There is an effort making to induce the proprietors of the Shore mail boats, to leave Bay City early in the morning, instead of the afternoon, and make most of the trip to Alpena by daylight. We see some objections in the change, and that is, the shore people would not receive as late Detroit mail as per the present arrangement. That will be considerable of an objection, too. Undoubtedly the talked of change might benefit the hotel keepers of Bay City, but it would be of no practical benefit to the people of the shore who go to the city to do business. The time intervening between the arrival of the boat at Bay City, in the evening, and its departure in the morning, would not furnish time or opportunity for the transaction of business, we imagine.