The Committee of the Petersfield British Schools, which were established in 1845, intend shortly having a public examination of the children of both sexes, previous to their Midsummer vacation, on which occasion the nobility and gentry are especially invited to attend, as well as the parents of the children. Every preparation is being made by the principal master, Mr. Fairbairn, for the accommodation of a large number of persons, which are expected to be present. Since the formation of this most useful and unsectarian school many hundred children have been turned out first-class scholars, and are now filling very superior situations, vide advertisement in another part of the paper.