After a week's postponement, rendered necessary by the unripe condition of the crops on the first of the month, the trials of sheaf-binding machines, using any other binding material than wire, instituted by the Royal Agricultural Society of England, began on Monday morning, the 8th of August. By nine o'clock, the time appointed for beginning operations, there was a very large number of gentlemen interested in these trials already collected on the farm of Mr. Hall, at Thulston, and the distances that many of them had come testified to the importance of the interests involved. The morning was perfect for reaping, though ominous clouds in the southwest led many to hazard conjectures, which unfortunately turned out too well founded, that the Royal Agricultural Society would not on this occasion escape the fate which had visited them so often. The corn stood ripe and upright in the various plots into which the fields had been divided, and the ground was level and dry. The published list of the competitors contained twenty entries, not by as many firms, however, for many names appeared more than once; but the rules of the society, which objects to different machines being used for different kinds of corn in these trials, together with non-attendance for unknown reasons, had reduced the actual list of competing machines to seven. These were as follows: Mr. W. A. Wood, the McCormick Harvesting Machine Company, the Johnston Harvester Company, Messrs. Samuelson & Company, Messrs. J. & F. Howard, Messrs. Aultman & Company, and Mr. H.J.H. King. All these machines were to be seen at the show, except the second named, which was delayed by the stranding of the steamship Britannic, and had only lately arrived in rather a weather-beaten condition. The trials were to be made upon oats, barley, and wheat, and the plots for the preliminary trials were about half an acre in extent. Shortly after half-past nine o'clock, the judges and engineers of the society having arrived upon the ground, a start was made upon the oats by the three machines belonging to Mr. Wood, Messrs. Samuelson & Co., and the Johnston Harvester Company. It should, perhaps, be mentioned that the strength of this crop of oats varied a good deal in different parts of the field. These three machines all belong to the class which has the automatic trip--that is, the binding gear is thrown into action by the pressure of the straw accumulated arriving at a certain value, independently of any special action on the part of the driver. The sheaves from Messrs. Samuelson's machines were extremely neat and well separated from each other, a point to which farmers attach great importance.