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A cosmic ray is a high-energy charged particle propagating through space. Galactic cosmic-ray electrons emit synchrotron and inverse-Compton radiation, while cosmic-ray nuclei produce gamma rays through collisions with gas.

In modern terminology, a primary cosmic ray arriving at Earth's atmosphere is usually a proton or another atomic nucleus, with an Electron component as well. Atmospheric collisions generate secondary cosmic rays and air showers, including muons, Electrons and photons. A gamma ray can also initiate an air shower, although it is electrically neutral. Consequently, detecting atmospheric ionization does not establish that an incoming primary cosmic ray passed through the detector. Magnetic fields bend charged particles, while gamma rays provide a more direct directional connection to their sources.^[ref]

The Hess cosmic-ray balloon experiment asks how atmospheric shielding and separation from the ground affect ionization. Its power comes from changing the environment around an enclosed detector instead of identifying each incoming particle.

An original cosmic-ray altitude attenuation model illustrates how competing origins can produce a dip followed by a rise. It is a hypothetical absorption calculation, not a reconstruction or fit of Hess's measurements, and it excludes air shower production. Put $z$ for height above a flat ground surface and assume gas density $\rho (z)={\rho }_0{e}^{-z/H}$ with constant scale $H$. The overlying atmospheric mass per unit area isLet $G$ denote a ground-origin contribution attenuated by material below the chamber, and $E$ a downward extraterrestrial contribution attenuated by material above it. Assume constant attenuation mass columns ${\Lambda }_g,{\Lambda }_e>0$:These are rates at a fixed detector gas density, in arbitrary common units. The constant $B$ represents residual background. The equation $dI/dX=-I/\Lambda$ gives exponential function attenuation along each propagation direction. Thus $G$ decreases and $E$ increases as $z$ increases; their sum need not be monotone. The different arguments of the two exponential functions encode the entire geometric idea.

The figure chooses $H=8\mathrm{km}$, $G_0=0.8$, $E_{\mathrm{top}}=6$, $B=0.15$, ${\Lambda }_g=0.08X_0$ and ${\Lambda }_e=0.45X_0$, all for illustration. Differentiation givesThe minimum occurs where $E/{\Lambda }_e=G/{\Lambda }_g$, at approximately $1.13\mathrm{km}$ for these invented parameters. At $6\mathrm{km}$ the fixed-gas response is about $1.41$ times its ground value, but multiplying by $\rho (z)/{\rho }_0$ gives an uncorrected vented-chamber response of only $0.66$ times its ground value. A real increase in radiation response per gas mass can therefore be hidden by a decrease in target gas density. This is the reason to distinguish radiation from the amount of gas being irradiated.

The model treats propagation as attenuation without generating new particles. Real primary cosmic rays interact, redistribute energy and produce air showers; an atmospheric profile need not follow either simple exponential function. The model also holds backgrounds and detector response fixed. Its value is to expose the sign of competing effects and the density confound, while Hess's experimental argument depends on his actual comparisons and instrument limitations.

Victor Franz Hess's 1912 series used two sealed, 3-mm-walled ionization chambers with Theodor Wulf's fiber electrometers. Karl Bergwitz suggested internal plating; Günther & Tegetmeyer improved focusing. Basket-mounted ground comparisons, insulation-loss measurements, simultaneous detectors and barograph-derived heights supplied checks. The highest flight reached 5350 m; its comparisons came from Vienna and after landing, without a launch-site baseline.^[ref]

A third, thin-walled chamber admitted ambient air. Hess multiplied its readings by $750/b$, with pressure $b$ in millimeters of mercury, warning that vessel-wall contributions might violate this scaling. He recorded outside temperature but applied no absolute-temperature correction. Night flights, an eclipse and weather observations constrained alternatives to radiation from above; the eclipse argument addressed directly propagating solar radiation.^[ref]

The electrometers read gradual electric potential loss caused by continuing air ionization. The low-altitude dip and strong high-altitude rise favored an extraterrestrial contribution, without measuring proton composition.^[ref] An ionization chamber integrates electric charge: one energetic particle may create many ion pairs, several particles may contribute to one reading, and a photon can create charged particles in the gas or walls. A voltage-loss reading is therefore neither a count of primary cosmic rays nor a chemical analysis of them.

Domenico Pacini supplied independent evidence: in June 1911 he compared a copper-box-enclosed electroscope at the sea surface and 3 m underwater, more than 300 m offshore above an 8-m-deep seabed. Reduced underwater ionization, stable electrical loss between runs, and a lake comparison supported an external contribution independent of soil radioactive decay. Water provided shielding; this established a different constraint from Hess's altitude comparison.^[ref]

An elementary ionization-chamber charge-loss model makes the inference explicit. Let a positively charged electrode and its electrometer have effective capacitance $C$, electric potential difference $U$, and enclosed gas volume $\mathcal{V}$. Assume constant $C$, a short enough interval that collection conditions remain stable, and no multiplication of charge in the gas. If ionization produces $q$ ion pairs per unit volume per unit time and a fraction $\eta$ is collected, thenHere $e$ is the elementary charge and $I_{\mathrm{leak}}$ is the parasitic electric current through imperfect insulation. Each fully collected ion pair transfers one elementary charge through the measuring circuit; counting its two opposite carriers as two transfers would introduce a factor-of-two error. The relation follows from charge conservation, rather than from a model of the incoming particle's identity.

For an invented example, take $C=2.00\mathrm{pF}$, $\mathcal{V}=2.00\mathrm{L}$, $\eta =1$, a measured fall of $6.00\mathrm{V}{\mathrm{h}}^{-1}$, and a separately determined leakage-equivalent fall of $0.60\mathrm{V}{\mathrm{h}}^{-1}$. The leakage-subtracted fall is $5.40\mathrm{V}{\mathrm{h}}^{-1}$, soThis is about $1.87\times 10^4$ collected ion pairs per second throughout the chamber, not that many primary cosmic rays. Unknown collection losses make $\eta <1$ another uncertainty; changes in capacitance would require differentiating $Q=CU$ with both factors variable.

Gas density is a separate issue. Under a fixed radiation field, fixed gas composition and approximately constant energy deposited per unit gas mass, the volume-based ionization rate scales as $q\propto \rho$. For a vented ionization chamber, the ideal gas law gives the illustrative correctionwhere $T$ is absolute temperature. A pressure-only correction presumes equal temperature. A sealed rigid chamber instead fixes gas number density as it rises: its internal pressure may change with temperature without losing gas. This does not make its insulation, electrometer calibration or collection efficiency insensitive to temperature. Nor can dividing by gas density correct arbitrary radiation from the vessel walls or changing particle energies. Those are distinct effects, not a universal normalization recipe.

Here a primary cosmic ray means a particle arriving from space before its first atmospheric collision.

A secondary cosmic ray here is a particle produced by an atmospheric interaction of a primary cosmic ray or its descendants. A muon at ground level need not have traveled from the original astronomical source.