Report consisting of an expository account of the theory of modular forms and its application to number theory and analysis.

The abscissas and weights for Gaussian Quadrature of order N = 2 to 100,and N = 125, 150, 175, and 200 are given. The abscissas are given to twenty-four places and the error is estimated to be no more than 1 unit in the last place. The weights are given to twenty-three places and the error is estimated to be no more than 1 unit in the last place.

From Abstract: "Numerical results, in table form, on the required phases, the directive gain, the current excitations, the location of all the sidelobes and nulls, and the beamwidths for uniformly spaced optimum endfire arrays with equal sidelobes are given."

Description of a computer program for searching chemical information on magnetic tape.

From Abstract: "This document is the final report of research carried on in the Electron Physics Section of the National Bureau of Standards during the period from February 1, 1955 to March 1962 in developing an electron optical method for the visualization of low-pressure gas flow."

From Introduction: "The data are presented with the idea that an engineer who is making initial calculations on equipment for operation at cryogenic temperatures is more interested in obtaining quickly a definite figure that he in evaluating the experimental data given in several detailed reports on the same material. The graphs and tables presented here, consequently, represent an attempt by the authors to perform evaluation of data which have appeared in the literature and to present the design engineer with the result."

Abstract: "These data are presented by element in part I, and all 39,000 observed lines are given in order of wavelength in Part II." From Introduction: "In the beginning, most intensity data were reported on an arbitrary scale of 10 steps, weak lines being assigned an intensity of 1, and the strongest line intensity 10."

From Abstract: "Comparisons with other intensity measurements in individual spectra indicate that the National Bureau of Standards spectral-line intensities may have average errors of 20 percent, but first of all they provide uniform quantitative values for the seventy chemical elements commonly determined by spectrochemists. These data are presented by element in part I, and all 39,000 observed lines are given in order of wavelength in part II."

From Introduction: "This symposium focuses attention on the growing awareness of the necessity for developing and using better methods for characterizing solids. Many of the most interesting properties of solids depend directly upon these small concentrations of impurities and defects, and the illustration of this is a principal theme of this paper."

From Introduction: "The purpose of this work is to give the results of a detailed computation of antenna patterns in the ionosphere at VHF over a spherical earth."

From Abstract: "An introductory text gives a detailed description of each column of the solar ledger. Tables include counts of lines of each spectrum recorded in the identification column, leading lines in the first and second spectra, and summaries of molecules and elements present in the sun. About 73 percent of the lines are wholly or partially identified. Sixty-three elements are recorded as present."

From Introduction: "The present report describes the condition of all of the porcelain enamels after exposure for 3 yr."

From Introduction: "Following the guidelines established by this committee, several commercially developed precision connectors have appeared on the market which have led to the wide use of the precision coaxial lines as immittance standards. This paper has been prepared to alleviate this situation by providing graphs from which the electrical parameters of the lines may be determined rapidly and accurately."

"The definition of color, as a characteristics of light, and the basic principles of its measurement are given. The reduction of spectrophotometric data to three chromaticity coordinates by means of the three-function CIE standard observer system for colorimetry is described. Various methods of direct colorimetry, and visual and photoelectric methods of colorimetry by differences from material standards are treated" (p. 1).

From Introduction: "The purpose of this report is to present an analysis of time variations in: (1) the phase (relative to a stable phase reference) if a 9414 Mc/s signal transmitted over this path, referred to hereafter as single-path phase data; (2) the phase observed at one receiving antenna relative to that observed at an adjacent antenna, referred to as phase difference data; (3) atmospheric refractivity as recorded by a microwave refractometer located at the Haleakala terminal; (4) the wind velocity at both ends of the path, and (5) surface atmospheric refractivity measured at 5 stations located on or near the path."

Report combining National Bureau of Standards Monograph 27 with the references given in Supplement 1 (May 13, 1963) and issued as a single publication to assist users of this material. References concern the field of temperature measurement. These references were collected from two general sources: Scientific and technical literature and government reports. References are divided into a number of categories based on the type of instrument used. Some references to calibration of instruments and to scientific theories upon which temperature measurement is based are also presented.

Report discussing the transient magnetic behavior of a paramagnetic substance, after an initial disturbance, considered theoretically for a variety of situations in which the lattice temperature rises as a result of energy flow from the magnetic (electron spin) system. Next, the opposite extreme is considered - that in which the resonant and remaining modes are totally uncoupled. Finally, there is a consideration of the case of spins coupled only to the resonant phonons, which in turn are coupled to a constant temperature bath, whether this be the helium or the remaining modes.

From Introduction: "An improved high-temperature gage was needed, and in an attempt to fill this need an investigation was initiated in February 1954 in the Enameled Metals Laboratory at the National Bureau of Standards. The present Monograph constitutes a final summary on this program."

Reports discussing bands of common gases that have been tabulated and remeasured wherever necessary from 2 to 16 microns to obtain an accuracy of about 0.03 cm-1 throughout the region and to provide good calibrating points at frequent intervals. Some 600 rotation-vibration lines are illustrated in 20 spectrograms and wavenumbers are listed in companion tables with considerable intercomparison with worthy data obtained in other laboratories. The absorption bands were remeasured or calibrated by using either a precisely graduated grating circle or standard atomic lines with the fringe system formed by a Fabry-Perot interferometer. Characteristic features of the individual bands are discussed briefly and references to other publications are given. The substances used for calibration include H2O, CO2, CO, HCl, HBr, NH3, C2H2, CH4, N2O, and polystyrene film.

Report presenting a table of corrected optical pyrometer readings which enables optical pyrometer users to convert observed temperature immediately to the true temperature, if the effective emissivity of the material being observed is known. The table gives observed temperatures from 1,000 to 3,000ºK in increments of 5 degrees, from 3,000 to 5,000ºK in increments of 10 degrees, from 5,000 to 10,000ºK in increments of 50 degrees, and from 10,000 to 39,900ºK in increments of 100 degrees. For these, true temperatures are tabulated for 49 emissivities ranging from 0.02 to 0.98 in increments of 0.02.

From Abstract: "This paper gives a review of the concepts and operations involved in measuring the mass of an object. The importance of viewing measurement as a production process is emphasized and methods of evaluating process parameters are presented."

Report discussing discrete energy levels observed within certain crystals which are due to perturbations of energy levels of the free ion by an electrostatic field arising from the crystal lattice. The analytic procedures for determining the field from the charge configuration are given, and the resulting fields are classified according to their symmetry. After a general survey of group-theoretical ideas, the applicable groups are analyzed in detail, and characters appropriate for both integral and half-integral angular momenta of the free ion are tabulated. Text includes tabulations, equations, and matrices using Wigner and Racah coefficients.

From Abstract: "This report describes the use of an air-filled aluminum-alloy ionization chamber to determine the energy transported by a bremsstrahlung beam with maximum photon energy in the range 6 to 170 Mev. This report can be used to construct a replica chamber to determine its absolute calibration between 6 and 170 Mev under a variety of experimental conditions."

From Abstract: "In the past 60 years considerable data have been accumulated concerning the mechanical properties of copper and its alloys.It was felt that there was great need to adequately document these results in one publication. Therefore a unique type of compilation is presented. The compilation is divided into four parts. The first section is intended for quick reference use for those who are interested in average values. The second section includes data from most of the investigators who have published results on the mechanical properties of copper and its alloys. The third section is composed of tables classifying the investigations which were not in section two. The fourth section section lists, in alphabetical order, all references used."