Interesting Chess Match. - We have the pleasure of announcing that a match has been arranged between Mr. Reichhelm and Captain Mackenzie, the champion of the New York Tournament. The match will commence, in New York, in a few days, and will be a very exciting contest.

Chess. - An Important Match Forthcoming. - A match of great interest to the chess players of this country, and one which will not be without its influence upon the estimation of American chess players abroad, will be commenced, at the New-York Chess Club, early next week. The contestants are Mr. Geo. H. Mackenzie, one of the best of the English players, and victor in the late tournament, and Mr. G. Richelm [sic], the best player in Philadelphia, and, after Mr. Murphy [sic], the first of American players. The match is to be decided by the winning of seven games by either player, and it is stipulated that neither shall consume more than an hour in making 12 moves. No money is to be staked upon the match, as the New-York and Philadelphia Chess Clubs object to the practice of betting upon chess, but the expenses of each player will be met by the opposing Club. Mr. Morphy, having practically retired from the game, the winner of this match will have a title to be considered the chess champion of the United States.

Chess - Philadelphia vs. New-York. As a sequel to the late Tournament of the New-York Chess Club, a match has at length been definitely arranged between Capt. G. H. Mackenzie, of the New-York clubs, and Mr. Reichelen [sic], champion of the Philadelphian chess-players. The conditions of the encounter are that the first winner of seven games is to be declared the conqueror; that the time allowed for consideration of each move shall not exceed an average of five minutes, but may be vided in such manner as may suit the player, provided that he does not consume more than two hours for twenty-four moves, and that the hours of play shall be daily from 2 to 5 and 8 to 11 P.M. Mr. Reichelin [sic] arrived in this City yesterday afternoon, and the commencement of play was agreed upon for 8 o'clock in the evening, with scarcely a possibility, however, of getting through the first game without adjournment.

Chess - Commencement of the Reichhelm-Mackenzie Match. - The match at chess between Messrs. Mackenzie and Reichhelm, to which we referred a few days ago, was commenced last night at the New-York Chess Club. Although but a short notice of Mr. Reichhelm's arrival had been given, the play was witnessed by about 50 gentlemen, among them Messrs. Irving, the President of the Club, Mead, Stanley, Wells of Philadelphia, Ware of Boston, Breutzinger [sic], Zerega, Berneir, Barnet [sic] and Warner. The first game between the distinguished contestants was begun at 8 p.m., and at 11 o'clock, the hour of adjournment, the board had been pretty well cleared of pieces, and Mr. Reichhelm was the gainer of a pawn. Capt. Mackenzie had the opening and played the "Ruy Lopez Knight's Game." The game will be continued this afternoon at 2 p.m.

The Philadelphia-New York Match. We alluded, last week, briefly to the fact that a match has been arranged between Mr. Reichhelm, of this city, and Mr. George H. Mackenzie, the champion of the New York Tournament. It has been the intention of the Philadelphia Club to challenge whoever might be the winner in the late contest in New York, and the match which we have had the pleasure of arranging between Messrs. Reichhelm and Mackenzie is the result of that purpose. [...]

The present match, which commenced last evening, at the New York Chess Club, is for the first seven games. By mutual consent, the moves are to be limited to an average of five minutes, and only one game is to be played at each sitting, unless otherwise agreed upon. Mr. Mackenzie has already played several important matches with Messrs. Anderssen, Deacon, McDonnell and Medley, besides his recent play in the New York Tournament, while Mr. Reichhelm has as yet played none but unimportant matches with members of the Philadelphia Club, and occasional off-hand contests with visitors from abroad. We shall report the progress of the match from day to day, in our regular editions.

An Interesting Match At Chess. One which will no doubt prove to be of great interest to the chess players of this country, and one which is calculated to have its influence upon the estimation of American chess players abroad, will be commenced, at the New York Chess Club, early next week. The combatants are Mr. Geo. H. Mackenzie, one of the best of English players, and victor in the late tournament, and Mr. G. Richelm [sic], the best player in Philadelphia, and, after Mr. Morphy, the first of American players. The match is to be decided by the winning of seven games by either player, and it is stipulated that neither shall consume more than an hour in making 12 moves. No money is to be staked upon the match, as the New York and Philadelphia Chess Clubs object to the practice of betting upon chess, but the expenses of each player will be met by the opposing club. Mr. Morphy, having practically retired from the game, the winner of this match will have a title to be considered the Chess Champion of the United States.

Philadelphia and New York. A match of seven games is pending, between Captain Mackenzie, the winner in the late N. Y. Club tournament, and Mr. G. Reichhelm, the strongest player amount the Philadelphians. It comes off here, at the Club Room in the University Building. The first game was to be played on Thursday evening.

The Grand Match Between Philadelphia and New-York. In conformity with a previous announcement in this paper, the grand trial of skill between the well-known chess players, Mr. Reichhelm and Capt. Mackenzie, the respective representatives of the Philadelphia and New-York amateurs, was commenced on Thursday evening, at 8 o'clock precisely. The attendance both of members and visitors at the rooms of the New-York Club was very large, and represented the elite of the chess fraternity of this City and its environs, several gentlemen from Philadelphia being likewise present.

