How can a charge of a particle be determined through its cloud chamber photograph? Specifically in reference to Carl Anderson's famous cloud chamber photograph providing evidence of a positron. Any insight is appreciated.

 A: In that experiment there exists  a magnetic field perpendicular to the plane of the photo.
The motion of the charged particle in a magnetic field is used ,  equating the centrifugal with the centripetal force one gets
Bqv=mv^2/R
where B is the magnetic field, q is the charge ( with its sign) v the velocity m the mass and R the radius.
From the incoming direction and the right hand rule one knows the charge of the particle, in this case it has to be positive from the setup.
From the curvature one gets the momentum , thus the energy.
There exist ionization curves (fig10)for a given particle mass

Ionization is proportional to the number of ions scattered off as the particle moves through  the cloud or bubble chamber, and is a function of the mass.
From the ionization characteristic for the measured energy, it could not be a proton, (at that small momentum the proton would have a much thicker ionization deposit and subsequent energy loss)  it was consistent with an electron track which confirmed it as the proposed by Dirac positron.
A: The cloud chamber was in a magnetic field which resulted in the trajectories of the particle being curved.
From the known directions of the magnetic field, the particle motion and the particles direction of deflection the sign of the charge can be inferred.

In this example produced in a bubble chamber the incident beam of gamma ray photons is coming from the top right and interacting to produces charged particles of opposite sign shown by the curvature being in the opposite direction.  
The particle trajectory are spirals because they lose kinetic energy by collision as they traverse the chamber.
A: If the direction of the magnetic field is known, the charge of the particle can be determined by looking in which direction the particle has been deflected and applying the right-hand rule.
In this particular image an electron would be deflected in the opposite direction.
