The little borough of Petersfield is in a state of great excitement, owing to the approaching dissolution of Parliament, and war is openly declared by the two parties which are nearly on a balance, but which would be very different if every elector was allowed the same privilege as the Duke of Newcastle claims, that is, to do as he likes with his own franchise. There is that good, consistent, and independent Liberal, C. J. Hector, Esq., M. P., again in the field, who has had the honour of representing the borough since 1831. Previous to the passing of the Reform Bill it was as close and corrupt a borough as Gatton, or Old Sarum. The present hon. member has just competed his canvass, with every prospect of being again the M.P., at the ensuing general election; but his friends must be up and doing and make every effort which possibly can be made considering that his election depends on their individual support. We hope to see the influential body of Dissenters in the town and neighbourhood strenuously exerting themselves on behalf of the hon. gentleman's cause, and especially the deacons, &c. of the Independent chapel. We recommend every Dissenter to read the spirited address which is just published to the Dissenters of Great Britain, hoping they will support all liberal members who are favourable to the young Queen's government. C. J. Hector has on all occasions been found at his post, supporting every liberal measure which has been introduced, whether civil or religious, for the good of the country at large. He is opposed by Sir W. Jolliffe, Bart., a Conservative, who has a great bulk of property in the town, consequently he commands a great deal of influence, but who is now canvassing the borough with a very faint hope of success; his party is to be seen wandering about catching at every doubtful voter, entreating them not to support Popery, but to uphold the church; but all this will not do—the Tories are completely chap-fallen. Electors of Petersfield rally round your independent member, and send him again to Parliament by a large majority at the election, which must shortly take place. (From a Correspondent.)