Public Gardens, and Mechanics' Exhibitions. - Among the best modes that we know of for improving the taste of the inhabitants of country towns and their neighbourhood are, the establishment of public gardens, such as those of Birmingham and Sheffield; and the opening of exhibitions, such as those of the mechanics' institutes in these towns, to which gentlemen in the neighbourhood are kind enough to send pictures, sculpture, and other articles of beauty, curiosity, or of scientific interest. These exhibitions, to which all are admitted on the payment of 6d.; or every day, as long as they are open, for 2s. 6d.; cannot fail to have an excellent effect. We learn, on good authority, that, at the end of a fortnight after the Derby exhibition was opened, more than 20,000 persons had been to see it.