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Full Article | PDF Article**Journal of the Optical Society of America**- Vol. 2,
- Issue 1,
- pp. 18-22
- (1919)
- •doi: 10.1364/JOSA.2.000018

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- The symbols are somewhat different from those used at the meeting, but the essential relation intended to be represented is the same, and more clearly expressed. This equation was first obtained by graphic transformations of the Planck equation.

- , Fig. 2, p. 476. Values have been scaled from the large original of figure, kindly loaned by Dr. Coblentz for this purpose.

- Merriman, Method of Least Squares, p. 25, 8th Ed. Revised, 1910.

- Since the meeting, the author has obtained (December 31, 1918) what appears to him to be a rigorous integration showing that the Stefan law may be derived mathematically from equation (1). In this connection he desires to acknowledge with thanks the advice and suggestions of his associate Mr. E. P. T. Tyndall, with whom he has discussed the problem of this integration.

- , Fig. 2, T = 1596.5 K.

- .

- , Fig. 2, T = 1596.5 K.

Merriman, Method of Least Squares, p. 25, 8th Ed. Revised, 1910.

The symbols are somewhat different from those used at the meeting, but the essential relation intended to be represented is the same, and more clearly expressed. This equation was first obtained by graphic transformations of the Planck equation.

, Fig. 2, p. 476. Values have been scaled from the large original of figure, kindly loaned by Dr. Coblentz for this purpose.

Merriman, Method of Least Squares, p. 25, 8th Ed. Revised, 1910.

Since the meeting, the author has obtained (December 31, 1918) what appears to him to be a rigorous integration showing that the Stefan law may be derived mathematically from equation (1). In this connection he desires to acknowledge with thanks the advice and suggestions of his associate Mr. E. P. T. Tyndall, with whom he has discussed the problem of this integration.

, Fig. 2, T = 1596.5 K.

.

, Fig. 2, T = 1596.5 K.

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$${\text{E}}_{\mathrm{\lambda}}={\text{D}}_{1}{\text{T}}^{5}{\text{e}}^{-{\text{D}}_{2}\hspace{0.17em}[{\text{A}}^{-{\scriptstyle \frac{1}{3}}}-{(\mathrm{\lambda}\text{T})}^{-{\scriptstyle \frac{1}{3}}}{]}^{2}}$$

$${\text{E}}_{\mathrm{\lambda}\text{r}}\equiv \frac{{\text{E}}_{\mathrm{\lambda}}}{{\text{E}}_{\text{m}}}{\text{e}}^{-{\text{D}}_{2}[{\text{A}}^{-{\scriptstyle \frac{1}{3}}}-{(\mathrm{\lambda}\text{T})}^{-{\scriptstyle \frac{1}{3}}}{]}^{2}}$$

$$\overline{\mathrm{\lambda}}\text{T}={\left(\frac{1}{{\text{A}}^{-{\scriptstyle \frac{1}{3}}}\pm \sqrt{\frac{{\text{log}}_{\text{e}}\hspace{0.17em}{\text{E}}_{\mathrm{\lambda}\text{r}}}{-{\text{D}}_{2}}}}\right)}^{3}$$

$$\mathrm{\lambda}={\mathrm{\lambda}}_{\text{m}}=\frac{\text{A}}{\text{T}}$$

$${\mathrm{\lambda}}_{\text{m}}=\frac{8}{{\left(\sqrt[3]{\frac{1}{{\mathrm{\lambda}}_{1}}}+\sqrt[3]{\frac{1}{{\mathrm{\lambda}}_{2}}}\right)}^{3}}$$

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