The steam-boat Walk-in-the-water arrived here last Tuesday morning, between the hour of one and two o'clock--(being her first trip this season.) She left Buffalo last Saturday, in the morning. Among the passengers were Maj. Douglass, of the corps of engineers, and Mr. Schoolcraft, the author of a treatise on the lead mines in Missouri, both of whom, we are informed, are to accompany Gov. Cass on his tour to Lake Superior, &c.--also, capt. Green and Lt. Clark, of the 3d infantry, with 120 handsome recruits for that regiment. We are also happy to state, that by this arrival of the steam-boat, some addition was made to our permanent population.
The passengers in the steam-boat expressed much surprise at the appearance of the fields, forests and gardens which border on the Detroit river, and all agree in the opinion that the vegitation [sic] here is at least three weeks in advance of that in the western part of New-York.
During the winter the Walk-in-the-water has been altered in a manner to render her very strong, and we were told by the engineer that she sails much better than she did last summer. It is to be regretted the proprietors continue the price for passage and freight that was demanded last season; but if they study their true interest, a reduction may be anticipated.