SECTION I: THE BLACKBODY PROBLEM

Chapter
1. Thermal radiation and the blackbody problem

1.1 Towards a solution to the blackbody problem

1.2 Planck and the blackbody problem

1.3 The work of the experimentalists

1.4 Thermal laws from dimensional analysis

1.5 Transition and new beginnings

SECTION II: THEORETICAL AND NUMERICAL MATTERS

Chapter
2. Theoretical developments

2.1 Spectral representations

2.2 Two important special functions

2.2.1 Polylogarithms

2.2.2 The Lambert W function

2.3 Two common spectral scales used to represent blackbody radiation

2.4 Other spectral scale representations

2.5 Ephemeral spectral peaks

2.6 Logarithmic spectral scales

2.7 The radiometric and actinometric cases

2.8 Normalized spectral exitance

2.9 The Stefan?Boltzmann law

2.9.1 The traditional approach

2.9.2 A polylogarithmic approach

2.10 Fractional functions of the ?rst kind

2.11 Fractional functions of other kinds

2.12 Centroid and median wavelengths

2.13 The standard probability distribution and cumulative probability distribution functions for blackbody radiation

2.14 Infrared, visible, and ultraviolet components in the spectral distribution of blackbody radiation

Chapter
3. Computational and numerical developments

3.1 Approximations to the spectral exitance

3.1.1 The laws of Wien and Rayleigh?Jeans

3.1.2 Extended Wien and Rayleigh?Jeans approximations

3.1.3 Polynomial interpolation and logarithmic correction factors

3.1.4 Laurent polynomials and non-rational approximations of Erminy

3.2 Computation of the fractional function of the ?rst kind

3.2.1 Series expansion methods

3.2.1.1 Large arguments

3.2.1.2 Small arguments

3.2.1.3 Division point

3.2.2 Approximation of the integrand ?rst

3.2.3 Gauss?Laguerre and generalized Gauss?Laguerre quadrature

3.2.4 Asymptotic expansion

3.2.5 Other methods

Chapter
4. Blackbody sources and basic radiometry

4.1 Blackbody sources

4.2 Goniometric characteristics of surfaces

4.3 Inverse square law

4.4 Extended source radiometry

4.5 Radiometry of images

4.6 Example problem

SECTION III: COMPUTATIONAL AIDS

Chapter
5. Nomograms and graphs used for thermal radiation calculations

5.1 Nomograms

5.2 Graphs

5.3 The legacy of graphical aids

Chapter
6. Slide rules used for thermal radiation calculations

6.1 Three early slide rules from Germany, England, and the United States

6.1.1 The System Czerny rule

6.1.2 General Electric Radiation Calculators

6.1.3 The Admiralty rule

6.2 Two mysterious rules

6.3 The DENEM Nuclear Radiation Calculator

6.4 A circular slide rule

6.5 "Do-it-yourself" slide rules and charts

6.6 Radiation slide charts from the 1960s

6.6.1 The Block rule

6.6.2 The Infrared Slide Rule

6.7 The last of the real slide rules

Chapter
7. Tables used for thermal radiation calculations

7.1 Notational conventions used for tables

7.2 From the earliest tables to 1939

7.3 Tables from 1940 to 1954

7.4 Tables from 1955 onwards

7.5 Tables then and now

Chapter
8. Beyond the analogue aids of old

Appendix A. Miscellaneous mathematical results

A.1 Series expansion for the Lambert W function

A.2 Bernoulli numbers and the Riemann zeta function

A.3 Number of real roots to an equation

Appendix B. Computer program for the fractional function of the ?rst kind

Appendix C. Chronological table of events

References

Reference Author Index

Index