THE United States' authorities in Utah are carrying forward their prosecution of Mormon polygamy in a commendable manner. Dispatches from Salt Lake, dated Oct. 21 and 22, give the following information: Oct. 20. The court was occupied all day by the Hawkins' adultery case. The cross-examination of Mrs. Hawkins elicited nothing materially new. She testified that Hawkins gave no reason for taking the other women for wives, except that he had had her day, and it was proper that he should have some one else. She said she had borne him seven children at the time he took another wife. The defense offered no testimony, except to prove the marriage of Hawkins with his second and third wives. Gen. Maxwell spoke for the prosecution, and assuming that the defense would rest upon the plural marriage as being a part of a religious faith, argued that polygamy was in direct violation of ecclesiastical and common law. Mr. Fitch concluded at a late hour for the defense. He contended that Hawkins, being a Mormon, had no intention of committing crime, and the intention was essential to conviction; that there was no law against polygamy when he took the second wife; and he could not be guilty of adultery, because he was legally married to the woman according to the usages and customs of the Mormon Church. United States Attorney Baskin will sum up this evening, after which the case will go to the jury. A number of additional arrests have been made. SALT LAKE, Oct. 21. The jury in the Hawkins' case came in last night with a sealed verdict, which, on being opened this afternoon, was found to be “guilty.” The court-room was crowded, and the announcement created much sensation. The counsel for The People moved the court that defendant be taken into custody, which motion was stoutly resisted by defendant's attorneys. The prosecution, however, were firm in their demand that the case should take the ordinary course, and the United States marshal accordingly was directed to hold Hawkins a prisoner. Time was allowed to prepare a motion for a new trial and arrest of judgment. The penalty of the Utah statutes for the crime of adultery is imprisonment not exceeding twenty years, and not less than three years, or by fine of not over $1,000, or both fine and imprisonment at the discretion of the court. This is a test case, and virtually places all polygamists at the mercy of the first wife, who, under the act, is the only party who can institute proceedings against the husband. The case was contested on both sides with great determination, and the charge of Chief Justice McKean to the jury last night is spoken of as being eminently able.