If the earth's core is regarded as a perfect conductor and the surrounding mantle as an insulator, then the unsigned magnetic flux, Po, crossing the core-mantle boundary remains constant in time. In practice this constancy is limited by the core's finite conductivity, but it is expected to hold for at least millenia. For such time spans an upper limit Gmn or Hmn may be derived for the magnitude of any geomagnetic Gauss coefficient gmn or hmn, by assuming that the entire value of Po is attributed to that coefficient alone. Such upper limits are evaluated here for n = 1--4, using a value of Po derived from Magsat data. The ratio ‖gmn/Gmn‖, ‖hmn/Hmn‖ between the observed magnitude of a coefficient and its upper limit defines a ''relative mulipole index'' for the present value of that coefficient. Using the Magsat model MGST 6/80 it is found that for the dipole term this ratio is about 0.72, suggesting that ‖g0l‖ is presently only about 28% lower than the maximum value during the past few millenia. Also, the largest of the other multipole indices calculated (‖g13/G13‖?0.23) is a factor of over 3 smaller, so presumably a dramatic change in field configuration outside the core is required before the next polarity reversal is completed.