30009 |
30 29 28 27 26 |
|
35 36 37 38 39_ |
59599 59622 59646 59669 . 59693^ |
80299 80282 80264 80247 80230 |
74221 74267 74312 74357 .74402 |
1.34732 1.34650 1-34568 1.34487 1-34405 |
.60991 .61015 •61038 •61061 •61084 |
79247 .79229 -79211 .79193 .79176 |
.76964 .77010 •77057 -77103 •77149 |
1-29931 1-29853 1.29775 1-29696 1-29318 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.59716 .59739 .59763 .59786 .59809 |
80212 80195 .80178 .80160 .80143 |
•74447 .74492 .74538 .74583 .74628 |
1.34323 1-34242 1.34160 1.34079 1.33998 |
•61107 .61130 •61153 •81176 •61199 |
-79158 -79140 .79122 .79105 .79087 |
•77196 -77242 •77289 •77335 .77382 |
1-29541 1-29463 1-29385 1.29307 1-29229 |
20 19 18 17 16 |
|
45 46 47 48 40 |
59832 .59856 .59879 .59902 .59926 |
.80125 •80108 .80091 .80073 .80056 |
.74674 .74719 .74764 .74810 •74855 |
1.33916 1.33835 1.33754 1.33673 1.33592 |
•61222 •61245 •61268 .61291 •61314 |
.79069 .79051 .79033 .79016 .78998 |
- 77428 -77475 -77521 -77568 -77615 |
•29152 •29074 •28997 .28919 .28842 |
15 14 13 12 11 |
|
50 51 52 53 54 |
.59949 .59972 •59995 •60019 .60042 |
.80038 .80021 .80003 .79986 .79968 |
.74900 .74946 .74991 .75037 .75082 |
1.33511 1.33430 1.33349 1.33268 1.33187 |
•61337 •61360 161383 j. 61406 .61429 |
.78980 .78962 .78944 .78926 .78908 |
-77661 .77708 .77754 .77801 .77848 |
.28764 •28687 .28610 .28533 .28456 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•60065 .60089 •60112 •60135 .60158 |
.79951 .79934 .79916 .79899 .79881 |
.75128 •75173 .75219 .75264 .75310 |
1.33107 1.33026 1-32946 1.32865 1.32785 |
•61451 .61474 .61497 •61520 .61543 |
-78891 •78873 .78855 -78837 78819 |
.77895 .77941 -77988 -78035 -78082 |
-28379 -28302 -28225 -28148 1.28071 |
5 4 3 2 |
|
60 |
.60182 |
.79864 |
.75355 |
1.32704 |
.61566 |
•78801 |
-78129 |
1-27994 |
0 |
|
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
'- |
|
|
I |
a* |
2'< |
VL |
i |
»• |
-NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 38° 39°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
0 1 2 3 4 |
.61566 •61589 •61612 •61635 •61658 |
•78801 •78783 .78765 •78747 •78729 |
•78129 .78175 •78222 -78269 •78316 |
1-27994 1.27917 1.27841 1.27764 1-27688 |
•62932 .62955 .62977 •63000 •63022 |
•77715 .77696 .77678 .77660 . 77641 |
.80978 •81027 .81075 •81123 •81171 |
1-23490 1-23416 1-23343 1.23270 1.23196 |
6O 59 58 57 56 |
|
5 6 7 8 9 |
•61681 .61704 •61726 .61749 •61772 |
.78711 .78694 •78676 78658 . 78640 |
.78363 •78410 . 78457 •78504 •78551 |
1.27611 1.27535 1.27458 1-27382 1.27306 |
. 63045 -63068 •63090 •63113 .63135 |
•77623 -77605 77586 -77568 -77550 |
81220 .81268 .81316 .81364 •81413 |
1.23123 1.23050 1-22977 1.22904 1-22831 |
55 54 53 52 51 |
|
10 11 12 13 14 |
•61795 .61818 .61841 •61864 .61887 |
.78622 •78604 .78586 •78568 -78550 |
.78598 78645 •78692 .78739 •78786 |
1.27230 1.27153 1.27077 1.27001 1.26925 |
.63158 •63180 .63203 •63225 •63248 |
.77531 .77513 . 77494 •77476 •77458 |
•81461 •81510 .81558 •81606 .81655 |
1.22758 1.22685 1-22612 1-22539 1-22467 |
50 49 48 47 46 |
|
15 16 17 18 19 |
•61909 •61932 .61955 •61978 •62001 |
.78532 •78514 •78496 •78478 -78460 |
•78834 .78881 .78928 -78975 -79022 |
1.26849 1.26774 1.26698 1.26622 1.26546 |
•63271 •63293 •63316 -63338 -63361 |
•77439 . 77421 . 77402 .77384 •77366 |
.81703 .81752 •81800 •81849 -81898 |
1-22394 1.22321 1.22249 1-22176 1.22104 |
45 44 43 42 41 |
|
20 21 22 23 24 |
•62024 .62046 •62069 .62092 •62115 |
. 78442 •78424 •78405 •78387 .78369 |
.79070 .79117 •79164 .79212 •79259 |
1-26471 1-26395 1.26319 1-26244 1.26169 |
-63383 -63406 -63428 -63451 -63473 |
•77347 .77329 .77310 .77292 •77273 |
-81946 -81995 -82044 •82092 .82141 |
1-22031 1-21959 1-21886 1-21814 1.21742 |
40 39 38 37 36 |
|
25 26 27 28 29 |
•62138 •62160 •62183 •62206 •62229 |
•78351 .78333 •78315 .78297 •78279 |
•79306 .79354 . 79401 . 79449 .79496 |
1-26093 1-26018 1-25943 1-25867 1-25792 |
-63496 -63518 -63540 -63563 .63585 |
•77255 •77236 -77218 .77199 •77181 |
•82190 •82238 •82287 .82336 .82385 |
1-21670 1.21598 1.21526 1.21454 1-21382 |
35 34 33 32 31 |
|
30 31 32 33 34 |
•62251 •62274 .62297 .62320 .62342 |
•78261 .78243 •78225 •78206 .78188 |
•79544 .79591 .79639 •79686 .79734 |
1.25717 1-25642 1.25567 1-25492 1.25417 |
•63608 .63630 .63653 •63675 -63698 |
-77162 . 77144 -77125 •77107 •77088 |
. 82434 •82483 .82531 -82580 -82629 |
1.21310 1-21238 1-21166 1-21094 1-21023 |
30 29 28 27 26 |
|
35 36 37 38 39 |
•62365 .62388 .62411 .62433 •62456 |
•78170 .78152 •78134 .78116 .78098 |
.79781 .79829 .79877 -79924 •79972 |
1.25343 1.25268 1.25193 1.25118 1.25044 |
.63720 .63742 -63765 -63787 -63810 |
•77070 •77051 •77033 .77014 •76996 |
-82678 •82727 •82776 •82825 .82874 |
1-20951 1-20879 1-20808 1-20736 1-20665 |
25 24 23 22 21 |
|
40 41 42 43 44 |
•62479 .62502 -62524 •62547 .62570 |
•78079 .78061 .78043 •78025 -78007 |
.80020 •80067 .80115 •80163 .80211 |
1.24969 1.24895 1-24820 1.24746 1.24672 |
•63832 .63854 •63877 •63899 .63922 |
•76977 •76959 . 76940 •76921 •76903 |
.82923 .82972 •83022 .83071 .83120 |
1-20593 -20522 •20451 -20379 •20308 |
2O 19 18 17 16 |
|
45 46 47 48 49 |
.62592 •62615 •62638 •62660 •62683 |
.77988 .77970 .77952 .77934 .77916 |
•80258 •80306 •80354 .80402 •80450 |
1.24597 1.24523 1.24449 1.24375 1.24301 |
•63944 •63966 -63989 •64011 .64033 |
•76884 •76866 •76847 •76828 •76810 |
.83169 .83218 •83268 •83317 -83366 |
.20237 •20166 •20095 1-20024 1-19953 |
15 14 13 12 11 |
|
50 51 52 53 54 |
•62706 •62728 •62751 •62774 .62796 |
•77897 .77879 .77861 . 77843 .77824 |
•80498 . 80548 -80594 •80642 .80690 |
1-24227 1.24153 1.24079 1.24005 1.23931 |
•64056 •64078 . 64100 .64123 •64145 |
-76791 -76772 -76754 .76735 •76717 |
-83415 -83465 -83514 -83564 -83613 |
1-19882 1-19811 1-19740 1-19669 1-19599 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•62819 •62842 •62864 •62887 .62909 |
•77806 -77788 .77769 •77751 .77733 |
•80738 .80786 .80834 •80882 •80930 |
1.23858 1-23784 1.23710 1-23637 1-23563 |
.64167 •64190 .64212 .64234 •64256 |
-76698 •76679 •76661 •76642 •76623 |
-83662 -83712 -83761 -83811 -83860 |
1-19528 1.19457 1.19387 1.19316 1-19246 |
5 4 3 2 1 |
|
60 |
•62932 |
•77715 |
80978 |
1-23490 |
-64279 |
-76604 |
-83910 |
1.19175 |
0 |
|
/ |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
51°
225
50°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 40° 41°
|
/ |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t |
|
0 2 3 4 |
64279 64301 64323 64346 64368 |
76604 76586 76567 76548 76530 |
83910 83960 84009 84059 84108 |
1.19175 1-19105 1-19035 1-18964 1-18894 |
65606 65628 65650 65672 65694 |
75471 75452 75433 75414 75395 |
86929 86980 87031 87082 87133 |
1.15037 1.14969 1-14902 1-14834 1-14767 |
60 69 58 57 56 |
|
5 6 7 8 9 |
64390 64412 64435 64457 64479 |
76511 76492 76473 76455 76436 |
84158 84208 84258 84307 84357 |
1.18824 1-18754 1.18684 1-18614 1.18544 |
65716 65738 65759 65781 65803 |
75375 75356 75337 75318 •75299 |
87184 87236 87287 87338 87389 |
1-14699 1-14632 1-14565 1.14498 1.14430 |
55 54 53 52 51 |
|
10 11 12 13 14 |
64501 64524 64546 64568 64590 |
76417 76398 76380 76361 76342 |
84407 84457 84507 84556 84606 |
1.18474 1 . 18404 1.18334 1-18264 1.18194 |
65825 65847 .65869 .65891 •65913 |
.75280 •75261 . 75241 •75222 .75203 |
87441 87492 87543 87595 87646 |
1-14363 1-14296 1-14229 1.14162 1.14095 |
50 49 48 47 46 |
|
15 16 17 18 19 , |
64612 64635 64657 64679 64701 |
76323 76304 •76286 .76267 76248 |
84656 84706 •84756 84806 84856 |
1.18125 1.18055 1-17986 1-17916 1-17846 |
.65935 .65956 •65978 - 66000 -66022 |
•75184 •75165 •75146 •75126 •75107 |
.87698 •87749 •87801 •87852 .87904 |
1-14028 1-13961 1.13894 1-13828 1-13761 |
45 44 43 42 41 |
|
2O 21 22 23 24 |
64723 . 64746 .64768 •64790 •64812 |
.76229 •76210 •76192 •76173 •76154 |
•84906 • ii4956 •85006 •85057 •85107 |
1.17777 1-17708 1-17638 1-17569 1.17500 |
. 66044 -66066 -66088 -66109 •66131 |
.75088 •75069 -75050 •75030 •75011 |
.87955 .88007 •88059 •88110 •88162 |
1-13694 1-13627 1-13561 1-13494 1-13428 |
40 39 38 37 36 |
|
25 26 27 28 29 |
.64834 .64856 •64878 .64901 .64923 |
-76135 •76116 .76097 .76078 .76059 |
•85157 •85207 •85257 •85308 •85358 |
1-17430 1.17361 1-17292 1.17223 1-17154 |
•66053 •66175 •66197 •66218 . 66240 |
.74992 •74973 •74953 . 74934 •74915 |
•88204 •88265 •88317 •88369 •88421 |
1.13361 1-13295 1-13228 1-13162 1-13096 |
35 34 33 32 31 |
|
30 31 32 33 34 |
. 64945 •64967 •64989 .65011 .65033 |
•76041 .76022 .76003 •75984 •75965 |
•85408 •85458 •85509 •85559 •85609 |
1-17085 1-17016 1-16947 1.16878 1.16809 |
•66262 .66284 •66306 •66327 •66349 |
•74896 -74876 -74857 •74838 •74818 |
•88473 •88524 •88576 -88628 -88680 |
1.13029 1.12963 1.12897 1-12831 1-12765 |
30 29 28 27 26 |
|
35 36 37 38 39 |
.65055 •65077 .65100 •65122 •65144 |
.75946 •75927 •75908 •75889 •75870 |
•85660 •85710 •85761 •85811 -85862 |
1-16741 1.16672 1-16603 1-16535 1-16466 |
•66371 •66393 •66414 •66436 -66458 |
•74799 • 74780 . 74760 . 74741 -74722 |
•88732 -88784 -88836 -88888 -88940 |
1-12699 1-12633 1-12567 1-12501 1-12435 |
25 24 23 22 21 |
|
40 41 42 43 44 |
•65166 •65188 •65210 •65232 •65254 |
•75851 •75832 -75813 •75794 •75775 |
-85912 -85963 •86014 •86064 -86115 |
1.16398 1.16329 1-16261 1-16192 1.16124 |
. 66480 •66501 .66523 •66545 •66566 |
- 74703 -74683 . 74664 • 74644 -74625 |
.88992 •89045 -89097 •89149 .89201 |
1.12369 1.12303 1.12238 1-12172 1.12106 |
20 19 18 17 16 |
|
45 46 47 48 49 |
•65276 •65298 •65320 •65342 •65364 |
.75756 •75738 •75719 •75700 •75680 |
•86166 86216 .86267 •86318 -86368 |
1.16056 1-15987 1-15919 1-15851 1-15783 |
•66588 •66610 •66632 •66653 •66675 |
. 74606 • 74586 •74567 • 74548 • 74528 |
•89253 .89306 •89358 -89410 .89463 |
1.12041 1-11975 1.11909 1-11844 1-11778 |
15 14 13 12 11 |
|
50 51 52 53 54 |
.65386 .65408 .65430 •65452 .65474 |
•75661 .75642 •75623 •75604 •75585 |
•86419 •86470 •86521 •86572 •86623 |
1-15715 1.15647 1-15579 1-15511 1-15443 |
•66697 •66718 •66740 •66762 •66783 |
. 74509 . 74489 . 74470 . 74451 .74431 |
•89515 •89567 •89620 •89672 •89725 |
1-11713 1.11648 1.11582 1.11517 1-11452 |
10 9 8 7 6 |
|
55 56 57 58 59 |
•65496 .65518 •65540 .65562 •65584 |
•75566 •75547 •75528 .75509 .75490 |
•86674 •86725 .86776 .86827 .86878 |
1.15375 1.15308 1-15240 1-15172 1-15104 |
-66805 •66827 •66848 •66870 •66891 |
.74412 •74392 •74373 •74353 . 74334 |
.89777 .89830 •89883 •89935 •89988 |
1-11387 1-11321 1-11256 1-11191 1.11126 |
5 3 2 |
|
60 |
.65606 |
.75471 |
-86929 |
1.15037 |
-66913 |
-74314 |
-90040 |
1-11061 |
0 |
|
' |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
' |
49°
226
48°
-NATURAL SINES, COSINES, TANGENTS, AND COTANuENTS. 43° 43°
|
t |
Sin. |
Cos. |
Tan. |
Cot. |
Sin. |
Cos. |
Tan. |
Cot. |
t |
|
o 2 8 |
.66913 66935 .66956 .66978 .66999 |
•74314 74295 74276 74256 74237 |
.90040 •90093 •90146 •90199 .90251 |
1-11061 1 10996 1-10931 1.10867 1.10802 |
68200 68221 68242 68264 68285 |
73135 -73116 73096 -73076 -73056 |
93252 -93306 -93360 -93415 -93469 |
1-07237 1-07174 1-07112 1-07049 1-06987 |
60 59 58 57 56 |
|
5 6 7 8 9 |
.67021 67043 .67064 •67086 .67107 |
74217 74198 74178 74159 74139 |
90304 90357 90410 90463 90516 |
1-10737 1.10672 1-10607 1-10543 1 • 10478 |
68306 68327 68349 68370 68391 |
73036 -73016 72996 72976 -72.957 |
-93524 -93578 •93633 -93688 -93742 |
1-06925 1-06862 1-06800 1-06738 1-06676 |
55 54 53 52 51 |
|
10 11 12 13 14 |
.67129 .67151 67172 67194 67215 |
74120 74100 74080 74061 74041 |
90569 90621 90674 90727 90781 |
1-10414 1-10349 1-10285 1-10220 1.10156 |
68412 68434 68455 68476 68497 |
-72937 72917 72897 72877 72857 |
-93797 -93852 -93906 -93961 -94016 |
1-06613 1-06551 1-06489 1-06427 1 06365 |
5O 49 48 47 46 |
|
15 16 17 18 19 |
67237 67258 67280 67301 87333 |
74022 74002 73983 73963 73944 |
90834 90887 90940 90993 91046 |
1.10091 1.10027 1.09963 1.09899 1-09834 |
68518 68539 68561 68582 68603 |
72837 72817 72797 72777 72757 |
.94071 -94125 -94180 -94235 -94290 |
-06303 -06241 -06179 -06117 .06056 |
45 44 43 42 .41 |
|
20 21 22 23 24 |
67344 67366 67387 67409 67430 |
73924 73904 73885 73865 73846 |
91099 91153 91206 91259 91313 |
1.09770 1-09706 1.09642 1-09578 1-09514 |
68624 68645 68666 68688 68709 |
72737 72717 72697 72677 72657 |
-94345 -94400 94455 -94510 -94565 |
-05994 -05932 1-05870 1-05809 1-05747 |
40 39 38 37 36 |
|
25 26 27 28 29 |
67452 67473 67495 67516 67538 |
73826 73806 73787 73767 73747 |
91368 91419 91473 91526 91580 |
1-09450 1-09386 1-09322 1-09258 1-09195 |
68730 68751 68772 68793 68814 |
72637 72617 72597 72577 72557 |
.94620 .94676 .94731 •94786 . 94841 |
1-05685 1-05624 1-05562 1-05501 1-05439 |
35 34 33 32 31 |
|
30 31 32 33 34 |
67559 67580 67602 67623 67645 |
73728 73703 73688 73669 73849 |
91633 91687 91740 91794 91847 |
1-09131 1-09067 1-09003 1-08940 1-08876 |
68835 68857 68378 68899 68920 |
72537 72517 72497 72477 .72457 |
•94896 •94952 •95007 •95062 .95118 |
1-05378 1-05317 1-05255 1-05194 1-05133 |
30 29 28 le |
|
35 36 37 38 39 |
•67666 •67688 -67709 •67730 67752 |
73629 73810 73590 73570 73551 |
91901 91955 92008 92062 92116 |
1-08813 1-08749 1.08686 1-08622 1-08559 |
68941 68962 68983 69004 69025 |
.72437 -72417 -72397 -72377 -72357 |
•95173 •95229 •95284 •95340 .95395 |
1.05072 1.05010 1 . 04949 1-04888 1.04827 |
25 24 23 22 21 |
|
40 41 42 43 44 |
.67773 •67795 •67816 •67837 .67859 |
73531 73511 73491 73472 73452 |
92170 92224 92277 92331 92385 |
1-08496 1-08432 1.08369 1-08306 1-08243 |
69046 69067 69088 69109 .69130 |
-72337 -72317 •72297 .72277 .72257 |
.95451 .95506 .95562 .95618 .95673 |
1-04766 1-04705 1.04644 1-04583 1-04522 |
20 19 18 17 _16 |
|
45 46 47 48 49 |
-67880 •67901 .67923 •67944 •67965 |
73432 73413 73393 73373 73353 |
92439 92493 92547 92601 .92655 |
1.08179 1-08118 1.08053 1.07990 1.07927 |
-69151 -69172 -69193 -69214 .69235 |
.72236 .72216 •72196 •72176 .72156 |
.95729 .95785 -95841 .95897 .95952 |
1-04461 1-04401 1-04340 1 . 04279 1-04218 |
15 14 13 12 11 |
|
50 51 52 53 54_ |
.67987 •68008 •68029 •68051 •68072 |
73333 73314 73294 73274 •73254 |
•92709 •92763 .92817 •92872 .92926 |
1-07864 1-07801 1-07738 1-07676 1-07613 |
-69256 •69277 -69298 .69319 - 69340 |
.72136 .72116 .72095 .72075 .72055 |
.96008 .96064 .96120 .96176 .98232 |
1.04158 1.04097 1-04038 1.03976 1-03915 |
10 9 ? _6 |
|
55 56 57 58 59 |
•68093 •68115 .68138 •68157 .68179 |
•73234 .73215 .73195 •73175 •73155 |
.92980 •93034 .93088 •93143 •93197 |
1.07550 1.07487 1-07425 1-07362 1-07299 |
-69361 .69382 .69403 •69424 . 69445 |
•72035 .72015 .71995 .71974 .71954 |
.96288 -96344 -96400 96457 .96513 |
1-03855 1.03794 1.03734 1-03674 1.03613 |
5 3 2 |
|
60 |
.68200 |
.73135 |
•93252 |
1-07237 |
69466 |
71934 |
-96569 |
1.03553 |
0 |
|
— 7— |
Cos. |
Sin. |
Cot. |
Tan. |
Cos. |
Sin. |
Cot. |
Tan. |
47°
227
46°
TABLE 10.— NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS 44° 44°
|
/ 0 2 3 ,4 5 6 7 8 9 |
Sin. |
Cos. |
Tan. |
Cot. |
' |
; |
Sin. |
Cos. |
Tan. |
Cot. |
/ |
|
.69466 •69487 .69508 •69529 •69549 |
•71934 .71914 •71894 •71873 •71853 |
.96569 .96625 .96681 .96738 .96794 |
1.03553 1.03493 1.03433 1-03372 1-03312 |
60 59 58 57 56 |
3O 31 32 33 34 |
.70091 .70112 .70132 •70153 .70174 |
•71325 -71305 -71284 -71264 -71243 |
.98270 -98327 .98384 -98441 .98499 |
1-01761 1-01702 1-01642 1.01583 1-01524 |
30 29 28 27 26 25 24 23 22 21 20 19 18 17 -IS 15 14 13 12 11 |
|
|
.69570 •69591 •69612 •69633 •69654 |
•71833 .71813 .71792 .71772 .71752 |
•96850 •96907 .96963 .97020 .97076 |
1.03252 1.03192 1-03132 1.03072 1.03012 |
55 54 53 52 51 |
35 36 37 38 39 |
•70195 •70215 •70236 •70257 .70277 |
•71223 -71203 -71182 -71162 •71141 |
.98556 .98613 •98671 .98728 .98786 |
1-01465 1.01406 1.01347 1.01288 1-01229 |
||
|
10 11 12 13 ii_ 15 16 17 18 i£- 20 21 22 23 24_ 25 26 27 28 29_ &L |
•69675 •69696 .69717 •69737 .69758 •69779 .69800 .69821 .69842 .69862 |
•71732 .71711 .71691 •71671 .71650 |
.97133 .97189 .97246 •97302 •97359 |
1-02952 1.02892 1.02832 1.02772 1.02713 |
50 49 48 47 46 |
40 41 42 43 44 |
-70298 -70319 . 70339 .70360 .70381 |
-71121 .71100 . 71080 .71059 .71039 |
98843 .98901 •98958 .99016 -99073 |
1-01170 1.01112 1.01053 1-00994 1.00935 |
|
|
.71630 .71610 .71590 .71569 •71549 |
•97416 .97472 •97529 .97586 .97643 |
1-02653 1.02593 1.02533 1.02474 1-02414 |
45 44 43 42 41 |
45 46 47 48 49 |
• 70401 - 70422 70443 -70463 - 70484 |
. 71019 •70998 -70978 -70957 70937 |
-99131 -99189 -99247 .99304 -99362 |
1.00876 1.00818 1-00759 1.00701 1.00642 |
|||
|
.69883 •69904 .69925 .69946 .69966 |
.71529 .71508 •71488 .71468 •71447 |
• 97700 .97756 •97813 .97870 .97927 |
1-02355 1.02295 1.02236 1.02176 1.02117 1-02057 1.01998 1-01939 1-01879 1.01820 |
40 39 38 37 36 |
50 51 52 53 54 |
•70505 •70525 •70546 .70567 •70587 |
•70916 •70896 • 70875 • 70855 • 70834 |
.99420 •99478 -99536 .99594 .99652 |
1.00583 1.00525 1-00467 1-00408 1.00350 |
10 9 8 7 6 |
|
|
•69987 • 70008 . 70029 . 70049 . 70070 |
.71427 . 71407 •71386 •71366 .71345 •71325 |
•97984 98041 .98098 •98155 .98213 |
35 34 33 32 31 |
55 56 57 58 59 |
- 70608 -70628 - 70649 -70670 . 70690 |
. 70813 • 70793 - 70772 - 70752 -70731 |
.99710 .99768 .99826 .99884 .99942 |
1-00291 1-00233 1-00175 1-00116 1-00058 |
5 4 3 2 1 -P |
||
|
•70091 |
.98270 |
1-01761 |
30 |
6O |
.70711 |
•70711 |
1 • 00000 |
1-00000 |
|||
|
Cos. |
Sin. |
Cot. |
Tan. |
' |
' |
Cos. |
Sin. |
Cot. |
Tan. |
45°
228
45°
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 0° 1° 2° 3°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
0 2 3 4 |
.00000 •00000 • 00000 .00000 -00000 |
.00000 .00000 .00000 .00000 .00000 |
•00015 .00016 .00016 .00017 •00017 |
.00015 .00016 .00016 .00017 .00017 |
.00061 .00062 •00063 •00064 •00065 |
.00061 .00062 .00063 .00064 .00065 |
•00137 •00139 •00140 •00142 •00143 |
.00137 .00139 •00140 •00142 •00143 |
0 1 2 3 |
|
5 6 7 8 9 |
.00000 .00000 .00000 .00000 .00000 |
.00000 .00000 .00000 .00000 . 00000 |
•00018 .00018 .00019 .00020 .00020 |
.00018 .00018 .00019 .00020 .00020 |
.00066 .00067 .00068 .00069 .00070 |
.00066 •00067 .00068 .00069 •00070 |
•00145 •00146 •00148 •00150 •00151 |
.00145 .00147 •00148 .00150 •00151 |
5 6 7 8 9 |
|
10 11 12 13 14 |
.00000 •00001 .00001 .00001 .00001 |
.00000 .00001 .00001 .00001 .00001 |
•00021 •00021 •00022 •00023 •00023 |
.00021 .00021 .00022 .00023 .00023 |
•00071 •00073 •00074 •00075 -00076 |
.00072 .00073 .00074 .00075 .00076 |
•00153 •00154 •00156 .00158 .00159 |
.00153 .00155 .00156 .00158 .00159 |
1O 11 12 13 14 |
|
15 16 17 18 19 |
.00001 .00001 .00001 .00001 .00002 |
.00001 .00001 .00001 .00001 -00002 |
•00024 •00024 •00025 •00026 -00026 |
.00024 •00024 .00025 .00026 .00026 |
•00077 .00078 .00079 .00081 -00082 |
.00077 .00078 •00079 .00081 .00082 |
.00161 •00162 •00164 •00166 •00168 |
.00161 .00163 .00164 •00166 .00168 |
15 16 17 18 19 |
|
20 21 22 23 24 |
.00002 -00002 00002 -00002 00002 |
.00002 .00002 .00002 .00002 .00002 |
-00027 •00028 .00028 .00029 -00030 |
•00027 .00028 .00028 .00029 .00030 |
•00083 -00084 00085 -00087 •00088 |
.00083 •00084 .00085 •00087 .00088 |
•00169 •00171 •00173 •00174 •00176 |
.00169 .00171 •00173 •00175 •00176 |
20 21 22 23 24 |
|
25 26 27 28 29 |
-00003 00003 -00003 -00003 - 00004 |
.00003 .00003 .00003 .00003 •00004 |
•00031 .00031 •00032 .00033 00034 |
.00031 .00031 .00032 •00033 •00034 |
-00089 00090 •00091 •00093 •00094 |
•00089 .00090 .00091 •00093 •00094 |
•00178 •00179 •00181 •00183 •00185 |
•00178 .00180 .00182 .00183 .00185 |
25 26 27 28 29 |
|
30 31 32 33 34 |
.00004 .00004 . 00004 - 00005 -00005 |
.00004 .00004 .00004 •00005 .00005 |
-00034 •00035 •00036 •00037 .00037 |
•00034 .00035 •00036 .00037 •00037 |
00095 .00096 -00098 .00099 .00100 |
•00095 -00097 •00098 •00099 •00100 |
00187 00188 •00190 •00192 •00194 |
.00187 •00189 .00190 •00192 .00194 |
3O 31 32 33 34 |
|
35 36 37 38 39 |
00005 .00005 .00006 .00006 • 00006 |
.00005 .00005 •00006 00006 .00006 |
-00038 .00039 •00040 -00041 -00041 |
•00038 .00039 •00040 • 00041 -00041 |
•00102 •00103 •00104 •00106 -00107 |
.00102 •00103 •00104 •00106 .00107 |
•00196 •00197 •00199 •00201 •00203 |
.00196 .00198 •00200 •00201 -00203 |
35 36 37 38 39 |
|
40 41 42 43 44 |
-00007 00007 -00007 00008 -00008 |
•00007 •00007 .00007 •00008 00008 |
. 00042 •00043 00044 •00045 . 00046 |
•00042 •00043 •00044 .00045 •00046 |
-00108 •00110 •00111 •00112 •00114 |
•00108 •00110 .00111 •00113 •00114 |
•00205 •00207 •00208 •00210 00212 |
•00205 •00207 .00209 .00211 .00213 |
40 41 42 43 44 |
|
45 46 47 47 49 |
-00009 00009 00009 -00010 00010 |
•00009 .00009 .00009 .00010 .00010 |
•00047 00048 -00048 •00049 -00050 |
.00047 .00048 •00048 •00049 .00050 |
•00115 •00117 •00118 •00119 -00121 |
.00115 •00117 •00118 •00120 •00121 |
•00214 •00216 .00218 •00220 •00222 |
00215 .'0216 .00218 .00220 .00222 |
45 46 47 48 49 |
|
50 51 52 53 54 |
-00011 00011 -00011 00012 •00012 |
.00011 •00011 .00011 •00012 .00012 |
•00051 •00052 •00053 •00054 •00055 |
.00051 .00052 .00053 •00054 .00055 |
•00122 •00124 •00125 •00127 •00128 |
•00122 •00124 •00125 •00127 •00128 |
•00224 •00226 •00228 -00230 •00232 |
.00224 •00226 .00228 .00230 •00232 |
5O 51 52 53 54 |
|
55 56 57 58 59 |
-00013 -00013 -00014 -00014 .00015 |
.00013 •00013 •00014 .00014 .00015 |
00056 •00057 .00058 •00059 •00060 |
.00056 •00057 .00058 .00059 00060 |
•00130 •00131 •00133 •00134 -00136 |
.00130 •00131 00133 .00134 .00136 |
•00234 •00236 -00238 •00240 .00242 |
•00234 .00236 .00238 .00240 -00242 |
55 56 57 58 59 |
|
60 |
-00015 |
•00015 |
•00061 |
•00061 |
•00137 |
.00137 |
•00244 |
.00244 |
60 |
229
Inserted by permission from Webb's Railroad Construction.
