The royal mail-steamer, "Hibernia, CAPTAIN JUD*INS, has arrived at Liverpool, on Tuesday from Halifax and Boston, after a passage of ten days from the former place.

She has brought home thirty-four passengers, and letters, and papers from New York to the 31st ult.;  Boston to the 1st;  and  Halifax to the 3d inst.;  all inclusive.

The "Britannia" which sailed hence on the 19th ult., reached Halifax on the 2d inst., after a very fair passage.

The news received by the "Hibernia", in a political point of view, is meagre and unimportant, public attention being almost wholly absorbed in the elections.

The commercial advices are important - in so far as we are informed of the probable failure of the cotton crop.  The setting in of frost in many districts of the South, had caused a sudden change in the prospect of the crop, and the condition of the markets throughout the Union, and prices have in consequence advanced;  and at the sailing of the "Hibernia" they were nearly one halfpenny per pound higher than at the date of the sailing of the previous steamer.

In the condition of the money market, there had been no change of moment.  Money continues abundant.  There was a fair inquiry for bills on London, at 108 to 108-3/4, but the majority of the transactions for the steamer were done at 10-1/4 to 10-3/4.