As you ar aware, our gunboats are not well adapted to fighting downstream, for want of steam power and other causes, while the exposed state of the river above in case of defeat would prove extremely disastrous. The fall of this stronghold was predicated upon the fall of Memphis or our having a large land force to co-operate with us, and now we are left without means hardly commensurate with the work we are expected to accomplish; we have not troops enough to occupy, even if we take, this place.

I have to-day, as well as previously, informed the Secretary of the Navy of the state of things here, and from the most reliable authority I can command the rebels have at least 6,000 men in their fortifications and eleven gunboats. The latter we keep mostly below the forts with our mortars. It is reported that the heavy iron-clad steamer Louisiana is daily expected, with several other gunboats, from New Orleans. We are as well prepared as possible, with our means, for an attack, offensive or defensive, and I shall do all in my power to secure the great object of the expedition.

I am, very respectfully, your obedient servant,

A. H. FOOTE,

Flag-Officer.

P. S.-In a picket skirmish yesterday the rebels lost 1 killed and 1 or 2 wounded; no loss on our side.

[Inclosure.]

SAINT LOUIS, April 20, 1862.

Flag-Officer ANDREW H. FOOTE:

SIR: The Essex will be off the dock on Tuesday next. I have only received in money a little over $3,000, and in consequence of delays, under your order to postpone the work for a time, my expenses have increased. At the time you required my estimates, and the delay caused by the time required to furnish them, I could have purchased timber for $27 per thousand, but in the mean time this material was bought up for private purposes, and I was therefore compelled to pay a higher price; and, besides this, the want of funds placed me completely at the mercy of the dock company, as I was compelled to take their materials very much against my own inclination.

I purchased the Alec Scott for the sum of $8,500. The hull of this vessel I had examined before making the purchase. Her machinery, with some little repairs, as well as boilers, are good enough. Besides, she is fast, and has a spacious hold. I expect her here next week, when I will at once get to work on her. I have already opened negotiations for another, which will be closed in a day or two. The War Department informs me the funds will be supplied here.

If you want the services of the Essex, funds must be at once supplied to complete her. At present we must pay for labor or stop the work; if so, she will be a serious loss to the squadron. The materials are all here. We now only want money for labor. This is indispensable. I have done all in my power to push the work, and no doubt the mental anxiety which I have undergone has retarded my recovery, but at present I am improving rapidly and am out of the hands of he doctor.

You are well aware I do not seek personal aggrandizement, but only aim to be useful to the Government, and hence when I complain it is not on my own account, but it is that the affairs of the vessel that I command or am attending to should progress rapidly and be made