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 4° 5° 6° 7°
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
o 1 2 8 4 |
00244 •00246 .00248 .00250 •00252 |
•00244 .00246 .00248 .00250 .00252 |
.00381 00383 •00386 -00388 .00391 |
.00382 .00385 .00387 .00390 •00392 |
-00548 •00551 .00554 •00557 -00560 |
•00551 •00554 •00557 •00560 •00563 |
.00745 •00749 00752 .00756 .00760 |
•00751 •00755 •00758 •00762 00765 |
0 1 2 3 4 |
|
5 6 7 8 9 |
.00254 .00256 .00258 •00260 .00262 |
.00254 .00257 •00259 .00261 00263 |
.00393 •00396 .00398 .00401 .00404 |
.00395 •00397 •00400 • 00403 •00405 |
•00563 .00566 •00569 •00572 .00576 |
•00566 .00569 .00573 .00576 •00579 |
00763 -00767 •00770 -00774 .00778 |
•00769 •00773 •00776 •00780 -00784 |
6 7 8 9 |
|
1O 11 12 13 1.4 |
00264 -00266 .00269 .00271 00273 |
•00265 .00267 .00269 .00271 •00274 |
• 00406 .00409 •00412 .00114 •00417 |
•00408 •00411 .00413 •00416 •00419 |
00579 .00582 00585 00588 •00591 |
.00582 .00585 •00588 •00592 •00595 |
•00781 •00785 -00789 00792 •00796 |
•00787 -00791 •00795 •00799 •00802 |
10 11 12 13 14 |
|
15 16 17 18 19 |
-00275 .00277 .00279 .00281 -00284 |
-00276 .00278 •00280 •00282 •00284 |
.00420 .00422 .00425 .00428 -00430 |
•00421 .00424 .00427 •00429 -00432 |
00594 -00598 -00601 .00604 -00607 |
•00598 •00601 •00604 .00608 •00611 |
. 00800 . 00803 •00807 •00811 -00814 |
.00806 .00810 •00813 •00817 .00821 |
15 16 17 18 19 |
|
20 21 22 23 24 |
-00286 -00288 •OC290 .00293 -00295 |
•00287 •00289 .00291 •00293 •00296 |
.00433 •00436 •00438 - 00441 •00444 |
.00435 •00438 •'00440 .00443 .00446 |
-00610 •00614 •00617 •00620 -00623 |
00614 •00617 •00621 -00624 •00627 |
•00818 •00822 •00825 •00829 -00833 |
.00825 •00828 •00832 .00836 .00840 |
20 21 22 23 24 |
|
25 26 27 28 29 |
•00297 •00299 •C0301 •00304 -00306 |
.00298 .00300 .00302 .00305 .00307 |
•00447 . 00449 •00452 •00455 •00458 |
.00449 .00451 .00454 .00457 .00460 |
•00626 •00630 -00633 •00636 -00640 |
.00630 .00634 .00637 •00640 •00644 |
•00837 •00840 .00844 •00848 •00852 |
.00844 •00848 •00851 .00855 .00859 |
25 26 27 28 29 |
|
30 31 32 33 34 |
•00308 .00311 •C0313 -00315 -00317 |
.00309 •00312 .00314 •00316 .00318 |
•00460 •00463 •00466 •00469 •00472 |
•004b3 .00465 .00468 .00471 •00474 |
•00643 -00646 •00649 -00653 -00656 |
•00647 .00650 •00654 •00657 •00660 |
.00856 00859 -00863 •00867 •00871 |
-00863 .00867 -00871 -00875 .00878 |
30 31 32 33 34 |
|
35 36 37 38 39 |
•00320 •00322 •00324 -00327 -00329 |
.00321 .00323 .00328 .00328 .00330 |
.00474 .00477 •00480 -00483 •00486 |
•00477 .00480 -00482 .00485 -00488 |
•00659 •00663 -00666 •00669 -00673 |
.00664 -00667 -00671 -00674 •00677 |
•00875 -OC878 -00882 -00886 -00890 |
-00882 -00886 •00890 -00894 •00898 |
35 36 37 38 39 |
|
40 41 42 43 44 |
•00332 •00334 -00336 -00339 •00341 |
.00333 •00335 •00337 •00340 .00342 |
•00489 •00492 •00494 •00497 •00500 |
•00491 .00494 -00497 .00500 .00503 |
-00676 •00680 •00683 -00686 -00690 |
-00681 .00684 .00688 -00691 •00695 |
•00894 •00898 •00902 •00908 •00909 |
•00902 -00906 -00910 -00914 •00918 |
40 41 42 43 44 |
|
45 46 47 48 49 |
•00343 •00346 •00348 00351 00353 |
.00345 •00347 •00350 .00352 •00354 |
•00503 •00506 •00509 •00512 •00515 |
-00506 -00509 -00512 •00515 .00518 |
-00693 00607 •00700 •00703 .00707 |
-00698 -00701 -00705 .00708 .00712 |
•00913 00917 00921 00925 •00929 |
-00922 -00926 .00930 -00934 00938 |
45 46 47 4& 49 |
|
50 5i 52 53 54 |
•00356 .00358 00361 •0036d -00365 |
•00357 .00359 .00362 •00364 .00367 |
•00518 •00521 •00524 •00527 .00530 |
-00521 -00524 -00527 .00530 .00533 |
• 007.10 •00714 •00717 •00721 .00724 |
-00715 .00719 -00722 -00726 -00730 |
.00933 00937 •00941 .00945 .00949 |
-00942 -00946 .00950 .00954 •00958 |
50 51 52 53 54 |
|
55 56 57 58 59. |
•00368 .00370 •00373 .00375 -00378 |
.00369 .00372 •00374 00377 •00379 |
.00533 .00536 •00539 .00542 00545 |
-00536 -00539 •00542 -00545 00548 |
•00728 -00731 •00735 •00738 •00742 |
-00733 .00737 -00740 -00744 •00747 |
•00953 •00957 •00961 .00965 •00969 |
.00962 -00966 -00970 .00975 -00979 |
55 56 57 58 ,59 |
|
60 |
•00381 |
.00382 |
00548 |
-00551 |
-00745 |
.00751 |
•00973 |
-00983 |
60 |
230
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 8° 9° 10° 11°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
/ |
|
0 2 3 4 |
.00973 •00977 .00981 .00985 -00989 |
.00983 .00987 •00991 •00995 .00999 |
•01231 .01236 •01240 .01245 .01249 |
.01247 .01251 .01256 .01261 •01265 |
-01519 .01524 .01529 .01534 .01540 |
•01543 .01548 .01553 .01558 .01564 |
-01837 -01843 •01843 .01854 .01860 |
•01872 .01877 •01883 .01889 •01895 |
O 2 3 |
|
5 6 7 9 |
00994 00998 .01002 .01006 .01010 |
-01004 •01008 .01012 .01016 .01020 |
•01254 •01259 •01263 -01268 -01272 |
•01270 .01275 .01279 -01284 .01289 |
•01545 •01550 .01555 •01560 .01565 |
.01569 .01574 .01579 •01585 .01590 |
•01865 01871 •01876 .01382 -01888 |
.01901 .01906 .01912 .01918 •01924 |
5 6 7 8 9 |
|
10 11 12 13 14 |
.01014 •01018 .01022 •01027 .01031 |
•01024 .01029 .01033 -01037 .01041 |
•01277 .01282 •01286 .01291 .01296 |
.01294 •01298 •01303 •01308 •01313 |
•01570 .01575 •01580 .01586 .01591 |
.01595 .01601 .01606 .01611 .01616 |
•01893 •01899 •01904 •01910 .01916 |
.01930 •01936 .01941 •01947 .01953 |
10 11 12 13 14 |
|
15 16 17 18 19 |
.01035 -01039 •01043 -01047 .01052 |
.01046 .01050 -01054 •01059 .01063 |
.01300 .01305 •01310 •01314 01319 |
•01318 •01322 •01327 •01332 •01337 |
•01596 -01601 .01606 •01612 -01617 |
•01622 .01627 .01633 .01638 .01643 |
•01921 .01927 .01933 •01939 •01944 |
•01959 •01965 •01971 .01977 •01983 |
15 16 17 18 -19 |
|
20 21 22 23- 24 |
-01056 01060 01064 -01069 •01073 |
.01067 .01071 .01076 .01080 .01084 |
•01324 •01329 -01333 •01338 .01343 |
.01342 •01346 •01351^ .01356 .01361 |
.01622 •01627 .01632 •01638 •01643 |
•01649 •01654 .01659 .01665 .01670 |
-01950 •01956 •01961 •01967 •01973 |
.01989 •01995 •02001 •02007 •02013 |
2O 21 22 23 24 |
|
25 26 27 28 29 |
.01077 .01081 .01086 -01090 .01094 |
.01089 .01093 .01097 .01102 .01106 |
.01348 •01352 .01357 •01362 .01367 |
.01366 .01371 .01376 .01381 .01386 |
•01648 -01653 •01659 •01664 •01669 |
.01676 .01681 .01687 .01692 .01698 |
-01979 •01984 •01990 -01996 •02002 |
•02019 •02025 .02031 .02037 .02043 |
25 28 27 28 29 |
|
30 31 32 33 34 |
•01098 .01103 -01107 .01111 .01116 |
.01111 .01115 .01119 .01124 .01128 |
•01371 .01376 •01381 .01386 .01391 |
.01391 •01395 •01400 .01405 .01410 |
.01675 •01680 •01685 •01690 .01696 |
.01703 .01709 .01714 .01720 .01725 |
.02008 .02013 •02019 .02025 -02031 |
.02049 .02055 .02061 •02067 .02073 |
30 31 32 33 34 |
|
35 36 37 38 39 |
•01120 .01124 .01129 •01133 -01137 |
.01133 .01137 .01142 .01146 -01151 |
•01396 -01400 .01405 •01410 •01415 |
.01415 .01420 •01425 .01430 • OUS'i |
•01701 •01706 •01712 -01717 -01723 |
.01731 -01736 .01742 .01747 .01753 |
•02037 .02042 •02048 •02054 .02060 |
.02079 .02085 .02091 •02097 •02103 |
35 36 37 38 39 |
|
40 41 42 43 44 |
01142 .01148 •01151 -01155 -01159 |
•01155 .01160 •01164 .01169 01173 |
-01420 .01425 •01430 -01435 .01439 |
•01440 .01445 01450 -01455 .01461 |
•01728 01733 .01739 .01744 .01750 |
•01758 .01764 .01769 .01775 .01781 |
.02066 .02072 •02078 •02084 -02090 |
•02110 •02116 •02122 .02128 •02134 |
40 41 42 43 44 |
|
45 46 47 48 49 |
.01164 -01168 01173 -01177 -01182 |
.01178 -01182 .01187 .01191 •01196 |
•01444 •01449 •01454 •01459 .01464 |
.01466 •01471 .01476 •01481 •01486 |
.01755 •01760 01766 •01771 .01777 |
01786 .01792 .01793 .01803 .01809 |
•02095 •02101 •02107 .02113 -02119 |
•02140 •02146 •02153 •02159 •02165 |
45 48 47 48 49 |
|
50 51 R2 53 54 |
01186 -01191 .01195 -01200 -01204 |
.01200 •01205 .01209 .01214 .01219 |
•01469 •01474 •01479 •01484 .01489 |
•01491 •01496 •01501 •01506 .01512 |
•01782 •01788 .01793 .0179^ -01804 |
.01815 .01820 •01826 •01832 01837 |
.02125 •02131 .02137 .02143 •02149 |
.02171 .02178 •02184 •02190 •02196 |
50 51 52 53 54 |
|
55 56 57 58 59, |
.01209 .01213 -01218 -01222 -01227 |
.01223 •01228 .01233 .01237 .01242 |
•01494 •01499 •01504 •01509 -01514 |
.01517 .01522 .01527 .01532 .01537 |
.01810 •01815 •01821 .01826 .01832 |
•01843 •01849 .01854 •01860 •01866 |
.02155 •02161 .02167 •02173 .02179 |
•02203 •02209 •02215 -02221 .02228 |
55 58 57 58 59 |
|
6O |
01231 |
.01247 |
.01519 |
.01543 |
.01837 |
.01872 |
•02185 |
.02234 |
60 |
231
TABLE 11— NATURAL VERSED SINES AND EXTERNAL SECANTS. 12° 13° 14° 15°
|
t |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
o 1 2 3 4 |
02185 02191 02197 .02203 02210 |
.02234 .02240 .02247 .02253 .02259 |
.02563 .02570 .02576 •02583 .02589 |
•02630 .02637 •02644 .02651 •02658 |
02970 02977 02985 02992 02999 |
.03081 •03069 .03076 •03084 •03091 |
03407 •03415 -03422 •03430 •03438 |
•03528 •03536 •03544 •03552 •03560 |
O 2 3 4 |
|
5 6 7 8 9 |
.02216 .02222 .02228 02234 02240 |
.02266 .02272 .02279 .02285 -02291 |
•02596 •02602 .02609 -02616 .02622 |
•02665 .02672 .02679 .02686 .02693 |
03006 03013 03020 •03027 •03034 |
•03099 .03106 •03114 .03121 .03129 |
-03445 •03453 03460 •03468 .03476 |
.03568 .03576 -03584 -03592 •03601 |
5 6 7 8 9 |
|
10 11 12 13 14 |
.02246 •02252 •02258 .02265 02271 |
.02298 -02304 .02311 .02317 •02323 |
•02629 -02635 •02642 .02649 .02655 |
.02700 .02707 •02714 .02721 .02728 |
.03041 •03048 •03055 •03063 •03070 |
•03137 .03144 .03152 .03159 •03167 |
•03483 •03491 -03498 -03506 -03514 |
-03609 -03617 -03625 -03633 -03642 |
10 11 12 13 14 |
|
15 16 17 18 19 |
02277 .02283 •02289 .02295 •02302 |
•02330 .02336 .02343 .02349 .02356 |
.02662 •02669 •02675 •02682 .02689 |
.02735 .02742 .02749 .02756 •02763 |
.03077 .03084 .03091 .03098 •03106 |
•03175 .03182 •03190 -03198 -03205 |
•03521 •03529 •03537 •03544 •03552 |
-03650 -03658 •03666 .03674 •03683 |
15 16 17 18 19 |
|
20 21 22 23 24 |
•02308 •02314 •02320 •02327 . 02333 |
.02362 •02369 •02375 .02382 •02388 |
•02696 •02702 •02709 .02716 •02722 |
.02770 .02777 .02784 .02791 .02799 |
•03113 •03120 •03127 •031S4 •03142 |
•C3213 •03221 •03228 .03236 .03244 |
.03560 •03567 •03575 .03583 •03590 |
-03691 -03699 .03708 •03716 •03724 |
20 21 22 23 24 |
|
25 26 27 28 29 |
.02339 •02345 •02352 -02358 •02364 |
.02395 •02402 •02408 •02415 .02421 |
•02729 •02736 •02743 .02749 .02756 |
.02806 .02813 .02820 .02827 .02834 |
.03149 .03156 •03163 -03171 •03178 |
.03251 .03259 .03267 .03275 •03282 |
.03598 •03606 .03614 •03621 •03629 |
•03732 •03741 •03749 •03758 .03766 |
25 26 27 28 29 |
|
30 31 32 33 34 |
•02370 •02377 -02383 •02389 -02396 |
•02428 .02435 .02441 .02448 •02454 |
.02763 •02770 •02777 •02783 •02790 |
.02842 •02C49 .02856 .02863 .02870 |
-03185 •03193 •03200 •03207 •03214 |
•03290 •03298 •03306 •03313 •03321 |
•03637 •03645 •03653 •03660 •03668 |
•03774 •03783 •03791 •03799 •03808 |
30 31 32 33 34 |
|
3o 36 37 38 39 |
•02402 -02408 •02415 02421 -02427 |
.02461 •02468 •02474 .02481 .02488 |
•02797 •02804 •02811 •02818 -02824 |
.02878 .02885 .02892 .02899 •02907 |
•03222 •03229 •03236 •03244 •03251 |
.03329 -03337 .03345 •03353 03360 |
•03676 •03684 .03692 •03699 •03707 |
•03816 •03825 -03833 -03842 •03850 |
35 36 37 38 39 |
|
40 41 42 43 44 |
-02434 -02440 •02447 •02453 •02459 |
•02494 .02501 •02508 •02515 •02521 |
•02831 •02838 •02845 02852 •02859 |
.02914 .02921 .02928 .02936 •02943 |
•03258 •03266 •03273 •03281 •03288 |
-03368 •03376 •03384 •03392 .03400 |
03715 -03723 •03731 •03739 •03747 |
•03858 .03867 -03875 .03884 .03892 |
40 41 42 43 44 |
|
45 46 47 48 49 |
• 02466 •02472 •02479 •02485 •02492 |
•02528 •02535 •02542 •02548 •02555 |
•02866 •02873 •02880 •02887 •02894 |
.02950 .02958 .02965 .02972 .02980 |
•03295 •03303 •03310 •03318 03325 |
•03408 •03416 .03424 .03432 •03439 |
•03754 •03762 03770 •03778 •03786 |
.03901 .03909 .03918 .03927 .03935 |
45 46 47 48 49 |
|
50 51 52 53 54 |
•02498 -02504 •02511 •02517 -02524 |
•02562 •02569 •02576 •02582 •02589 |
•02900 •02907 •02914 •02921 .02928 |
.02987 •02994 •03002 •03009 .03017 |
03333 •03340 -03347 .03355 •03362 |
•03447 •03455 .03463 •03471 •03479 |
•03794 .03802 .03810 •03818 •03826 |
.03944 -03952 .03961 .03969 •03978 |
50 51 52 53 54 |
|
55 56 57 58 59 |
-02530 •02537 •02543 •02550 -02556 |
•02596 •02603 •02610 •02617 -02624 |
•09935 -02942 02949 •02956 •02963 |
.03024 •03032 .03039 03046 •03054 |
.03370 .03377 03385 •03392 .03400 |
•03487 -03495 .03503 •03512 •03520 |
.03834 .03842 •03850 •03858 •03866 |
.03987 -03995 •04004 .04013 .04021 |
55 56 57 58 59 |
|
60 |
•02563 |
02630 |
•02970 |
.03061 |
03407 |
.03528 |
•03874 |
.04030 |
60 |
232
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 16° 17° 18° 19°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec |
I |
|
o 1 2 3 |
03874 03882 03890 03898 03906 |
.04030 .04039 .04047 .04056 .04065 |
04370 04378 04387 04395 04404 |
•04569 •04578 -04588 .04597 -04606 |
04894 04903 04912 04921 04930 |
.05146 -05156 .05166 •05176 .05186 |
05448 05458 05467 05477 05486 |
.05762 -05773 •05783 •05794 .05805 |
0 1 2 3 4 |
|
5 6 7 8 9 |
03914 J3922 03930 03938 03946 |
•04073 .04082 .04091 .04100 -04108 |
04412 04421 04429 04438 04446 |
.04616 •04625 04635 .04644 .04653 |
04939 04948 04957 04967 04976 |
.05196 •05206 .05216 .05226 • 05'236 |
05496 05505 05515 05524 05534 |
•05815 •05826 -05836 •05847 .05858 |
5 6 7 8 9 |
|
10 11 12 13 14 |
03954 03963 03971 03979 03987 |
.04117 04126 .04135 •04144 .04152 |
04455 04464 04472 04481 04489 |
.04663 .04672 •04682 .04691 .04700 |
04985 04904 05003 05012 05021 |
.05246 .05256 .05266 -05276 .05286 |
.05543 •05553 •05562 •05572 .05582 |
•05869 -05879 •05890 •05901 .05911 |
10 11 12 13 14 |
|
15 16 17 18 19 |
03995 04003 04011 04019 04028 |
.04161 •04170 •04179 •04188 -04197 |
04498 04507 04515 04524 04533 |
.04710 .04719 .04729 .04738 -04748 |
05030 05039 05048 05057 05067 |
.05297 .05307 .05317 .05327 .05337 |
•05591 .05601 05610 •05620 .05630 |
.05922 .05933 .05944 .05955 .05965 |
15 16 17 18 19 |
|
20 21 22 23 24 |
04036 04044 04052 04060 04069 |
•04206 .04214 .04223 .04232 .04241 |
04541 04550 0455S 04567 04576 |
.04757 .04767 .04776 .04786 .04795 |
05076 05085 .05094 .05103 .05112 |
-05347 .05357 .05367 .05378 -05388 |
.05639 .05649 .05688 .05668 .05678 |
•05976 .05987 .05998 .06009 .06020 |
20 21 22 23 24 |
|
25 26 27 28 29 |
04077 04085 04093 04102 04110 |
•04250 •04259 .04268 .04277 •04286 |
04585 04593 .04602 .04611 .04620 |
.04805 .04815 .04824 04834 •04843 |
.05122 .05131 .05140 •05149 .05158 |
05398 -05408 .05418 .05429 -05439 |
.05687 •05697 05707 •05716 .05726 |
.06030 .06041 .06052 .06063 .06074 |
25 26 27 28 29 |
|
30 31 32 33 34 |
04118 04126 04135 04143 .04151 |
•04295 .04304 .04313 .04322 .04331 |
-04628 •04637 -04646 04655 .04663 |
.04853 .04863 •04872 .04882 .04891 |
.05168 .05177 .05186 .05195 .05205 |
.05449 .05460 .05470 .05480 .05490 |
.05736 .05746 .05755 .05765 .05775 |
.06085 .06096 .06107 -06118 .06129 |
30 31 32 33 34 |
|
35 36 37 38 39 |
•04159 .04168 .04176 .04184 .04193 |
•04340 •04349 •04358 •04367 .04376 |
.04672 •04681 .04690 -04699 -04707 |
.04901 •04911 04920 •04930 -04940 |
-05214 .05223 .05232 .05242 .05251 |
.05501 •05511 .05521 •05532 .05542 |
.05785 .05794 .05804 .05814 .05824 |
•06140 .06151 •06162 •06173 .06184 |
35 - 36 37 38 -39 |
|
40 41 42 43 44 |
-04201 .04209 .04218 .04226 .04234 |
.04385 .04394 .04403 .04413 .04422 |
-04716 .04725 .04734 .04743 -04752 |
-04950 •04959 •04969 -04979 .04989 |
.05260 .05270 .05279 .05288 .05298 |
.05552 .05563 .05573 .05584 .05594 |
.05833 .05843 .05853 .05863 .05873 |
.06195 .06206 •06217 -06228 .06239 |
40 41 42 43 44 |
|
45 46 47 48 49 |
.04243 .04251 04260 •04268 •04276 |
.04431 •04440 . 04449 •04458 .04468 |
-04760 •04769 .04778 .04787 .04796 |
.04998 •05008 .05018 .05028 .05038 |
.05307 .05316 .05326 .05335 .05344 |
.05604 .05615 .05625 .05636 .05646 |
.05882 .05892 -05902 .05912 .05922 |
.06250 .06261 -06272 .06283 .06295 |
45 46 47 48 49 |
|
50 51 52 53 54 |
04285 .04293 •04302 .04310 -04319 |
•04477 •04486 .04495 .04504 .04514 |
•04805 .04814 -04323 .04832 -04841 |
•05047 .05057 .05067 •05077 •05087 |
•05354 .05363 .05373 .05382 -05391 |
.05657 .05667 .05678 .05688 -05699 |
.05932 .05942 .05951 .05961 .05971 |
.06306 .06317 .06328 .06339 .06350 |
5O 51 52 53 54 |
|
55 56 57 58 59 |
.04327 .04336 •04344 .04353 .043fil |
•04523 •04532 .04541 .04551 -04560 |
-04850 •04858 -04867 -04876 04885 |
•05097 •05107 .05116 .05126 .05136 |
.05401 .05410 .05420 .05429 .05439 |
.05709 .05720 .05730 .05741 .05751 |
.05981 -05991 -06001 .06011 .06021 |
.06362 .06373 .06384 .06395 -06407 |
55 56 57 58 59 |
|
60 |
•04370 |
-04569 |
-04894 |
•05146 |
.05448 |
.05762 |
.06031 |
.06418 |
60 |
|
2 |
33 |
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 30° 21° 22° 23°
|
t |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
f |
|
0 2 3 4 |
-06031 .06041 •06051 •06061 .06071 |
•06418 .06429 .06440 .06452 06463 |
•06642 •06652 •06663 .06673 •06684 |
.07115 .07126 .07138 .07150 .07162 |
.07282 .07293 .07303 .07314 .07325 |
.07853 •07866 .07879 •07892 •07904 |
•07950 •07961 •07972 •07984 -07995 |
.08636 •08649 •08663 .08676 .08690 |
O 2 3 4 |
|
5 6 7 8 9 |
•06081 •06091 .06101 •06111 06121 |
.06474 .06486 06497 .06508 .06520 |
•06694 •06705 •06715 .06726 •06736 |
.07174 .07186 •07199 .07211 .07223 |
•07336 •07347 -07358 •07369 -07380 |
.07917 07930 •07943 •07955 .07968 |
-C8006 -C8018 -08029 •C8041 .08052 |
.08703 •08717 •08730 •08744 .08757 |
5 6 7 8 9 |
|
10 11 12 13 14 |
•06131 •06141 •06151 .06161 .06171 |
.06531 .06542 .06554 .06565 •06577 |
.06747 •06757 •06768 •06778 .06789 |
.07235 •07247 .07259 .07271 .07283 |
•07391 •07402 •07413 •07424 .07485 |
.07981 .07994 .08006 .08019 •08032 |
•08064 •08075 •08086 •08098 •08109 |
•08771 •08784 .08798 .08811 .08825 |
10 11 12 IS 14 |
|
15 16 17 18 19 |
•06181 •06191 •06201 •06211 .06221 |
•06588 .06600 .06611 .06622 .06634 |
•06799 •06810 •06820 •06831 .06841 |
•07295 .07307 .07320 .07332 •07344 |
.07446 .07457 •07468 .07479 .07490 |
.08045 .08058 .08071 -08084 .08097 |
.08321 .08132 .08144 .08155 08167 |
.08839 .08852 .08866 .08880 .08893 |
15 13 17 18 19 |
|
2O 21 22 23 24 |
•06231 •06241 •06252 •06262 .06272 |
.06645 .06657 •06668 .06680 .06691 |
•06852 .06863 •06873 •06884 •06894 |
-07356 .07368 .07380 .07393 .07405 |
.07501 .07512 .07523 .07534 .07545 |
•08109 .08122 .08135 .08148 .08161 |
.08178 •08190 •08201 •08213 •08225 |
.08907 .08921 08934 .08948 .08962 |
20 21 22 23 24 |
|
25 26 27 28 29 |
-06282 .06292 06302 06312 06323 |
.06703 .06715 .06726 .06738 .06749 |
•06905 .06916 .06926 .06937 .06948 |
.07417 .07429 .07442 .07454 .07486 |
.07556 .07568 .07579 .07590 •07601 |
.08174 .08087 .08200 .08213 •08226 |
•08236 08248 •08259 •08271 08282 |
.08975 .08989 .09003 •09017 .09030 |
25 26 27 28 29 |
|
30 31 32 33 34 |
08333 06343 06353 06363 06374 |
.06761 .06773 .06784 .06796 .06807 |
.06958 .06969 •06980 .06990 .07001 |
.07479 .07491 .07503 .07516 .07528 |
.07612 •07623 .07634 .07645 •07657 |
.08239 .08252 •08265 .08278 .08291 |
•08294 •08306 •08317 .'08329 . 08340 |
.09044 .09058 .09072 .09086 .09099 |
30 31 32 .33 34 |
|
35 36 37 38 39 |
06384 06394 06404 06415 06425 |
.06819 .06831 •06843 •06854 •06866 |
.07012 .07022 .07033 07044 07055 |
.07540 .07553 .07565 .07578 •07590 |
•07668 .07679 .07690 -07701 •07713 |
•08305 .08318 .08331 •08344 .08357 |
•08352 •08364 -08375 •08387 •08399 |
•09113 •09127 .09141 .09155 .09169 |
35 36 37 38 39 |
|
40 41 42 43 44 |
06435 06445 06456 06466 06476 |
.06878 .06889 •06901 .06913 .06925 |
07065 07076 07087 07098 07108 |
.07J02 .07615 .07627 •07U40 .07652 |
.07724 .07735 •07746 .07757 07769 |
.08370 .08383 08397 .08410 .08423 |
•08410 •08422 08434 •08445 •08457 |
•09183 .09197 .09211 •09224 .09238 |
40 41 42 48 44- |
|
45 46 47 48 49 |
06486 06497 06507 06517 06528 |
.06936 -06948 .06960 .06972 06984 |
07119 07130 07141 07151 07162 |
.07665 .07677 .07690 .07702 .07715 |
07780 07791 07802 07814 07825 |
.08436 .08449 .08463 •08476 .08489 |
