The concept of charges was known and Benjamin Franklin had already assigned the positive-negative convention (inconveniently, as it turned out). It is rather simple to determine the sign of the charge and the mass of the particle.
In a known electromagnetic field, a charged particle will move one way or the other depending on the sign of the charge of the particle. Electrons were already discovered so if the particle moves in the same direction as the electron, it must have the same charge as the electron.
From how much the particle moves (ie amount of deflection), the charge/mass ratio can be determined. This would be a relatively simple use of Newtonian equations of motion combined with Maxwell’s laws.
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