Saturday, June 25th, a committee from the Bricklayers' union, composed of A. E. Vorkeller, C. C. Scouller and C. J. Lindgren, met a committee of Master Masons, composed of C. A. Moses, Thomas Nicholson and E. S. Moss. The Union committee asked for and received an official copy of the proposition to allow a judge of the United States court to select four business men to arbitrate the case. They objected to the manner of selecting the arbitrators, and suggested that they be permitted to select their representatives, and the Master Masons do the same, and then select a judge as umpire. This action of the two committees was entirely unofficial, but the Union committeemen said they would officially present a proposition to the Master Masons on the subject. Monday, June 27th, the executive committee of the Bricklayers' union replied to the communication of President Downey, as follows: JOSEPH DOWNEY, President--_Dear Sir_: In reply to your communication of the 25th inst., submitting a proposition to settle permanently the differences existing between our union and your association, we beg leave to say that said proposition does not meet with our approval for the following reasons, viz: There is a want of confidence on the part of workingmen in such high officials as United States judges from the fact that they are not brought in close contact with workingmen in the settlement of their difficulties. Further, we believe a board of arbitration selected in the manner suggested by your committee would not be satisfactory to either side. Neither do we believe they would be as competent as a board selected from the employers and employes directly interested. We, therefore, take this opportunity to remind your association that we, on the 9th inst., appointed a committee of five from our organization to meet a like committee from your association (the joint committee to select an umpire) with full power to permanently settle the differences existing between our union and your association. By order of the executive committee of the United Order of American Bricklayers and Stonemasons. A. E. VORKELLER, CHARLES J. LINDGREN, [Seal.] FRED RECKLING, JAMES SIDLAK, JOHN PEARSON.