COMPUTATIOK OF MATHEMATICAL TABLES The following statement' with reference to a project for the computation of mathematical tables under the Work Projects Administration may be of interest to the readers of The Journal o j Physical Chemistry: A Project for the Computation of Mathematical Tables, sponsored by Dr. Lyman J. Briggs, Director of the National Bureau of Standards, is being conducted by the Work Projects Administration for the City of New York. The Project has been in operation since January 1, 1938, under the technical supervision of Dr. Arnold K. Lowan. An agenda of the Project, listing the tables completed, in progress, and under consideration, is given below: Completed tables
1. A table of exponentials for the following ranges, intervals, and number of decimals: Range
-2.5000 to 1.0000 to 2.500 to 5.00 to
1.oooo 2.5000 5.000 10.00
Interm1
Number of decimals
o.oO01 o.Ooo1 0.001 0.01
18
15 15 12
2. A table of sines and cosines for the range from 0 to 25 radians a t intervals of to eight places of decimals. 3. A table of the first ten powers of the integers from 1 to 1000. Tables i n progress
A. Computations completed; manuscripts in process of preparation 1. A table of the functions-
for the range between 0 and 2 a t intervals of lo-' to nine places of decimals. 2. A table of the functions defined in paragraph 1 for the range between 0 and 10 a t intervals of 10-8 to nine significant figures. 3. A table of circular and hyperbolic sines and cosines for the range between 0 and 2 a t intervals of 10-4. 4. A table of natural logarithms of integers from 0 to 100,000 to sixteen places of decimals. 5. A table of natural logarithms of decimal numbers from O.oo00 to 10.0000 a t intervals of 10-4 to sixteen places of decimals.
Issued July 1, 1939.
1099
1188
COMPUTATION OF MATHEMATICAL TABLES
6. A series of physical tables: (a) G = l / c p , for @ ranging from 0 to 0.9997 a t various intervals. This table also includes certain functions depending on G . ( b ) Table of Nh
P
- I)-'
2rch-4($
for h ranging between 0.25 and 10 microns a t various intervals, and for T = 1O00, 1500, 2000, 2500, 3000, 3500, 8000°K. (c) Table of
Jx
- I)-'
clh-5(eg
i
for T = lO00"K., ranging from 0.5 to 20 microns a t various intervals. ( d ) Table of
and Jo-r =
1'
JI dy
for T = 1000'K. Range of h the same as for J A . (e) Table of the ratios
Range for A same as under paragraph c.
B. Computations in progress 7. Table of the probability functions
for z ranging from 0 to 1 a t intervals of 10-4 and from 1 to 6 a t intervals of 108. Table of the probability functions
for z ranging between 0 and 1a t intervals of 10-4 and from 1 to 8.4 a t intervals of 10-8. 9, Table of Bessel functions J&) and J I ( z ) for complex arguments, z = re", where T ranges from 0 to 10 a t intervals of 0.01 and 0 ranges from 0 to 90" a t intervals of 5". 10. Table of tan z and cot z for x ranging between 0 and 2 a t intervals of 10-4. 11. Table of the integrals
l'&
sin nrz d z
for n = 0, 1, 2, 3,
. . . 100 and IC
and
1'
ZL cos nu2 dz
= 0, 1, 2, 3, 4, 5 .
COMPUTATION OF MATHEMATICAL TABLES
1101
Tables under consideration 1. A 12-decimal place table of inverse tangents to radian measure. The table will include the following ranges: from 0 to 3 a t intervals of 10-8; from 3 to 10 a t intervals of lo-*; from 10 to 40 a t intervals of 10-1; from 40 to 100 a t intervals of 1; and from 100 to 1000 a t intervals of 10. 2. Table of Bessel functions J * i / a ( z ) , J * l / s ( z ) ,J * I / , ( z ) Y , & ) , Y l ( z ) ,and K*i/a(z), for ranges and intervals similar to those for J o ( z )and Jl(z). 3. Table of
for z ranging between 0 and 10 a t intervals of 0.01 and for n = 1, 2, 3, . . . 10. 4. Table of gamma functions for complex arguments a bi, where a and b range from 0 to 5 a t intervals of 0.05. 5 . Table of elliptic functions for arguments z = z i y , where z and y range from 0 to r / 2 a t intervals of 0.01. 6 . Table of the function 1 zy A(2,Y) = -
+
+
-
1-2
where z ranges from 0 to A a t intervals of 0.01 and y ranges from 0 to 4 a t intervals of 0.01. 7. Table of temperature and density of stars, for “point-source” models. The directors of the Project are anxious to hear from scientific colleagues concerning work in progress elsewhere, as well a8 concerning suggestions for new tables. All suggestions will receive careful consideration. Communications concerning new tables or work in progress elsewhere should be addressed to Dr. Arnold N. Lowan, Chief Project Supervisor, Proj.ect for the Computation of Mathematical Tables, 475 Tenth Avenue, New York City, New York.
