I understand your question differently than boblet.
What I think you want is a the colour that is interpolated by the gradient at 78px from the bottom of the gradient.
I don't know a method to exactly determine it, only how to approximate it.
First create your original 348px gradient. For the colours I used black and white for clarity.
Then place a guide at 78px from the beginning of the gradient.
Now select the rectangle that has the gradient, go to
Object -> Expand, you will see this window:
Make sure you expand the gradient to objects, not as a gradient mesh.
Now you can double click the rectangle (which now is a group) to enter Isolation mode and select one "piece" of the gradient closest to the previously set guide.
The fill colour of that piece is displayed in the colour panel, you can drag it as a swatch to save it.
Now use that colour as the starting point of your new, 270px gradient.