The Analysis of the Cosmic-Ray Absorption Curve

A method of solving the integral equation of absorption $f\left(s\right)=\int 0^{\infty }\phi \left(\mu \right)\exp (-\mu s)d\mu$ is developed which gives the function $\phi$ as a series of Laguerre orthogonal functions, whose coefficients are determined from the power series expansion of a function $F\left(x\right)\mathrm{}$. This in turn is simply related to the given function $f\left(s\right)\mathrm{}$; in case the latter is given numerically, the expansion may be accomplished by the method of least squares. The function $\phi$ (called the absorption coefficient spectrum of the radiation) is determined for cosmic rays at several altitudes and latitudes. In each case there are two maxima of intensity, one at $\mu =0.06\mathrm{}$ and one at $\mu =0.6\mathrm{}$ ${\mathrm{}\left(\mathrm{meters}\mathrm{water}\right)\mathrm{}}^{-1\mathrm{}}$. The minimum of intensity occurs at $\mu =0.25\mathrm{}$, or $\frac{1}{\mu }=4\mathrm{}$ m water=30 cm mercury. This is also the range of the rays responsible for the inflection points of the Compton-Stephenson high altitude curve, but no consistent explanation of the correlation is found. The spectrum also shows a range of negative intensity, indicating the presence of secondary radiations. In no case is there any evidence for a line structure of the spectrum. No basis is found for restricting the assumption of exponential absorption to apply only to equatorial data; neither is any evidence discovered which makes the assumption a necessary one at any latitude. Only data on the absorption in air and water are considered; several points are indicated at which the existing data require extension.