Some of the State Legislatures are still in session, but their action is too local to excite general interest. A very important Act has passed the Legislature of the State of New York, re-organizing the Common School System of the State, and placing it partially upon the free basis. By the law of 1849 all the common schools of the State were made entirely free, their cost being paid by county, town, and district taxation. This was found to be highly obnoxious, chiefly from that provision which gave the _voters_ in any district power to tax the _property_ of the district _ad libitum_ for school purposes. The new law was passed to remedy those objections. By its provisions a State tax of $800,000 is annually imposed upon the property of the State, and distributed among the schools. The balance, if any should be required, is to be collected by rate-bill from those who send to school, indigent persons being exempt, at the expense of property of the town. The bill has become a law and will go into operation next fall. Another very important measure has been introduced into the Legislature, concerning the enlargement of the Erie Canal. The Constitution of the State sets apart the surplus revenues of the canals in each year, for the completion of the enlargement; but the rapidly increasing competition of railroads has led the Legislature to perceive the necessity of accomplishing this work more rapidly than it can be done in the way hitherto adopted. The bill referred to proposes to borrow money on the credit of the surplus revenues set apart by the Constitution; and with the money thus procured, to complete the enlargement forthwith, setting apart the revenues as a fund to redeem the certificates. The measure was very strenuously resisted by the Democratic party, chiefly on the ground that it was unconstitutional. This, however, was denied by the friends of the bill. It was argued with great ability and zeal on both sides. In the Assembly the bill passed, by a vote of 76 ayes and 21 nays In the Senate it is still under consideration. We have already recorded the attempt and failure of the Legislature to elect a Senator in the Congress of the United States. On the 18th of March the effort was renewed by a joint resolution, and after a session protracted until two hours after midnight, it resulted, through the absence of two Democratic Senators, in the choice, by separate nomination of each House, of HAMILTON FISH. In the Senate there were 16 votes for, and 12 against him. In the House he received 68 votes and there were but 8 against him. He has accepted the office.--The members of the Legislature and the State Officers paid a visit of three days to the City of New York, on the invitation of the Mayor and Common Council. They visited the different public and charitable institutions, of this city and Brooklyn; and were entertained at a public dinner at the Astor House, on the evening of March 22d. This is the first visit of the kind ever made.--A