08469 •08481 .08492 .08504 .08516 |
.09252 .09266 •09280 •09294 09308 |
45 46 47 48 49 |
|
5O 51 52 53 54 |
06538 06548 06559 06569 06580 |
.06995 .07007 .07019 -07031 • 07043 |
07173 07184 07195 07206 07216 |
.07727 .07740 .07752 .07765 .07778 |
07836 07848 07859 07870 07881 |
.08503 .08516 .08529 .08542 .08556 |
08528 08539 08551 08563 08575 |
.09323 -09337 .09351 •09365 09379 |
50 51 52 53 54 |
|
55 56 57 58 59 |
06590 06600 06611 06621 06632 |
.07055 .07067 .07079 .07091 .07103 |
07227 07238 07249 07260 07271 |
.07790 •07803 .07816 •07828 -07841 |
07893 07904 07915 07927 07938 |
.08569 •08582 .08596 .08069 •08623 |
08586 08598 08610 08622 08634 |
•09393 •09407 •09421 •09435 09449 |
55 56 57 58 59 |
|
60 |
06642 |
.07115 |
07282 |
•07853 |
07950 |
.08636 |
08645 |
•09464 |
60 |
234
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 24° 25° 26° 27°
|
0 2 3 ~5~ 6 7 8 _9_ 10 11 12 13 14 |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
t ~ 2 3 4 5 6 7 8 9 |
|
08645 .08657 •08669 •08681 .08693 |
.09464 .09478 .09492 .09506 .09520 |
.09369 .09382 .09394 •09406 -09418 |
•10338 .10353 .10368 .10383 •10398 |
10121 •10133 .10146 .10159 -10172 |
•11260 •11276 •11292 •11308 •11323 |
•10899 •10913 •10926 •10939 -10952 |
• 12233 -1224b •12266 -12283 •12299 |
||
|
.08705 .08717 .08728 .08740 .08752 |
•09535 •09549 .09563 .09577 .09592 |
•09431 •09443 •09455 09468 .09480 |
-10413 . 10428 .10443 .10458 .10473 |
•10184 •10197 .10210 •10223 •10236 |
•11339 11355 •11371 •11387 •11403 |
•10965 •10979 -10992 -11005 .11019 |
-12316 -12333 - 12349 .12366 -12383 |
||
|
.08764 •08776 .08788 .088CO .08812 |
.09608 •09620 .09635 .09649 .09663 |
.09493 .09505 •09517 •09530 .09542 |
.10488 •10503 10518 •10533 .10549 |
.10248 •10261 •10274 .10287 .10300 |
•11419 •11435 .11451 -11467 .11483 |
•11032 •11045 .11058 11072 .11085 |
•12400 •12416 •12433 •12450 .12467 |
10 11 12 13 14 |
|
|
15 16 17 18 19 |
.08824 •08836 .08848 .08860 .08872 |
.09678 .09692 .09707 .09721 -09735 |
09554 •09567 •09579 •09592 .09604 |
.10564 .10579 .10594 •10609 .10625 |
•10313 •10326 .10338 •10351 •10364 |
•11499 11515 •11531 •11547 .11563 |
•11098 •11112 •11125 -11138 •11152 |
.12484 .12501 .12518 -125b4 -12551 |
15 16 17 18 19 |
|
20 21 22 23 24 |
.08884 •08896 •08908 .08920 .08932 |
.09750 .09764 .09779 .09793 .09808 |
-09617 •09629 •09642 •09654 .09666 |
•10640 •10655 •10670 .10686 -10701 |
•10377 •10390 • 10403 •10416 10429 |
•11579 •11595 -11611 •11627 -11643 |
•11165 •11178 •11192 •11205 •11218 |
•12568 -12585 .12602 .12619 12636 |
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 |
|
25 26 27 28 29_ 30 31 32 33 34 35 36 37 38 39 |
.08944 .08956 .08968 .08980 .08992 |
.09822 •09837 .09851 .09866 •09880 |
•09679 •09691 .09704 •09716 •09729 |
.10716 .10731 •10747 •10762 •10777 |
. 10442 •10455 .10468 •10481 .10494 |
•11659 -11675 •11691 -11708 -11724 |
•11232 •11245 •11259 •11272 .11285 |
-12653 -12670 -12687 .12704 •12721 |
|
|
.09004 .09016 .09028 -.09040 .09052 |
.09895 •09909 .09924 -09939 •09953 |
•09741 .09754 •09767 .09779 .09792 |
.10793 10808 10824 -10839 -10854 |
•10507 •10520 .10533 •10546 .10559 |
.11740 •11756 -11772 -11789 11805 |
•11299 •11312 •11326 •11339 .11353 |
.12738 •12755 •12772 •12789 . 12807 |
||
|
.09064 .09076 .09089 .09101 .09113 |
.09968 •09982 .09997 .10012 .10026 |
.09804 09817 09829 •09842 .09854 |
.10870 .10885 -10901 •10916 .10932 |
•10572 -10585 .10598 •10611 • 10624 |
•11821 .11838 •11854 •11870 -11886 |
•11366 •11380 •11393 •11407 •11420 |
•12824 •12841 -12858 .12875 -12892 |
||
|
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 |
•09125 •09137 .09149 .09161 .09174 |
.10041 .10055 .10071 .10085 .10100 |
•09867 •09880 •09892 •09905, .09918 |
. 10947 •10963 .10978 .10994 •11009 |
•10637 .10650 .10663 •10676 .10689 |
•11903 •11919 •11936 •11952 .11968 |
•11434 •11447 •11461 •11474 .11488 |
12910 -12927 •12944 •12961 •12979 |
4O 41 42 43 44 45 46 47 48 49 50 51 52 53 54 |
|
.09186 •09198 •09210 .09222 -09234 |
.10115 .10130 .10144 .10159 .10174 |
•09930 •09943 •09955 •09968 -09981 |
-11025 •11041 -11056 •11072 •11087 |
•10702 •10715 -10728 •10741 •10755 |
•11985 •12001 •12018 •12034 •12051 |
•11501 •11515 -11528 -11542 -11555 |
•12996 •13013 -13031 • 13048 13065 |
||
|
.09247 •09259 •09271 -09283 .09296 |
•10189 .10204 .10218 .10233 .10248 |
•09993 •10006 •10019 •10032 . 10044 |
•11103 -11119 •11134 .11150 •11166 |
•10768 •10781 10794 -10807 10820 |
•12067 • 12084 •12100 •12117 •12133 |
-11569 •11583 -11596 11610 -11623 |
. 13083 •13100 •13117 •13135 13152 |
||
|
55 56 57 58 59 |
•09308 •09320 .09332 -09345 .09357 |
.10263 •10278 .10293 .10308 .10323 |
•10057 •10070 •10082 •10095 •10108 |
.11181 .11197 .11213 .11229 •11244 |
.10833 •10847 •10860 •10873 •10886 |
-12150 •12166 •12183 .12199 •12216 |
•11637 •11651 •11664 •11678 .11692 |
•13170 •13187 .13205 •13222 .13240 |
55 56 57 58 59 |
|
60 |
.09369 |
.10338 |
•10121 |
.11260 |
.10899 |
.12233 |
•11705 |
•13257 |
60 |
235
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS, 28° 29° 30° 31°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
0 2 3 4 |
•11705 •11719 .11733 •11746 •11760 |
.13257 .13275 •13292 •13310 •13327 |
.12538 .12552 •12566 •12580 •12595 |
•14335 -14354 .14372 .14391 • 14409 |
•13397 •13412 •13427 •13441 -13456 |
•15470 .15489 •15509 .15528 •15548 |
•14283 .14298 •14313 •14328 . 14343 |
•16663 •16684 •16704 .16725 .16745 |
O 1 2 3 •4 |
|
5 6 7 8 9 |
•11774 •11787 -11801 •11815 •11828 |
.13345 .13362 •13380 .13398 •13415 |
•12609 •12623 •12637 •12651 •12665 |
.14428 -14446 •14465 .14483 •14502 |
•13470 •13485 -13499 -13514 -13529 |
.15567 •15587 •15606 -15626 -15645 |
•14358 •14373 •14388 • 14403 -14418 |
.16766 .16786 .16806 •16827 •16848 |
5 6 7 8 9 |
|
10 11 12 13 14 |
•11842 •11856 •11870 •11883 •11897 |
•13433 •13451 •13468 •13486 -13504 |
•12679 •12694 .12708 •12722 •12736 |
•14521 .14539 .14558 .14576 •14595 |
.13543 •13558 .13573 -13587 -13602 |
-15665 -15684 •15704 •15724 •15743 |
. 14433 • 14449 . 14464 • 14479 . 14494 |
•16868 •16889 -16909 .16930 -16950 |
10 11 12 13 14 |
|
15 16 17 18 19 |
.11911 •11925 •11938 •11952 .11966 |
•13521 •13539 •13557 .13575 •13593 |
•12750 •12765 .12779 .12793 •12807 |
•14614 .14632 .14651 •14670 -14689 |
-13616 -13631 -13646 -13660 •13675 |
•15763 •15782 .15802 •15822 -15841 |
•14509 •14524 •14539 •14554 .14569 |
-16971 •16992 •17012 -17033 -17054 |
15 16 17 18 19 |
|
20 21 22 23 24 |
.11980 .11994 •12007 •12021 .12035 |
•13610 .13628 .13646 •13664 •13682 |
.12822 •12836 •12850 •12864 •12879 |
-14707 .14726 .14745 •14764 .14782 |
-13690 -13705 -13719 -13734 - 13749 |
.15861 .15881 .35901 .15920 .15940 |
-14584 -14599 -14615 •14630 •14645 |
•17075 •17095 •17116 -17137 •17158 |
20 21 22 23 24 |
|
25 26 27 28 29 |
. 12049 •12063 -12077 •12091 12104 |
-13700 •13718 .13735 .13753 .13771 |
.12893 •12907 •12921 .12936 .12950 |
.14801 .14820 .14839 .14858 .14877 |
•13763 •13778 •13793 •13808 .13822 |
•15960 •15980 .16000 •16019 -16039 |
•14660 •14675 •14690 •14706 .14721 |
-17178 .17199 .17220 •17241 •17262 |
25 28 27 28 29 |
|
30 31 32 33 34 |
•12118 .12132 •12146 12160 12174 |
.13789 .13807 .13825 .13843 .13861 |
•12964 .12979 .12993 .13007 .13022 |
.14896 .14914 .14933 -14952 .14971 |
•33837 •13852 •13867 •13881 -13896 |
•16059 .16079 .16099 .16119 .16139 |
•14736 •14751 •14766 •14782 •14797 |
•17283 •17304 •17325 •17346 •17367 |
30 31 32 33 34 |
|
35 36 37 38 39 |
.12188 •12202 •12216 •12230 •12244 |
•13879 .13897 .13916 •13934 13952 |
.13036 .13051 •13065 •13079 .13094 |
.14990 .15009 •15028 .15047 .15066 |
-13911 -13926 -13941 -13955 -18970 |
.16159 .16179 •16199 •16219 -16239 |
-14812 .14827 • 14843 •14858 -14873 |
•17388 •17409 •37430 •17451 -17472 |
35 36 37 38 39 |
|
40 41 42 43 44 |
.12257 •12271 •12285 .12299 .12313 |
•13970 .13988 •14006 •14024 • 14042 |
.13108 •13122 •13137 •13151 .13166 |
•15085 -1510u .15124 -15143 •15162 |
13985 - 14000 -14015 - 14030 -14044 |
.16259 .16279 .16299 9. 16319 -16339 |
•14888 •14904 •34819 •14934 •34949 |
•17493 •17514 -17535 •17556 •17577 |
40 41 42 43 44 |
|
45 46 47 48 49 |
-12327 .32341 .12355 .12369 12383 |
•14061 • 14079 •14097 •14115 •14134 |
•13180 -13195 .13209 .13223 .13238 |
-15181 .15200 .15219 .15239 .15258 |
-14059 14074 -14089 •14104 14119 |
16359 •16380 .16400 •16420 •16440 |
•14965 • 3 4980 •14995 •15011 15026 |
-17598 -17620 •17641 -17662 •176S3 |
45 46 47 48 49 |
|
50 51 52 53 54 |
.1239'/ •12411 .12425 . 12439 .12454 |
.14152 .14170 •14188 .14207 •14225 |
.13252 .13267 .13281 •13296 •13310 |
.15277 .15296 .15315 .15335 .15354 |
•14134 14149 •14164 14179 •14194 |
.16460 16481 •16501 .16521 .16541 |
15041 15057 15072 15087 35103 |
.17704 •17726 •17747 .17768 .17790 |
50 51 52 53 54 |
|
55 56 57 58 59 |
.12468 •12482 •12496 •12510 .12524 |
.14243 14262 •14280 .14299 .14317 |
.13325 .13339 .13354 .13368 .13383 |
.15373 .15393 .15412 .15431 -15451 |
14208 •14223 •14238 •14253 14268 |
•16562 •16582 •16602 •16623 -16643 |
15118 15134 15149 15164 15180 |
•17811 -17832 •17854 •17875 .17896 |
55 56 57 58 59 |
|
60 |
.12538 |
.14335 |
•13397 |
.15470 |
-14283 |
•16663 |
15195 |
•17918 |
60 |
236
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 32° 33° 34° 35°
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
t ~ 2 3 a 6 7 8 9 10 11 12 13 14 15 16 17 18 19 |
|
o 2 3 ~5~ 7 9 10 11 12 13 14 15 16 17 18 19- 20 21 22 23 24 25 26 27 28 29 |
•15195 .15211 .15226 .15241 •15257 |
•17918 •17939 .17961 .17982 .18004 |
•16133 .16149 .16165 -16181 -16196 |
.19236 •19259 •19281 .19304 -19327 |
.17096 .17113 •17129 .17145 .17161 |
.20622 .20645 •20669 •20693 -20717 |
-18085 -18101 -18118 .18135 -18152 |
-22077 •22102 •22127 •22152 -22177 |
|
|
•15272 .15288 .15303 .15319 .15334 |
.18025 •18047 •18068 •18090 .18111 |
.16212 .16228 .16244 .16260 .16276 |
•19349 •19372 •19394 -19417 - 19440 |
•17178 •17194 .17210 •17227 .17243 |
.20740 •20764 •20788 •20812 -20836 |
•18168 •18185 -18202 .18218 -18235 |
. 22202 •22227 •22252 .22277 -22302 |
||
|
.15350 -15365 .15381 -15396 -15412 |
-18133 .18155 .18176 •18198 .18220 |
•16292 •16308 -16324 .16340 -16355 |
.19463 .19485 .19508 -19531 -19554 |
.17259 .17276 -17292 .17308 •17325 |
.20859 •20883 -20907 .20931 .20955 |
-18252 -18269 -18286 -18302 -18319 |
•22327 .22352 •22377 . 22402 - 22428 |
||
|
.15427 •15443 .15458 .15474 .15489 |
.18241 •18263 •18285 .18307 .18328 |
-16371 -16387 -16403 -16419 -16435 |
.19576 •19599 .19622 -19645 -19668 |
.17341 •17357 •17374 -17390 -17407 |
.20979 -21003 •21027 -21051 -21075 |
-18336 -18353 -18369 -18386 -18403 |
.22453 .22478 .22503 •22528 •22554 |
||
|
.15505 -15520 -15536 -15552 -15567 |
-18350 -18372 .18394 •18416 .18437 |
.16451 -16467 -16483 .16499 .16515 |
-19691 .19713 .19736 .19759 .19782 |
-17423 -17439 -17456 •17472 .17489 |
-21099 •21123 -21147 -21171 -21195 |
•18420 •18437 -18454 -18470 -18487 |
-22579 •22604 •22629 -22655 -22680 |
20 21 22 23 24 25 26 27 28 29 |
|
|
-•15583 -15598 -15614 -15630 .15645 |
.18459 .18481 •18503 .18525 .18547 |
- 16531 •16547 •16563 •16579 -16595 |
.19805 .19828 •19851 .19874 -19897 |
•17505 -17522 -17538 .17554 .17571 |
•21220 •21244 •21268 •21292 -21316 |
•18504 -18521 -18538 -18555 .18572 |
. 22706 -22731 .22756 -22782 •22807 |
||
|
30 31 32 33 34 |
.15661 •15676 •15692 •15708 •15723 |
.18569 .18591 .18613 .18635 -18657 |
.16611 -16627 •16644 •16660 -16676 |
.19920 •19944 •19967 •19990 -20013 |
•17587 •17604 -17620 •17637 -17653 |
.21341 •21365 -21389 -21414 -21438 |
-18588 •18605 -18622 -18639 -18656 |
•22833 -22858 •22884 . 22909 .22935 |
30 31 32 33 34 |
|
35 36 87 38 39 |
.15739 -15755 -15770 •15786 .15802 |
-18679 .18701 .18723 .18745 •18767 |
-16692 -16708 -16724 -16740 -16756 |
•20036 •20059 •20083 •20106 •20129 |
-17670 -17686 -17703 -17719 -17736 |
•21462 .21487 .21511 -21535 -21560 |
•18673 -18690 -18707 -18724 .18741 |
-22960 -22986 •23012 -23037 .23063 |
35 36 37 38 _39 4O 41 42 43 44 |
|
40 41 42 43 44 45 46 47 48 49 |
.15818 -15833 •15849 -15865 .15880 |
.18790 .18812 •18834 -18856 .18878 |
•16772 -16788 -16805 -16821 -16837 |
-20152 -20176 -20199 .20222 -20246 |
•17752 .17769 •17786 .17802 .17819 |
-21584 -21609 -21633 -21658 -21682 |
-18758 -18775 •18792 •18809 -18826 |
.23089 •23114 .23140 -23166 •23192 |
|
|
•15896 .15912 •15928 -15943 •15959 |
-18901 -18923 -18945 -18967 -18990 |
-16853 -16869 -16885 -16902 -16918 |
-20269 -20292 -20316 -20339 -20363 |
-17835 -17852 -17868 -17885 -17902 |
•21707 .21731 •21756 •21781 -21805 |
-18843 •18860 -18877 •18894 •18911 |
.23217 .23243 -23269 .23295 -23321 |
45 46 47 48 49 5O 51 52 53 _5J 55 56 57 58 59 |
|
|
50 51 52 53 54 55 56 57 58 59 |
•15975 •15991 .16006 -16022 •18038 |
-19012 .19034 .19057 •19079 -19102 |
-16934 -16950 -16966 -16983 -16999 |
.20386 •20410 •20433 .20457 - 20480 |
-17918 .17935 -17952 •17968 -17985 |
•21830 •21855 •21879 •21904 •21929 |
-18928 .18945 •18962 •18979 18996 |
.23347 .23373 .23399 . 23424 -23450 |
|
|
•16054 -16070 •16085 .16101 .16117 |
.19124 .19146 .19169 .19191 -19214 |
.17015 .17031 •17047 •17064 •17080 |
-20504 -20527 •20551 -20575 -20598 |
-18001 •18018 •18035 .18051 -18068 |
.21953 .21978 .22003 .22028 -22053 |
19013 19030 19047 19064 19081 |
.23476 .23502 -23529 -23555 •23581 |
||
|
60 |
•16133 |
.19236 |
-17096 |
.20622 |
-18085 |
.22077 |
19098 |
•23607 |
60 |
237
TABLE 11— NATURAL VERSED SINES AND EXTERNAL SECANTS 36° 37° 38° 39°
|
/ o 2 8 ~6~ 6 8 G 1O 11 12 13 li- 15 16 17 18 -L9_ 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39_ 40 41 42 43 44 |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
» ~0 2 _! 5 8 9 10 11 12 13 -I* 15 16 17 18 19 |
|
•19098 •19115 •19133 .19150 -19167 |
.23607 •23633 .23659 .23685 •23711 |
.20136 -20154 .20171 •20189 •20207 |
.25214 •25241 .25269 .25296 •25324 |
.21199 .21217 .21235 •21253 .21271 |
.26902 .26931 •26960 .26988 .27017 |
.22285 •22304 •22322 .22340 •22359 |
.28676 -28706 -28737 -28767 •28797 |
||
|
.19184 .19201 .19218 .19235 .19252 |
.23738 .23764 .23790 .23816 .23843 |
.20224 .20242 .20259 .20277 .20294 |
.25351 •25379 •25406 .25434 .25462 |
•21289 •21307 •21324 .21342 .21360 |
•27046 .27075 •27104 •27133 •27162 |
•22377 •22395 •22414 •22432 . 22450 |
•28828 .28858 .28889 .28919 •28950 |
||
|
.19270 .19287 •19304 .19321 •19338 |
.23869 .23895 .23922 .23948 .23975 |
•20312 .20329 .20347 •20365 .20382 |
.25489 .25517 .25545 .25572 .25600 |
•21378 .21396 .21414 .21432 •21450 |
.27191 •27221 .27250 .27279 •27308 |
.22469 -22487 -22506 •22524 .22542 |
.28980 •29011 .29042 •29072 •29103 |
||
|
.19356 .19373 .19390 •19407 -19424 |
.24001 .24028 .24054 .24081 .24107 |
•20400 .20417 .20435 .20453 .20470 |
.25628 .25656 .25683 .25711 .25739 |
•21468 •21486 .21504 .21522 .21540 |
.27337 .27366 .27396 .27425 -27454 |
•22561 .22579 -22598 •22616 •22634 |
.29133 .29164 .29195 .29226 •29256 |
||
|
•19442 •19459 •19476 •19493 .19511 |
.24134 -24160 .24187 .24213 .24240 |
.20488 .20506 •20523 •20541 .20559 |
•25767 .25795 .25823 .25851 .25879 |
.21558 .21578 •21595 •21613 .21631 |
•27483 .27513 .27542 .27572 .27601 |
.22653 •22671 •22690 •22708 .22727 |
•29287 •29318 -29349 .29380 .29411 |
20 21 22 23 24 25 26 27 28 _29 30 31 32 33 34 |
|
|
.19528 •19545 •19562 .19580 •19597 |
.24267 .24293 . 24320 .24347 •24373 |
•20576 •20594 .20612 .20629 .20647 |
.25907 .25935 •25963 .25991 .26019 |
•21649 .21667 .21685 •21703 .21721 |
.27630 .27660 •27689 .27719 .27748 |
•22745 .22764 .22782 .22801 -22819 |
-29442 -29473 .29504 .29535 •29566 |
||
|
.19614 .19632 .19649 .19666 -19684 |
. 24400 .24427 .24454 .24481 .24508 |
•20665 .20682 .20700 .20718 •20736 |
.26047 .26075 .26104 .26132 .26160 |
.21739 •21757 •21775 .21794 •21812 |
-27778 -27807 -27837 .27867 .27896 |
.22838 .22856 22875 .22893 •22912 |
.29597 .29628 .29659 .29690 •29721 |
||
|
.19701 .19718 •19736 •19753 .19770 |
.24534 .24561 .24588 .24615 . 24642 |
•20753 •20771 •20789 .20807 .20824 |
.26188 .26216 .26245 .26273 •26301 |
•21830 .21848 .21866 •21884 -21902 |
-27926 .27956 .27985 •28015 .28045 |
•22930 •22949 •22967 •22986 . 23004 |
.29752 -29784 -29815 -29846 -29877 |
35 38 37 38 -39 40 41 42 43 _44 45 46 47 48 49 |
|
|
•19788 .19805 •19822 .19840 .19857 |
.24669 .24696 .24723 .24750 •24777 |
•20842 •20860 •20878 •20895 .20913 |
.26330 .26358 .26387 •26415 . 26443 |
.21921 •21939 -21957 •21975 .21993 |
•28075 .28105 -28134 .28164 •28194 |
•23023 .23041 •23060 .23079 .23097 |
- 29909 -29940 -29971 .30003 •30034 |
||
|
45 46 47 48 49 50 51 52 53 54 |
•19875 •19892 •19909 •19927 .19944 |
.24804 .24832 24859 .24886 •24913 |
.20931 •20949 •20967 •20985 .21002 |
•26472 .26500 .26529 .26557 •26586 |
•22012 .22030 •22048 •22066 . 22084 •22103 •22121 •22139 •22157 •22176 |
-28224 -28254 •28284 .28314 •28344 |
•23116 •23134 -23153 •23172 -23190 |
.30066 .30097 .30129 .30160 •30192 |
|
|
•19962 .19979 •19997 •20014 •20032 |
. 24940 .24967 .24995 .25022 - 25049 |
•21020 .21038 .21056 •21074 .21092 |
.26615 .26643 .26672 .26701 .26729 |
.28374 - 28404 -28434 •28464 •28495 |
•23209 -23228 -23246 •23265 -23283 |
.30223 .30255 •30287 .30318 .30350 |
50 51 52 53 54 55 56 57 58 -fifl 60 |
||
|
55 56 57 58 M. 60 |
.20049 •20066 •20084 •20101 -20119 |
.25077 .25104 .25131 .25159 .25186 |
•21109 •21127 •21145 •21163 -21181 |
.26758 .26787 .26815 .26844 .26873 |
•22194 •22212 •22231 •22249 .22267 |
-28525 •28555 .28585 .28615 .28646 |
•23302 •23321 -23339 •23358 -23377 |
.30382 .30413 .30445 .30477 -30509 |
|
|
•20136 |
•25214 |
.21199 |
.26902 |
•22285 |
•28676 |
•23396 |
.30541 |
238
|
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 40° 41° 43° 43° |
|||||||||
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
|
|
O 1 2 3 4 5 6 7 9 |
•23396 .23414 •23433 .23452 .23470 |
.30541 .30573 .30605 .30636 .30668 |
.24529 .24548 •24567 •24586 .24605 |
,32501 .32535 .32568 .32602 .32636 |
.25686 •25705 .25724 .25744 .25763 |
.34563 .34599 .34634 .34669 .34704 |
.26865 •26884 •26904 .26924 .26944 |
•36733 .36770 .36807 .36844 .36881 |
0 2 3 _1 5 6 7 8 9 1O 11 12 13 14 "15 16 17 18 19 |
|
•23489 .23508 .23527 .23545 •23564 |
.30700 •30732 .30764 .30796 .30829 |
•24625 .24644 •24663 •24682 .24701 |
.32669 .32703 .32737 .32770 .32804 |
.25783 •25802 •25822 .25841 •25861 |
.34740 .34775 .34811 •34846 •34882 |
•26964 •26984 •27004 •27024 • 27043 |
•36919 .36956 .36993 .37030 •37068 |
||
|
10 11 12 13 14 15 16 17 18 19 |
.23583 .23602 .23620 .23639 •23658 |
.30801 .30393 .30925 .30957 .30989 |
. 24720 •24739 .24759 .24778 .24797 |
.32838 .32872 .32905 .32939 .32973 |
.25880 •25900 .25920 .25939 •25959 |
.34917 •34953 .34988 .35024 .35060 |
27063 •27083 •27103 .27123 •27143 |
•37105 .37143 •37180 .37218 .37255 |
|
|
.23677 •23696 •23714 •23733 -23752 |
•31C22 .31054 .31086 •31119 .31151 |
•24816 •24835 .24854 .24874 .24893 |
.33007 .33041 .33075 .33109 •33143 |
.25978 .25998 .26017 .26037 .26056 |
.35095 .35131 .35167 .35203 .35238 |
.27163 .27183 .27203 .27223 . 27243 |
.37293 .37330 .37368 .37406 •37443 |
||
|
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
•23771 •23790 .23808 .23827 •23846 |
•31183 .31216 .31248 .31281 .31313 |
24912 24931 24950 24970 24989 |
.33177 .33211 .33245 .33279 .33314 |
.26076 .26096 .26115 .26135 .26154 |
.35274 .35310 .35346 .35382 .35418 |
.27263 .27283 .27303 •27323 .27343 |
.37481 .37519 •37556 .37594 .37632 |
2O 21 22 23 _24 25 28 27 28 29 30 31 32 33 34 |
|
•23865 23884 •23903 •23922 23941 |
.31346 .31378 .31411 .31443 .31476 |
25008 25027 25047 25066 25085 |
.33348 .33382 .33416 .33451 .33485 |
.26174 .26194 .26213 •26233 .26253 |
.35454 .35490 .35526 .35562 .35598 |
.27363 27383 27403 27423 .27443 |
•37670 .37708 .37746 .37784 .37822 |
||
|
.23959 .23978 23997 24016 24035 |
.31509 •31541 .31574 .31607 .31640 |
25104 25124 25143 25162 25182 |
.33519 .33554 .33588 .33622 .33657 |
26272 26292 26312 26331 26351 |
.35634 .35670 •35707 .35743 •35779 |
