I have just received the inclosed note from General Cooper, and inclose it, together with the article in question, for your perusal.

I am, very respectfully, &c.,

R. E. LEE,

General.

[Inclosure.]

APRIL 25, 1862.

General R. E. LEE, &c.:

GENERAL: In the Examiner of to-day is published an article from the New York Herald, giving verbation the telegraphic dispatch of General Beauregard of the 9th instant to me, which was in cipher.

This information appears to have been communicate from Nashville under date of April 15. The only copy that was made from the original dispatch was sent to you, together with the telegraph, in cipher; the rough, from which the copy sent you was made, has never been out of my possession, and I am therefore led to the conclusion that the telegraph communicated from Nashville must have been obtained somewhere in that quarter.

Under the circumstances would it not be well to advise General Beauregard of the fact, an suggest a change in his cipher or the adoption of an entirely new one?

Very respectfully,

S. COOPER,

Adjutant and Inspector General.

P. S.-I inclose the article referred to.

[Subinclosure.]

We take the following from the New York Herald of the 21st:

HIGHLY IMPORTANT.-INTERCEPTION OF A VALUABLE DISPATCH FROM GENERAL BEAUREGARD.

NASHVILLE, TENN., April 15, 1862.

The latest information from the South is of the utmost importance. Beauregard's army had been terribly demoralized, and, according to his own confession, he has now only 35,000 men. The following telegram has been intercepted by General Mitchel, and is a full confession of the hopelessness of the rebel cause in the West. I append it verbation, leaving you to comment on its importance:

CORINTH, April 9, 1862.

General S. COOPER,

Richmond, Va.:

All present probabilities are that whenever the enemy move on this position he will do so with an overwhelming force of not less than 85,000 men. We can now muster only about 35,000 effectives. Van Dorn may possibly join us in a few days with about 15,000 more. Can we not be re-enforced from Pemberton's army? If defeated here, we lose the Mississippi Valley and probably our cause; whereas we could even afford to lose for a while Charleston and Savannah for the purpose of defeating Buell's army, which would not only insure us the valley of the Mississippi but our independence.

G. T. BEAUREGARD.