Why is a Riemannian metric $g$? A Riemannian metric on a manifold is universally denoted with the letter $g$, but unlike many other mathematical objects like a function $f$, a distance $d$, a manifold $M$ or a group $G$ there does not seem to be a connection to the name or meaning of the actual quantity, neither in English nor German.

Questions:


When and where has this notation been introduced?
Is there an evident reason why the letter $g$ was chosen and accepted by everyone?




Some Remarks: 


Of course $g$ carries a lot of information about the geometry of a manifold, but this seems to be a little too unspecific to me. 
In his book on Riemannian geometry, Do Carmo only uses $g_{ij}$ but never $g$ for the metric. On the other hand at some point he uses $g$ for the Gauss-map of a surface, but that also does not directly relate to the metric tensor.
Do Carmo also points out that Riemann introduced the concept of a quadratic form assigned to each point of a manifold in his paper "Über die Hypothesen, welche der Geometrie zugrunde liegen." But in there I did not find the notation $g$ as well.
I always thought it was $g$ for the Gram matrix, which, after picking a basis, specifies the component of an inner product:

$g_{ij} = \langle \hat{e}_i, \hat{e}_j \rangle$

On a Riemannian manifold, the metric is just an inner product-valued field.
The symbol $\mathbb Z$ is used because the German word for number is Zahlen.

In German, "gestalt" means "shape", "form", "figure", etc.

Perhaps this is the reason behind the choice of $g$.