27463 27483 27503 27523 27543 |
.37860 .37898 .37936 .37974 •38012 |
||
|
35 36 37 38 39 |
24054 24073 24092 24111 24130 |
.31672 .31705 .31738 .31771 .31804 |
25201 25220 25240 25259 25278 |
.33691 .33726 .33760 .33795 .33830 |
26371 26390 26410 26430 26449 |
.35815 •35852 .35888 .35924 .35961 |
27563 27583 27603 27623 27643 |
.38051 .38089 .38127 .38165 .38204 |
35 36 37 38 -39 40 41 42 43 44 |
|
40 41 42 43 44 |
24149 24168 24187 24206 24225 |
.31837 .31870 .31903 .31936 •31969 |
25297 25317 25336 25356 25375 |
.33864 .33899 .33934 .33968 .34003 |
26469 26489 26509 26528 26548 |
.35997 .36034 .36070 .36107 .36143 |
27663 27683 27703 27723 27743 |
•38242 .38280 .38319 .38357 .38396 |
|
|
, 45 46 :• 47 48 49 |
24244 24262 24281 24300 24320 |
.32002 .32035 .32068 .32101 .32134 |
25394 25414 25433 25452 25472 |
.34038 .34073 .34108 .34142 .34177 |
26568 26588 26607 26627 26647 |
.36180 .36217 .36253 .36290 •36327 |
27764 27784 27804 27824 27844 |
.38434 .38473 .38512 .38550 .38589 |
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 |
|
5O 51 52 53 54 |
24339 24358 24377 24396 24415 |
.32168 .32201 •32234 .32267 .32301 |
25491 25511 25530 25549 25569 |
.34212 .34247 •34282 •34317 •34352 |
26667 26686 26706 26726 26746 |
.36363 .36400 .36437 .36474 .36511 |
27864 27884 27905 27925 27945 |
.38628 .38666 .38705 .38744 .38783 |
|
|
55 56 57 58 59 |
24434 24453 24472 24491 24510 |
.32334 .32368 .32401 •32434 .32468 |
25588 25608 25627 25647 25666 |
•34387 .34423 .34458 .34493 .34528 |
26766 26785 26805 26825 26845 |
.36548 •36585 .36622 .36669 .36696 |
27965 27985 28005 28026 28046 |
.38822 .38860 .38899 .38938 .38977 |
|
|
60 |
24529 |
.32501 |
25686 |
.34563 |
26865 |
.36733 |
28066 |
.39016 |
60 |
239
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 44° 45° 46° 47°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
0 1 2 3 4 |
.28066 .28086 .28106 .28127 .28147 |
.39016 .39055 .39095 .39134 .39173 |
•29289 -29310 •29330 •29351 •29372 |
.41421 .41463 .41504 .41545 .41586 |
.30534 .30555 .30576 •30597 .30618 |
•43956 .43999 .44042 .44086 -44129 |
•31SOO •31821 •31843 •31864 •311*5 |
•46628 •46674 .46719 •46765 -46811 |
0 1 2 3 4 |
|
5 6 7 8 9 |
.28167 .28187 •28208 .28228 .28248 |
.39212 .39251 .39291 .39330 •39369 |
•29392 .29413 .29433 29454 .29475 |
.41627 .41669 .41710 •41752 •41793 |
•30639 .30660 •30681 .30702 •30723 |
.44173 .44217 •44260 •44304 . 44347 |
•31907 •31928 •31949 •31971 •31992 |
•46857 .46903 •46949 •46995 47041 |
5 6 7 8 9 |
|
10 11 12 13 14 |
.28268 .28289 •28309 •28329 .28350 |
.39409 .39448 .39487 .39527 .39566 |
.29495 .29516 .29537 •29557 •29578 |
.41835 .41876 .41918 .41959 •42001 |
.30744 .30765 .30786 .30807 .30828 |
•44391 .44435 .44479 .44523 •44567 |
•32013 •32035 •32C56 -32077 •32099 |
.47087 .47134 •47180 .47226 47272 |
10 11 12 13 14 |
|
15 16 17 18 19 |
.28370 .28390 .28410 .28431 .28451 |
.39606 •39646 .39685 .39725 •39764 |
.29599 .29619 .29640 .29661 •29681 |
.42042 .42084 .42126 .42168 .42210 |
.30849 .30870 .30891 .30912 -30933 |
•44610 .44654 .44698 .44742 -44787 |
•32120 -32141 -32163 -32184 •32205 |
.47319 .47365 .47411 •47458 -47504 |
15 16 17 18 19 |
|
20 21 22 23 24 |
.28471 .28492 .28512 .28532 .28553 |
•39804 .39844 .39884 .39924 .39963 |
29702 .29723 .29743 •29764 -29785 |
.42251 .42293 .42335 .42377 .42419 |
-30954 .30975 -30996 -31017 -31038 |
.44831 .44875 .44919 .44963 .45007 |
-32227 •32248 •32270 •32291 •32312 |
.47551 •47598 .47644 .47691 -47738 |
20 21 22 23 24 |
|
25 26 27 28 29 |
•28573 •28593 .28614 .28634 .28655 |
•40003 .40043 .40083 .40123 .40163 |
,29805 .29826 .29847 •29868 .29888 |
.42461 .42503 .42545 .42587 .42630 |
-31059 .31080 .31101 •31122 -31143 |
.45052 .45096 .45141 .45185 .45229 |
32334 -32355 •32377 •32398 -32420 |
•47784 .47831 •47878 •47925 -47972 |
25 26 27 28 29 |
|
30 31 32 33 34 |
.28675 .28695 •28716 •28736 •28757 |
.40203 .40243 .40283 .40324 .40364 |
•29909 .29930 •29951 •29971 .29992 |
.42672 .42714 .42756 .42799 .42841 |
•11165 •31186 -31207 -31228 .31249 |
.45274 .45319 .45363 .45408 -45452 |
•32441 -32462 •32484 •32505 •32527 |
•48019 •48066 .48113 .48160 •48207 |
30 31 32 33 34 |
|
35 36 37 38 39 |
.28777 •28797 •28818 .28838 .28859 |
.40404 .40444 •40485 .40525 •405P5 |
.30013 •30034 •30054 •30075 •30096 |
•42883 .42926 .42968 .43011 .43053 |
•31270 -31291 -31312 -31334 -31355 |
.45497 .45542 .45587 •45631 -45676 |
-32548 -32570 -32591 -32613 •32634 |
•48254 •48301 -48349 •48396 •48443 |
35 36 37 38 39 |
|
40 41 42 43 44 |
.28879 •28900 .28920 .28941 .28961 |
.40606 . 40646 .40687 .40727 .40768 |
•30117 •30138 •30158 .30179 .30200 |
.43096 .43139 .43181 .43224 .43267 |
-31376 -31397 •31418 •31439 .31461 |
•45721 •45766 .45811 .45856 .45901 |
•32656 -32677 -32699 -32720 -32742 |
•48491 -48538 •48586 •48633 •48681 |
40 41 42 43 44 |
|
45 46 47 48 49 |
•28981 •29002 •29022 •29043 .29063 |
.40808 .40849 .40890 .40930 .40971 |
•30221 •30242 •30263 •30283 .30304 |
.43310 .43352 .43395 .43438 -43481 |
•31482 •31503 •31524 •31545 -31567 |
.45946 .45992 .46037 -46082 46127 |
•32763 -32785 -32806 -32828 - 32849 |
•48728 .48776 •48824 •48871 -48919 |
45 46 47 48 49 |
|
50 51 52 53 54 |
•29084 .29104 ..'39125 .29145 •29166 |
.41012 .41053 .41093 .41134 .41175 |
•30325 •30346 -30367 •30388 . 30409 |
.43524 .43567 .43610 .43653 .43696 |
•31588 •31609 •31630 •31651 •31673 |
•46173 •46218 •46263 •46309 •46354 |
-32871 •32893 •32914 32936 3?957 |
•48967 •49015 •49063 .49111 .49159 |
50 51 52 53 54 |
|
55 56 57 58 59 |
.29187 •29207 •29228 •29248 29269 |
.41216 .41257 .41298 .41339 .41380 |
•30430 -30451 •30471 .30492 -30513 |
.43739 .43783 .43826 .43869 .43912 |
•31694 31715 31736 31758 31779 |
.46400 .46445 •46491 .46537 -46582 |
32979 33001 33022 33044 330P5 |
.49207 •49255 .49303 .49351 .4P399 |
55 56 57 58 59 |
|
60 |
•29289 |
.41421 |
-30534 |
.43956 |
31800 |
.46628 |
33087 |
•49448 |
60 |
240
TABLE 11— NATURAL VERSED SINES AND EXTERNAL SECANT3. 48* 49° 50° 51°
|
• |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
o 1 2 3 4 |
33087 33109 33130 33152 33173 |
.49448 .49496 .49544 .49593 .49641 |
34394 34416 34438 34400 34482 |
•52425 .52476 .52527 .52579 -52630 |
35721 35744 35766 35788 35810 |
•55572 •55626 .55680 .55734 .55789 |
37068 37091 37113 37136 37158 |
•58902 •58959 •59016 .59073 -59130 |
0 1 2 3 4 |
|
5 6 7 8 9 10 11 12 13 14 |
33195 33217 33238 33260 33282 |
•49690 .49738 .49787 .49835 .49884 |
34504 34526 34548 34570 34592 |
.52681 .52732 .52784 .52835 .52886 |
35833 35855 35877 35900 35922 |
.55843 .55897 .55951 .56005 . 56.060 |
37181 37204 37226 37249 37272 |
-59188 -59245 •59302 .59360 -59418 |
5 6 7 8 9 |
|
33303 33325 33347 33368 33390 |
.49933 .49981 .50030 .50079 .50128 |
34614 34636 34658 34680 34702 |
.52938 .52989 .53041 .53092 .53144 |
35944 35967 35989 36011 36034 |
.56114 .56169 .56223 .56278 .56332 |
37294 37317 37340 37362 37385 |
.59475 .59533 •59590 .59648 .59706 |
10 11 12 13 14 |
|
|
15 16 17 18 19 |
33412 33434 33455 33477 33499 |
.50177 .50226 .50275 .50324 .50373 |
34724 34746 34768 34790 34815? |
.53196 .53247 .53299 .53351 .53403 |
36056 36078 36101 36123 36146 |
.56387 .56442 .56497 .56551 .56606 |
37408 37430 37453 37476 37498 |
.59764 .59822 .59880 .59938 .59996 |
15 16 17 18 19 |
|
20 21 22 23 24 . 25 26 27 28 29 |
33520 33542 33564 33586 33607 |
•50422 .50471 .50521 .50570 .50619 |
34834 34856 34878 34900 34923 |
.53455 .53507 .53559 .53611 .53663 |
36168 36190 36213 36235 36258 |
•56661 .56716 .56771 .56826 .56881 |
37521 37544 37567 37589 37612 |
.60054 .60112 .60171 .60229 .60287 |
20 21 22 23 24 25 26 27 28 29 |
|
33629 33651 33673 33694 33716 |
•50669 .50718 •50767 .50817 .50866 |
34945 34967 34989 35011 35033 |
.53715 .53768 .53820 .53872 .53924 |
36280 36302 36325 36347 36370 |
.56937 .56992 .57047 .57103 .57158 |
37635 37658 .37680 .37703 .37726 |
.60346 .60404 .60463 .60521 -60580 |
||
|
30 31 32 33 ! 34 |
33738 33760 33782 33803 33825 |
•50916 •50966 •51015 .51065 .51115 |
35055 35077 35099 35122 35144 |
.53977 . 54029 •54082 .54134 .54187 |
36392 36415 36437 36460 36482 |
.57213 -57269 .57324 .57380 .57436 |
.37749 •37771 -37794 .37817 .37840 |
.60639 .60698 .60756 .60815 .60874 |
3O 31 32 33 34 35 36 37 38 -39 4O 41 42 43 44 45 46 47 48 49 5O 51 52 53 54 55 56 57 58 59 60 |
|
35 36 37 38 39_ 40 41 42 43 44 45 46 47 48 49 |
33847 33869 33891 33912 33934 |
.51165 .51215 .51265 .51314 .51364 |
35166 35188 35210 35232 35254 |
.54240 .54292 . 54345 .54398 .54451 |
36504 •36527 .36549 •36572 .36594 |
-57491 .57547 .57603 .57659 .57715 |
-37862 -37885 -37908 -37931 .37954 |
.60933 .60992 .61061 .61111 -61170 |
|
|
33958 •33978 •34000 •34022 •34044 |
.51415 .51465 .51515 .51565 .51615 |
35277 35299 35321 35343 35365 |
.54504 .54557 .54610 .54663 .54716 |
.36617 •36639 •36662 •36684 .36707 |
•57771 .57827 .57C83 .57939 .57995 |
.37976 .37999 .38022 -38045 -38068 |
.61229 . 61288 .61348 •61407 .61467 |
||
|
•34065 -34087 •34109 •34131 -34153 |
.51665 .51716 .51766 .51817 .51867 |
35388 35410 35432 .35454 •35476 |
.54769 .54822 .54876 .54929 .54982 |
•36729 •36752 -36775 •36797 -36820 |
.58051 .58108 .58164 .58221 .58277 |
-38091 -38113 •38136 •38159 .38182 |
.61526 .61586 .61646 .61705 .61765 |
||
|
50 51 52 53 54 |
-34175 •34197 -34219 •34241 • 34262 |
.51918 .51968 .52019 .52069 .52120 |
-35499 •35521 •35543 .35565 .35588 |
.55036 .55089 .55143 .55196 .55250 |
.36842 •36865 •36887 .36910 .36932 |
.58333 .58390 . 58447 .58503 .58560 |
.38205 •38228 •38251 -38274 .38296 |
- 61825 .61885 .61945 .62005 .62065 |
|
|
'55 56 57 58 59 60 |
•34284 •34306 •34328 •34350 -34372 |
.52171 .52222 .52273 .52323 .52374 |
.35610 •35632 •35654 •35677 •35699 |
.55303 .55357 .55411 .55465 .55518 |
.36955 -36978 .37000 -37023 -37045 |
.58617 .58674 .58731 .58788 .58845 |
-38319 .38342 .38365 .38388 .38411 |
.62125 .62185 .62246 .62306 -62366 |
|
|
•34394 |
.52425 |
.35721 |
.55572 |
-37068 |
.58902 |
•38434 |
.62427 |
||
|
241 |
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANT& 53° 53° 54° 55°
|
' |
Vers. |
Ex. sec |
Vers. |
Ex. sec |
Vers. |
Ex. sec |
Vers. |
Ex. sec |
|
|
I |
. 38434 .38457 .38480 .38503 •38526 |
.62427 . 62487 .62548 .62609 •62669 |
.39819 •39842 •39865 •39888 •39911 |
.66164 .66228 .66292 .66357 •66421 |
•41221 •41245 •41269 •41292 •41316 |
.70130 .70198 .70267 •70335 . 70403 |
•42642 .42666 •42690 .42714 •42738 |
. 74345 •74417 . 74490 •74562 •74635 |
0 2 3 4 |
|
1 e 1 8 9 |
•38549 •38571 •38594 •38617 .38640 |
.62730 .62791 .62852 •62913 .62974 |
•39935 •39958 .39981 •40005 .40028 |
•66486 •66550 .66615 .66679 •66744 |
•41339 •41363 •41386 •41410 •41433 |
. 70472 . 70540 . 70609 •70677 •70746 |
•42762 •42785 •42809 •42833 •42857 |
•74708 . 74781 .74854 .74927 •75000 |
5 6 7 8 g |
|
10 11 12 13 14 |
•38663 .38686 .38709 •38732 •38755 |
.63035 .63096 .63157 .63218 .63279 |
•40051 •40074 .40098 •40121 .40144 |
.66809 .66873 •66938 .67003 •67068 |
.41457 •41481 •41504 •41528 -41551 |
• 70815 .70884 .70953 . 71022 •71091 |
•42881 .42905 •42929 •42953 •42976 |
.75073 .75146 .75219 .75293 •75366 |
10 11 12 13 14 |
|
15 16 17 18 -L2L |
.38778 .38801 .38824 •38847 •38870 |
.63341 .63402 .63464 .63525 .63587 |
•40168 •40191 •40214 •40237 •40261 |
.67133 .67199 .67264 .67329 .67394 |
•41575 •41599 .41622 •41646 .41670 |
.71160 •71229 .71298 .71368 •71437 |
.43000 .43024 •43048 •43072 |
. 75440 .75513 •75587 .75661 •75734 |
15 16 17 18 19 |
|
20 21 22 23 24_ |
•38893 .38916 .38939 .38962 .38985 |
.63648 .63710 .63772 .63834 .63895 |
.40284 •40307 .40331 •40354 .40378 |
.67460 .67525 .67591 .67656 .67722 |
•41693 •41717 •41740 -41764 .41788 |
•71506 .71576 .71646 .71715 •71785 |
•43120 •43144 •43168 •43192 43216 |
.75808 .75882 .75956 .76031 •76105 |
20 21 22 23 24 |
|
25 26 27 28 |
39009 39032 39055 39078 39101 |
.63957 .64019 .64081 •64144 •64206 |
.40401 .40424 .40448 •40471 •40494 |
.67788 .67853 •67919 •67985 •68051 |
•41811 •41835 •41859 •41882 .41906 |
•71855 .71925 .71995 .72065 •72135 |
•43240 •43264 •43287 •43311 •43335 |
•76179 .76253 .76328 .76402 •76477 |
25 26 27 28 29 |
|
30 31 32 33 34 |
39124 39147 39170 39193 39216 |
.64268 .64330 .64393 .64455 .64518 |
-40518 •40541 40565 40588 40611 |
.68117 .68183 •68250 .68316 .68382 |
•41930 .41953 .41977 •42001 .42024 |
.72205 . 72275 .72346 •72416 .72487 |
•43359 •43383 •43407 •43431 •43455 |
•76552 .76626 .76701 .76776 •76851 |
~3O 31 32 33 34 |
|
(CO CO CO CO CO kOCO-JCDOl |
39239 39262 39286 39309 39332 |
.64580 .64643 .64705 .64768 .64831 |
40635 40658 40682 40705 40728 |
. 68449 •68515 .68582 •68648 •68715 |
•42048 •42072 42096 42119 42143 |
.72557 .72628 .72698 .72769 . 72840 |
•43479 •43503 •43527 •43551 .43575 |
•76926 .77001 .77077 .77152 |
35 36 37 38 39 |
|
40 41 42 43 44 |
39355 39378 39401 39424 39447 |
•64894 •64957 .65020 .65083 •65146 |
40752 40775 40799 40822 40846 |
•68782 .68848 .68915 .68982 •69049 |
42167 42191 42214 42238 42262 |
.72911 •72982 .73053 .73124 .73195 |
•43599 •43623 •43647 •43671 43695 |
.77303 .77378 .77454 •77530 •77606 |
40 41 42 43 44 |
|
45 46 47 48 49 |
39471 39494 39517 39540 39563 |
.65209 .65272 .65336 .65399 •65462 |
40869 40893 40916 40939 40963 |
.69116 .69183 .69250 .69318 .69385 |
42285 42309 42333 42357 42381 |
.73267 .73338 . 73409 .73481 .73552 |
43720 43744 43768 43792 43816 |
•77681 •77757 .77833 .77910 •77986 |
45 46 47 48 49 |
|
50 51 52 53 54 |
39586 39610 39633 9656 9679 |
65526 65589 65653 65717 65780 |
40986 41010 41033 41057 41080 |
.69452 .69520 .69587 .69655 .69723 |
42404 42428 42452 42476 42499 |
.73624 .73696 .73768 .73840 .73911 |
43840 43864 43888 43912 43936 |
.78062 .78138 .78215 .78291 •78368 |
50 51 52 53 54 |
|
55 56 57 58 -fiL. |
9702 9726 9749 9772 9795 |
65844 65908 65972 66036 66100 |
41104 41127 41151 41174 41198 |
.69790 •69858 .69926 .69994 •70062 |
42523 42547 42571 42595 42619 |
.73983 .74056 .74128 . 74200 •74272 |
43960 43984 44008 44032 44057 |
.78445 .78521 .78598 .78675 78752 |
55 56 57 58 59 |
|
60 |
9819 |
66164 |
41221 |
70130 |
42642 |
•74345 |
44081 |
78829 |
60 |
242
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 56° 57° 58° 59°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
9 |
|
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 |
•44081 .44105 •44129 •44153 •44177 |
.78829 .78906 .78984 .79061 •79138 |
.45536 •45560 .45585 -45609 .45634 |
.83608 .83690 .83773 .83855 .83938 |
•47008 •47033 •47057 .47082 .47107 |
.88708 .88796 .88884 .88972 .89060 |
•48496 •48521 •48546 •48571 -48596 |
.94160 .94254 . 94349 .94443 .94537 |
0 2 3 4 5 6 7 9 |
|
•44201 .44225 •44250 -44274 -44298 |
.79216 .79293 .79371 . 79449 .79527 |
-45658 •45683 -45707 •45731 .45756 |
.84020 .84103 .84186 .84269 .84352 |
.47131 .47156 .47181 •47206 .47230 |
.89148 •89237 .89325 .89414 .89503 |
•48621 -48646 •48671 .48696 -48721 |
.94632 .94726 .94821 .94916 .95011 |
||
|
•44322 •44346 .44370 •44395 .44439 |
.79604 .79682 .79761 .79839 .79917 |
.45780 -45805 •45829 .45854 .45878 |
.84435 •84518 •84601 .84685 -84768 |
•47255 .47280 .47304 .47329 .47354 |
.89591 .89680 .89769 .89858 .89948 |
•48746 -48771 .48796 .48821 .48846 |
.95106 •95201 .95296 .95392 .95487 |
10 11 12 13 14 15 16 17 18 19 |
|
|
•44443 •44467 •44491 .44516 .4454.0 |
.79995 .80074 •80152 .80231 .80309 |
.45903 •45927 .45951 •45976 .46000 |
.84852 .84935 .85019 •85103 •85187 |
.47379 •47403 .47428 •47453 •47478 |
.90037 .90126 •90216 .90305 .90395 |
•48871 •48896 •48921 .48946 .48971 |
.95583 -95678 .95774 .95870 •95966 |
||
|
20 21 22 23 24 25 28 27 28 29 |
•44564 .44588 •44612 .44637 •44661 |
.80388 .80467 .80546 .80625 .80704 |
.46025 -46049 •46074 •46098 .46123 |
•85271 .85355 .85439 •85523 .85608 |
.47502 .47527 .47552 .47577 .47601 |
.90485 .90575 .90665 .90755 .90845 |
.48996 •49021 •49046 •49071 •49096 |
.96062 .96158 .96255 .96351 .96448 |
20 21 22 23 24 25 26 27 28 29 30 3] 32 33 34 35 36 37 38 -39 40 41 42 43 44 45 46 47 48 49 5O 51 52 53 54 55 56 57 58 59 |
|
•44685 .44709 •44734 •44758 •44782 |
.80783 .80862 .80942 .81021 .81101 |
•46147 •46172 -46196 -46221 •46246 |
.85692 .85777 .85861 .85946 .86031 |
•47626 •47651 •47676 .47701 •47725 |
.90935 .91026 .91116 .91207 .91297 |
•49121 •49146 -49171 -49196 .49221 |
.96544 .96641 .96738 .96835 .96932 |
||
|
30 31 32 33 84 35 36 37 38 39 |
•44806 .44831 .44855 •44879 .44903 |
.81180 •81260 •81340 .81419 .81499 |
-46270 •46295 •46319 •46344 -46368 |
.86116 .86201 .86286 .86371 .86457 |
•47750 .47775 -47800 •47825 .47849 |
.91388 .91479 .91570 .91661 •91752 |
.49246 .49271 •49296 .49321 .49346 |
.97029 .97127 .97224 .97322 .97420 |
|
|
•44928 •44952 44976 •45001 .45025 |
•81579 .81659 .81740 .81820 .81900 |
-46393 •46417 - 46442 •46466 -46491 |
•86542 .86627 •86713 .86799 •86885 |
•47874 .47899 .47924 •47949 -47974 |
.91844 .91935 .92027 .92118 .92210 |
•49372 •49397 •49422 -49447 -49472 |
.97517 .97615 .97713 .97811 .97910 |
||
|
40 41 42 43 44 45 46 47 48 49 |
•45049 -45073 •45098 •45122 -45146 |
•81981 .82061 •82142 •82222 •82303 |
•46516 -46540 •46565 •46589 .46614 |
•86970 .87056 .87142 •87229 •87315 |
•47998 .48023 •48048 •48073 .48098 |
.92302 .92394 .92486 .92578 .92670 |
•49497 •49522 .49547 .49572 .49597 |
.98008 .98107 .98205 .98304 .98403 |
|
|
-45171 45195 -45219 -45244 -45268 |
•82384 •82465 •82546 .82627 .82709 |
•46639 •46663 •46688 •46712 .46737 |
.87401 •87488 •87574 .87661 .87748 |
•48123 .48148 •48172 .48197 -48222 |
.92762 •92855 .92947 .93040 .93133 |
•49623 •49648 •49673 •49698 .49723 |
.98502 .98601 .98700 .98799 .98899 |
||
|
50 51 52 53 54 55 56 57 58 59 |
•45292 •45317 •45341 -45365 -45390 |
•82790 •82871 •82953 .83034 .83116 |
•46762 •46786 •46811 •46836 •46860 |
.87834 .87921 .88008 .88095 •88183 |
.48247 -48272 .48297 •48322 -48347 |
.93226 .93319 .93412 .93505 .93598 |
-49748 -49773 -49799 49824 49849 |
.98998 .99098 •99198 .99298 .99398 |
|
|
•45414 •45439 -45463 •45487 •45512 |
.83198 .83280 .83362 .83444 .83526 |
•46885 •46909 •46934 -46959 •46983 |
.88270 •88357 •88445 .88532 •88620 |
-48372 •48396 •48421 -48446 48471 |
.93692 .93785 .93879 .93973 .94066 |
49874 49899 49924 49950 49975 |
.99498 .99598 .99698 •99799 -99899 |
||
|
60 |
•45536 |
.83608 |
•47008 |
.88708 |
.48496 |
.94160 |
50000 |
1.00000 |
6O |
243
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 60° 61° 63° 63°
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
t |
|
0 1 2 3 4 |
50000 50025 50050 50076 50101 |
1.00000 1-00101 1-00202 1-00303 1 - 00404 |
51519 51544 51570 51595 51621 |
1-06267 1-06375 1.06483 1-06592 1-06701 |
53053 53079 53104 53130 -53156 |
1.13005 1.13122 1-13239 1-13356 1-13473 |
54601 54627 54653 54679 54705 |
1-20269 1-20395 1-20521 1-20647 1-20773 |
0 1 2 3 4 |
|
~~5~ 6 7 8 g |
50126 50151 50176 50202 50227 |
1-00505 1-00607 1-00708 1-00810 1-00912 |
51646 51672 51697 51723 -51748 |
1-06809 1-06918 1-07027 1-07137 1-07246 |
-53181 •53207 -53233 .53258 .53284 |
1-13590 1.13707 1-13825 1-13942 1.14060 |
54731 .54757 - 54782 -54808 . 54834 |
1-20900 1-21026 1.21153 1.21280 1-21407 |
5 6 7 8 9 |
|
ib~ 11 12 13 14 |
50252 50277 50303 50328 50353 |
1-01014 1-01116 1-01218 1-01320 1-01422 |
-51774 -51799 -51825 -51850 -51876 |
1-07356 1.07465 1.07575 1-07685 1-07795 |
-53310 •53336 .53361 .53387 -53413 |
1-14178 1.14296 1-14414 1-14533 1-14651 |
- 54860 .54886 -54912 •54938 -54964 |
1-21535 1.21662 1.21790 1-21918 1.22045 |
10 11 12 13 14 |
|
15 16 17 18 19 |
50378 50404 50429 50454 50479 |
1.01525 1-01628 1-01730 1-01833 1.01936 |
-51901 •51927 .51952 .51978 .52003 |
1-07905 1.08015 1.08126 1.08236 1-08347 |
-53439 -53464 -53490 -53516 -53542 |
1.14770 1.14889 1.150C8 1.15127 1-15246 |
•54990 -55016 . 55042 .55068 - 55094 |
1-22174 1-22302 1-22430 1-22559 1.22688 |
15 16 17 18 19 |
|
20 21 22 23 24 |
50505 -50530 .50555 .50581 .50606 |
1-02039 1-02143 1-02246 1.02349 1.02453 |
-52029 -52054 -52080 -52105 -52131 |
1-08458 1.08569 1.08680 1.08791 1-08903 |
