The pulsation periods of long period variables (LPVs) depend on their mass
and helium abundance as well as on their luminosity and metal abundance.
Comparison of the observed periods of LPVs in globular clusters with models is
capable of revealing the amount of mass lost on the giant branch and the helium
abundance.} {We aim to determine the amount of mass loss that has occurred on
the giant branches of the low metallicity globular clusters NGC 362 and NGC
2808. We also aim to see if the LPVs in NGC 2808 can tell us about helium
abundance variations in this cluster.} We have used optical monitoring of NGC
362 and NGC 2808 to determine periods for the LPVs in these clusters. We have
made linear pulsation models for the pulsating stars in these clusters taking
into account variations in mass and helium abundance. Reliable periods have
been determined for 11 LPVs in NGC 362 and 15 LPVs in NGC 2808. Comparison of
the observed variables with models in the logP - K diagram shows that mass loss
of ~0.15-0.2 Msun is required on the first giant branch in these clusters, in
agreement with estimates from other methods. In NGC 2808, there is evidence
that a high helium abundance of Y~0.4 is required to explain the periods of
several of the LPVs. It would be interesting to determine periods for LPVs in
other Galactic globular clusters where a helium abundance variation is
suspected to see if the completely independent test for a high helium abundance
provided by the LPVs can confirm the high helium abundance estimates.Comment: 13 pages, 12 figures, accepted for publication in Astronomy &
Astrophysic