The length of the latus rectum of a parabola, whose vertex and focus are on the positive $$x$$-axis at a distance $$R$$ and $$S (> R)$$ respectively from the origin, is:

We are told that the vertex and the focus both lie on the positive $$x$$-axis. Hence we can assign the vertex the coordinates $$(R,0)$$ and the focus the coordinates $$(S,0)$$ with the given condition $$S > R$$. Because the focus is to the right of the vertex, the parabola opens towards the positive $$x$$-direction.

For any parabola that opens to the right, the standard form of the equation, when its vertex is at $$(h,k)$$, is stated first:

$$ (y-k)^2 = 4a\,(x-h) $$

In this form, $$a$$ is defined as the distance from the vertex to the focus, and we also know the following fact:

The length of the latus rectum of such a parabola is $$4a$$.

Now, for our particular parabola we have

$$h = R, \quad k = 0$$

and the distance from $$(R,0)$$ to $$(S,0)$$ is simply the difference of their abscissae:

$$ a = S - R. $$

Substituting this value of $$a$$ into the standard statement for the latus-rectum length, we obtain

$$ \text{Length of latus rectum} = 4a = 4(S - R). $$

Hence, the correct answer is Option C.