  Photometric data for 593 Cepheids in the LMC, measured by Udalski et al. in
the OGLE survey, augmented by 92 longer period Cepheids from other sources, are
analyzed for the P-C and P-L relations, and for the variations of amplitude,
light curve shape, and period across the instability strip at constant absolute
magnitude. Both the P-C and P-L relations have different slopes for periods
smaller and larger than 10 days. The break at 10 days is also seen in the
period-amplitude relations, and the compound Fourier combinations of R_21 and
Phi_21 introduced by Simon and Lee.
  The LMC Cepheids are bluer than Galactic Cepheids in the B,V,I color bands,
part of which is due to differential Fraunhofer line blanketing and part to
real differences in the temperature boundaries of the instability strip. The
LMC strip is hotter by between 80K and 350K depending on the period. Hence,
both the slopes and (necessarily) the zero points of the P-L relations in B,V,I
must differ between LMC and the the Galaxy, and in fact they do. The LMC
Cepheids are brighter by up to 0.5 mag at log P=0.4 (2 days) and fainter by 0.2
mag at log P=1.5 (32 days). These facts complicate the use of Cepheid as
precision distance indicators until the reason is found for the
non-universality of the P-L and P-C relations.
  The very large data base permits mapping of various Cepheid properties at
different positions within the instability strip, both at constant period and
at constant absolute magnitude over the range of 2 < P < 40 days and -2 > M_V >
-5. (...)
