#### Abstract

An investigation at sea level of cosmic-ray showers with sizes from 5×${10}^{5}$ to over ${10}^{9}$ particles is described. The core locations, arrival directions, and particle density distributions of several thousand showers whose cores landed within an area of ${10}^{5}$ ${\mathrm{m}}^{2}$ were determined by the techniques of fast-timing and density sampling. The most important results are as follows: (1) The existence of primary particles with energies greater than ${10}^{18}$ ev is established by the observation of one shower with more than ${10}^{9}$ particles. (2) The function $f\left(r\right)=0.45\left(\frac{N}{{{R}_{0}}^{2}}\right){r}^{-0.7\mathrm{}}{\mathrm{}(1+r)\mathrm{}}^{-3.2\mathrm{}}$, where $r=\frac{R}{{R}_{0}}$ and ${R}_{0}=79\mathrm{}$ m, describes the lateral distribution of particles at distances in the range $50\mathrm{m}R\mathrm{}400\mathrm{}\mathrm{m}$ and for showers with sizes in the range $5\times {10}^{5}<N<\mathrm{}{10}^{8}$. (3) At distances greater than 50 m from the core the density fluctuations in individual showers have a Poisson distribution. (4) The size and zenith angle distribution can be represented by the formula $s(N,x)={s}_{0}{\left(\frac{{10}^{6}}{N}\right)}^{\Gamma +1\mathrm{}}\mathrm{exp}[-\frac{(x-{x}_{0})}{\Lambda}]$, where $x={x}_{0}sec\theta $, ${x}_{0}=1040\mathrm{}$ g ${\mathrm{cm}}^{-2\mathrm{}}$, ${s}_{0}=(6.6\mathrm{}\pm 1.0)\times {10}^{-8\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{sec}}^{-1\mathrm{}}$ ${\mathrm{sterad}}^{-1\mathrm{}}$, $\Gamma =1.9\mathrm{}\pm 0.1$, $\Lambda =(113\mathrm{}\pm 9)$ g ${\mathrm{cm}}^{-2\mathrm{}}$, ${x}_{0}<x<\mathrm{}1.3\mathrm{}{x}_{0}$, and $7\times {10}^{5}<N<\mathrm{}7\mathrm{}\times {10}^{8}$. (5) No evidence is found of anisotropy in the arrival directions or of a break in the energy spectrum of the primaries up to the largest energies observed. (6) Assuming a specific model for shower development and taking into account fluctuations in the depth of the first interaction, the integral energy spectrum of the primaries is $J\left(E\right)={J}_{0}{\left(\frac{{10}^{15}}{E}\right)}^{\gamma}$, where ${J}_{0}=(8.1\mathrm{}\pm 3.1)\times {10}^{-11\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{sec}}^{-1\mathrm{}}$ ${\mathrm{sterad}}^{-1\mathrm{}}$, $\gamma =2.17\mathrm{}\pm 0.1$, and $3\times {10}^{15}\mathrm{ev}E\mathrm{}{10}^{18}\mathrm{ev}$.

DOI: http://dx.doi.org/10.1103/PhysRev.122.637

- Received 13 December 1960
- Published in the issue dated April 1961

© 1961 The American Physical Society