  Red giants are unstable to radial pulsation. About a third of them also show
a long secondary period, 5 to 10 times the pulsation period. The long secondary
periods were recently ascribed to eclipses of the red giant by a low-mass
dust-enshrouded companion. Long secondary periods have been known for over a
century. In this paper, I use primarily American Association of Variable Star
Observers visual and photoelectric observations to look for evidence of long
secondary periods in 103 red giant stars listed by Nancy Houk in 1963 as having
long secondary periods, based mostly on photographic photometry. I have
determined long secondary periods in 37 stars, and upper limits (some of them
not very stringent) in 25. In the former, the ratio of long secondary period to
pulsation period peaks strongly at 10, which suggests that most of the stars
are pulsating in the first overtone. The loong secondary periods are consistent
with those o0f Houk in 33 of the 37 stars. I have identified 16 stars as
bimodal pulsaters;their period ratios are consistent with previous
observational and theoretical results. For 14 stars,the periods in the General
Catalogue of Variable Stars are incorrect or absent.
