Extract of a Letter from a i/hfiizuishe I fairer of Gen. IIooTs comtnan /. c *hitntiica!c l to tin ll'ushiir'ton Lilian, dated:—“fc\vN rr. BisMii,) i«N //. -.*2, I b 16. $'I hr knowing onrt» hero say that we •diall have a clever fight before reaching Chihuahua, am! some of lliem predict a defeat. Perhaps sil’ier all« we may reap laurels if peace does not arrest us.We are getting on well and harrnoni-ou*!y. The Illinois volunteers are reailv * + £ood soldiers, and I think will prove efficient,den. Wool is very popular and very ri^id. He talks plainly to the volunteers, but they serin to like it. The general hnlt; exhibited creat knowledge of the detail* of service and a high degree of adn cmini.-trative talent. On the whole, 1 think we m:*v look forward to an inn r- 10e«tin*T arid mtrcessful campaign, hut it \\ ill!4 be one of hardships and privations.”The movements of (ten. \\ ool are now watched with interest. It will be seen that his presence h anxiously wished for, ( to r inf rce (Jen. Tavlor. The N. O.*I i i * - - V t!i »i on the id S •ptcm* hi r, he had his headquarters in San Antonio. Hut a le’ter of a later date M ites ihat if»e writ* r had met the advancc •ni; nl of Ceil. Wool's armv, destined toJM *occupy Chihuahua, on the banks of theLeon, a small river three miles from San \ntnnin. It was cimmandtd by Col.■ rII rnev, and e moted of the Washington*Vrtillerv, i ao enrninnie* of the 2 I dra*• • goons two companies of regular infantry, i regiment of Illinois volunteers and thlt;* Arkansas Mounted (iunmen. The ad-vanced guard began their march on the 2(itli nil., accompanied by 200 w igons. (ien. Wool w;»* expected to follow tip the remainder ol the troops with all expedition. I he roids the r uy will have to traverse, to reach the point indicated in (Jen. Wool's instructions, arc said to be almost impracticable, very poorly supplied with water; hut nothing can daunt ilie ardor and energy of our brave soldiers. Though not numbering in all 11.000 men, they are advancing into the hear* ol Mexico; and their only desire i« to meet the foe in arm*, in order to em- j ul «te the glorious deeds of their brethren at Monterey.—lki'hmonl /Inquirer,