The Analysis of the Cosmic-Ray Absorption Curve

A method of solving the integral equation of absorption f(s)=∫0^∞φ(μ)exp(-μs)dμ is developed which gives the function φ as a series of Laguerre orthogonal functions, whose coefficients are determined from the power series expansion of a function $F(x)$. This in turn is simply related to the given function $f(s)$; in case the latter is given numerically, the expansion may be accomplished by the method of least squares. The function φ (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 μ=0.06 and one at μ=0.6 (meterswater)^-1. The minimum of intensity occurs at μ=0.25, or 1μ=4 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.