Henderson had an engagement yesterday near Mexico, and capture 40 prisoners. He expected another fight this morning. If any of our troops are withdrawn from there at present the scattered insurgents will collect, and again destroy the railroad and telegraph line. We may expect, however, that most of these gangs will be broken up in the course of the next two or three weeks.

Price's army is still near Springfield. His forces are variously estimated from 12,000 to 40,000. About 50 miles farther south it is said there is a force of 18,000 Arkansas, Texan, and Indian troops marching to his assistance. Such is the substance of the telegrams from General Curtis and Colonel Steele. In order to ascertain the truth as to Price's position and numbers as nearly as possible, I sent out the cavalry from Rolla to drive in his pickets and feel his position and strength, intending to move the infantry and artillery to their support. On receiving the President's telegrams I suspended the latter movement, and for several days have heard nothing from Carr's cavalry. If Price should be found to have anything like his reputed forces, it would probably be necessary to send against him also most of the available forces near Sedalia not now absent north of the river pursuing rebel bands and bridge-burners. For the reasons already given, these troops are still held in position.

If the troops at Sedalia and Rolla are not either sent against Price or put in position to keep him in check, he will unquestionably return to the Missouri River, where he will be received a very large mass of insurgents, who have concealed arms and ammunition. This information comes from so many reliable sources that I cannot doubt its correctness. The question is therefore a very plain one. If a sufficient number of troops are to be withdrawn from Missouri at the present time to constitute an expedition up the Cumberland strong enough to afford any reasonable hope of resisting an attack of the enemy, we must seriously peril the loss of this State. I can make with the gunboats and available troops a pretty formidable demonstration, but no real attack. The gunboats are not yet ready, but probably will be within a week or two. With good luck here, and the receipt of the 11,000 arms ordered by you a month ago, we can by their early part of February throw some 15,000 or 20,000 additional troops on that line. If you insist upon my doing this now, your orders will be obeyed, whatever may be the result in Missouri.

Advices received yesterday from Cairo are to the effect that no large forces have moved the vicinity of Columbus in the direction of Bowling Green.

Pillow was ordered forward, but, disapproving order, he resigned and went South.

Very respectfully, your obedient servant,

H. W. HALLECK,

Major-General.

CAIRO, ILL., January 9, 1862.

Major-General HALLECK, Saint Louis:

The fog is so dense that it is impossible to cross the river. This will defer any movement for on day. A steamer is now lying across the channel at Dogtooth Bend, which will prevent re-enforcements arriving by river until she is removed. Have re-enforcements started?

U. S. GRANT.