THE VARIABLE-STARS OF NGC 1866

New multiepoch CCD photometry of the populous LMC cluster NGC 1866 has been obtained to search for new variables and confirm the variable candidates of Storm et al. (1988). In addition, we have acquired high-dispersion, photon-counting echelle spectra of 18 variables in the field of NGC 1866 which have been used to obtain 106 radial velocities. From these data, we find: (1) Eight previously unknown Cepheid variables, most near the cluster core. (2) Of the new variables reported by Storm et al. (1988), only six (V1, V4, V5, V6, V7, and V8) out of ten appear to be Cepheids and one of these (V5) is not a member. (3) Periods and mean magnitudes and colors for sufficiently uncrowded variables. (4) One red giant variable of long period. (5) One Cepheid (HV 12202) which is a single-lined spectroscopic binary with a velocity semiamplitude greater than or equal to 10.5 km s.-1 (6) The blue and large-amplitude Cepheid HV 12204 is a nonmember from radial velocities. (7) The variation of light-curve amplitude with position in the Instability Strip. (8) An apparently nonvariable star, which is a radial velocity member, in the Instability Strip. (9) A true distance modulus of 18.57 +/- 0.01 mag for the cluster. We determine the color coefficient beta of the Cepheid P-L-C to be 2.03 +/- 0.38 from all uncrowded variables with good phase coverage in the field of the cluster. The scatter in the P-L-C for the nonbinary field variables is only 0.047 mag, which can be accounted for by photometric errors. This indicates that the P-L-C is practically disperionless. There is no evidence for Cepheids in more than one crossing of the Instability Strip.