The MACHO Project LMC Variable Star Inventory. VI. The Second-overtone   Mode of Cepheid Pulsation From First/Second Overtone (FO/SO) Beat Cepheids
  MACHO Project photometry of 45 LMC FO/SO beat Cepheids which pulsate in the first and second overtone (FO and SOo, respectively) has been analysed to determine the lightcurve characteristics for the SO mode of Cepheid pulsation. We predict that singly-periodic SO Cepheids will have nearly sinusoidal lightcurves; that we will only be able to discern SO Cepheids from fundamental (F) and (FO) Cepheids for P <= 1.4 days; and that the SO distribution will overlap the short-period edge of the LMC FO Cepheid period-luminosity relation (when both are plotted as a function of photometric period).   We also report the discovery of one SO Cepheid candidate, MACHO*05:03:39.6$-$70:04:32, with a photometric period of 0.775961 +/- 0.000019 days and an instrumental amplitude of 0.047 +/- 0.009 mag in V. 
The MACHO Collaboration: C. Alcock, R.A. Allsman, D.R. Alves, T.S.   Axelrod, A. Becker, D.P. Bennett, K.H. Cook, K.C. Freem...