A measurement of the Stark-induced amplitudes a and P for the 6P, iz~7P, i2 transition in atomic thallium is reported. Absorption of cw laser light tuned to this transition at 293 nm was compared to absorption of 378-nm cw laser light tuned to the allowed 6Pl/2~7Sl/2 transition. The absorption sample was an intense atomic beam in the presence of a strong electric field. The measured values are a = 2.01(4)X 10 s P s / (V/cm) and P = 1.67(4) X 10 'Ps / (V/cm), where iss is the Bohr magneton.These results are in agreement with semiempirical theory, but disagree with previous measurements of these amplitudes in this laboratory. A critical analysis of the previous measurement is given to explain the discrepancy. The newly measured value of P makes it necessary to reinterpret previous measurements of parity nonconservation in the 6Pl/2~7Pl/2 transition. In the course of the present experiment, Stark shifts of the 6P l /2~7 P l /2 and 6P l /2~7 S l /2 transitions were also measured: Av(6Pl/2~7Sl/2) = -112(6) kHz/(kV/cm) and hv(6Pl/2~7Pl/2) = -618(31) kHz/(kV/cm) . These results are also in good agrement with semiempirical theory.