July 29.--The waters this day subsided rapidly. It is evident that there has been no flood in the river for a very considerable period prior to the present one, there being no marks of wreck or rubbish on the trees or banks. Now the quantity of matter is astonishing, and, such as must take some years to remove. The rapid rise and fall in the water would seem to indicate that neither its source nor its embouchure can be at any great distance. The former is probably not far east of Arbuthnot's Range. August 2.--It was not until this morning that the river had fallen sufficiently to allow us to ford it. Though the morning was unpromising with slight rain, it was not deemed prudent to lose a moment in passing it, while in our power; and by one o'clock every thing was safely over, to our great satisfaction. Before this, it had begun to rain hard, and it continued to do so throughout the day, and great part of the night. Our observations place this part of Castlereagh River in lat. 31. 14. 14. S., long. 148. 18. E., variation 8. 14. E. August 3.--A dark cloudy morning. At nine o'clock proceeded on our eastern course towards Arbuthnot's Range. The river had risen in the night so considerably, that had we delayed until this morning, we should have been unable to pass it. The rain had rendered the ground so extremely soft and boggy, that we found it impossible to proceed above three-quarters of a mile on our eastern course. We therefore returned, resolving to keep close to the river's edge, until we should be enabled to sound the vein of quagmire, with which we appeared to be hemmed in. In this attempt we were equally unfortunate, the horses falling repeatedly: one rolled into the river, and it was with difficulty we saved him: my baggage was on him, and was entirely spoiled; the chart case and charts were materially damaged, and our spare thermometer broken: we therefore unladed the horses where they stood, and the men carried the provisions to a firmer spot, where they were reladen. We again proceeded easterly, and for upwards of a mile we travelled up to our knees in water and mud: the horses were here stopped by running waters from the marshes, encircling a spot of comparatively dry ground; they were again unladen, and with the utmost difficulty we got every thing safe over. Both men and horses were so much exhausted by the constant labour they had undergone, that I determined to halt, in order to restore our baggage to some order. Our ardent hopes are fixed upon the high lands of Arbuthnot's Range, which I estimate to be about twenty miles off. The intermediate country, we fear, will be one continued morass.