New York, May 27. Tlie HcrahPs correspondent reports that the Fourth Michigan Regiment, in the recent skirmish on the Chickahominy, iought and routed ao entire rebel brigade. A letter to the Herald gives a list of the losses n the Fourth Michigan Regiment in the recent skirraish. Kil1 cd. Private Abel M. D. Piper, company B, shot through the heart. Wounded. Piivates Franklin Drake, Company B, mortally ; AVni. II. Ohase, company 0, rnortally, compound fracture of the thigh ; M. Young, company B, fie.sk wound in arm ; Corporal John Campbell, company 3, fiesii wound in thigh ; Piivates Martin Brockway, companv 3, compound fracture oí the torearm ; Charles Bruner, company A, flash vound in thigii ; Charles Burow, company I, wounded n the mouth.