-53567 -53593 -53619 -53645 -53670 |
1-15366 1-15485 1-15605 1-15725 1-15845 |
-55120 -55146 •55172 •55198 .55224 |
1-22817 1-22946 1-23075 1-23205 ] .23334 |
20 21 22 23 24 |
|
25 26 27 28 29 |
•50631 .50656 .50682 .50707 .50732 |
1-02557 1-02661 1-02765 1-02869 1-02973 |
-52156 -52182 .52207 -52233 .52259 |
1-09014 1.09126 1-09238 1.09350 1-09462 |
.53696 -53722 -53748 -53774 .53799 |
1-15965 1-16085 1.16206 1.16326 1-16447 |
•55250 •55276 •55302 •55328 .55354 |
1-23464 1-23594 1-23724 1-23855 1-23985 |
25 26 27 28 29 |
|
30 81 32 33 34 |
.50758 .50783 -50808 .50834 -50859 |
1-03077 1-03182 1-03286 1-03391 1-03496 |
.52284 -52310 .52335 -52361 .52386 |
1-09574 1-09686 1-09799 1-09911 1-10024 |
-53825 -53851 -53877 -53903 .53928 |
1-16568 1.16689 1.16810 1.16932 1-17053 |
•55380 -55406 •55432 •55458 -55484 |
1-24116 1-24247 1-24378 1-24509 1-24640 |
30 31 32 33 34 |
|
35 36 37 38 39 |
.50884 -50910 .50935 -50960 . 50986 |
1-03601 1-03706 1-03811 1-03916 1-04022 |
.52412 -52438 . 52463 .52489 .52514 |
1-10137 1-10250 1-10363 1-10477 1-10590 |
•53954 -53980 - 54006 -54032 . RAO 58 |
1-17175 1.17297 1-17419 1.17541 1.17663 |
•55510 •55536 •55563 •55589 -FF615 |
1-24772 1-24903 1-25035 1-25167 1 .95300 |
35 36 37 38 39 |
|
40 41 42 43 44 |
•51011 -51036 -51062 .51087 .51113 |
1-04128 1-04233 1-04339 1 - 04445 1-04551 |
-52540 •52566 -52591 •52617 .52642 |
1-10704 1.10817 1-10931 1.11045 1-11159 |
-54083 -54109 .54135 -54161 -54187 |
1-17786 1-17909 1.18031 1-18154 1-18277 |
•55641 •55667 -55693 -55719 -55745 |
1-25432 1-25565 1-25697 1-25830 1.25963 |
40 41 42 43 44 |
|
45 46 47 48 49 |
•51138 •51163 •51189 .51214 -51239 |
1-04658 1-04764 1.04870 1-04977 1-05084 |
•52668 •52694 •52719 •52745 .52771 |
1-11274 1-11388 1-11503 1.11617 1-11732 |
-54213 -54238 -54264 -54290 .54316 |
1-18401 1-18524 1-18648 1-18772 1-18895 |
•55771 •55797 -55823 -55849 -55876 |
1-26097 1-26230 1-26364 1-26498 1-26632 |
45 46 47 48 49 |
|
50 51 52 53 54 |
•51265 •51290 •51316 •51341 .51366 |
1-05191 1-05298 1-05405 1-05512 1-05619 |
.52796 •52822 .52848 .52873 -52899 |
1.11847 1.11963 1.12078 1-12193 1-12309 |
-54342 •54368 -54394 - 54420 . 54446 |
1-19019 1-19144 1.19268 1-19393 1-19517 |
.55902 -55928 -55954 -55980 -56006 |
1-26766 1-26900 1-27035 1-27169 1-27304 |
50 51 52 53 54 |
|
55 66 57 58 59 |
•51392 •51417 .51443 •51468 -51494 |
1-05727 1-05835 1-05942 1-06050 1-06158 |
•52924 •52950 -52976 .53001 .53027 |
1-12425 1.12540 1.12657 1-12773 1-12889 |
- 54471 •54497 -54523 . 54549 .54575 |
1-19642 1-19767 1-19892 1-20018 1-20143 |
-56032 .56058 .56084 -56111 56137 |
1-27439 1-27574 1-27710 1.27845 1-27981 |
bb 56 57 58 -§C |
|
60 |
•51519 |
1-06267 |
.53053 |
1-13005 |
-54601 |
1-20269 |
-56163 |
1-28117 |
60 |
244
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 64° 65° 66° 67°
|
• |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
r |
|
o 1 2 3 4 |
•56163 .56189 .56215 .56241 .56267 |
1.28117 1-28253 1-28390 1.28526 1-28663 |
.57738 .57765 .57791 .57817 . 57844 |
1-36620 1-36768 1.36916 1-37064 1.37212 |
-59326 .59353 .59379 .59406 .59433 |
.45859 .46020 .46181 .46342 -46504 |
-60927 •60954 .60980 •61007 .61034 |
•55930 •56106 .56282 .56458 .56634 |
O 3 |
|
5 6 7 8 9 |
.56294 .56320 .56346 .56372 .56398 |
1.28800 1-28937 1-29074 1-29211 1.29349 |
.57870 .57896 •57923 .57949 .57976 |
1-37361 1.37509 1.37658 1-37808 1.37957 |
. 59459 .59486 •59512 •59539 .59566 |
.46665 •46827 1.46989 1-47152 1-47314 |
-61061 .61088 -61114 •61141 -61168 |
•56811 -56988 •57165 -57342 .57520 |
5 6 8 9 |
|
1O 11 12 13 14 |
.56425 .56451 •56477 •56503 .56529 |
1.29487 1-29625 .29763 .29901 . 30040 |
.58002 .58028 .58055 .58081 .58108 |
1-38107 1-38256 1.38406 1.38556 1-38707 |
.59592 -59619 -59645 -59672 -59699 |
1-47477 1-47640 1-47804 1-47967 1.48131 |
-61195 -61222 -61248 -61275 -61302 |
1-57698 1.57876 1-58054 1-58233 1.58412 |
1O 11 12 13 14 |
|
15 16 17 18 19 |
•56555 .56582 .56608 .56634 .56660 |
•30179 .30318 -30457 -30596 -30735 |
.58134 -58160 -58187 .58213 -58240 |
1-38857 1-39008 1-39159 1.39311 1-39462 |
-59725 •59752 -59779 -59805 .59832 |
1.48295 1.48459 1.48624 1.48789 1-48954 |
.61329 -61356 -61383 -61409 .61436 |
1.58591 1.58771 1-58950 1-59130 1-59311 |
15 16 17 18 19. |
|
20 21 22 23 24 |
.56687 •56713 •56739 .56765 •56791 |
•30875 •31015 •31155 •31295 -31436 |
-58266 •58293 .58319 .58345 .58372 |
1.39614 1.39766 1-39918 1.40070 1.40222 |
-59859 -59885 .59912 -59938 .59965 |
1-49119 1-49284 1-49450 1-49616 1-49782 |
. 61463 .61490 .61517 .61544 -61570 |
1-59491 1-59672 1-59853 1.60035 1-60217 |
20 21 22 23 24 |
|
25 2G 27 28 29 |
•56818 56844 56870 56896 56923 |
•31576 •31717 .31858 .31999 .32140 |
-58398 .58425 .58451 58478 58504 |
1.40375 1.40528 1.40681 1-40835 1.40988 |
-59992 -60018 -60045 • 60072 .60098 |
1 - 49948 1-50115 1-50282 1 . 50449 1.50617 |
•61597 •61624 .61651 .61678 .61705 |
1-60399 1-60581 1-60763 1-60946 1-61129 |
25 26 27 28 29 |
|
30 31 32 33 34 |
56949 56975 57001 57028 57054 |
•32282 •32424 .32566 1-32708 1-32850 |
58531 58557 58584 58610 58637 |
1-41142 1.41296 1.41450 1.41605 1.41760 |
•60125 •60152 •60178 -60205 .60232 |
1.50784 1.50952 1.51120 1.51289 1-51457 |
.61732 .61759 -61785 •61812 .61839 |
1-61313 1-61496 1.61680 1-61864 1 • 62049 |
30 S 33 34 |
|
35 36 37 38 39_ |
57080 57106 57133 57159 57185 |
1-32993 1.33135 1-33278 1-33422 1-33565 |
58663 58690 58716 58743 58769 |
1-41914 1.42070 1.42225 1.42380 1-42536 |
•60259 -60285 •60312 •60339 -60365 |
1.51626 1-51795 1.51965 1.52134 1 . 52304 |
•61866 •61893 -61920 -61947 -61974 |
1-62234 1.62419 1-62604 1.62790 1-62976 |
35 36 37 38 39 |
|
40 41 42 43 44 |
57212 57238 •57264 .57291 .57317 |
1-33708 1-33852 1-33996 1-34140 1-34284 |
-58796 58822 58849 -58875 .58902 |
1.42692 1-42848 1.43005 1.43162 1-43318 |
•60392 •60419 - 60445 •60472 . 60499 |
1.52474 1.52645 1.52815 1.52986 1.53157 |
-62001 -62027 -62054 -62081 -62108 |
1-63162 1.63348 1-63535 1-63722 1-63909 |
40 41 42 43 44 |
|
45 46 47 48 49 |
•57343 •57369 -57396 . 57422 . 57448 |
1 . 34429 1.34573 1-34718 1-34863 1-35009 |
.58928 •58955 -58981 •59008 -59034 |
1.43476 1-43633 1.43790 1.43948 1.44106 |
.60526 •60552 .60579 .60606 •60633 |
1.53329 1.53500 1.53672 1.53845 1-54017 |
•62135 -62162 •62189 -62216 - 62243 |
1.64097 1-64285 1-64473 •64662 •64851 |
45 46 47 48 49 |
|
50 51 52 53 54 |
.57475 -57501 .57527 .57554 -57580 |
1.35154 1.35300 1.35446 1-35592 1-35738 |
•59061 -59087 •59114 •59140 .59167 |
1.44264 1 • 44423 1.44582 1-44741 1-44900 |
.60659 •60886 .60713 . 60740 •60766 |
1.54190 1-54363 1-54536 1 - 54709 1 - 54883 |
- 62270 -62297 •62324 .62351 -62378 |
.65040 •65229 •65419 1-65609 1.65799 |
5O 51 52 53 54 |
|
55 56 57 58 .59. |
.57606 •57633 •57659 .57685 .57712 |
1-35885 1-36031 1-36178 1-36325 1-36473 |
•59194 •59220 -59247 -59273 -59300 |
1-45059 1-45219 1.45378 1.45539 1.45699 |
•60793 •60820 •60847 -60873 -60900 |
1-55057 1-55231 1.55405 1.55580 1.55755 |
. 62405 .62431 -62458 -62485 -62512 |
1-65989 1.66180 1 66371 1-66563 1-66755 |
55 56 57 58 59 |
|
60 |
•57738 |
1-36620 |
-59326 |
1-45859 |
.60927 |
1.55930 |
.62539 |
1-66947 |
60 |
245
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 68° 69° 70° 71°
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
0 2 3 |
.62539 .62566 .62593 • 62620 •62647 |
1-66947 1.67139 1-67332 1.67525 1-67718 |
•64163 -64190 .64218 -64245 - 64272 |
1-79043 1.79254 1.79466 1-79679 1-79891 |
•65798 •65825 •65853 .65880 .65907 |
1-92380 1-92614 1-92849 1-93083 1.93318 |
- 67443 • 67471 - 67498 -67526 -67553 |
2.07155 2-07415 '2-07675 2-07936 2-08197 |
0 2 3 4 |
|
5 6 7 8 . 9 |
.62674 .62701 .62728 •62755 .62782 |
1-67911 1.68105 1-68299 1.68494 1-68689 |
-64299 •64326 •64353 .64381 . 64408 |
1.80104 1.80318 1-80531 1-80746 1-80960 |
•65935 -65962 -65989 -66017 •66044 |
1-93554 1-93790 1.94026 1-94263 1-94500 |
-67581 -67608 -67636 -67663 -67691 |
2-08459 2-08721 2-08983 2-09246 2-09510 |
5 6 7 8 9 |
|
10 11 12 13 14 |
•62809 •62836 •62863 .62890 •62917 |
1.68884 1-69079 1.69275 1.69471 1-69667 |
. 64435 - 64462 . 64489 -64517 - 64544 |
1-81175 1.81390 1-81605 1-81821 1-82037 |
-66071 -66099 -66126 -66154 -66181 |
1-94737 1-94975 1-95213 1-95452 1.95691 |
-67718 -67746 -67773 -67801 -67829 |
2.09774 2-10038 2-10303 2.10568 2-10834 |
10 11 12 13 34 |
|
15 16 17 18 19 |
•62944 •62971 •62998 •63025 .63052 |
1.69864 1-70061 1.70258 1.70455 1.70653 |
-64571 .64598 •64625 •64653 . 64680 |
1-82254 1-82471 1-82688 1-82906 1-83124 |
-66208 -66236 -66263 -66290 •66318 |
1-95931 1.96171 1-96411 1-96652 1-96893 |
-67856 -67884 -67911 -67939 -67966 |
2-11101 2-11367 2-11635 2.11903 2-12171 |
15 16 17 18 19 |
|
20 21 22 23 24 |
.63079 •63106 •63133 •63161 •63188 |
1.70851 1.71050 1.71249 1 • 71448 1.71647 |
. 64707 . 64734 .64761 •64789 .64816 |
1-83342 1-83561 1.83780 1-83999 1-84219 |
•66345 -66373 • 66400 •66427 •66455 |
1 97135 1-97377 1-97619 1-97862 1.98106 |
-67994 -68021 -68049 -68077 -68104 |
2-12440 2-12709 2-12979 2-13249 2-13520 |
20 21 22 23 24 |
|
25 26 27 28 29 |
•63215 -63242 •63269 •63296 63323 |
1-71847 1 . 72047 1.72247 1 . 72448 1.72649 |
. 64843 . 64870 .64898 . 64925 •64952 |
1.84439 1.84659 .84880 .85102 •85323 |
•66482 •66510 •66537 •66564 .66592 |
1-98349 1-98594 1-98838 1-99083 1-99329 |
•68132 •68159 •68187 •68214 - 68242 |
2-13791 2-14063 2-14335 2-14608 2-14881 |
25 26 27 28 29 |
|
30 31 32 33 34 |
63350 •63377 63404 63431 63458 |
1-72850 1-73052 1-73254 1-73456 1-73659 |
-64979 •65007 •65034 •65061 •65088 |
-85545 -85767 .85990 -86213 1.86437 |
•66619 •66647 •66674 • 66702 •66729 |
1-99574 1-99821 2-00067 2-00315 2-00562 |
• 68270 -68297 •68325 •68352 -68380 |
2-15155 2-15429 2.15704 2.15979 2-16255 |
30 sa 32 33 34 |
|
35 36 37 38 39 |
63485 63512 63539 63566 63594 |
1.73862 1-74065 1.74269 1 - 74473 1-74677 |
65116 65143 65170 65197 65225 |
1.86661 1-86885 1-87109 1-87334 1-87560 |
•66756 •66784 •66811 •66839 -6R866 |
2-00810 2-01059 2-01308 2-01557 2-01807 |
• 68408 •68435 -68463 •68490 .68518 |
2-16531 2-16808 2-17085 2-17363 2-17641 |
35 36 37 38 39 |
|
40 41 42 43 44 |
63621 63648 63675 63702 63729 |
1.74881 1.75086 1.75292 1.75497 1-75703 |
65252 65279 65306 65334 65361 |
1-87785 1-88011 1-88238 1-88465 1-88692 |
•66894 •66921 •66949 •66976 . 67003 |
2-02057 2-02308 2-02559 2-02810 2-03062 |
-68546 •68573 •68601 .68628 -68656 |
2-17920 2-13199 2-18479 2-18759 2-19040 |
40 41 42 43 44 |
|
45 46 47 48 49 |
63756 63783 63810 63838 63865 |
1.75909 1-76116 1.76323 1.76530 1.76737 |
65388 65416 65443 65470 65497 |
1-88920 1-89148 1.89376 1-89605 1.89834 |
-67031 •67058 •67086 67113 67141 |
2-03315 2-03568 2-03821 2-04075 2-04329 |
.68684 •68711 •68739 •68767 .68794 |
2-19322 2-19604 2-19886 2-20169 2-20453 |
45 46 47 48 49 |
|
50 51 52 53 54 |
63892 63919 63946 63973 64000 |
1.76945 1-77154 1-77362 1.77571 1.77780 |
65525 65552 65579 65607 65634 |
.90063 .90293 .90524 •90754 -90986 |
67168 67196 67223 67251 67278 |
2-04584 2-04839 2-05094 2-05350 2-05607 |
-68822 . 68849 •68877 •68905 68932 |
2-20737 2-21021 2-21306 2-21592 2-21878 |
50 51 52 53 54 |
|
55 56 57 58 1L. |
64027 64055 64082 64109 64136 |
1.77990 1-78200 1-78410 1.78621 1-78832 |
65661 65689 65716 65743 65771 |
-91217 -91449 1-91681 1.91914 1-92147 |
67306 67333 67361 67388 67416 |
2-05864 2-06121 2-06379 2-06637 2-06896 |
68960 68988 69015 69043 69071 |
2-22165 2-22452 2-22740 2-23028 2.23317 |
55 56 57 58 59 |
|
60 |
64U63 |
1.79043 |
657.98 |
1-92380 |
67443 |
2-07155 |
69098 |
2-23607 |
60 |
246
TABLE 11.— NATURAL VERSED STNES AND EXTERNAL SECANTS. 72° 73° 74° 75°
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
o 1 2 3 | |
-69098 .69126 .69154 •69181 .69209 |
2-23607 2.23897 2-24187 2-24478 2-24770 |
-70763 -70791 -70818 -70846 -70874 |
2-42030 2-42356 2-42683 2-43010 2-43337 |
-72436 -72464 -72492 .72520 . 72548 |
2-62796 2.63164 2-63533 2-63903 2-64274 |
-74118 -74146 -74174 -74202 -74231 |
2-86370 2-86790 2-87211 2-87633 2-88056 |
O 1 2 3 |
|
5 6 7 8 9 |
.69237 .69264 .69292 .69320 .69347 |
2-25062 2-25355 2-25648 2-25942 2-26237 |
.70902 .70930 .70958 -70985 .71013 |
2-43666 2-43995 2-44324 2-44655 2.44986 |
•72576 -72604 •72632 -72660 .72688 |
2.64645 2.65018 2-65391 2-65765 2.66140 |
-74259 .74287 .74315 .74343 .74371 |
2-88479 2-88904 2-89330 2-89756 2-90184 |
5 6 7 8 9 |
|
10 11 12 13 14 |
-69375 - 69403 -69430 .69458 .69486 |
2-26531 2-26827 2-27123 2-27420 2-27717 |
-71041 -71069 -71097 -71125 -71153 |
2-45317 2-45650 2-45983 2-46316 2-46651 |
.72716 - 72744 -72772 -72800 .72828 |
2-66515 2-66892 2-67269 2-67647 2-68025 |
•74399 . 74427 •74455 - 74484 .74512 |
2.90613 2-91042 2-91473 2.91904 2-92337 |
10 11 12 13 14 |
|
15 16 17 18 19 |
•69514 .69541 -69569 -69597 -69624 |
2-28015 2-28313 2-28612 2-28912 2-29212 |
-71180 .71208 -71236 -71264 -71292 |
2-46986 2-47321 2-47658 2-47995 2 48333 |
.72856 -72884 -72912 -72940 .72988 |
2-68405 2-68785 2-69167 2-69549 2-69931 |
. 74540 -74568 -74596 -74624 -74652 |
2-92770 2-93204 2-93640 2-94076 2-94514 |
15 16 17 18 19 |
|
20 21 22 23 24 |
-69652 -69680 .69708 .69735 .69763 |
2-29512 2-29814 2-30115 2-30418 2.30721 |
-71320 -71348 -71375 •71403 .71431 |
2-48671 2-49010 2-49350 2-49691 2-50032 |
-72996 -73024 -73052 •73080 -73108 |
2-70315 2-70700 2-71085 2.71471 2-71858 |
- 74680 - 74709 -74737 -74765 . 74793 |
2.94952 2-95392 2-95832 2-96274 2-96716 |
20 21 22 23 24 |
|
25 26 27 28 29 |
.69791 .69818 -69846 -69874 -69902 |
2.31024 2.31328 2-31633 2-31939 2-32244 |
-71459 -71487 -71515 .71543 .71571 |
2-50374 2-50716 2-51060 2-51404 2-51748 |
-73136 -73164 -73192 .73220 -73248 |
2.72246 2-72635 2-73024 2-73414 2-73806 |
. 74821 . 74849 .74878 - 74906 - 74934 |
2.97160 2-97604 2.98050 2.98497 2-98944 |
23 26 27 28 29 |
|
30 31 32 33 34 |
-69929 -69957 -69985 -70013 - 70040 |
2.32551 2-32858 2-33166 2-33474 2-33783 |
•71598 -71626 -71654 -71682 -71710 |
2.52094 2-52440 2-52787 2-53134 2-53482 |
-73276 -73304 73332 -73360 -73388 |
2-74198 2-74591 2-74984 2-75379 2-75775 |
-74962 -74990 -75018 .75047 .75075 |
2-99393 2-99843 3-00293 3-00745 3-01198 |
3O 31 32 33 34 |
|
35 36 37 38 19- |
•70068 •70096 -70124 •70151 -70179 |
2-34092 2-34403 2-34713 2-35025 2-35336 |
-71738 -71766 -71794 -71822 .71850 |
2-53831 2-54181 2-54531 2-54883 2-55235 |
-73416 - 73444 - 73472 -73500 -73529 |
2-76171 2-76568 2-76966 2-77365 2-777R5 |
-75103 -75131 -75159 -75187 .75216 |
3-01652 3.02107 3-02563 3-03020 3-03479 |
35 36 37 38 39 |
|
40 41 42 43 44 |
-70207 -70235 - 70263 - 70290 -70318 |
2-35649 2-35962 2-36276 2.36590 2-36905 |
-71877 -71905 -71933 -71961 -71989 |
2-55587 2-55940 2.56294 2-56649 2.57005 |
-73557 -73585 -73613 -73641 -73669 |
2-78166 2-78568 2-78970 2-79374 2-79778 |
- 75244 -75272 -75300 -75328 -75356 |
3-03938 3-04398 3-04860 3-05322 3-05786 |
40 41 42 43 44 |
|
45 46 47 48 49 |
- 70346 -70374 - 70401 . 70429 -70457 |
2-37221 2-37537 2-37854 2.38171 2-38489 |
-72017 - 72045 -72073 -72101 .72129 |
2-57361 2-57718 2-58076 2-58434 2-58794 |
-73697 -73725 -73753 -73781 -73809 |
2-80183 2-80589 2-80996 2-81404 2-81813 |
-75385 -75413 - 75441 .75469 -75497 |
3-06251 3-06717 3-07184 3-07652 3-08121 |
45 46 47 48 49 |
|
50 51 52 53 54 |
-70485 -70513 -70540 •70568 .70596 |
2-38808 2-39128 2-39448 2.39768 2.40089 |
.72157 •72185 .72213 •72241 •72269 |
2.59154 2-59514 2-59876 2-60238 2.60601 |
-73837 -73865 -73893 -73921 -73950 |
2-82223 2-82633 2-83045 2-83457 2-83871 |
-75526 -75554 -75582 -75610 -75639 |
3-08591 3-09063 3-09535 3-10009 3-10484 |
5O 51 52 53 54 |
|
55 56 57 58 59. |
.70624 •70652 •70679 •70707 -70735 |
2-40411 2-40734 2-41057 2-41381 2-41705 |
•72296 -72324 -72352 •72380 -72408 |
2-60965 2-61330 2-61695 2-62061 2-62428 |
-73978 -74006 - 74034 -74062 -74090 |
2-84285 2-84700 2-85116 2-85533 2-85951 |
-75667 -75695 -75723 -75751 -75780 |
3-10960 3.11437 3-11915 3.12394 3-12875 |
55 56 57 58 59 |
|
60 |
•70763 |
2-42030 |
.72436 |
2-62796 |
-74118 |
2-86370 |
-75808 |
3-13357 |
60 |
247
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 76° 77° 78° 79°
|
' |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
0 2 3 4 |
-75808 •75836 •75864 •75892 •75921 |
3-13357 3-13839 3.14323 3-14809 3-15295 |
•77505 •77533 •77562 •77590 •77618 |
3-44541 3-45102 3-45664 3-46228 3-46793 |
.79209 •79237 •79266 •79294 -79323 |
3-80973 3-81633 3-82294 3-82956 3-83621 |
-80919 •80948 -80976 -81005 •81033 |
4-24084 4-24870 4-25658 4-26448 4-27241 |
O 1 2 3 4 |
|
5 6 7 8 9 |
•75949 •75977 •76005 •76034 •76062 |
3-15782 3.16271 3-16761 3-17252 3-17744 |
•77647 •77675 •77703 •77732 •77760 |
3-47360 3-47928 3-48498 3-49069 3-49642 |
•79351 .79380 •79408 -79437 -79465 |
3.84288 3-84956 3.85627 3-86299 3-86973 |
-81062 •81090 •81119 •81148 •81176 |
4.28036 4-28833 4-29634 4-30436 4-31241 |
5 6 7 8 9 |
|
10 11 12 13 14 |
•76090 •76118 •76147 •76175 •76203 |
3-18238 3.18733 3-19228 3.19725 3.20224 |
.77788 .77817 .77845 .77874 •77902 |
3-50216 3-50791 3-51368 3-51947 3-52527 |
- 79493 -79522 -79550 -79579 - 79607 |
3-87649 3-88327 3-89007 3-89689 3-90373 |
.81205 •81233 •81262 -81290 -81319 |
4-32049 4.32859 4.33671 4.34486 4-35304 |
10 11 12 13 14 |
|
15 16 17 18 19 |
•76231 •76260 •76288 •76316 •76344 |
3-20723 3-21224 3-21726 3-22229 3-22734 |
.77930 .77959 -77987 •78015 -78044 |
3-53109 3-53692 3.54277 3 - 54863 3-55451 |
-79636 -79664 -79693 .79721 -79750 |
3.91058 3-91746 3.92436 3-93128 3-93821 |
•81348 •81376 •81405 -81433 .81462 |
4-36124 4-36947 4-37772 4-38600 4-39430 |
15 16 17 18 19 |
|
20 21 22 23 24 |
•76373 . 76401 •76429 •76458 •76486 |
3-23239 3-23746 3-24255 3-24764 3-25275 |
. 78072 .78101 .78129 •78157 •78186 |
3 . 56041 3-56632 3.57224 3.57819 3-58414 |
-79778 -79807 -79835 •79864 •79892 |
3-94517 3-95215 3-95914 3-96616 3-97320 |
•81491 -81519 .81548 .81576 .81605 |
4-40263 4-41099 4-41937 4-42778 4-43622 |
20 2. 2i. 23 24 |
|
25 26 27 28 29 |
•76514 •76542 •76571 •76599 .76627 |
3.25787 3-26300 3-26814 3-27330 3-27847 |
. 78214 . 78242 . 78271 . 78299 -78328 |
3-59012 3-59611 3-60211 3.60813 3-61417 |
•79921 •79949 •79978 •8C006 •80035 |
3-98025 3-98733 3-99443 4-00155 4-00869 |
•81633 •81662 •81691 •81719 -81748 |
4-44468 4-45317 4-46169 4-47023 4-47881 |
25 26 27 28 29 |
|
30 31 32 33 34 |
•76655 •76684 .76712 • 76740 76769 |
3-28366 3-28885 3 - 29406 3-29929 3-30452 |
•78356 • 78384 •78413 . 78441 . 78470 |
3 - 62023 3-62630 3-63238 3 • 63849 3-64461 |
-80063 -80092 -80120 -80149 -80177 |
4-01585 4-02303 4-03024 4-03746 4-04471 |
•81776 •81805 -81834 •31862 •81891 |
4-48740 4-49603 4-50468 4-51337 4-52208 |
30 31 32 33 34 |
|
35 36 37 38 2* |
•76797 •76825 76854 76882 76910 |
3-30977 3-31503 3-32031 3-32560 3-33090 |
. 78498 •78526 •78555 .78583 •78612 |
3-65074 3-65690 3-66307 3-66925 3-67545 |
-80206 -80234 -80263 -80291 .80320 |
4-05197 4-05926 4-06657 4-07390 4.08125 |
•81919 •81948 •81977 •82005 -82034 |
4-53081 4-53958 4-54837 4-55720 4.56605 |
35 36 37 38 -29 |
|
40 41 42 43 44 |
76938 76967 76995 77023 77052 |
3-33622 3-34154 3-34689 3-35224 3-35761 |
•78640 •78669 •78697 78725 78754 |
3-68167 3-68791 3.69417 3 - 70044 3 - 70673 |
•80348 •80377 -80405 • 80434 •80462 |
4-08863 4-09602 4-10344 4-11088 4-11835 |
•82063 •82091 •82120 •82148 -82177 |
4-57493 4-58383 4-59277 4-60174 4-61073 |
40 41 42 43 44 |
|
45 46 47 48 49 |
77080 77108 77137 77165 77193 |
3-36299 3-36839 3-37380 3-37923 3-38466 |
78782 78811 78839 78868 78896 |
3-71303 3-71935 3-72569 3-73205 3-73843 |
-80491 •80520 80548 80577 80605 |
4-12583 4-13334 4-14087 4-14842 4-15599 |
•82206 •82234 -82263 82292 82320 |
4-61976 4-62881 4-63790 4-64701 4-65616 |
45 46 47 48 49 |
|
50 51 52 53 54 |
77222 77250 77278 77307 77335 |
3-39012 3-39558 3-40106 3-40656 3-41206 |
78924 78953 78981 79010 79038 |
3 • 74482 3-75123 3-75766 3-76411 3-77057 |
80634 80662 80691 80719 80748 |
4-16359 4-17121 4-17886 4-18652 4-19421 |
82349 82377 82406 82435 82463 |