Up to a late hour last evening, this eventful encounter had progressed as follows:

Chess in New York. First game in the match between Mr. G. Reichhelm, of Philadelphia, and Captain Mackenzie, of New York.

GAME II. After a short recess, at about 3 P.M., hostilities were resumed and a second game commenced, when Mr. Reichhelm, having the first move, led off in very dashing style, with the attack known as the Evans Gambit, wherein, for strategic reasons, on the thirteenth move he sacrificed his king's knights for adverse king's bishop's pawns. At the usual hour for adjournment, 5 P.M., 26 moves had been made on either side, the attitude of the contending forces being highly critical, and the evening session awaited with corresponding interest by a large and critical gallery of spectators. Punctually at 8 o'clock play was again resumed, and notwithstanding a desperate struggle, in the course of which Mr. Reichhelm succeeded in recovering a portion of the advantage lost, he succumbed to an inevitable checkmate, occurring on the fifty-fifth move, at 9:30 o'clock.

The second game began on Friday afternoon, Mr. Reichhelm opening an Evans's Gambit. Much fine play was exhibited in this game, which was a beautiful specimen of this celebrated opening. [From To-day's New York Tribune.] The second game was immediately commenced, and Mr. Reichhelm, having the move, adopted the aggressive opening known as the Evans's Gambit. In the early part of the game, to maintain his attacks, he sacrifices a Knight, and, with the same object, declined a subsequent chance to regain. The assault, which he gained, did not, however, prove compensative for the price paid for it; and, after a lengthened contest, during which the game was reduced to an interesting end-position, Mr. Reichhelm resigned upon the fifty-fifth move.

GAME III. Immediately after the conclusion of Game II., the pieces were reset for number three; when Capt. Mackenzie once more attacked after the manner of Ruy Lopez. We left the scene of conflict at a late hour, and although lookers-on have no right to make remarks upon a game during its progress, there can be little harm in stating that all the advantages of position appeared to us to be in favor of the New-York player.

In the blind game, which was immediately begun, Mr. Mackenzie again opened with the Ruy Lopez Knight's Game. Mr. Reichhelm made a disastrous mistake by hasty play, in the opening, losing a piece, and no subsequent efforts, although he struggled gallantly, were efficacious to save the game, which he resigned on the thirty-first move.

The fourth game will be commenced this afternoon at 2 o'clock.

The Reichhelm-Mackenzie Match. [From To-day's Tribune.] The progress of this match, which is being observed with greatest possible interest by chess-players, has, thus far, been of a rather unanticipated nature. Mr. Reichhelm, although he has in parts of the games contested exhibited great skill, has as yet failed to maintain his high reputation by any sustained effort. In the last three games his play has been marked by lamentable and disastrous oversight. On Saturday afternoon the fourth game was commenced, and through one of these slips was finished in favor of Mr. Mackenzie in 1 ¾ hours. The game for the evening was postponed, at the request of Mr. Mackenzie, until this afternoon, when it was expected the Philadelphia player will display his undoubted ability, and that there will be a rough fight.

[The result of the game of Saturday afternoon is more remarkable, as Mr. Reichhelm's position, after an hour's play, was apparently a very fine one. He was laboring, on Saturday morning, under a temporary indisposition, but we did not suppose it would be sufficient to affect his play as it seems to have done. It must have been some most extraordinary oversight that lost the game.-Ed. Bulletin.]

Chess - The Reichhelm-Mackenzie Match. - The way in which this match has progressed, thus far, is exciting great astonishment among those who are familiar with the respective strength of the two contestants, and seems to prove that chess, as well as other games, is pervaded by a "glorious uncertainty." Mr. Reichhelm the American player, has exhibited some exceedingly fine play, but has managed, through some lamentable mischance, to make some blunder in the early part of each game, except the first, from the effect of which no after-efforts have been able to shield him. Yesterday afternoon he lost his fourth game, by weak play in the opening, Mr. Mackenzie having again attacked him with the formidable "Ruy Lopez." In the evening Mr. Reichhelm commenced with his favorite "Evan' Gambit," and the game was proceeding lively when on the 18th move he perpetrated a mistake, which lost him a couple of pawns, and allowed an exchange of queens. After this he made a grand rally, organized a powerful assault upon his adversary's king, and the "exchange" converted that gain into a piece, but finally lost through his minority of pawns. He played this part of the game in a style worthy of Labourdonnais. The score now stands, Mackenzie, 5. Reichhelm, 0. Drawn 1.

