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( ∈ vs. ε): Why Physicists Use 2 Forms of the Greek Letter Epsilon

Michael Faraday / By /

When I learned Maxwell’s equations in college, I was taught to draw the permittivity with a Greek letter epsilon that looked like a c with a line in it and not like a backwards 3 like usual. 

Table Of Contents

Why Physicists Use 2 Forms of the Greek Letter Epsilon

Image References

Reference

Why Physicists Use 2 Forms of the Greek Letter Epsilon

It turns out that this alternative epsilon is a mistake that happened when an English printing company accidentally used a newly minted math symbol and ancient version of epsilon in an English translation of Heinrich Hertz’s papers in 1893. 

The reason I know it was a mistake is because Hertz’s original papers in German from 1890 and the German collection of his papers from 1894 use the normal form of epsilon. 

Soon people started to write Maxwell’s equations with an epsilon that looks like the math symbol because people thought that was what Hertz intended. Physicists have used two versions of epsilon ever since!

Image References

( ∈ vs. ε): Why Physicists Use 2 Forms of the Greek Letter Epsilon
Figure 1: Feynman Teaching Maxwell’s Laws in 1963, note how he drew epsilon
Figure 2: The misprint of epsilon in Hertz's English book (1893)
Figure 2: The misprint of epsilon in Hertz’s English book (1893)
Figure 3: Hertz's original paper from 1890 (note the form of epsilon)
Figure 3: Hertz’s original paper from 1890 (note the form of epsilon)
Figure 4: Hertz's collection of edited papers from 1894
Figure 4: Hertz’s collection of edited papers from 1894

References

 1 Hertz, Heinrich “On the Fundamental Equations of Electromagnetics for Bodies at Rest” (March 19, 1890) Electric Waves (1893) p. 200  https://www.google.com/books/edition/_/EJdAAAAAIAAJ?sa=X&ved=2ahUKEwiaiYT93Mv5AhUDJn0KHZ44DnQQ7_IDegQIExAC 

2 Hertz, Heinrich “Ueber die Grundgleichungen der Elektrodynamik” (March, 1890) Annalen der Physik vol. 277 issue 11, p. 110 https://www.deutsche-digitale-bibliothek.de/item/E4EHCECIDIMIFJQCP6HXHJCDYPXNMEZZ  

3 Hertz, Heinrich “Ueber die Grundgleichungen der Elektrodynamik” Untersuchungen über die Ausbreitung der elektrischen Kraft (1894) p. 213 https://www.google.com/books/edition/Untersuchungen_über_die_Ausbreitung_der/WWcSAAAAIAAJ?hl=en&gbpv=0 

For example, Feynman Lectures of Physics (1964) https://www.feynmanlectures.caltech.edu/flpphotos.html#S18 

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