4-66533 4-67454 4-68377 4-69304 4.70234 |
50 51 52 53 54 |
|
55 56 57 58 19 |
77363 77392 77420 77448 77477 |
3-41759 3-42312 3-42867 3-43424 3.43982 |
79067 79095 79123 79152 79180 |
-77705 -78355 -79007 -79661 -80316 |
80776 80805 80833 80862 80891 |
4.20193 4-20966 4-21742 4-22521 4-23301 |
82492 82521 82549 82578 82607 |
4-71166 4-72102 4-73041 4-73983 4-74929 |
55 56 57 58 59 |
|
60 |
77505 |
8-44541 |
79209 |
.80973 |
80919 |
4-24084 |
82635 |
4-75877 |
60 |
248
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 80° 81° 82° 83°
|
/ |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
t |
|
0 2 3 4 |
-82635 •82664 .82692 .82721 -82750 |
4-75877 4-76829 4.77784 4-78742 4.79703 |
.84357 .84385 .84414 .84443 . 84471 |
5-39245 5-40422 5.41602 5.42787 5-43977 |
-86083 -86112 -86140 -86169 -86198 |
6-18530 6-20020 6.21517 6.23019 6-24529 |
.87813 .87842 -87871 -87900 .87929 |
7.20551 7.22500 7.24457 7-26425 7-28402 |
O 2 3 |
|
5 6 7 8 9 |
•82778 -82807 •82836 •82864 -82893 |
4.80667 4-81635 4-82606 4-83581 4.84558 |
.84500 -84529 -84558 .84586 .84615 |
5-45171 5-46369 5.47572 5.48779 5-49991 |
-86227 -86256 -86284 •86313 .86342 |
6-26044 6-27566 6-29095 6-30630 6-32171 |
•87957 .87986 •88015 . 88044 •88073 |
7-30388 7-32384 7-34390 7-36405 7-38431 |
5 6 7 8 9 |
|
10 11 12 13 14 |
•82922 •82950 -82979 .83008 •83036 |
4.85539 4-86524 4-87511 4-88502 4-89497 |
.84644 .84673 .84701 .84730 .84759 |
5.51208 5-52429 5-53655 5.54886 5-56121 |
-86371 •86400 -86428 -86457 .86486 |
6-33719 6-35274 6-36835 6-38403 6-39978 |
.88102 •88131 -88160 .88188 .88217 |
7-40466 7-42511 7-44566 7-46632 7-48707 |
10 11 12 13 14 |
|
15 16 17 18 19 |
•83065 -83094 -83122 -83151 .83180 |
4.90495 4-91496 4-92501 4-93509 4-94521 |
.84788 .84816 .84845 .84874 . 84903 |
5.57361 5-58606 5.59855 5-61110 5-62369 |
-86515 -86544 -86573 -86601 -86630 |
6-41560 6-43148 6-44743 6-46346 6-47955 |
-88246 •88275 -88304 -88333 •88362 |
7-50793 7-52889 7-54996 7-57113 7-59241 |
15 16 17 18 19 |
|
20 21 22 23 24 |
•83208 •83237 -83266 •83294 83323 |
4-95536 4-96555 4-97577 4-98603 4-99633 |
-84931 -84960 -84989 .85018 .85046 |
5.63633 5-64902 5-66176 5-67454 5-68738 |
-86659 -86688 -86717 •86746 .86774 |
6-49571 6-51194 6-52825 6-54462 6-56107 |
-88391 -88420 •88448 -88477 .88506 |
7-61379 7-63528 7-65688 7-67859 7-70041 |
20 21 22 23 24 |
|
25 26 27 28 29 |
83352 83380 83409 83438 83467 |
5-00666 5-01703 5.02743 5-03787 5-04834 |
.85075 .85104 .85133 85162 .85190 |
5-70027 5-71321 5-72620 5-73924 5-75233 |
•86803 .86832 •86861 .86890 .86919 |
6-57759 6-59418 6-61085 6-62759 6 - 64441 |
•88535 •88564 -88593 -88622 -88651 |
7-72234 7.74438 7.76653 7.78880 7.81118 |
25 26 27 28 29 |
|
30 31 32 33 34 |
83495 83524 83553 83581 83610 |
5-05886 5-06941 5-08000 5-09062 5-10129 |
.85219 -85248 -85277 -85305 -85334 |
5-76547 5-77866 5-79191 5-80521 5-81856 |
-86947 -86976 -87005 -87034 -87063 |
6.66130 6-67826 6-69530 6-71242 6-72962 |
-88680 -88709 •88737 .88766 .88795 |
7.83367 7-85628 7-87901 7.90186 7-92482 |
30 31 32 33 34 |
|
35 36 37 38 39- |
83639 83667 83696 -83725 •83754 |
5-11199 5.12273 5-13350 5-14432 5-15517 |
-85363 .85392 .85420 .85449 .85478 |
5-83196 5-84542 5-85893 5-87250 5-88612 |
.87092 .87120 -87149 -87178 -87207 |
6-74689 6-76424 6-78167 6-79918 6-81677 |
-88824 -88853 .88882 .88911 - 88940 |
7,94791 7-97111 7-99444 8-01788 8.04146 |
35 36 37 38 -39 |
|
40 41 42 43 44 |
-83782 -83811 •83840 -83868 -83897 |
5-16607 5-17700 5-18797 5.19898 5-21004 |
-85507 -85536 -85564 -85593 -85622 |
5-89979 5.91352 5.92731 5.94115 5-S5505 |
-87236 -87265 -87294 •87322 -87351 |
6.83443 6-85218 6-87001 6-88792 6-90592 |
-88969 -88998 •89027 .89055 -89084 |
8-06515 8-08897 8-11292 8-13699 8-16120 |
40 41 42 43 44 |
|
45 46 47 48 49 |
.83926 .83954 .83983 -84012 . 84041 |
5.22113 5-23226 5.24343 5.25464 5.26590 |
-85651 -85680 -85708 •85737 .85766 |
5.96900 5.98301 5-99708 6-01120 6-02538 |
-87380 -87409 •87438 •87467 -87496 |
6-92400 6.94216 6-96040 6-97873 6-99714 |
•89113 •89142 .89171 -89200 .89229 |
8-18553 8-20999 8-23459 8-25931 8-28417 |
45 46 47 48 49 |
|
50 51 52 53 54 |
-84069 •84098 .84127 .84155 .84184 |
5-27719 5.28853 5-29991 5-31133 5-32279 |
.85795 .85823 .85852 -85881 -85910 |
6-03962 6-05392 6-06828 6-08269 6.09717 |
-87524 -87553 -87582 -87611 -87640 |
7-01565 7-03423 7-05291 7-07167 7.09052 |
-89258 -89287 .89316 .89345 .89374 |
8-30917 8-33430 8-35957 8-38497 8-41052 |
5O 51 52 53 54 |
|
55 56 57 58 59 |
.84213 . 84242 .84270 •84299 -84328 |
5.33429 5-34584 5-35743 5-36906 5-38073 |
.85939 -85967 -85996 .86025 .86054 |
6.11171 6.12630 6.14096 6.15568 8-17046 |
•87669 .87698 -87726 .87755 .87784 |
7.10946 7.12849 7.14760 7-16681 7-18612 |
-89403 .89431 •89460 .89489 .89518 |
8-43620 8-46203 8.48800 8-51411 8-54037 |
55 56 57 58 59 |
|
60 |
•84357 |
5-39245 |
.86083 |
6.18530 |
-87813 |
7-20551 |
-89547 |
8-56677 |
60 |
249
TABLE 11.— NATURAL VERSED SINES AND EXTERNAL SECANTS. 84° 85° 86°
|
/ |
Vers. |
Ex. sec. |
Vers. |
JSx. sec. |
Vers. |
Ex. sec. |
t |
|
0 2 3 4 |
•89547 •89576 .89605 .89634 .89663 |
8.56677 8.59332 8.62002 8-64687 8.67387 |
.91284 .91313 .91342 .91371 •91400 |
10.47371 10.51199 10.55052 10.58932 10-62837 |
.93024 .93053 .93082 .93111 •93140 |
13.33559 13.39547 13-45586 13-51676 13.57817 |
O I 2 3 4 5 6 7 8 9 |
|
5 6 7 8 JL 10 11 12 13 14 |
.89692 .89721 .89750 .89779 .89808 |
8.70103 8-72833 8.75579 8-78341 8.81119 |
.91429 .91458 .91487 -91516 .91545 |
10.66769 10.70728 10.74714 10.78727 10-82768 |
.93169 .93198 .93227 .93257 •93286 |
13-64011 13-70258 13-76558 13-82913 13.89323 |
|
|
.89836 •89865 .89894 •89923 •89952 |
8.83912 8-86722 8.89547 8.92389 8-95248 |
•91574 .91603 .91632 .91661 .91690 |
10.86837 10-90934 10.95060 10.99214 11.03397 |
.93315 .93344 .93373 •93402 •93431 |
13-95788 14-02310 14-08890 14-15527 14-22223 |
1O 11 12 13 14 |
|
|
15 16 17 18 2L. 20 21 22 23 24 |
•89981 •90010 •90039 •90068 •90097 |
8-98123 9.01015 9-03923 9.06849 9.09792 |
•91719 .91748 .91777 .91806 -91835 |
11.07610 11.11852 11.16125 11.20427 11.24761 |
.93460 .93489 .93518 .93547 -93576 |
14-28979 14-35795 14-42672 14-49611 14-56614 |
15 16 17 18 19 |
|
•90126 .90155 •90184 •90213 .90242 |
9.12752 9.15730 9.18725 9.21739 9-24770 |
•91864 .91893 .91922 •91951 .91980 |
11.29125 11.33521 11.37948 11.42408 11.46900 |
•93605 -93634 .93663 .93692 .93721 |
14-63679 14-70810 14-78005 14-85268 14.92597 |
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
|
|
25 26 27 28 29 |
•90271 -90300 .90329 .90358 .90386 |
9.27819 9.30887 9.33973 9.37077 9.40201 |
.92009 .92038 •92067 .92096 -92125 |
11.51424 11.55982 11.60572 11.65197 11.69856 |
.93750 •93779 .93808 •93837 •93866 |
14-99995 15-07462 15-14999 15-22607 15-30287 |
|
|
30 31 32 33 34 |
•90415 •90444 •90473 •90502 .90531 |
9.43343 9.46505 9.49685 9.52886 9-56106 |
.92154 .92183 •92212 .92241 .92270 |
11.74550 11.79278 11.84042 11.88841 11-93677 |
.93895 -93924 .93953 -93982 .94011 |
15-38041 15-45869 15-53772 15-61751 15.69808 |
|
|
35 36 37 38 39 |
.90560 .90589 .90618 .90647 .90676 |
9.59346 9-62605 9.65885 9.69186 9-72507 |
.92299 .92328 .92357 •92386 .92415 |
11.98549 12.03458 12.08040 12.13388 12.18411 |
- 94040 .94069 -94098 .94127 •94156 |
15-77944 15-86159 15-94456 16-02835 16.11297 |
35 36 37 38 39 |
|
40 41 42 43 44 |
.90705 .90734 .90763 .90792 .90821 |
9.75849 9.79212 9.82596 9.86001 9-89428 |
.92444 .92473 .92502 -92531 -92560 |
12-23472 12.28572 12.33712 12.38891 12.44112 |
.94186 .94215 . 94244 - 94273 .94302 |
16-19843 16-28476 16.37196 16-46005 16-54903 |
40 41 42 43 44 45 46 47 48 49 |
|
45 46 47 48 49 |
.90850 .90879 .90908 .90937 .90966 |
9-92877 9.96348 9.99841 10-03356 10.06894 |
•92589 -92618 .92647 .92676 -92705 |
12.49373 12.54676 12.60021 12.65408 12.70838 |
-94331 -94360 -94389 -94418 . 94447 |
16-63893 16-72975 16-82152 16-91424 17-00794 |
|
|
50 51 52 53 54 |
.90995 •91024 .91053 .91082 .91111 |
10-10455 10-14039 10.17646 10.21277 10-24932 |
.92734 .92763 .92792 .92821 -92850 |
12.76312 12-81829 12-87391 12-92999 12-98651 |
-94476 .94505 -94534 .94563 .94592 |
17.10262 17.19830 17.29501 17-39274 17-49153 |
5O 51 52 53 54 |
|
55 56 57 58 59 |
.91140 .91169 .91197 .91226 •91255 |
10-28610 10.32313 10-36040 10.39792 10-43569 |
.92879 .92908 .92937 .92966 .92995 |
13.04350 13.10096 13.15889 13.21730 13-27620 |
-94621 -94650 .94679 .94708 -94737 |
17-59139 17.69233 17.79438 17-89755 18-00185 |
55 56 57 58 59 |
|
60 |
.91284 |
10.47371 |
.93024 |
13-33559 |
.94766 |
18-10732 |
60 |
250
TABLE 11. —NATURAL VERSED SINES AND EXTERNAL SECANTS. 87° 88° 89°
|
1 |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
Vers. |
Ex. sec. |
' |
|
o 2 3 4 |
•94766 .94795 .94825 .94854 .94883 |
18-10732 18-21397 18-32182 18.43088 18-54119 |
.96510 .96539 .96568 •96597 .96626 |
27.65371 27.89440 28-13917 28-38812 28-64137 |
.98255 .98284 •98313 .98342 -98371 |
F.3- 29869 57.26976 58-27431 59-31411 60.39105 |
O 1 2 3 4 |
|
5 6 7 8 9 |
.94912 .94941 .94970 .94999 .95028 |
18.65275 18.76560 18-87976 18-99524 19.11208 |
.96655 .96684 •96714 .96743 .96772 |
28-89903 29-16120 29.42802 29.69960 29.97607 |
•98400 .98429 -98458 -98487 -98517 |
61-50715 62.66460 63-86572 65-11304 66-40927 |
5 6 7 8 9 |
|
10 11 12 13 14 |
.95057 .95086 .95115 .95144 .95173 |
19.23028 19.34989 19-47093 19.59341 19-71737 |
.96801 .96830 .96859 .96888 .96917 |
30.25758 30-54425 30.83623 31-13366 31-43671 |
.98546 •98575 .98604 .98633 -98662 |
67-75736 69-16047 70-62285 72-14583 73-73586 |
10 11 12 13 14 |
|
15 16 17 18 J9 |
.95202 .95231 .95260 .95289 .95318 |
19-84283 19-96982 20-09838 20.22852 20.36027 |
.96946 .96975 .97004 .97033 •970R2 |
31-74554 32.06030 32-38118 32-70835 33-04199 |
-98691 .98720 .98749 .98778 .98807 |
75-39655 77.13274 78.94968 80-85315 82-84947 |
15 16 17 18 19 |
|
20 21 22 23 24 |
.95347 .95377 .95406 •95435 .95464 |
20.49368 20-62876 20.76555 20.90409 21-04440 |
.97092 .97121 .97150 .97179 .97208 |
33-38232 33.72952 34-08380 34-44539 34-81452 |
-98836 -98866 .98895 •98924 .98953 |
84-94561 87-14924 89-46886 91-91387 94-49471 |
20 21 22 23 24 |
|
25 26 27 28 29 |
.95493 .95522 .95551 .95580 .95609 |
21.18653 21.33050 21-47635 21-62413 21-77386 |
.97237 .97266 .97295 .97324 .97353 |
35-19141 35-57633 35-96953 36-37127 36.78185 |
.98982 .99011 .99040 .99069 .99098 |
97-22303 100-1119 103-1757 106-4311 109-8966 |
25 26 27 28 29 |
|
30 31 32 33 34 |
.95638 •95667 .95696 .95725 .95754 |
21-92559 22-07935 22-23520 22-39316 22-55328 |
.97382 .97411 .97440 .97470 -97499 |
37.20155 37-63068 38-06957 38.51855 38-97797 |
.99127 .99156 .99186 .99215 -99244 |
113-5930 117-5444 121-7780 126-3253 131-2223 |
30 31 32 33 34 |
|
35 36 37 38 39 |
.95783 .95812 .95842 •95871 .95900 |
22-71563 22-88022 23-04712 23-21637 23-38802 |
.97528 .97557 •97586 .97615 97644 |
39-44820 39-92963 40-42266 40-92772 41-44525 |
.99278 .99302 •99331 .99360 .99389 |
136-5111 142-2406 148-4684 155-2623 162-7033 |
35 36 37 38 39 |
|
40 41 42 43 44 |
.95929 .95958 .95987 .96016 .96045 |
23-56212 23-73873 23-91790 24-09969 24-28414 |
•97673 .97702 .97731 .97760 .97789 |
41-97571 42-51961 43-07746 43-64980 44-23720 |
.99418 •99447 .99476 .99505 -99535 |
170-8883 179-9350 189-9868 201-2212 213-8600 |
40 41 42 43 44 |
|
45 46 47 48 49 |
•96074 .96103 .96132 .96161 .96190 |
24-47134 24-66132 24-85417 25-04994 25-24869 |
.97819 .97848 .97877 .97906 .97935 |
44-84026 45-45963 46-09596 46-74997 47-42241 |
.99564 .99593 .99622 .99651 .99680 |
228-1839 244-5540 263-4427 285-4795 311-5230 |
45 46 47 48 49 |
|
50 51 52 53 54 |
.96219 .96248 .96277 .96307 .96336 |
25-45051 25.65546 25.86360 26.07503 26-28981 |
.97964 .97993 .98022 •98051 -98080 |
48.11406 48-82576 49-55840 50.31290 51-09027 |
.99709 .99738 •99767 .99796 .99825 |
342-7752 380.9723 428.7187 490-1070 571-9581 |
50 51 52 53 54 |
|
55 56 57 58 59 |
.96365 .96394 .96423 .96452 .96481 |
26-50804 26-72978 26-95513 27-18417 27-41700 |
.98109 .98138 .98168 .98197 .98226 |
51.89156 52.71790 53-57046 54.45053 55-35946 |
.99855 .99884 .99913 .99942 .99971 |
686.5496 858-4369 1144-916 1717-874 3436-747 |
55 56 57 58 59 |
|
60 |
•96510 |
27-65371 |
.98255 |
56-29869 |
1.00000 |
Infinite |
60 |
251
252 12. —CUBIC YARDS PER 100 FEET. SLOPES i : 1.
|
Depth |
Base |
Base |
Base |
Base |
Base |
Base |
Base |
Base |
|
12 |
14 |
16 |
18 |
22 |
24 |
26 |
28 |
|
|
1 |
45 |
53 |
60 |
68 |
82 |
90 i 97 |
105 |
|
|
2 |
93 |
107 |
122 |
137 |
167 |
181 |
196 |
211 |
|
3 |
142 |
163 |
186 |
208 |
253 |
275 |
297 |
319 |
|
4 |
193 |
222 |
252 |
281 |
341 |
370 |
400 |
430 |
|
5 |
245 |
282 |
319 |
356 |
431 |
468 |
605 |
542 |
|
6 |
300 |
344 |
389 |
433 |
522 |
567 |
611 |
656 |
|
7 |
356 |
408 |
460 |
512 |
616 |
668 |
719 |
771 |
|
8 |
415 |
474 |
533 |
593 |
711 |
770 |
830 |
889 |
|
9 |
475 |
542 |
608 |
675 |
808 |
875 |
942 |
1008 |
|
10 |
537 |
611 |
685 |
759 |
907 |
981 |
1056 |
1130 |
|
11 |
601 |
682 |
764 |
845 |
1008 |
1090 |
1171 |
1253 |
|
12 |
667 |
756 |
844 |
933 |
1111 |
1200 |
1289 |
1378 |
|
13 |
734 |
831 |
926 |
1023 |
1216 |
1312 |
1408 |
1505 |
|
14 |
804 |
907 |
1010 |
1115 |
1322 |
1426 |
1530 |
1633 |
|
15 |
8<3 |
986 |
1096 |
1208 |
1431 |
1542 |
1653 |
1764 |
|
16 |
948 |
1067 |
1184 |
1304 |
1541 |
1659 |
1778 |
1896 |
|
17 |
1023 |
1149 |
1274 |
1401 |
1653 |
1779 |
1905 |
2031 |
|
18 |
1100 |
1233 |
1366 |
1500 |
1767 |
1900 |
2033 |
2167 |
|
19 |
1179 |
1319 |
1460 |
1601 |
1882 |
2023 |
2164 |
2305 |
|
20 |
1259 |
1407 |
1555 |
1704 |
2000 |
2148 |
2296 |
2444 |
|
21 |
1342 |
1497 |
1653 |
1808 |
2119 |
2275 |
2431 |
2586 |
|
22 |
1426 |
1589 |
1752 |
1915 |
2241 |
2404 |
2567 |
*730 |
|
23 |
1512 |
1682 |
1853 |
2023 |
2364 |
2534 |
2705 |
2875 |
|
24 |
1600 |
1778 |
1955 |
2133 |
2489 |
2667 |
2844 |
3022 |
|
25 |
1690 |
1875 |
2060 |
2245 |
2616 |
J2801 |
2986 |
3171 |
|
26 |
1781 |
1974 |
2166 |
2359 |
2744 |
2937 |
3130 |
3322 |
|
27 |
1875 |
2075 |
2274 |
2475 |
2875 |
3075 |
3275 |
3475 |
|
28 |
1970 |
2178 |
2384 |
2593 |
3007 |
3215 |
8422 |
3630 |
|
29 |
2068 |
2282 |
2496 |
2712 |
3142 |
3356 |
3571 |
3786 |
|
30 |
2167 |
2389 |
2610 |
2833 |
3278 |
3500 |
3722 |
3944 |
|
31 |
2288 |
2497 |
2726 |
2956 |
3416 |
3645 |
3875 |
4105 |
|
32 |
2370 |
2607 |
2844 |
3081 |
3556 |
3793 |
4030 |
4267 |
|
33 |
2475 |
2719 |
2964 |
3208 |
3697 |
3942 |
4186 |
4431 |
|
34 |
2581 |
2833 |
3085 |
3337 |
3841 |
4093 |
4344 |
4596 |
|
35 |
2690 |
2949 |
3208 |
3468 |
3986 |
4245 |
4505 |
4764 |
|
36 |
2800 |
3067 |
3333 |
3600 |
4133 |
4400 |
4667 |
4933 |
|
37 |
2912 |
3186 |
3460 |
3734 |
4282 |
4556 |
4831 |
5105 |
|
38 |
3026 |
3307 |
3589 |
3870 |
4433 |
4715 |
4996 |
5278 |
|
39 |
3142 |
3431 |
3719 |
4008 |
4586 |
4875 |
6164 |
5453 |
|
40 |
3259 |
3556 |
3852 |
4148 |
4741 |
5037 |
5333 |
6630 |
|
41 |
3379 |
3682 |
3986 |
4290 |
4897 |
5201 |
5505 |
5808 |
|
42 |
3500 |
3811 |
4122 |
4433 |
5056 |
5367 |
6678 |
5989 |
|
43 |
3623 |
3942 |
4260 |
4579 |
5216 |
5534 |
5853 |
6171 |
|
44 |
3748 |
4074 |
4400 |
4726 |
5378 |
5704 |
6030 |
6356 |
|
45 |
3875 |
4208 |
4541 |
4875 |
5542 |
5875 |
6208 |
6542 |
|
46 |
4004 |
4344 |
4684 |
5026 |
5707 |
6048 |
6389 |
6730 |
|
47 |
4134 |
4482 |
4830 |
5179 |
5875 |
6223 |
6571 |
6919 |
|
48 |
4267 |
4622 |
4978 |
5333 |
6044 |
6400 |
6756 |
7111 |
|
49 |
4401 |
4764 |
5127 |
5490 6216 |
6579 |
6943 |
7305 |
|
|
50 |
4537 |
4907 |
5278 |
5648 |
6389 |
6759 |
7130 |
7500 |
|
51 |
4675 |
5053 |
5430 |
5808 |
6564 |
6942 |
7319 |
7697 |
|
52 |
4815 |
5200 |
5584 |
597'0 |
6741 |
7126 |
7511 |
7896 |
|
53 |
4956 |
5349 |
5741 |
6134 i 6919 |
7312 |
7705 |
8097 |
|
|
54 |
5100 |
5500 |
5900 |
6300 ! 7100 |
7500 |
7900 |
&300 |
|
|
55 |
5245 |
5653 |
6060 |
6468 |
7282 |
7690 |
8097 |
8505 |
|
56 |
5393 |
5807 |
6222 |
6637 |
7467 |
7881 |
8296 |
8711 |
|
57 |
5542 |
5964 |
6386 |
6808 |
7653 |
8075 |
8497 |
8919 |
|
58 |
5693 |
6122 |
6552 |
6981 |
7841 |
8270 |
8700 |
9130 |
|
59 |
5845 |
6282 |
6719 |
7156 |
8031 |
3468 |
8905 |
9342 |
|
60 |
6000 |
6444 |
6889 |
7333 |
8222 |
8667 |
9111 |
9556 |
12.— CUBIC YARDS PER 100 FEET. SLOPES * : 1. 253
|
Depth |
Base 12 |
Base 14 |
Base 1G |
Base 13 |
Base 22 |
Base 24 |
Base 26 |
Base 28 |
|
1 |
46 |
54 |
Cl |
CD |
83 |
91 |
98 |
106 |
|
2 |
96 |
111 |
126 |
141 |
170 |
185 |
200 |
215 |
|
3 |
150 |
172 |
194 |
217 |
261 |
283 |
306 |
328 |
|
4 |
207 |
237 |
267 |
296 |
356 |
385 |
415 |
444 |
|
5 |
269 |
306 |
343 |
380 |
454 |
491 |
528 |
565 |
|
6 |
333 |
378 |
422 |
467 |
556 |
600 |
644 |
689 |
|
7 |
402 |
454 |
506 |
557 |
661 |
713 |
765 |
817 |
|
8 |
474 |
533 |
593 |
652 |
770 |
830 |
889 |
948 |
|
9 |
550 |
617 |
683 |
750 |
883 |
950 |
1017 |
1083 |
|
10 |
630 |
704 |
778 |
852 |
1000 |
1074 |
1148 |
1222 |
|
11 |
713 |
794 |
876 |
957 |
1120 |
1202 * |
1283 |
1365 |
|
12 |
800 |
889 |
978 |
1067 |
1244 |
1333 |
1422 |
1511 |
|
13 |
891 |
987 |
1083 |
1180 |
1372 |
1469 |
1565 |
1661 |
|
14 |
985 |
1089 |
1193 |
1296 |
1504 |
1607 |
1711 |
1815 |
|
15 |
1083 |
1194 |
1306 |
1417 |
1639 |
1750 |
1861 |
1972 |
|
16 |
1185 |
1304 |
1422 |
1541 |
1779 |
1896 |
2015 |
2133 |
|
17 |
1291 |
1417 |
1543 |
1669 |
1920 |
2046 |
2172 |
2298 |
|
18 |
1400 |
1533 |
1667 |
1800 |
2067 |
2200 |
2333 |
2467 |
|
19 |
1513 |
1654 |
1794 |
1935 |
2217 |
2357 |
2498 |
2639 |
|
20 |
1630 |
1778 |
1926 |
2074 ' |
2370 |
2519 |
2667 |
2815 |
|
21 |
1750 |
1906 |
2061 |
2217 |
2528 |
2683 |
2839 |
2994 |
|
22 |
1874 |
2037 |
2200 |
2363 |
2689 |
2852 |
3015 |
3178 |
|
23 |
2002 |
2172 |
2343 |
2513 |
2854 |
3024 |
3194 |
8365 |
|
24 |
2133 |
2311 |
2489 |
2667 |
3022 |
3200 |
3378 |
3556 |
|
25 |
2269 |
2454 |
2639 |
2824 |
3194 |
3380 |
3565 |
3750 |
|
26 |
2407 |
2600 |
2793 |
2985 |
3370 |
35C3 |
3756 |
3948 |
|
27 |
2550 |
2750 |
2950 |
3150 |
3550 |
3750 |
3950 |
4151 |
|
28 |
2696 |
2904 |
3111 |
3319 |
3733 |
3941 |
4148 |
4356 |
|
29 |
2846 |
3061 |
3276 |
3491 |
3920 |
4135 |
4350 |
4565 |
|
30 |
3000 |
3222 |
3444 |
3667 |
4111 |
4333 |
4556 |
4778 |
|
31 |
3157 |
3387 |
3617 |
3846 |
4306 |
4535 |
4765 |
4994 |
|
32 |
3319 |
3556 |
3793 |
4030 |
4504 |
4741 |
4978 |
5215 |
|
33 |
3483 |
3728 |
3972 |
4217 |
4706 |
4950 |
5194 |
5439 |
|
34 |
3652 |
3904 |
4156 |
4407 |
4911 |
5163 |
5415 |
5667 |
|
35 |
3824 |
4083 |
4343 |
4602 |
5120 |
5380 |
5639 |
5898 |
|
36 |
4000 |
4267 |
4533 |
4800 |
5333 |
5600 |
5867 |
6133 . |
|
37 |
4180 |
4454 |
4728 |
5002 |
5550 |
5824 |
6098 |
6372 |
|
38 |
4363 |
4644 |
4926 |
5207 |
5770 |
6052 |
6333 |
6615 |
|
39 |
4550 |
4839 |
5128 |
5417 |
5994 |
6283 |
6572 |
6861 |
|
40 |
4741 |
5037 |
5333 |
5630 |
6222 |
6519 |
6815 |
7111 |
|
41 |
4935 |
5239 |
5543 |
5846 |
6454 |
6757 |
7061 |
7365 |
|
42 |
5133 |
5444 |
5756 |
6067 |
6689 |
7000 |
7311 |
7623 |
|
43 |
5335 |
5654 |
5972 |
6291 |
6928 |
7246 |
7565 |
7883 |
|
44 |
5541 |
5867 |
6193 |
6519 |
7170 |
7496 |
7822 |
8148 |
|
45 |
5750 |
60&3 |
6417 |
6750 |
7417 |
7750 |
8083 |
8417 |
|
46 |
5963 |
6304 |
6644 |
6985 |
7667 |
8007 |
8348 |
8689 |
|
47 |
6180 |
6528 |
6876 |
7224 |
7920 |
8269 |
8617 |
8965 |
|
48 49 |
6400 6624 |
6756 6987 |
7111 7350 |
m |
m |
8889 9165 |
||
|
50 |
6852 |
7222 |
7593 |
7963 |
87C4 |
9074 |
9444 |
9815 |
|
51 |
7083 |
7461 |
7839 |
8217 |
8972 |
9350 |
9728 |
10106 |
|
52. |
7319 |
7704 |
8089 |
8474 |
9244 |
9630 |
10015 |
10400 |
|
53 |
7557 |
7950 |
8343 |
8735 |
9520 |
9913 |
10306 |
10698 |
|
54 |
7800 |
8200 |
8600 |
9000 |
9800 |
10200 |
10600 |
11000 |
|
55 |
8046 |
8454 |
8861 |
9269 |
10083 |
10491 |
10898 |
11306 |
|
56 |
8296 |
8711 |
9126 |
9541 |
10370 |
10785 |
11200 |
11615 |
|
57 |
8550 |
8972 |
9394 |
9817 |
10661 |
11083 |
11506 |
11928 |
|
58 |
8807 |
9237 |
9667 |
10096 |
10956 |
11385 |
11815 |
12244 |
|
59 |
9069 |
9506 |
9943 |
10380 |
11254 |
11691 |
12128 |
12565 |
|
60 |
9333 |
9778 |
10222 |
10667 |
11556 |
12000 |
12444 |
12889 |
254 12.— CUBIC YARDS PER 100 FEET. SLOPES 1 : 1.
