A Converting JJ Thomson's q/m Units to Modern Standards

[adamws]

TL;DR Summary

How to convert from the units used to report q/m by JJ Thomson to the units used in the now accepted form of q/m.

Summary: How to convert from the units used to report q/m by JJ Thomson to the units used in the now accepted form of q/m.

Referencing the below paper... The q/m measurement was first done in 1897 and reported by JJ Thomson. Numerous others measured the same in the early 1900's. The paper below gives a chronicle of those measurements which appear to converge on a value of 1.76x10^7 and they refer to units of this measurement as "electrostatic units". Today's accepted value is different by several orders of magnitudes; 1.75882001076(53)×10^11 C/kg. This leads me to believe that "electrostatic units" are not the same as C/kg but I cannot find a source that can confirm the conversion. It appears that one can just multiply by 10,000 but that is conjecture... I really would like to have a source.

https://www.cs.princeton.edu/courses/archive/fall05/frs119/papers/smith97_thomson.pfg.pdf

 

[vanhees71]

It's obviously not in electrostatic units. In the original paper

https://doi.org/10.1080/14786449708621070
Thomson quote the value for $m/e$ of being around $0.5 \cdot 10^{-7}$ (without giving a unit; he'd not pass the intro lab in our university today ;-)). Let's see which units he most probably has used. In matters of absolute values the SI is the save ground to start from: $m/e \simeq 5.70 \cdot 10^{-12} \text{kg} \, \text{C}^{-1}$. Now in science even in England masses were measured in grams. So we have $m/e \simeq 5.70 \cdot 10^{-9} \text{g} \, \text{C}^{-1}$. Now there's only a discrepancy of a factor of 10.

Checking Wikipedia for historical units of electromagnetism, we find that thus he must have used the electromagnetic charge unit, the socalled absolute Coulomb. Now $1 \; \text{C} \widehat{=}0.1 \, \text{abC}$, i.e., we have $m/e \simeq 5.70 \cdot 10^{-8} \text{g} \, \text{abC}^{-1}=0.570 \cdot 10^{-7} \text{g} \, \text{abC}^{-1}$ in accordance with Thomson's measurements.

Unfortunately the English Wikipedia has not that very useful table the German Wikipedia has:

https://de.wikipedia.org/wiki/Elektromagnetische_Maßeinheiten#Elektromagnetische_Einheiten_in_verschiedenen_Systemen

The most convenient system of units for electromagnetism, used today in theoretical high-energy physics, are the rationalized Gaussian units, also known as Heaviside-Lorentz units (usually taken in natural units, where $\hbar=c=1$. In the letter form it's identical with the SI setting $\mu_0=\epsilon_0=1$. If it comes to concrete numbers, the one and only system is of course the modern SI units with all the (now exactly defined!) values for the fundamental constants left intact.

 

[adamws]

Makes complete sense! Thank you kindly for your effort and well written response.