NEW YORK, August 25, 1864.

Honorable W. H. SEWARD:

MY DEAR SIR: As I omitted to send you the inclosed, I now take the liberty to present it for your consideration, with the hope that the Government will take this favorable opportunity to avoid a most calamitous extremity. It is not for a head of one of the departments to overlook the importance of yielding to the cogent necessity of circumstances, and the more especially when in coercing a rigid execution of the law, the highest interests of the country are placed in jeopardy. I come in contact with so many Honorable and patriotic gentlemen entertaining the same opinions I do with regard to the draft, and one this morning who was wounded in the recent riot, who would like an opportunity to revenge himself, that I cannot hesitate in a proffer of my views.

If you can quiet the fears of this city you will gain strength everywhere, and the sooner the decision be made the more certain will be its beneficial effects. A disturbance in this place will be followed with great embarrassments elsewhere, in the promotion of which we have many politicians of the worst kind of grade. I shall see Mr. Blunt in the course of the day and learn from him what are our dangers and what may be our hopes. It has afforded me much satisfaction to see the conservative conduct of the people of Indianapolis since the exposure. It looks as if the West has not run mad hopelessly.

Yours, truly,

A. HAMILTON.

[Inclosure.]

THE DRAFT.

Credit claimed for 26,000 naval recruits.

On Monday the county volunteer committee forwarded to Governor Seymour and Major Townsend, the Commission appointed by the Secretary of War to ascertain the number of naval enlistments in this State since the commencement of this war, a voluminous report containing the names, ages, and residences of over 26,000 naval recruits.

This report will be forwarded immediately to the War Department by the commissioners, and every possible exertion will be made to have this county credited with these 26,000 men. If they are successful in their efforts, and many who are in positions to be able to judge think they will be, this city will have a surplus of some 6,000 men and there will be no necessity for a draft.

Important meeting of the Board of Supervisors-Resolutions adopted asking for a postponement of the draft.

The Board of Supervisors met yesterday afternoon, Supervisor Blunt occupying the chair in the absence of the president.

The quota of this city.-Supervisor Purdy offered the following resolution respecting the adjustment of the city's quota, which was adopted unanimously:

Whereas, it is currently reported that no correction of the error and injustice done in estimating the quota for the county of New York, under the call of the President of the United States for 500,000 men for the Army, has as yet been made; and

Whereas, the county of New York has ever promptly responded to the call of the President and sent to the Army over 100,000 men, and expended over $15,000,000