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Fourier decompositions have been made of the light curves of a large sample of RR Lyrae field stars. The coefficients have been tabulated. Following the scheme of an earlier investigation of classical Cepheids, certain combinations of the low-order coefficients-21' R 21' and 31-are plotted against period. The Bailey-type c pulsators stand out from the type ab stars, particularly on the R21 plot which is found to be a more sensitive discriminator of Bailey type than is the traditionally employed amplitude-period diagram. We compare the RR Lyrae plots of 21' R 21 , and 31 with those previously obtained for classical Cepheids. It is noted that, while the Cepheid plots display a tightly defined progression with period, reflecting the influence of a modal resonance, in the RR Lyrae case there is much more scatter. However, some evidence is shown to exist for a Cepheid-like progression appearing among the longer period RR Lyrae pulsators and culminating in the unique small-amplitude variable XZ Ceti. New observations will be required to confirm the reality of such a progression.

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The peculiar pulsating variable XZ Ceti has a period of 0.8231 day, suggesting that it is a Bailey type ab RR Lyrae star, but it has a light curve shape and amplitude which is like that of the Bailey type c variables. Fourier decomposition analysis verifies that the parameters of its light curve match those of the type c variables, except for its unacceptably long period. We have obtained a new photometric light curve which verifies this long period. We have also obtained energy distributions from spectrum scans, which are used to derive a temperature and approximate surface gravity of this star. These results are used to construct pulsation models so as to attempt to identify the. nature of XZ Ceti. The models suggest the possibility that XZ Ceti is an anomalous Cepheid or, perhaps, an overtone BL Her star.

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