Officers on detached Service and doing Duty at the South.—S. Hensley, captain; S. Gibson, do. (lanced through the body at San Pascual); Miguel Pedrorena, do., Spaniard (appointed by Stockton); Stgo. Arguello, do., Californian (appointed by do.); Bell, do. (appointed by do.), old resident of California (Los Angeles); H. Rhenshaw, 1st lieutenant, (appointed by do.); A. Godey, do. (appointed by do.); Jas. Barton, do. (appointed by do.); L. Arguello, do., Californian (appointed by do.).

After a march of six or eight hours, up the valley of the arroyo, through a heavy rain, and mud so deep that several of our horses gave out from exhaustion, we encamped in a circular bottom, near a deserted adobe house. A caballada, of some 500 or 600 loose horses and mules is driven along with us, but many of them are miserable sore-backed skeletons, having been exhausted with hard usage and bad fare during the summer campaign. Besides these, we have a large number of pack-mules, upon which all our baggage and provisions are transported. Distance 10 miles.

We did not move on the 1st and 2d of December. There being no cattle in the vicinity of our camp, a party was sent back to the mission, on the morning of the 1st, who in the afternoon returned, driving before them about 100 head, most of them in good condition. After a sufficient number were slaughtered to supply the camp with meat for the day, the remainder were confined in a corral prepared for the purpose, to be driven along with us, and slaughtered from day to day. The rain has continued, with short intermissions, since we commenced our march on the 30th of November. The ground has become saturated with water, and the small branches are swollen into large streams. Notwithstanding these discomforts, the men are in good spirits, and enjoy themselves in singing, telling stories, and playing monte.

December 3.—The rain ceased falling about 8 o'clock this morning; and, the clouds breaking away, the sun cheered us once more with his pleasant beams. The battalion was formed into a hollow square, and, the order of the day being read, we resumed our march. Our progress, through the deep mud, was very slow. The horses were constantly giving out, and many were left behind. The young and tender grass upon which they feed affords but little nourishment, and hard labour soon exhausts them. We encamped on a low bluff, near the arroyo, timbered with evergreen oak. Distance 8 miles.

December 4.—I was ordered with a small party in advance this morning. Proceeding up the valley a few miles, we left it, crossing several steep hills sparsely timbered with oak, from which we descended into another small valley, down which we continued to the point of its termination, near some narrow and difficult mountain gorges. In exploring the gorges, we discovered the trail of a party of Californians, which had passed south several days before us, and found a horse which they had left in their march. This, doubtless, was a portion of the party which captured Mr. Larkin, and had the engagement between Monterey and St. Juan, on the 17th ult. The main body coming up, we encamped at three o'clock. The old grass around our camp is abundant; but having been so much washed by the rains, and consequently exhausted of its nutritious qualities, the animals refused to eat it. The country over which we have travelled to-day, and as far as I can see, is mountainous and broken, little of it being adapted to other agricultural purposes than grazing.

Thirteen beeves are slaughtered every afternoon for the consumption of the battalion. These beeves are generally of good size, and in fair condition. Other provisions being entirely exhausted, beef constitutes the only subsistence for the men, and most of the officers. Under these circumstances, the consumption of beef is astonishing. I do not know that I shall be believed when I state a fact, derived from observation and calculation, that the average consumption per man of fresh beef is at least ten pounds per day. Many of them, I believe, consume much more, and some of them less. Nor does this quantity appear to be injurious to health, or fully to satisfy the appetite. I have seen some of the men roast their meat and devour it by the fire from the hour of encamping until late bed-time. They would then sleep until one or two o'clock in the morning, when, the cravings of hunger being greater than the desire for repose, the same occupation would be resumed, and continued until the order was given to march. The Californian beef is generally fat, juicy, and tender, and surpasses in flavour any which I ever tasted elsewhere. Distance 10 miles.

December 5.—I rose before daylight. The moon shone brightly. The temperature was cold. The vapour in the atmosphere had congealed and fallen upon the ground in feathery flakes, covering it with a white semi-transparent veil, or crystal sheen, sparkling in the moonbeams. The smoke from the numerous camp-fires soon began to curl languidly up in graceful wreaths, settling upon the mountain summits. The scene was one for the pencil and brush of the artist; but, when the envious sun rose, he soon stripped Madam Earth of her gauzy holiday morning-gown, and exposed her every-day petticoat of mud.

Our march to-day has been one of great difficulty, through a deep brushy mountain gorge, through which it was almost impossible to force the field-pieces. In one place they were lowered with ropes down a steep and nearly perpendicular precipice of great height and depth. We encamped about three o'clock, P.M., in a small valley. Many of the horses gave out on the march, and were left behind by the men, who came straggling into camp until a late hour of the evening, bringing their saddles and baggage upon their shoulders. I noticed, while crossing an elevated ridge of hills, flakes of snow flying in the air, but melting before they reached the ground. The small spring-branch on which we encamped empties into the Salinas River. The country surrounding us is elevated and broken, and the soil sandy, with but little timber or grass upon it. Distance 12 miles.

December 6.—Morning clear and cool. Crossed an undulating country, destitute of timber and water, and encamped in a circular valley surrounded by elevated hills, through which flows a small tributary of the Salinas. The summits of the mountains in sight are covered with snow, but the temperature in the valleys is pleasant. Distance 15 miles.

December 7.—Ice, the first I have seen since entering California, formed in the branch, of the thickness of window-glass. We reached the valley of the Salinas about eleven o'clock A.M., and encamped for the day. The river Salinas (laid down in some maps as Rio San Buenaventura) rises in the mountains to the south, and has a course of some sixty or eighty miles, emptying into the Pacific about twelve miles north of Monterey. The valley, as it approaches the ocean, is broad and fertile, and there are many fine ranchos upon it. But, higher up, the stream becomes dry in the summer, and the soil of the valley is arid and sandy. The width of the stream at this point is about thirty yards. Its banks are skirted by narrow belts of small timber. A range of elevated mountains rises between this valley and the coast. A court-martial was held to-day, for the trial of sundry offenders. Distance 8 miles.