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We have conducted an extensive wide-field imaging survey for Cepheidvariables in the Local Group irregular galaxy WLM. From data obtained on 101nights, we have discovered 60 Cepheids which include 14 of the 15 Cepheidvariables previously detected by Sandage and Carlson. Down to a period of 3days, our Cepheid survey in WLM should be practically complete. Importantly, wehave found for the first time a long-period Cepheid (P=54.2 days) in thisgalaxy, alleviating the puzzle that WLM with its many blue, massive stars doesnot contain Cepheids with periods longer than about 10 days. Our data definetight period-luminosity relations in V, I and the reddening-free Wesenheitmagnitude ${\rm W}_{\rm I}$ which are all extremely well fit by thecorresponding slopes of the LMC Cepheid PL relation, suggesting no change ofthe PL relation slope down to a Cepheid metal abundance of about -1.0 dex, inagreement with other recent studies. We derive a true distance modulus to WLMof 25.144 $\pm$0.03 (r) $\pm$0.07 (s) mag from our data, in good agreement withthe earlier 24.92 $\pm$ 0.21 mag determination of Lee, Freedman and Madore(1993a) from Cepheid variables. The quoted value of the systematic uncertaintydoes not include the contribution from the LMC distance which we have assumedto be 18.50 mag, as in the previous papers in our project.

The Araucaria Project. The Distance to the Local Group Galaxy WLM from Cepheid Variables discovered in a Wide-Field Imaging Survey