Natural Trigonometric Functions [math tables]

343 Pages·1931·17.162 MB·English

by  H. Ives

NATURAL TRIGONOMETRIC FUNCTIONS
WORKS OF
HOWARD CHAPIN
IVES, C.E.
PUBLISHEDBY
JOHN WILEY & SONS, Inc.
NaturalTrigonometricFunctions.
To seven decimal places for every ten seconds of
arc,togetherwith manyspecial tables. 329pages
f>2by92 Cloth
HighwayCurves.
Full text and comprehensive tables 402 pag ^
4 byGJ 50 figures Flexiblebinding.
Surveying Manual.
Designed for the Use of First-vear Students
in Surveying and Especially for the L'se of Non-
Civil Engineering Students Second edition
29f> pages 1 by 64 ">."> figures Flexible bind-
in*?
SevenPlace NaturalTrigonometricalFunctions.
Together with m.im miscellaneous tables and
appendices on the adjustment ot the engineer's
transit and level, area computation, \ertic,d
curves, simple curves, and determination of
latitude, longitude and azimuth 222 pane--
4 by(\i Flexible binding
TheAdjustmentsoftheEngineer'sTransitandLevel.
Sfiegcuorensd BEodiatridosn 1"> pages 4J by f\] 11
m
W. IT. SEARLES AND II. C. IVES
Field Engineering.
A Handbook of the Theory and Practice of Rail-
way Surveying, Location, and Construetion,
designed for Classroom, Field, and Olhce I se,
and containing a large number of Kseful Tables,
<>riginal and Selected B\ the late \V 11 Krjuhs
Twentieth Edition, Revised and Cnlaiged b\
Howard ("hapin I\es, C10
Vol. I. Text. 342 pages. 4 by 6^ l^i figure-
Flexible binding
Vol. II. Tables. 3S6 pages 4 by (>] FloMblo
binding
Complete. TextandTables. Flexiblebinding
Mathematical Tables.
nHceeprrinmgt,e"dwiftrhomAd<Sehatrulnrss,aCnodmpIi\lees'd a"nFdnAIrdraInng^eid-
by Howard Chapin Ives 1^0 pages t bv t>^
Flexible binding
NATURAL TRIGONOMETRIC FUNCTIONS
TO
SEVEN DECIMAL PLACES
FOR
EVERY TEN SECONDS OF ARC
TOGETHER WITH
MISCELLANEOUS TABLES
BY
HOWARD CHAP1N
IVES, C.E.
CONSULTING ENOINLEh
NEW YORK
JOHN WILEY &
SONS, INC.
LONDON: CHAPMAN & HALL, LIMITED
1931
COPYRIGHT, 1931,
BY HOWARD CHAPIN IVES
All Rights Reserved
Thisbookor anypartthereofmustnot
be reproduced ^n any form wxthout
thewrittenpermissionofthepublisher*
Printed in U. S. A.
Printing CompositionandPlates Binding
.H.BGOFSLTSOONN co. TECHNICACLAMCBORMIPDOGSEITION co. STANHOBPOSETOBNINDERY
PREFACE
This book is divided into two parts: The first gives 270 pages of the seven
place natural sines, cosines, tangents and cotangents to ten seconds together
with proportional parts to seconds. The second part consists of a variety of
miscellaneous tables, information and examples especially adapted to subdi-
vision work. The result is that a large amount of material previously scattered
or not available is made accessible.
Much thought was spent on selection and arrangement of the material.
Several specimen pages were set up before a final selection was made.
In the case of cotangents which change rapidly, the differences in some
cases appear to change irregularly. This is due to the fact that all quantities
are given to the nearest place and were checked by fifteen place tables.
The original manuscript was twice checked. The pages when set in type
were proof read four times and by three different persons. It is confidently
believed that the book is unusually accurate.
Thanks are due: Mr. Herbert E. Hayes, C. E. who checked the entire
manuscript and who also gave valuable suggestions and advice; Mr. Alfred B.
Osborne, C. E. Industrial Engineer for Larkin Co., Inc., Buffalo, N. Y., who
read the entire proof besides giving expert advice; and to the publishers, com-
positors, printers and binders who have spared no thought, time or expense in
the endeavor.
H. C. I.

CONTENTS
PART
I
PAGES
TABLE 1. SINES, COSINES, TANGENTS AND COTANGENTS 1-270
PART
II
MISCELLANEOUS TABLES
TABLE 2. LENGTH OF ARC TO RADIUS UNITY 273
TABLE 3. COEFFICIENT K FOR CENTRAL ANGLES OF CERTAIN CURVES 291
TABLE 4. RADII FROM ARC DEFINITION 292
TABLE 5. RADII FROM CHORD DEFINITION 295
TABLE 6. CURVES WITH EVEN FOOT RADII 300
TABLE 7. FUNCTIONS OF A 1 CURVE 302
TABLE 8. CORRECTIONS TO TANGENT DISTANCES 308
TABLE 9. CORRECTIONS TO EXTERNAL DISTANCES 308
TABLE 10. TRIGONOMETRIC FUNCTIONS, FORMULASANDSOLUTIONOFTRIANGLES 309
TABLE 11. MINUTES IN DECIMALS OF A DEGREE 318
TABLE 12. UNITS OF LENGTH AND OF SURFACE 319
DEFINITIONS AND THEORY 320
USE OF TABLES 326

SINES, COSINES, TANGENTS AND COTANGENTS
00'
89 50'
TEN SECOND NATURAL TRIGONOMETRIC FUNCTIONS
010'
89 40'