Abstract

The witch of Agnesi, y=ha²/(a²+x²) is of importance to physicists because it approximates the spectral energy distribution of spectral lines, particularly x-ray lines. This paper reviews the known properties of the witch such as graphical construction, parametric form of the equation and nth derivatives. New series for these derivatives are developed which are better adapted for use in correcting experimental curves by the method derived by the author. The points on the curve whose ordinates are $\frac{1}{4},\frac{1}{2}$ and $\frac{3}{4}$ of the maximum have special properties which are described.

© 1940 Optical Society of America

The Optical Properties of the Grating Interferometer

J. H. Schroeder and B. P. Ramsay
J. Opt. Soc. Am. 30(8) 355-361 (1940)

Spectral Luminosity Factors*

Kasson S. Gibson
J. Opt. Soc. Am. 30(2) 51-61 (1940)

The Dispersion of Magnetic Double Refraction in the Short Infra-Red Spectrum

Francis J. Davis
J. Opt. Soc. Am. 30(10) 488-494 (1940)

Visibility Through Haze and Smoke, and a Visibility Meter

G. D. Shallenberger and E. M. Little
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The Density of Silicate Glasses as a Function of Composition*

Maurice L. Huggins
J. Opt. Soc. Am. 30(9) 420-430 (1940)