The observation comes before the picture
A discharge tube and a spectroscope measure where spectral lines fall and how bright they are. They do not follow an electron around a nucleus. The same wavelengths return each time a sample is prepared, and a theory has to explain why atomic energy differences are so reproducible. The regular pattern of hydrogen lines was already known, so it was a test for any theory, not something found by drawing quantized circles.
Bohr’s 1913 paper starts from a conflict. Rutherford’s nuclear atom explains scattering, but in ordinary electrodynamics an orbiting electron is accelerating and must radiate. Mechanical orbits alone explain neither why atoms are stable nor why they have one definite size. A working theory has to account for stable atoms and for their characteristic radiation. Read Part I, the introduction and §1, with those two requirements in mind.
Read the evidence: N. Bohr (1913), On the Constitution of Atoms and Molecules, Part I, §§1–3
The decisive change was the rule for radiation
Bohr introduced stationary states and tied the frequency of emitted light to the energy difference between two of them. In general that frequency differs from the electron’s orbital frequency. Bohr broke with classical radiation theory exactly where the spectrum needed a new explanation.
In the relation below, the initial state has the higher energy, the frequency is positive, and the Planck constant converts frequency to energy. One set of states, through the differences between their energies, can account for many lines at once. That is a tighter test than giving each observed wavelength its own unrelated oscillator.
Read the evidence: N. Bohr (1913), On the Constitution of Atoms and Molecules, Part I, §§1–3
What the agreement shows, and what it does not
Part I, §2 compares the theory with the hydrogen spectrum and discusses lines attributed to helium. One electron gives an especially sharp test, because the Coulomb force fixes the scale and the pattern of the lines together. Matching a series of lines supports the energy levels and the transition rule. It does not, on its own, show that electrons follow the proposed circular paths.
The 1922 Nobel Prize recognized Bohr’s investigation of atomic structure and radiation, not every mechanical detail of the 1913 model. Modern orbital probability densities and the historical orbit picture are different descriptions of the atom. The hydrogen Lab lets you compare states and spectra; it does not reconstruct a 1913 measurement.
Read the evidence: N. Bohr (1913), On the Constitution of Atoms and Molecules, Part I, §§1–3Nobel Prize in Physics 1922 — official award record
A second kind of measurement checks the same energies
A spectrum measures energy that atoms give off as light. Electron-impact experiments measure something else: how much kinetic energy an atom can take from an incoming electron. If the two methods agree, the same energy levels appear in two different observables, and an explanation that covers only light is no longer enough. The next article follows that link through the work of Franck and Hertz.
In the linked Lab, note which transition produced each line, and treat its position separately from its displayed width and brightness. A hydrogen teaching model cannot give you a historical absolute intensity calibration, the many-electron spectrum of mercury or a test of the Lamb shift. Each of those needs its own apparatus assumptions and evidence.
Read the evidence: N. Bohr (1913), On the Constitution of Atoms and Molecules, Part I, §§1–3