SENATOR BRODERICK KILLED IN A DUEL. News is brought by the overland mail of the death of United States Senator Broderick of California. All the particulars forwarded by telegraph from St Louis, are given in another column. Mr Broderick was a native of Washington city, but removed at an early age to New York, where he was conspicuous in political matters up to the time of his removal to California. He was about forty years of age, and took his seat as a senator at the second session of the 34th congress. His term would have extended to March 4, 1863. The hostile meeting grew out of language used at the dinner table of a hotel, by the deceased, reflecting severely upon Terry’s moral character. The challenge was sent by the aggrieved party in June last, soon after the language had been uttered. Since that time the friends of both had endeavored to compromise matters, but to no effect. The Tribune’s correspondent states that Terry is a lawyer, about 40 years of age. The only public position which he ever held there was chief justice of the supreme court, a position for which he was not fit in either learning, talent, or moral character. He was on the bench during the vigilance committee time, and he was for a long time held a prisoner by that body for having stabbed a member of the committee.