The Great Match Between Philadelphia and New-York. The exciting contest between Mr. Reichhelm, the Philadelphia Chess champion, and Capt. Mackenzie, winner of the late Tournament of New-York amateurs, has been brought to a sudden termination by the resignation of the former player. According to the terms of the match the winning of seven games became necessary to constitute a victory on either side; and so far as the play progressed, six games only had been played, of which number Capt. Mackenzie had won five, the one remaining having been drawn. A defeat so signal is certainly somewhat unusual among players deemed at all well matched; but the effects of that to which Mr. Reichhelm has now so courteously succumbed, will be greatly diminished from the consideration of the far greater opportunities for good practice which his able antagonist has enjoyed than could have fallen to his lot of late years in Philadelphia; and we doubt not that the fulsome and absurd adulation from which Mr. Reichhelm has suffered at the hands of certain ill-advised admirers having access, strangely enough, to the columns of a portion of the press have been as annoying to him as they have been offensive to good taste generally, and the feelings of true chess players in particular.

The below printed is the sixth and last game occurring in this match, and, with exception of Game I, given in the Times of last Saturday, will be found the best contested and most interesting of the series.

Termination of the Chess Match - Mackenzie the Winner. [From the N. Y. Tribune.] The match between Messrs. Reichhelm and Mackenzie was brought to a termination yesterday, by the resignation of the former player. He attributes his incapacity to bring the contest to a successful conclusion, to an attack of illness, which since Friday, has seriously affected his mental powers, and destroyed that fine balance of mind which is so necessary to a match of this important and taxing kind. The score remained as stated in yesterday's Tribune, no additional games having been contested.

The Reichhelm-Mackenzie Match. We doubt if anybody has been as much astonished at the result of this match as Captain Mackenzie himself. In six sittings the contest was decided by the resignation of Mr. Reichhelm, he having failed to score a single game against Captain Mackenzie's five. We regret, on some accounts, that the battle was not fought out, but Mr. Reichhelm is, of course, the best judge of the propriety of continuing such up-hill work.

We have no intention of making excuses for this unexpected result of the match. We are naturally disappointed at it, as we had every reason to expect a very different issue, both from our general knowledge of our colleague's real Chess strength and from the result of his former play with his recent antagonist. We have no fault to find with anything or anybody connected with this match. Mr. Reichhelm and our self were received and treated with every courtesy, as might have been expected, and we are satisfied that the disappointment felt in Philadelphia is shared by many of the New York gentlemen who witnessed the match.

There are one or two remarks which we may make without at all detracting from the laurels of the winner of this contest. In our judgment the result illustrates very strongly the advantage of practice in match playing. Out of sheer nervousness arising from the novelty of his position, Mr. Reichhelm played a full Knight below his ordinary strength, all through the match. In every instance (at least in the four games which we have seen at this time of writing) Mr. Reichhelm committed blunders so glaring as to prove that he was not at all in training for a contest with an experienced steady opponent. In the actual matter of Chess-play, we do not hesitate to express the opinion that the superiority was on Mr. Reichhelm's side. In no case was he outplayed by his adversary. Captain Mackenzie very sensibly adopted the wary policy of husbanding his forces, and allowing his antagonist to exhaust himself in his powerful attacks, counting upon the losses in the early part of the games to tell, as they always did, upon the issue.

We do not like to refer to the theory advanced by the New York Tribune, in explanation of Mr. Reichhelm's failure. We were aware of his indisposition as early in the match as Saturday morning, but urged him to play at the usual hour. Knowing how liable any proposition for postponement was to misrepresentation, we thought it better to risk the loss of a game than to be thought desirous of evading the issue.

Mr. Reichhelm is yet a comparatively you Chess player, and we believe that the effect of this match will not be lost upon him. The experience, bought at so high a price, is most valuable, and we hope at some future day to see him again cross swards with his late antagonist.

Captain Mackenzie has fairly won the American championship, but we doubt if he will long be allowed to enjoy his laurels unchallenged. These contests give a greatly increased interest to the noble game, and there are not a few ambitious aspirants for Captain Mackenzie's laurels. He has gained them in a fair fight, and we congratulate him upon his victory.

The Match Between Philadelphia and New York. Captain Mackenzie, the winner in the late N. Y. Chess Club Tournament, has also won the match above-named. A drawn game at the start led to the hope that the contest would be a close one; but the Captain, having subsequently won five games in succession, Mr. Reichhelm, on Tuesday afternoon, abandoned the conflict as a hopeless one on his side. The games have been so widely published by the daily papers, that we do not give them place.

Chess In The Metropolis. - Last week we gave the result of the great chess match between Captain Mackenzie, of this city, and Mr. Reichhelm, of Philadelphia, up to that time, when, it will be remembered, the former had gained considerable advantage. Play was resumed on Monday, and the match resulted on Tuesday in the victory of the Captain, by the resignation of Mr. Reichhelm, on the plea of sickness, under which he had labored since the Friday previous. It is unfortunate that Mr. Reichhelm should have been obliged to resign for such a cause, as this match was looked upon as a test of strength between the leading players of the two cities. We therefore hope that another meeting may be arranged so soon as the gentleman from the Quaker City shall have recovered his health. The result of the late encounter was: Captain Mackenzie won five; drawn, one.