|
Depth |
Base 12 |
Base 14 |
Base 16 |
Base 18 |
Base 20 |
Base 28 |
Base 30 |
Base 32 |
|
1 |
48 |
56 |
63 |
70 |
78 |
107 |
115 |
122 |
|
• |
104 |
119 |
133 |
148 |
163 |
222 |
237 |
252 |
|
3 |
167 |
189 |
211 |
233 |
256 |
344 |
367 |
389 |
|
237 |
267 |
296 |
326 |
356 |
474 |
504 |
533 |
|
|
5 |
315 |
352 |
389 |
426 |
463 |
611 |
648 |
685 |
|
6 |
400 |
444 |
489 |
533 |
578 |
756 |
800 |
844 |
|
7 |
493 |
544 |
596 |
648 |
700 |
907 |
959 |
1011 |
|
8 |
693 |
652 |
711 |
77'0 |
830 |
1067 |
1126 |
1185 |
|
9 |
700 |
767 |
833 |
900 |
967 |
1233 |
1300 |
1367 |
|
10 |
815 |
889 |
963 |
1037 |
1111 |
1407 |
1481 |
1556 |
|
11 |
937 |
1019 |
1100 |
1181 |
1263 |
1589 |
1670 |
1752 |
|
12 |
1067 |
1156 |
1244 |
1333 |
1422 |
1778 |
1867 |
1956 |
|
13 |
1204 |
1300 |
1396 |
1493 |
1589 |
1974 |
2070 |
2167 |
|
14 |
1348 |
1452 |
1556 |
1659 |
1763 |
2178 |
2281 |
2385 |
|
15 |
1500 |
1611 |
1722 |
1833 |
1944 |
2389 |
2500 |
2611 |
|
16 |
1659 |
1778 |
1896 |
2015 |
2133 |
2607 |
2726 |
2844 |
|
17 |
1826 |
1952 |
2078 |
2204 |
2330 |
2833 |
2959 |
3085 |
|
18 |
2000 |
2133 |
2267 |
2400 |
2533 |
3067 |
3200 |
3333 |
|
19 |
2181 |
2322 |
2463 |
2604 |
2744 |
3307 |
3448 |
3589 |
|
20 |
2370 |
2519 |
2667 |
2815 |
2963 |
3556 |
3704 |
3852 |
|
21 |
2567 |
27£2 |
2878 |
3033 |
3189 |
3811 |
3967 |
4122 |
|
22 |
2770 |
2933 |
3096 |
3259 |
3422 |
4074 |
4237 |
4444 |
|
23 |
2981 |
8152 |
3322 |
3493 |
3663 |
4344 |
4515 |
4685 |
|
24 |
3200 |
3378 |
3556 |
3733 |
3911 |
4622 |
4800 |
4978 |
|
25 |
3426 |
3611 |
3796 |
3981 |
4167 |
4907 |
5093 |
5278 |
|
26 |
8659 |
3852 |
4044 |
4237 |
4430 |
5200 |
5393 |
5585 |
|
27 |
3900 |
4100 |
4300 |
4500 |
4700 |
5500 |
5700 |
5900 |
|
28 |
4148 |
4356 |
4563 |
4770 |
4978 |
5807 |
6015 |
6222 |
|
29 |
4404 |
4619 |
4833 |
5048 |
5263 |
6122 |
6337 |
6552 |
|
30 |
4667 |
4889 |
5111 |
5333 |
5556 |
6444 |
6667 |
6889 |
|
31 |
4937 |
5167 |
5396 |
5626 |
5856 |
6774 |
7004 |
7233 |
|
32 |
5215 |
5452 |
5689 |
5926 |
6163 |
7111 |
7348 |
7585 |
|
33 |
5500 |
5744 |
5989 |
6233 |
6478 |
7456 |
7700 |
7944 |
|
34 |
6793 |
6044 |
6296 |
6548 |
6800 |
7807 |
8059 |
8311 |
|
35 |
6093 |
6352 |
6611 |
6870 |
7130 |
8167 |
8426 |
8685 |
|
, 36 |
6400 |
6667 |
6933 |
7200 |
7467 |
8533 |
8800 |
9067 |
|
37 |
6715 |
6989 |
7263 |
7537 |
7811 |
8907 |
9181 |
9456 |
|
38 |
7037 |
7319 |
7600 |
7881 |
8163 |
9289 |
9570 |
9852 |
|
39 |
7367 |
7656 |
7944 |
8233 |
8522 |
9678 |
9967 |
10256 |
|
40 |
7704 |
8000 |
8296 |
8593 |
8889 |
10074 |
10370 |
10667 |
|
41 |
8048 |
8352 |
8656 |
8959 |
9263 |
10478 |
10781 |
11085 |
|
42 |
8400 |
8711 |
9022 |
9333 |
9644 |
10889 |
11200 |
11511 |
|
43 |
8759 |
9078 |
9396 |
9715 |
10033 |
11307 |
11626 |
11944 |
|
44 |
9126 |
9452 |
9778 |
10104 |
10430 |
11733 |
12059 |
12385 |
|
45 |
9500 |
9833 |
10167 |
10500 |
10833 |
12167 |
12500 |
12833 |
|
46 |
9881 |
10222 |
10563 |
10904 |
11244 |
12607 |
12948 |
13289 |
|
47 |
10270 |
10619 |
10967 |
11315 |
11663 |
13056 |
13404 |
13752 |
|
48 |
10667 |
11022 |
11378 |
11733 |
12089 |
13511 |
13867 |
14222 |
|
49 |
11070 |
11433 |
11796 |
12159 |
12522 |
13974 |
14337 |
14700 |
|
60 |
11481 |
11852 |
12222 |
12593 |
12963 |
14444 |
14815 |
15185 |
|
51 |
11900 |
12278 |
12656 |
13033 |
13411 |
14922 |
15300 |
15678 |
|
62 |
12326 |
12711 |
13096 |
13481 |
13867 |
15407 |
15793 |
16178 |
|
63 |
12759 |
13152 |
13544 |
13937 |
14330 |
15900 |
16293 |
16G85 |
|
64 |
13200 |
13600 |
14000 |
14400 |
14800 |
16400 |
16800 |
17200 |
|
65 |
13648 |
14056 |
14463 |
14870 |
15278 |
16907 |
17315 |
17722 |
|
66 |
14104 |
14519 |
14933 |
15348 |
15763 |
17422 |
17837 |
18252 |
|
67 |
14567 |
14989 |
15411 |
15833 |
16256 |
17944 |
18367 |
18789 |
|
68 |
15037 |
15467 |
15896 |
16326 |
16756 |
18474 |
18904 |
19333 |
|
69 |
15515 |
15952 |
16389 |
16826 |
17263 |
19011 |
19448 |
19885 |
|
60 |
16000 |
16444 |
16889 |
17333 |
17778 |
19556 |
20000 |
20444 |
12.— CUBIC YARDS PER 100 FEET. SLOPES H : 1. 255
|
Depth |
Base 12 |
Base 14 |
Base 16 |
Base 18 |
Base 20 |
Base 28 |
Base 30 |
Base 32 |
|
1 |
50 |
57 |
65 |
72 |
80 |
109 |
117 |
124 |
|
2 |
111 |
126 |
141 |
156 |
170 |
230 |
244 |
259 |
|
3 |
183 |
206 |
228 |
250 |
272 |
361 |
383 |
406 |
|
4 |
267 |
296 |
326 |
356 |
385 |
504 |
533 |
563 |
|
6 |
361 |
398 |
435 |
472 |
509 |
657 |
694 |
731 |
|
6 |
467 |
511 |
556 |
600 |
644 |
822 |
867 |
911 |
|
7 |
583 |
635 |
687 |
739 |
791 |
998 |
1050 |
1102 |
|
8 |
71i |
770 |
830 |
889 |
948 |
1185 |
1244 |
1304 |
|
9 |
850 |
917 |
983 |
1050 |
1116 |
1383 |
1450 |
1517 |
|
10 |
1000 |
1074 |
1148 |
1222 |
1296 |
1593 * |
1667 |
1741 |
|
11 |
1161 |
1243 |
1324 |
1406 |
1487 |
1813 |
1894 |
1976 |
|
12 |
1333 |
1422 |
1511 |
1600 |
1689 |
2044 |
2133 |
2222 |
|
13 |
1517 |
1613 |
1709 |
1806 |
1902 |
2287 |
2383 |
2480 |
|
14 |
1711 |
1815 |
1919 |
2022 |
2126 |
2541 |
2644 |
2748 |
|
15 |
1917 |
2028 |
2139 |
2250 |
2361 |
2806 |
2917 |
3028 |
|
16 |
2133 |
2252 |
2370 |
2489 |
2607 |
3081 |
3200 |
3319 |
|
1? |
2361 |
2487 |
2613 |
2739 |
2865 |
3369 |
3494 |
3620 |
|
18 |
2600 |
2733 |
2867 |
3000 |
3133 |
3667 |
3800 |
3933 |
|
19 |
2850 |
2991 |
3131 |
3272 |
3413 |
3976 |
4117 |
4257 |
|
20 |
3111 |
3259 |
3407 |
3556 |
3704 |
4296 |
4444 |
4592 |
|
21 |
3383 |
3539 |
3694 |
3850 |
4005 |
4628 |
4783 |
4939 |
|
22 |
3667 |
3830 |
3993 |
4156 |
4318 |
4970 |
5133 |
5296 |
|
23 |
3961 |
4131 |
4302 |
4472 |
4642 |
5324 |
5494 |
5665 |
|
24 |
4267 |
4444 |
4622 |
4800 |
4978 |
5689 |
5867 |
6044 |
|
25 |
4583 |
4769 |
4954 |
5139 |
5324 |
6065 |
6250 |
6435 |
|
26 |
4911 |
5104 |
5296 |
5489 |
5681 |
6452 |
6644 |
6837 |
|
2? |
5250 |
5450 |
5650 |
5850 |
6050 |
6850 |
7050 |
7250 |
|
28 |
5600 |
5807 |
6015 |
6222 |
6430 |
7259 |
7467 |
7674 |
|
2ft |
5961 |
6176 |
6391 |
6606 |
6820 |
7680 |
7894 |
8109 |
|
30 |
6333 |
6556 |
6778 |
7000 |
7222 |
8111 |
8333 |
8555 |
|
31 |
6717 |
6946 |
7176 |
7406 |
7635 |
8554 |
8783 |
9013 |
|
32 |
7111 |
7348 |
7585 |
7822 |
8059 |
9007 |
9244 |
9482 |
|
33 |
7517 |
7761 |
8006 |
8250 |
8494 |
9472 |
9717 |
9962 |
|
34 |
7933 |
8185 |
8437 |
8689 |
8941 |
9948 |
10200 |
10452 |
|
35 |
8361 |
8620 |
8880 |
9139 |
9398 |
10435 |
10694 |
10954 |
|
36 |
8800 |
9067 |
9333 |
9600 |
9867 |
10933 |
11200 |
11467 |
|
37 |
9250 |
9524 |
9798 |
10072 |
10346 |
11443 |
11717 |
11991 |
|
38 |
9711 |
9993 |
10274 |
10556 |
10837 |
11963 |
12244 |
12526 |
|
39 |
10183 |
10472 |
10761 |
11050 |
11339 |
12494 |
12783 |
13072 |
|
40 |
10667 |
10963 |
11259 |
11556 |
11852 |
13037 |
13333 |
13630 |
|
41 |
11161 |
11465 |
11769 |
12072 |
12376 |
13591 |
13894 |
14198 |
|
42 |
11667 |
11978 |
12289 |
12600 |
12911 |
14156 |
14467 |
14778 |
|
43 |
12183 |
12502 |
12820 |
13139 |
13457 |
14731 |
15050 |
15369 |
|
44 |
12711 |
13037 |
13363 |
13689 |
14015 |
15319 |
15644 |
15970 |
|
45 |
13250 |
13583 |
13917 |
14250 |
14583 |
15917 |
16250 |
16583 |
|
46 |
13800 |
14141 |
14481 |
14822 |
15163 |
16526 |
16867 |
17207 |
|
47 |
14361 |
14709 |
15057 |
15406 |
15754 |
17146 |
17494 |
17843 |
|
48 |
14933 |
15289 |
15644 |
16000 |
16356 |
17778 |
18133 |
18489 |
|
49 |
15517 |
15880 |
16243 |
16606 |
16968 |
18420 |
18783 |
19146 |
|
50 . |
16111 |
16481 |
16852 |
17222 |
17592 |
19074 |
19444 |
19815 |
|
51 |
16717 |
17094 |
17472 |
17850 |
18228 |
19739 |
20117 |
20494 |
|
52 |
17333 |
17719 |
18104 |
18489 |
18874 |
20415 |
20800 |
21185 |
|
53 |
17961 |
18354 |
18746 |
19139 |
19531 |
21102 |
21494 |
21887 |
|
54 |
18600 |
19000 |
19400 |
19800 |
20200 |
21800 |
22200 |
22600 |
|
55 |
19250 |
19657 |
20065 |
20472 |
20880 |
22509 |
22917 |
23324 |
|
56 |
19911 |
20326 |
20741 |
21156 |
21570 |
23230 |
23644 |
24059 |
|
57 |
20583 , |
21006 |
21428 |
21850 |
22272 |
23961 |
24383 |
24805 |
|
58 |
21267 |
21696 |
22126 |
22556 |
22985 |
24704 |
25133 |
25563 |
|
59 |
21961 |
22398 |
22835 |
23272 |
23709 |
25457 |
25894 |
26332 |
|
60 |
22667 |
23111 |
23556 |
24000 |
24444 |
26222 |
26667 |
27111 |
256 12.— CUBIC YARDS PER 100 FEET. SLOPES 2 : 1.
