Why does “Fresnel'sche” have an apostrophe and “Gaußsche” doesn't?

Question

In German physics literature, I often see adjectives like “Gaußsche” and “Fresnel'sche”. I know what they mean in the context, that Gauß (or Fresnel) invented something or that it is named after them. But why does one have an apostrophe in it, and the other does not? What does that mean (i. e. what am I leaving out?) and which is the right way?

Answer 1

Firstly, it is never required that the apostrophe be used, but it is acceptable when used as a noun.

When used as an adjective, it would be written lower-case and without the apostrophe.

Die gaußsche Glockenkurve

If it's used as a noun, both with or without the apostrophe would be acceptable.

die Gauß'sche Glockenkurve -or- die Gaußsche Glockenkurve

Note that all three of these mean exactly the same thing, and it's just a matter of preference. It would be preferred that you were consistent throughout a text with one style.