Certainly, I can provide a brief overview of the steps involved in replicating Compton's experiment using language that might have been used in the early 20th century:
Obtain a source of X-rays: The first step in this undertaking shall be to secure an apparatus capable of generating a beam of X-rays of suitable energy and intensity. This may take the form of a Crookes tube, an X-ray machine, or other such device capable of producing a beam of penetrating radiation.
Choose a scattering medium: The next step shall be to select a suitable material to serve as the scattering medium. This material should possess a high electron density and a large atomic number, so as to effectively scatter the X-rays. Commonly employed materials include graphite, aluminum, copper, and lead.
Set up the experimental apparatus: The apparatus shall be arranged such that the X-ray beam is directed at the scattering medium, and the scattered X-rays are detected using a suitable detector, such as a Geiger-Müller tube or photographic plate.
Conduct the experiment: The experiment shall proceed by measuring the energy and intensity of the scattered X-rays at various scattering angles, and comparing the results to theoretical predictions based on the principles of Compton scattering.
Analyze the results: The results of the experiment shall be analyzed by calculating the energy and momentum of the scattered X-rays, as well as the scattering angle and other relevant parameters, and comparing them to theoretical predictions. Any discrepancies between the experimental and theoretical results shall be carefully scrutinized and interpreted in the light of existing physical theories.
Overall, this undertaking shall require the employment of precision instruments and the exercise of great care and patience, in order to elucidate the nature of X-ray scattering and the properties of matter.