|The MicroCoulomb Experiment page 6|
Science. It is furthermore inadmissible and constitutes a petitis principii, if assumptions are made concerning the existence and uniqueness of a smallest charge, and of the fact that the differences of successive charge of the same particle are multiples of a same small charge and that this charge equals the above mentioned smallest charge.
The author therefore intended to clarify the basic properties of the method and to investigate critically the premises, in order to determine beyond any doubt the electronic charge. The method was to be as direct and as empirical as possible, and was certainly not to presuppose anything about the charges to be measured, which were to be found as a result of this method. The author hopes to have succeeded, after having worked at this problem for 30 years, and he aims in this paper to present some technical features of what he would call the micro-Coulomb experiment which have not been published yet, and some optical studies which he has made at the occasion of this experiment, and which are also of general interest for microscopy.
2. The Problem.
In essence the determination of the charge e of a test particle is done in a homogeneous vertical electric field E, by comparing the force on the particle which is due to the electric field to the force on it due to the field of gravity. The force exerted upon a particle of charge e is then P=eE. If the particle rest suspended at a field E*, then the charge is determined from the equation
where mg is the weight of the test-particle. This suspension experiment can be done in a vacuum or at nay gas pressure what ever. If the weight of the test-particle is known, then the determination of the charge is entirely independent of any laws of friction. Thus the determination of the charge is reduced to the precise mesurement of the field E* and the weigh of the test particle.
The weight of a particle of spherical shape is given by
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