The case began with a covered tube, not the famous hand
Röntgen’s 1895 report describes a discharge tube wrapped in black cardboard. A barium platinocyanide screen nearby still glowed. The cardboard blocked the tube’s ordinary light, so something else had to be reaching the screen. Placing different materials in its path turned the surprise into a series of comparisons.
The hand shadow was striking because bone and the surrounding tissue weaken the rays by different amounts. On its own it gave no wavelength and no account of how the rays were produced. The discovery came before the 1901 prize, and before the rays were identified as short-wavelength electromagnetic radiation.
Equal thickness did not mean equal transmission
Materials of the same thickness let through different amounts of the rays. The report compares stacked foil, several metals and glasses with different lead content, and Röntgen noted that density alone could not explain every result. These comparisons say more than the modern shorthand that dense objects look dark.
Whenever he could, Röntgen checked what he saw on the screen with photographic plates. A plate builds up its response over the exposure; a screen can be inspected at once. Neither response is automatically proportional to the incident intensity, so exposure, detector response and background must be stated before numbers are compared.
Sources: [1]
A magnet told the new rays apart from cathode rays
Inside the tube, a magnet deflected the cathode rays. Outside the tube, the new rays showed no comparable deflection in Röntgen’s tests. Bending the cathode rays moved the spot where they struck, and the apparent source of the X-rays moved with it. This tied X-ray production to the impact region without treating the emitted rays as the incoming electrons.
The report also describes unsuccessful searches for refraction and interference, and it suggests the rays might be longitudinal waves in the ether. That conjecture did not survive. The report shows what Röntgen observed and argued at the time, uncertainties included; it is not a list of conclusions that all held up.
Sources: [1]
The modern exponential law needs extra assumptions
Transmitted intensity falls exponentially with thickness for a narrow, single-energy beam in a uniform absorber, provided no scattered photons reach the detector. Thickness is measured along the ray, and the linear attenuation coefficient has units of inverse length. This is a modern explanatory model; Röntgen did not fit it to his data.
A discharge tube emits a broad spectrum, and the spectrum changes shape as it passes through matter. A single effective coefficient can then depend on thickness, and scattered radiation can fill in the shadow. A radiograph adds up the attenuation along each path, so it is neither a depth map nor a chemical-state spectrum.
How to read the report, and what came next
Read the covered-tube and material comparisons in sections 1–6 of the report, then the magnetic tests in sections 10–12. For each comparison, ask which competing explanation it argues against. The Laue and Bragg article takes up a later question: how a crystal can probe wavelength and the arrangement of atoms.
Sources: [1]