A great event has just been decided in this city. The ceremony of the election of a president of the United States, for the four years which shall commence on the fourth day of March next, took place yesterday. The circumstances which led to the peculiar forms of this choice, the characters of the candidates, and the probable result that it will have on the policy of the country, may not be without interest to one who studies mankind as generally as yourself.

The first president, you know, was Washington. He was succeeded by the vice-president, the elder Adams. At the end of four, years, a hot contest occurred between Mr. Adams and Mr. Jefferson, the president and vice-president of the day, for the chair. In order to give you a proper understanding of the case, it will be necessary to explain the law for the election to this high office.

You know that the sovereignty of the states is represented by the senate. Thus, Rhode Island, with 70,000 inhabitants, has two members in the senate, as well as New York with 1,700,000. But the members of the lower house, which is the connecting link between the states, are apportioned according to the population. The state of Rhode Island has, therefore, two representatives, and the state of New York thirty-seven. In all ordinary cases of legislation, each individual, whether a senator or a representative, gives one vote.