This paper distinguishes in Maxwell’s thought between “atomic molecules” and “ultimate atoms,” and arrives at a set of properties that characterize each type of atom. It concludes that Maxwell is a mathematical atomist, an approach that entails the notion that although it is impossible to observe the ultimate atoms as free particles, we can nevertheless study them as mathematical observables, on the caveat that mathematical formalism remains tied to phenomenalism and to theoretical interpretations of such phenomena as, for example, mass (...) and force variations, gravitational pull, gas diffusion and viscosity, and heat conduction. (shrink)