|
Depth |
Base 12 |
Base 14 |
Base 16 |
Base 18 |
Base 20 |
Ba«e 28 |
Base 30 |
Base 32 |
|
1 |
52 |
59 |
67 |
74 |
81 |
111 |
119 |
126 |
|
2 |
119 |
133 |
143 |
1C3 |
178 |
237 |
252 |
267 |
|
3 |
200 |
222 |
244 |
267 |
289 |
878 |
400 |
422 |
|
4 |
296 |
326 |
856 |
385 |
415 |
5-33 |
563 |
693 |
|
5 |
407 |
444 |
481 |
519 |
556 |
V04 |
741 |
778 |
|
6 |
533 |
578 |
622 |
637 |
711 |
889 |
933 |
979 |
|
7 |
674 |
726 |
778 |
830 |
881 |
1089 |
1141 |
1193 |
|
8 |
830 |
889 |
948 |
1007 |
1067 |
1304 |
1363 |
1422 |
|
9 |
1000 |
1067 |
1133 |
1200 |
1267 |
1533 |
1600 |
1667 |
|
10 |
1185 |
1259 |
1333 |
1407 |
1481 |
1778 |
1852 |
1926 |
|
11 |
1385 |
1467 |
1548 |
1630 |
1711 |
2037 |
2119 |
2200 |
|
12 |
1600 |
1689 |
1778 |
1867 |
1956 |
2311 |
2400 |
2489 |
|
13 |
1830 |
1926 |
2022 |
2119 |
2215 |
2600 |
2696 |
2793 |
|
14 |
2074 |
2178 |
2281 |
2385 |
2489 |
2904 |
3007 |
3111 |
|
15 |
2333 |
2444 |
2356 |
2667 |
2778 |
3222 |
3333 |
3444 |
|
16 |
2607 |
2726 |
2844 |
2963 |
3081 |
&55(3 |
3674 |
3793 |
|
17 |
2896 |
3022 |
8148 |
3274 |
3400 |
3904 |
4030 |
4156 |
|
18 |
3200 |
8333 |
3457 |
3600 |
3733 |
4207 |
4400 |
4533 |
|
19 |
3519 |
3059 |
3800 |
3941 |
4081 |
4644 |
4785 |
4926 |
|
20 |
3852 |
4000 |
4148 |
4296 |
4444 |
5037 |
5185 |
5333 |
|
21 |
4200 |
4356 |
4511 |
4667 |
4822 |
5444 |
5600 |
5756 |
|
22 |
4563 |
4730 |
4889 |
5053 |
5215 |
5867 |
6030 |
6193 |
|
23 |
4941 |
5111 |
5281 |
5452 |
5622 |
6304 |
6474 |
6644 |
|
24 |
5333 |
5511 |
5689 |
5867 |
6044 |
6756 |
6933 |
7111 |
|
25 |
5741 |
5926 |
6111 |
6296 |
6481 |
7222 |
7407 |
7593 |
|
26 |
6163 |
6356 |
6548 |
6741 |
6933 |
7704 |
7896 |
8089 |
|
27 |
6600 |
6800 |
7000 |
7200 |
7400 |
8200 |
8400 |
8600 |
|
28 |
7052 |
7259 |
7467 |
7674 |
7881 |
8711 |
8919 |
9126 |
|
29 |
7519 |
7733 |
7948 |
8163 |
8378 |
9237 |
9452 |
9667 |
|
30 |
8000 |
8222 |
8444 |
8667 |
8889 |
9778 |
10000 |
10222 |
|
31 |
8496 |
8726 |
8956 |
9185 |
9415 |
10333 |
10563 |
10793 |
|
32 |
9007 |
9244 |
9481 |
9719 |
9956 |
10904 |
11141 |
11378 |
|
33 |
9533 |
9778 |
10022 |
10267 |
10511 |
11489 |
11733 |
11978 |
|
34 |
10074 |
10326 |
10378 |
10830 |
11081 |
12089 |
12341 |
12593 |
|
35 |
10630 |
10889 |
11148 |
11407 |
11667 |
12704 |
12963 |
13222 |
|
36 |
11200 |
11467 |
11733 |
12000 |
12267 |
13333 |
13600 |
13867 |
|
37 |
11785 |
12059 |
12333 |
12607 |
12881 |
13978 |
14252 |
14526 |
|
38 |
12385 |
12667 |
12948 |
13230 |
13511 |
14637 |
14919 |
15200 |
|
39 |
13000 |
13289 |
13578 |
13867 |
14156 |
15311 |
15GOO |
15889 |
|
40 |
13630 |
13926 |
14223 |
14519 |
14815 |
16000 |
16296 |
16593 |
|
41 |
14274 |
14578 |
14881 |
15185 |
15489 |
16704 |
17007 |
17311 |
|
42 |
14'.)33 |
15244 |
15556 |
15867 |
16178 |
17422 |
17733 |
18044 |
|
43 |
15607 |
15926 |
16224 |
16563 |
16881 |
18156 |
18474 |
18793 |
|
44 |
16296 |
16622 |
16948 |
17274 |
17600 |
16904 |
19230 |
19556 |
|
45 |
17000 |
17333 |
17667 |
18000 |
18333 |
19667 |
20000 |
20333 |
|
46 |
17719 |
18059 |
18400 |
18741 |
19081 |
20444 |
20785 |
21126 |
|
47 |
18452 |
18800 |
19148 |
19496 |
19844 |
21237 |
21585 |
21933 |
|
48 |
19200 |
19556 |
19911 |
20267 |
20622 |
22044 |
22400 |
22756 |
|
49 |
19963 |
20326 |
20689 |
21052 |
21415 |
22867 |
23230 |
23593 |
|
50 |
20741 |
20711 |
21481 |
21852 |
22222 |
23704 |
24074 |
24444 |
|
51 |
21533 |
21911 |
22289 |
22667 |
23044 |
24556 |
24933 |
25311 |
|
*2 |
22341 |
22726 |
23111 |
23496 |
23881 |
25422 |
25807 |
26193 |
|
53 |
23163 |
2J556 |
23948 |
24341 |
24733 |
26304 |
26696 |
2?089 |
|
54 |
24000 |
21400 |
24800 |
25200 |
25600 |
27200 |
27600 |
28000 |
|
55 |
24852 |
25259 |
25667 |
26074 |
26481 |
28111 |
28519 |
28926 |
|
56 |
25719 |
26133 |
26548 |
26963 |
27378 |
29037 |
29452 |
29867 |
|
57 |
26600 |
27022 |
27444 |
27867 |
28289 |
20978 |
30400 |
30822- |
|
58 |
27496 |
27926 |
28356 |
28785 |
29215 |
30933 |
31363 |
31793 |
|
59 |
28407 |
28844 |
29281 |
29719 |
30156 |
31904 |
32341 |
32778 |
|
60 |
89333 |
29778 |
30222 |
30667 |
31111 |
32889 |
33333 |
33778 |
12.— CUBIC YARDS PER 100 FEET. SLOPES 3 : 1. 257
|
Depth |
Base 12 |
Base 14 |
Base 16 |
Base 18 |
Base 20 |
Base 28 |
Base 30 |
Base 32 |
|
1 |
56 |
63 |
70 |
78 |
85 |
115 |
122 |
130 |
|
2 |
133 |
148 |
163 |
178 |
193 |
252 |
267 |
281 |
|
3 |
233 |
256 |
278 |
300 |
322 |
411 |
433 |
456 |
|
4 |
356 |
385 |
415 |
444 |
474 |
593 |
622 |
652 |
|
5 |
500 |
537 |
574 |
611 |
648 |
796 |
833 |
870 |
|
6 |
667 |
711 |
756 |
800 |
&44 |
1022 |
1067 |
1111 |
|
7 |
856 |
907 |
959 |
1011 |
1063 |
1270 |
1322 |
1374 |
|
8 |
1067 |
1126 |
1185 |
1244 |
1304 |
1541 |
1600 |
1659 |
|
9 |
1300 |
1367 |
1433 |
1500 |
1567 |
1833 |
1900 |
1967 |
|
10 |
1556 |
1630 |
1704 |
1778 |
1852 |
2148 |
2222 |
2296 |
|
11 |
1833 |
1915 |
1996 |
2078 |
2159 |
2485 |
2567 |
2648 |
|
IS |
2133 |
2222 |
2311 |
2400 |
2489 |
2844 |
2933 |
3022 |
|
13 |
2456 |
2552 |
2648 |
2744 |
2841 |
3226 |
3322 |
3419 |
|
14 |
2800 |
2904 |
3007 |
3111 |
3215 |
3630 |
3733 |
3837 |
|
15 |
3167 |
3278 |
3389 |
3500 |
3611 |
4056 |
4167 |
4278 |
|
16 |
3556 |
3674 |
3793 |
3911 |
4030 |
4504 |
4622 |
4741 |
|
17 |
3967 |
4093 |
4219 |
4344 |
4470 |
4974 |
5100 |
5226 |
|
18 |
4400 |
4533 |
4667 |
4800 |
4933 |
5467 |
5600 |
5733 |
|
19 |
4856 |
4996 |
5137 |
5278 |
5419 |
5981 |
6122 |
6263 |
|
20 |
5333 |
5481 |
5630 |
5778 |
5926 |
6519 |
6667 |
6815 |
|
21 |
5833 |
5989 |
6144 |
6300 |
6456 |
7078 |
7233 |
7389 |
|
22 |
6356 |
6519 |
6681 |
6844 |
7007 |
7659 |
7822 |
7985 |
|
23 |
6900 |
7070 |
7241 |
7411 |
7581 |
8263 |
8433 |
8504 |
|
24 |
7467 |
7644 |
7822 |
8000 |
8178 |
8889 |
9067 |
9144 |
|
25 |
8056 |
8241 |
8426 |
8611 |
8796 |
9537 |
9722 |
9807 |
|
26 |
8667 |
8859 |
9052 |
9244 |
9437 |
10207 |
10400 |
10593 |
|
27 |
9300 |
9500 |
9700 |
9900 |
10100 |
10900 |
11100 |
11300 |
|
28 |
9956 |
10163 |
10370 |
10578 |
10785 |
11615 |
11822 |
12030 |
|
29 |
10633 |
10848 |
11063 |
11278 |
11493 |
12352 |
12567 |
12781 |
|
30 |
11333 |
11556 |
11778 |
12000 |
12222 |
13111 |
13333 |
13556 |
|
31 |
12056 |
12285 |
12515 |
12744 |
12974 |
13893 |
14122 |
14352 |
|
32 |
12800 |
13037 |
13274 |
13511 |
13748 |
14696 |
14933 |
15170 |
|
as |
13567 |
13811 |
14056 |
14300 |
14544 |
15522 |
15767 |
16011 |
|
34 |
14356 |
14607 |
14859 |
15111 |
15363 |
16370 |
16622 |
16874 |
|
35 |
15167 |
15426 |
15685 |
15944 |
16204 |
17241 |
17500 |
17759 |
|
36 |
16000 |
16267 |
16533 |
1G800 |
17067 |
18133 |
18400 |
18667 |
|
37 |
16856 |
17130 |
17404 |
17678 |
17959 |
19048 |
19322 |
19596 |
|
38 |
17733 |
18015 |
18296 |
18578 |
18859 |
19985 |
20267 |
20548 |
|
89 |
18633 |
18922 |
19211 |
19500 |
19789 |
20944 |
21233 |
21522 |
|
40 |
19556 |
19852 |
20148 |
20444 |
20741 |
21926 |
22222 |
22516 |
|
41 |
20500 |
20804 |
21107 |
21411 |
21715 |
22930 |
23233 |
23537 |
|
42 |
21467 |
21778 |
22089 |
22400 |
22711 |
23956 |
24267 |
24578 |
|
43 |
22456 |
22774 |
23093 |
23411 |
23730 |
25004 |
25322 |
25641 |
|
44 |
23467 |
23793 |
24119 |
24444 |
24770 |
26074 |
26400 |
26726 |
|
45 |
24500 |
24833 |
25167 |
25500 |
25833 |
27167 |
27500 |
27833 |
|
46 |
25556 |
25896 |
26237 |
26578 |
26919 |
28281 |
28622 |
28963 |
|
47 |
26633 |
26981 |
27330 |
27678 |
28026 |
29419 |
29767 |
30115 |
|
48 |
27733 |
28089 |
28800 |
29156 |
30578 |
30938 |
31289 |
|
|
49 |
28856 |
20219 |
21)581 |
29944 |
30307 |
31759 |
32122 |
32485 |
|
50 |
30000 |
30370 |
30741 |
31111 |
31481 |
32963 |
33333 |
33704 |
|
51 |
31167 |
31544 |
31922 |
32300 |
32678 |
34189 |
34567 |
34944 |
|
52 |
32356 |
32741 |
33126 |
33511 |
33396 |
35437 |
35822 |
36207 |
|
53 |
33567 |
33959 |
34352 |
34744 |
35137 |
36707 |
37100 |
87493 |
|
54 |
34800 |
35200 |
35600 |
36000 |
36400 |
38000 |
38400 |
38800 |
|
55 |
36056 |
36463 |
36870 |
37278 |
37685 |
39315 |
39722 |
4€130 |
|
56 |
37333 |
37748 |
38163 |
38578 |
38993 |
40652 |
41067 |
41481 |
|
5? |
38633 |
39056 |
39478 |
39900 |
40322 |
42011 |
42433 |
42856 |
|
58 |
39956 |
40385 |
40815 |
41244 |
41674 |
43393 |
43822 |
44252 |
|
59 |
41300 |
41737 |
42174 |
42611 |
43048 |
44796 |
45233 |
45670 |
|
60 |
42667 |
43111 |
43556 |
44000 |
44444 |
46222 |
46667 |
47111 |
258 TABLE 13.— CUBIC YARDS IN 100 FEET LENGTH.
|
Area. IS: |
Cubic Yards. |
Area. ft |
Cubic Yards. |
Area. ft |
Cubic Yards. |
Area. Sq, Ft. |
Cubic Yards. |
Area. Sq. Ft. |
Cubic Yards. |
|
1 |
3.7 |
51 |
188.9 |
101 |
374.1 |
151 |
559.3 |
201 |
744.4 |
|
2 |
7.4 |
52 |
192.6 |
102 |
377.8 |
152 |
563.0 |
202 |
748.2 |
|
3 |
11.1 |
53 |
196.3 |
103 |
381.5 |
153 |
566.7 |
203 |
751.9 |
|
4 |
14.8 |
54 |
200.0 |
104 |
385.2 |
154 |
570.4 |
204 |
755.6 |
|
5 |
18.5 |
55 |
203.7 |
105 |
388.9 |
155 |
574.1 |
905 |
759.3 |
|
6 |
22.2 |
56 |
207.4 |
106 |
392.6 |
156 |
577.8 |
206 |
763.0 |
|
7 |
25.9 |
57 |
211.1 |
107 |
396.3 |
157 |
581.5 |
207. |
766.7 |
|
8 |
29.6 |
58 |
214.8 |
108 |
400.0 |
158 |
585.2 |
208 |
770.4 |
|
9 |
33.3 |
59 |
218.5 |
109 |
403.7 |
159 |
588.9 |
209 |
774.1 |
|
10 |
37.0 |
60 |
222.2 |
110 |
407.4 |
160 |
592.6 |
210 |
777.8 |
|
11 |
40.7 |
61 |
225.9 |
111 |
411.1 |
161 |
596.3 |
211 |
781 5 |
|
12 |
44.4 |
62 |
229.6 |
112 |
414.8 |
162 |
600.0 |
212 |
785.2 |
|
13 |
48.1 |
63 |
233.3 |
113 |
418.5 |
163 |
603.7 |
213 |
788.9 |
|
14 |
51.9 |
64 |
237.0 |
114 |
422.2 |
164 |
607.4 |
214 |
792.6 |
|
15 |
55.6 |
65 |
240.7 |
115 |
425.9 |
165 |
611.1 |
215 |
796.3 |
|
16 |
59.3 |
66 |
244 .4 |
116 |
429.6 |
166 |
614.8 |
216 |
800.0 |
|
17 |
63.0 |
67 |
248.2 |
117 |
433.3 |
167 |
618.5 |
217 |
803.7 |
|
18 |
66.7 |
68 |
251.9 |
118 |
437.0 |
168 |
622.2 |
218 |
807.4 |
|
19 |
70.4 |
69 |
255.6 |
119 |
440.7 |
169 |
625.9 |
219 |
811.1 |
|
20 |
74.1 |
70 |
259.3 |
120 |
444.4 |
170 |
629.6 |
220 |
814.8 |
|
21 |
77.8 |
71 |
263.0 |
121 |
448.2 |
171 |
633.3 |
221 |
818.5 |
|
22 |
81.5 |
72 |
266.7 |
123 |
451.9 |
172 |
637.0 |
222 |
822.2 |
|
23 |
85.2 |
73 |
270.4 |
123 |
455 6 |
173 |
640.7 |
223 |
825.9 |
|
24 |
88.9 |
74 |
274.1 |
124 |
459.3 |
174 |
644.4 |
224 |
829.6 |
|
25 |
92.6 |
75 |
277.8 |
125 |
463.0 |
175 |
648.2 |
225 |
833.3 |
|
26 |
96.3 |
76 |
281.5 |
126 |
466.7 |
176 |
651.9 |
226 |
837.0 |
|
27 |
100.0 |
77 |
285 2 |
127 |
470.4 |
177 |
655.6 |
227 |
840.7 |
|
28 |
103.7 |
78 |
, 288.9 |
128 |
474 1 |
178 |
659.3 |
228 |
844.4 |
|
29 |
107.4 |
79 |
292.6 |
129 |
477.8 |
179 |
663.0 |
229 |
848.2 |
|
30 |
111.1 |
80 |
296.3 |
130 |
481.5 |
180 |
666.7 |
230 |
851.9 |
|
31 |
114.8 |
81 |
300.0 |
131 |
485.2 |
181 |
670.4 |
231 |
855.6 |
|
32 |
118.5 |
82 |
303.7 |
132 |
488 9 |
182 |
674.1 |
232 |
859.3 |
|
33 |
122.2 |
83 |
307.4 |
133 |
492.6 |
183 |
677.8 |
233 |
863.0 |
|
34 |
125.9 |
84 |
311.1 |
134 |
496.3 |
184 |
681.5 |
234 |
866.7 |
|
35 |
129 6 |
85 |
314.8 |
135 |
500.0 |
185 |
685.2 |
235 |
870.4 |
|
36 |
133.3 |
86 |
318.5 |
136 |
503.7 |
186 |
688.9 |
236 |
874.1 |
|
37 |
137.0 |
87 |
322.2 |
137 |
507.4 |
187 |
692.6 |
237 |
877.8 |
|
38 |
140.7 |
88 |
325.9 |
138 |
511.1 |
188 |
696.3 |
238 |
881.5 |
|
39 |
144 4 |
89 |
329.6 |
139 |
514.8 |
189 |
700.0 |
235 |
885.2 |
|
40 |
148.2 |
90 |
333.3 |
140 |
518.5 |
190 |
703.7 |
240 |
888.9 |
|
41 |
151.9 |
91 |
337.0 |
141 |
522.2 |
191 |
707.4 |
241 |
892.6 |
|
42 |
155.6 |
92 |
340.7 |
142 |
525.9 |
192 |
711.1 |
242 |
896.3 |
|
43 |
159 3 |
93 |
344.4 |
143 |
529.6 |
193 |
714.8 |
243 |
900.0 |
|
44 |
163.0 |
94 |
348.2 |
144 |
533.3 |
194 |
718.5 |
244 |
903.7 |
|
45 |
166.7 |
95 |
351.9 |
145 |
537.0 |
195 |
722.2 |
245 |
907.4 |
|
46 |
170.4 |
96 |
355.6 |
146 |
540.7 |
196 |
725.9 |
246 |
911.1 |
|
47 |
174.1 |
97 |
359.3 |
147 |
544.4 |
197 |
729.6 |
247 |
914.8 |
|
48 |
177.8 |
96 |
363.0 |
148 |
548.2 |
198 |
733.3 |
248 |
918.5 |
|
49 |
181.5 |
99 |
366.7 |
149 |
551.9 |
199 |
737.0 |
249 |
922.2 |
|
50 |
185.2 |
100 |
370.4 |
150 |
555.6 |
200 |
740.7 |
250 |
925.9 |
TABLE 13.— CUBIC YARDS IN 100 FEET LENGTH. 259
|
Area * |
Cubic Yards. |
Area. ft |
Cubic Yards. |
Area ft |
Cubic Yards. |
Area •ft |
Cubic Yards. |
Area ft |
Cubic Yards. |
|
251 |
929.6 |
301 |
1114.8 |
351 |
1300.0 |
401 |
1485.2 |
451 |
1670.4 |
|
252 |
933.3 |
302 |
1118.5 |
352 |
1303.7 |
402 |
1488.9 |
152 |
1674.1 |
|
253 |
93?. 0 |
303 |
1122.2 |
353 |
1307.4 |
403 |
1492.6 |
453 |
1677.8 |
|
254 |
940.7 |
304 |
1125.9 |
a54 |
1311.1 |
404 |
1496.3 |
454 |
1681.5 |
|
255 |
944.4 |
305 |
1129.6 |
355 |
1314.8 |
405 |
1500.0 |
455 |
1685.2 |
|
256 |
948.2 |
306 |
1133.3 |
356 |
1318.5 |
406 |
1503.7 |
456 |
1688.9 |
|
1 257 |
951.9 |
307 |
1137.0 |
357 |
1322.2 |
407 |
1507.4 |
457 |
1692.6 |
|
258 |
955.6 |
308 |
1140.7 |
358 |
1325.9 |
408 |
1511.1 |
458 |
1696.3 |
|
259 |
959.3 |
309 |
1144.4 |
359 |
1329.6 |
409 |
1514.8 |
459 |
1700.0 |
|
260 |
963.0 |
310 |
1148.2 |
360 |
1333.3 |
410 |
1518.5 |
460 |
1703.7 |
|
261 |
966.7 |
311 |
1151.9 |
361 |
1337.0 |
411 |
1522.2. |
461 |
1707.4 |
|
262 |
970.4 |
312 |
1155.6 |
362 |
1340.7 |
412 |
1525.9 |
462 |
1711.1 |
|
263 |
974.1 |
313 |
1159.3 |
363 |
1344.4 |
413 |
1529.6 |
463 |
1714.8 |
|
264 |
977.8 |
314 |
1163.0 |
364 |
1348.2 |
414 |
1533.3 |
-164 |
1718.5 |
|
265 |
981.5 |
315 |
1166.7 |
365 |
1351.9 |
415 |
1537.0 |
465 |
1722.2 |
|
266 |
985.2 |
316 |
1170.4 |
366 |
1355.6 |
416 |
1540.7 |
466 |
1725.9 |
|
267 |
988.9 |
317 |
1174.1 |
367 |
1359.3 |
417 |
1544.4 |
467 |
1729.6 |
|
268 |
992.6 |
318 |
1177.8 |
368 |
1363.0 |
418 |
1548.2 |
468 |
1733.3 |
|
269 |
996.3 |
319 |
1181.5 |
369 |
1366.7 |
419 |
1551.9 |
469 |
1737.0 |
|
270 |
1000.0 |
320 |
1185.2 |
370 |
1370.4 |
420 |
1555.6 |
470 |
1740.7 |
|
271 |
1003.7 |
321 |
1188.9 |
371 |
1374.1 |
421 |
1559.3 |
471 |
1744.4 |
|
272 |
1007.4 |
322 |
1192.6 |
372 |
1377.8 |
422 |
1563.0 |
472 |
1748.2 |
|
273 |
1011.1 |
323 |
1196.3 |
373 |
1381.5 |
423 |
1566.7 |
473 |
1751.9 |
|
274 |
1014.8 |
324 |
1200.0 |
374 |
1385.2 |
424 |
1570.4 |
474 |
1755.6 |
|
275 |
1018.5 |
325 |
1203.7 |
375 |
1388.9 |
425 |
1574.1 |
475 |
1759.3 |
|
276 |
1022.2 |
326 |
1207.4 |
376 |
1392.6 |
426 |
1577.8 |
476 |
1763.0 |
|
277 |
1025.9 |
327 |
1211.1 |
377 |
1396.3 |
427 |
1581.5 |
477 |
1766.7 |
|
278 |
1029.6 |
328 |
1214.8 |
378 |
1400.0 |
428 |
1585.2 |
478 |
1770.4 |
|
279 |
1033.3 |
329 |
1218.5 |
379 |
1403.7 |
429 |
1588.9 |
479 |
1774.1 |
|
280 |
1037.0 |
330 |
1222.2 |
380 |
1407.4 |
430 |
1592.6 |
480 |
1777.8 |
|
281 |
1040.7 |
331 |
1225.9 |
381 |
1411.1 |
431 |
1596.3 |
481 |
1781.5 |
|
282 |
1044.4 |
332 |
1229 6 |
382 |
1414.8 |
432 |
1600.0 |
482 |
1785.2 |
|
283 |
1048.2 |
333 |
1233.3 |
383 |
1418.5 |
433 |
1603.7 |
483 |
1788.9 |
|
284 |
1051.9 |
334 |
1237.0 |
384 |
1422.2 |
434 |
1607.4 |
484 |
1792.6 |
|
285 |
1055.6 |
335 |
1240.7 |
385 |
1425.9 |
435 |
1611.1 |
485 |
1796 3 |
|
286 |
1059.3 |
336 |
1244.4 |
386 |
1429.6 |
436 |
1614.8 |
486 |
1800.0 |
|
287 |
1063.0 |
337 |
1248.2 |
387 |
1433.3 |
437 |
1618.5 |
487 |
1803.7 |
|
288 |
1066.7 |
338 |
1251.9 |
388 |
1437.0 |
438 |
1622.2 |
488 |
1807.4 |
|
289 |
1070.4 |
339 |
1255.6 |
389 |
1440.7 |
439 |
1625.9 |
»89 |
1811.1 |
|
290 |
1074.1 |
340 |
1259.3 |
390 |
1444.4 |
440 |
1629.6 |
490 |
1814.8 |
|
291 |
1077.8 |
341 |
1263.0 |
391 |
1448.2 |
441 |
1633.3 |
491 |
1818.5 |
|
292 |
1081.5 |
342 |
1266.7 |
392 |
1451.9 |
442 |
1637.0 |
492 |
1822.2 |
|
293 |
1085.2 : |
343 |
1270.4 |
393 |
1455.6 |
443 |
1640.7 |
493 |
1825.9 |
|
294 |
1088.9 |
344 |
1274.1 |
394 |
1459.3 |
444 |
1644.4 |
494 |
1829.6 |
|
295 1092.6 |
345 |
1277.8 |
395 |
1463.0 |
445 |
1648.2 |
495 |
1833.3 |
|
|
296 1096.3 |
346 |
1281.5 |
396 |
1466.7 |
446 |
1651.9 |
496 |
1837.0 |
|
|
297 1100.0 |
347 |
1285.2 |
397 |
1470.4 |
447 |
1655.6 |
497 |
1840.7 |
|
|
298 1103.7 |
348 |
1288.9 |
398 |
1474.1 |
448 |
1659.3 |
498 |
1844.4 |
|
|
299 |
1107.4 |
349 |
1292.6 |
399 |
1477.8 |
449 |
1663.0 |
499 |
1848.2 |
|
300 |
1111.1 |
350 |
1296.3 |
400 |
1481.5 |
450 |
1G66.7 |
500 |
1851.9 |
260 TABLE 13.— CUBIC YARDS IN 100 FEET LENGTH.
|
Area. H: |
Cubic Yards. |
Area. 1?: |
Cubic Yards. |
Area. & |
Cubic Yards. |
Area. 1?: |
Cubic Yards. |
Area. 8t |
Cubic Yards. |
|
501 |
1855.6 |
551 |
2040.7 |
601 |
2225.9 |
651 |
2411.1 |
701 |
2596.3 |
|
502 |
1859.3 |
552 |
2044.4 |
602 |
2229.6 |
652 |
2414.8 I |
702 |
2000.0 |
|
503 |
1863.0 |
553 |
2048.2 |
603 |
2233.3 |
653 |
2418.5 i |
703 |
2603.7 |
|
504 |
1866.7 |
554 |
2051.9 |
604 |
2237.0 |
654 |
2422.2 |
704 |
2607.4 |
|
505 |
1870.4 |
555 |
2055.6 |
605 |
2240.7 |
655 |
2425.9 |
705 |
2611.1 |
|
506 |
1874.1 |
556 |
2059.3 |
606 |
2244.4 |
656 |
2429.6 |
706 |
2614.8 |
|
507 |
1877.8 |
557 |
2063.0 |
607 |
2248.2 |
657 |
2433.3 |
707 |
2618.5 |
|
508 |
1881.5 |
558 |
2066.7 |
608 |
2251.9 |
658 |
2437.0 |
708 |
2622.2 |
|
509 |
1885.2 |
559 |
2070.4 |
609 |
2255.6 |
659 |
2440.7 |
709 |
2625.9 |
|
510 |
1888.9 |
560 |
2074.1 |
610 |
2259.3 |
660 |
2444 .4 |
710 |
2629.6 |
|
511 |
1892.6 |
561 |
2077.8 |
611 |
2263.0 |
661 |
2448.2 |
711 |
2633.3 |
|
512 |
1896.3 |
562 |
2081.5 |
612 |
2266.7 |
662 |
2451.9 |
712 |
2637.0 |
|
513 |
1900.0 |
563 |
20&>.2 |
613 |
2270.4 |
663 |
2455.6 |
713 |
2640.7 |
|
514 |
1903.7 |
564 |
2088.9 |
614 |
2274.1 |
664 |
2459.3 |
714 |
2644.4 |
|
515 |
1907.4 |
565 |
2092.6 |
615 |
2277.8 |
665 |
2463.0 |
715 |
2648.2 |
|
516 |
1911.1 |
566 |
2096.3 |
616 |
2281.5 |
666 |
2466.7 |
716 |
2651.9 |
|
517 |
1914.8 |
567 |
2100.0 |
617 |
2285.2 |
667 |
2470.4 |
717 |
2655.6 |
|
518 |
1918.5 |
568 |
2103.7 |
618 |
2288.9 |
668 |
2474.1 |
718 |
2659.3 |
|
519 |
1922.2 |
569 |
2107.4 |
619 |
2292.6 |
669 |
2477.8 |
719 |
2663.0 |
|
520 |
1925.9 |
570 |
2111.1 |
620 |
2296.3 |
670 |
2481.5 |
720 |
2666.7 |
|
521 |
1929 6 |
571 |
2114.8 |
621 |
2300.0 |
671 |
2485.2 |
721 |
2670.4 |
|
522 |
1933.3 |
572 |
2118.5 |
622 |
2303.7 |
672 |
2488.9 |
722 |
2674.1 |
|
523 |
1937.0 |
573 |
2122.2 |
623. |
2307.4 |
673 |
2492 6 |
723 |
2677.8 |
|
524 |
1940.7 |
574 |
2125.9 |
624 |
2311.1 |
674 |
2496.3 |
724 |
2681.5 |
|
525 |
1944.4 |
575 |
2129.6 |
625 |
2314.8 |
675 |
2500.0 |
725 |
2685.2 |
|
526 |
1948.2 |
576 |
2133.3 |
626 |
2318.5 |
676 |
2503.7 |
726 |
2688.9 |
|
527 |
1951.9 |
577 |
2137.0 |
627 |
2322.2 |
677 |
2507.4 |
727 |
2692.6 |
|
528 |
1955.6 |
578 |
2140.7 |
628 |
2325.9 |
678 |
2511.1 |
728 |
2696.3 |
|
529 |
1959.3 |
579 |
2144.4 |
629 |
2329.6 |
679 |
2514.8 |
729 |
2700.0 |
|
530 |
1963.0 |
580 |
2148 2 |
630 |
2333.3 |
680 |
2518.5 |
730 |
2703.7 |
|
531 |
1966.7 |
581 |
2151.9 |
631 |
2337.0 |
681 |
2522.2 |
731 |
2707.4 |
|
532 |
1970.4 |
582 |
2155.6 |
632 |
2340.7 |
682 |
2525.9 |
732 |
2711.1 |
|
533 |
1974.1 |
583 |
2159.3 |
633 |
2344.4 |
683 |
2529.6 |
733 |
2714.8 |
|
534 |
1977.8 |
584 |
2163.0 |
634 |
2348.2 |
684 |
2533.3 |
734 |
2718.5 |
|
535 |
1981.5 |
585 |
2166.7 |
635 |
2351.9 |
685 |
2537.0 |
735 |
2722.2 |
|
536 |
1985.2 |
586 |
2170.4 |
636 |
2355.6 |
686 |
2540 7 |
736 |
2725.9 |
|
537 |
1988.9 |
587 |
2174.1 |
637 |
2359.3 |
687 |
2544.4 |
737 |
2729.6 |
|
538 |
1992.6 |
588 |
2177.8 |
638 |
2363 0 |
688 |
2548.2 |
738 |
2733.3 |
|
539 |
1996.3 |
589 |
2181.5 |
639 |
2366.7 |
689 |
2551.9 |
739 |
2737.0 |
|
540 |
2000.0 |
590 |
2185.2 |
640 |
2370.4 |
690 |
2555.6 |
740 |
2740.7 |
|
541 |
2003.7 |
591 |
2188.9 |
641 |
2374.1 |
691 |
2559.3 |
741 |
2744.4 |
|
542 |
2007.4 |
592 |
2192.6 |
642 |
2377.8 |
692 |
2563.0 |
742 |
2748.2 |
|
543 |
2011.1 |
593 |
2196.3 |
643 |
2381.5 |
693 |
2566.7 |
743 |
2751.9 |
|
544 |
2014.8 |
594 |
2200.0 |
644 |
2385.2 |
694 |
2570.4 |
744 |
2755.6 |
|
545 |
2018.5 |
595 |
2203.7 |
645 |
2388.9 |
695 |
2574.1 |
745 |
2759.3 |
|
546 |
2022.2 |
596 |
2207.4 |
646 |
2:592.6 |
696 |
2577.8 |
746 |
2763.0 |
|
547 |
2025.9 |
597 |
2211.1 ; |
647 |
2396.3 |
697 |
2581.5 |
747 |
2766.7 |
|
548 |
2029.6 |
598 |
2214.8 |
648 |
2400.0 |
698 |
2585.2 |
748 |
2770.4 |
|
549 |
2033.3 |
599 |
2218.5 |
649 |
2403.7 |
699 |
2588.9 |
749 |
2774.1 |
|
550 |
2037.0 |
600 |
2222.2 |
650 |
2407.4 |
700 |
2592.6 |
750 |
2777.8 |
TABLE 13.— CUBIC YARDS IN 100 FEET LENGTH. 261
|
Area. !?: |
Cubic Yards. |
Area. §q- tt. |
Cubic Yards. |
Area. SSq. i F<- |
Cubic Yards. |
Area. ft |
Cubic Yards. |
Area. St |
Cubic Yards. |
|
751 |
2781.5 |
801 |
2966.7 |
851 |
3151.9 |
901 |
3337.0 |
951 |
3522.2 |
|
752 |
2785.2 |
802 |
2970.4 |
852 |
3155.6 |
902 |
3340.7 |
952 |
3525.9 |
|
753 |
2788.9 |
803 |
2974 . 1 |
8o3 |
3159.3 |
9U3 |
3344.4 |
953 |
3529.6 |
|
754 |
2792.6 |
8o4 |
2977.8 |
854 |
3163.0 |
904 |
3348.2 |
954 |
3533.3 |
|
755 |
2796.3 |
805 |
2981.5 |
8f>5 |
3166.7 |
905 |
3351.9 |
955 |
3537.0 |
|
756 |
2800.0 |
806 |
2985.2 |
856 |
3170.4 |
906 |
3355.6 |
956 |
3540.7 |
|
757 |
2803.7 |
807 |
2988.9 |
857 |
3174.1 |
907 |
3359.3 |
957 |
3544.4 |
|
758 |
2807.4 |
808 |
2992.6 |
858 |
3177.8 |
908 |
3363.0 |
958 |
3548.2 |
|
759 |
2811.1 |
809 |
2996.3 |
859 |
3181.5 |
909 |
3366.7 |
959 |
3551.9 |
|
760 |
2814.8 |
810 |
3000.0 |
860 |
3185.2 |
910 |
3370.4 |
960 |
3555.6 |
|
761 |
2818.5 |
811 |
3003 7 |
861 |
3188.9 |
911 |
3374.1 |
961 |
3559.3 |
|
762 |
2822 2 |
812 |
3007.4 |
862 |
3192.6 |
912 |
3377.8 |
962 |
3563.0 |
|
763 |
2825.9 |
813 |
3011.1 |
863 |
3196.3 |
913 |
3381.5 |
963 |
3566.7 |
|
764 |
2829.6 |
814 |
3014.8 |
864 |
3200.0 |
914 |
3385.2 |
964 |
3570.4 |
|
765 |
2833 3 |
815 |
3018.5 |
865 |
3203.7 |
915 |
3388.9 |
965 |
3574.1 |
|
766 |
2837.0 |
816 |
3022.2 |
866 |
3207.4 |
916 |
3392.6 |
966 |
3577.8 |
|
767 |
2840.7 |
817 |
3025.9 |
867 |
3211.1 |
917 |
3396.3 |
967 |
3581.5 |
|
768 |
2844 4 |
818 |
3029.6 |
868 |
3214.8 |
918 |
3400.0 |
968 |
3585.2 |
|
769 |
2848.2 |
819 |
3033.3 |
869 |
3218.5 |
919 |
3403.7 |
969 |
3588.9 |
|
770 |
2851.9 |
820 |
3037.0 |
870 |
3222.2 |
920 |
3407.4 |
970 |
3592.6 |
|
771 |
2855.6 |
821 |
3040.7 |
871 |
3225.9 |
921 |
3411.1 |
971 |
3596.3 |
|
772 |
2859.3 |
822 |
3044.4 |
872 |
3229.6 |
922 |
3414.8 |
972 |
3600.0 |
|
773 |
2863.0 |
823 |
3048.2 |
873 |
3233.3 |
923 |
3418.5 |
973 |
3603.7 |
|
774 |
2866.7 |
824 |
3051.9 |
874 |
3237.0 |
924 |
3422.2 |
974 |
3607.4 |
|
775 |
2870.4 |
825 |
3055.6 |
875 |
3240.7 |
925 |
3425.9 |
975 |
3611.1 |
|
776 |
2874.1 |
826 |
3059.3 |
876 |
3244.4 |
926 |
3429.6 |
976 |
3614.8 |
|
777 |
2877.8 |
827" |
3063.0 |
877 |
3248.2 |
927 |
3433.3 |
977 |
3618.5 |
|
778 |
2S81.5 |
828 |
3066.7 |
878 |
3251.9 |
928 |
3437.0 |
978 |
3622.2 |
|
779 |
2885.2 |
829 |
3070.4 |
879 |
3255.6 |
929 |
3440.7 |
979 |
3625.9 |
|
780 |
2888.9 |
830 |
3074.1 |
880 |
3259.3 |
930 |
3444.4 |
980 |
3629.6 |
|
781 |
2892.6 |
831 |
3077.8 |
881 |
3263.0 |
931 |
3448.2 |
981 |
3633.3 |
|
782 |
2896.3 |
832 |
3081.5 |
882 |
3266.7 |
932 |
3451.9 |
9«2 |
3637.0 |
|
783 |
2900.0 |
833 |
3085.2 |
883 |
3270.4 |
933 |
3455.6 |
983 |
3640.7 |
|
784 |
2903 7 |
834 |
3088.9 |
884 |
3274.1 |
934 |
3459.3 |
984 |
3644.4 |
|
785 |
2907.4 |
835 |
3092.6 |
885 |
3277.8 |
935 |
3463.0 |
985 |
3648.2 |
|
786 |
'^91 1 . 1 |
836 |
3096.3 |
886 |
3281.5 |
936 |
3466.7 |
9*6 |
3651.9 |
|
787 |
2914.8 |
837 |
3100.0 |
887 |
3285.2 |
937 |
3470.4 |
987 |
3655.6 |
|
788 |
2918.5 |
838 |
3103.7 |
888 |
3288.9 |
938 |
3474.1 |
988 |
3659.3 |
|
789 |
2922.2 |
839 |
3107.4 |
889 |
3292.6 |
939 |
3477.8 |
Q?9 |
3663.0 |
|
790 |
2925.9 |
840 |
3111.1 |
890 |
3296.3 |
940 |
3481.5 |
990 |
3666.7 |
|
791 |
2929.6 |
841 |
3114.8 |
891 |
3300.0 |
941 |
8485.2 |
991 |
3670.4 |
|
792 |
2933.3 |
842 |
3118.5 |
892 |
3303.7 |
942 |
3488.9 |
992 |
3674.1 |
|
793 |
2937.0 |
843 |
3122.2 |
893 |
3307.4 |
943 |
3492.6 |
993 |
3677.8 |
|
?94 |
2940.7 |
844 |
3125.9 |
894 |
3311.1 |
9)4 |
3496.3 |
994 |
3681.5 |
|
795 |
2944.4 |
845 |
3129.6 |
895 |
3314.8 |
945 |
3MX).0 |
995 |
8685.2 |
|
796 |
2948.2 |
846 |
3133.3 |
896 |
3318.5 |
946 |
3503.7 |
996 |
3688.9 |
|
797 |
2051.9 |
847 |
3137.0 |
897 |
3322.2 |
947 |
3507.4 |
997 |
3692.6 |
|
798 |
2955.6 |
848 |
3140.7 |
• 808 |
3325.9 |
948 |
3511.1 |
998 |
3696.3 |
|
799 |
2959.3 |
849 |
3144.4 |
899 |
3329.6 |
949 |
3514.8 |
999 |
3700.0 |
|
800 |
2963.0 |
850 |
3148.2 |
900 |
3333.3 |
950 |
3518.5 |
1000 |
3703.7 |
262
TRIGONOMETRIC FORMULAS.
TABLE 14. — TRIGONOMETRIC FORMULAS.
FIG. 98.
RIGHT TRIANGLES. Z>
FIG. 99,
In Fig 99, let DCE be the arc of a quadrant, ABC a right triangle, the angle 13 A C subtended by the arc CE = A, and consider the radius A C = unity. Then
BC = am
AB = cosA. HE = tan A. DF =cotA. AH = sec A.
^ljP=cosec^.. J5£r = versinJ.. DI = co versing, CH= exsec-4. CF = coexsec^..
Using the small letters a, &, c, to represent the sides of a right triangle in Fig. 98 or 99, we may write
sin^l = -; eosec.4— -; .-. sin>4 = ...
6 a cosec^l
= -; sec A—--, .'.cosA=
6 c sec A
= -: cot A =-;.'. tan A = — L— . c a cot-4
OBLIQUE TRIANGLES 263
FORMULAS FOR LOGARITHMIC COMPUTATION.
Given one side, a, and the three angles A, B, and C.
The "sine proportion" states that each side of a triangle is proportional to the sine of the angle opposite it.
™, , a sin B . „ a sin C
Then, b = —-. — -r- and C =
Area
. cauu \s - . 4 .
sm A mnA
a2 sin B sin C
2 sin (B+ C) Given two sides a and 6 and the included angle C.
Ftrs/ method: — Determining the angles first.
$(A + B) = J (180 - C) tan \(A - B) = ~-^ tan J (A + B).
A = J (A + B) + | (A - B) B = i (A + B) - $(A - B).
The third side, c, can now be determined by the sine proportion. Second method: — Determining the third side first.
2 sin i C /-- tan x = — - Va h.
a — b
a - b c = —
COS X
The angles A and B can now be found by the sine proportion
Area = J a b sin C. Given the three sides a, 6, and c.
Let s = >- (a + 6 -f c).
\| — (s — a) (s — b) (s — c) Then *tan \A = — —
*tan
J -i- (s - a) (« - 6) (.s - c)
- (s — a) (s — b) (s — c)
Area = -y/ s (s — a) (s — 6) (s — c)
* It will be noted that the numerator is the same in each case and that the denominators are quantities whose logarithms are known and hence two additional logarithmic operations over that required for one angle gives all three angles and a complete check on the entire compu- tation since A + B + c = 180°.
THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW
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WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $I.OO ON THE SEVENTH DAY OVERDUE.
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JUN 11 |948 |
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FEB 0 5 2001 |
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U.C. BERKELEY |
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LD 21-95m-7,'37 .. . ._ _ - __ |
YA 01422
7
UNIVERSITY OF CALIFORNIA LIBRARY