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In his 1910 paper "On the Scattering of rapidly moving Electrified Particles", Thomson presented equations that modelled how [[beta particle]]s scatter in a collision with an atom.<ref name=ThomsonScattering1910>{{cite journal |author=J. J. Thomson |year=1910 |title=On the Scattering of rapidly moving Electrified Particles |journal=Proceedings of the Cambridge Philosophical Society |volume=15 |pages=465–471 |url=https://archive.org/details/proceedingsofcam15190810camb/page/464/mode/2up}}</ref><ref name=Heilbron1968/>{{rp|277}} His work was based on beta scattering studies by [[James Crowther]].
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Thomson typically assumed the positive charge in the atom was uniformly distributed throughout its volume, encapsulating the electrons. In his 1910 paper, Thomson presented the following equation which isolated the effect of this positive sphere:<ref name=ThomsonScattering1910/><ref name=Heilbron1968/>{{rp|278}}
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