This is from an on-line discussion in a long-forgotten forum:

The obvious application of the inverse square law is NOT correct
and the equations given below are close but not exact. This is due to
a common misconception. The reason is that when the print sizes is
changed, two distances are changed: the distance from the lens to the
print (or more accurately, from a nodal point to the image), and the
distance from the lens to the negative (or more accurately from the
other nodal point to the object). Changing the lens-print distance
obviously changes the light. Changing the lens-negative distance also
changes the light -- frequently this is explained as changing the
effective aperture.

The easiest way to express the correct equation is
t1 / t2 = ((m1 + 1) / (m2 + 1))**2

i.e., the ratio of the exposure times should
be the ratio of the terms (magnification plus one) squared. Without
the "plus one" it would be the inverse square law.