﻿JOURNAL 
  

  

  OF 
  THE 
  

  

  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  

  

  Vol.. 
  12 
  November 
  19, 
  1922 
  No. 
  19 
  

  

  MATHEMATICS. 
  — 
  Values 
  of 
  sine 
  6 
  and 
  cosine 
  d 
  to 
  jj 
  places 
  of 
  decimals 
  

   for 
  various 
  values 
  of 
  9 
  expressed 
  in 
  sexagesimal 
  seconds.^ 
  C. 
  B. 
  

   Van 
  Orstrand 
  and 
  Marvin 
  A. 
  Shoultes, 
  Geological 
  Survey. 
  

  

  One 
  hundred 
  preliminary 
  values 
  of 
  both 
  the 
  sine 
  and 
  cosine 
  were 
  

   computed 
  several 
  years 
  ago 
  in 
  collaboration 
  with 
  the 
  late 
  Dr. 
  George 
  

   F. 
  Becker 
  with 
  the 
  object 
  in 
  view 
  of 
  constructing 
  complete 
  tables 
  of 
  

   the 
  natural 
  values 
  of 
  the 
  six 
  trigonometric 
  functions. 
  In 
  the 
  mean- 
  

   time 
  Professor 
  J. 
  Peters- 
  published 
  870 
  values 
  of 
  the 
  sine, 
  and 
  cosine, 
  

   to 
  21 
  places 
  of 
  decimals, 
  the 
  interval 
  of 
  the 
  argument 
  for 
  the 
  first 
  

   10' 
  being 
  1", 
  and 
  for 
  the 
  remainder 
  of 
  the 
  semiquadrant, 
  10'. 
  During 
  

   the 
  interval 
  1911-18, 
  the 
  elaborate 
  tables 
  to 
  15 
  places 
  of 
  decimals 
  by 
  

   Professor 
  H. 
  Andoyer^ 
  of 
  the 
  University 
  of 
  Paris 
  were 
  published. 
  

   An 
  unnumbered 
  volume 
  contains 
  values 
  of 
  the 
  logarithmic 
  sines, 
  

   cosines, 
  tangents, 
  and 
  cotangents; 
  and 
  in 
  volumes 
  1 
  to 
  3, 
  respectively, 
  

   are 
  tabulated 
  natural 
  sines 
  and 
  cosines; 
  tangents 
  and 
  cotangents; 
  

   secants 
  and 
  cosecants. 
  The 
  interval 
  of 
  the 
  argument 
  in 
  all 
  of 
  the 
  

   tables 
  is 
  10". 
  Volume 
  1 
  contains 
  also 
  natural 
  values 
  of 
  each 
  of 
  the 
  

   six 
  trigonometric 
  functions 
  to 
  20 
  decimals 
  for 
  arguments 
  expressed 
  in 
  

   hundredths 
  of 
  a 
  quadrant. 
  Andoyer's 
  tables 
  are 
  the 
  first 
  to 
  replace 
  

   the 
  great 
  work 
  of 
  George 
  Joachim 
  Rheticus 
  consisting 
  of 
  the 
  Opus 
  

   Palatinum, 
  published 
  in 
  1596 
  and 
  containing 
  10 
  place 
  values 
  at 
  in- 
  

   tervals 
  of 
  10" 
  for 
  all 
  of 
  the 
  trigonometric 
  functions 
  ; 
  and 
  the 
  Thesaurus 
  

   Mathematicus 
  which 
  was 
  published 
  in 
  1613 
  and 
  contains 
  15 
  place 
  

   values 
  of 
  the 
  natural 
  sine 
  at 
  intervals 
  of 
  10" 
  throughout 
  the 
  entire 
  

   quadrant, 
  and 
  in 
  addition, 
  values 
  of 
  the 
  same 
  function 
  to 
  the 
  same 
  

  

  1 
  Published 
  with 
  the 
  permission 
  of 
  the 
  Director 
  of 
  the 
  U. 
  S. 
  Geological 
  Survey. 
  Received 
  

   June 
  30, 
  1922. 
  

  

  - 
  Peters. 
  J. 
  Einundzwanzigstellige 
  Werte 
  der 
  Funktionen 
  Sinus 
  und 
  Cosinus 
  zur 
  gen- 
  

   auen 
  Berechnung 
  von 
  zwanzigstelligen 
  Werten 
  sdmtlicher 
  trigonometrischen 
  Funktionen 
  eines 
  

   beliebigen 
  Arguments 
  sowie 
  ihrer 
  Logarithmen. 
  Abh. 
  Konigl. 
  Preuss. 
  Akad. 
  Wiss. 
  1-54. 
  

   1911. 
  

  

  3 
  Andoyer, 
  H. 
  Nouvelles 
  tables 
  trigonometriques 
  fondamentales 
  (logarithmes) 
  ; 
  same 
  

   (valeurs 
  naturelles). 
  •■■ 
  

  

  423 
  

  

  