[Sept. 19.] Some of the American scouting parties fall in with those of the British, and with great boldness begin the attack, about one o’clock at noon. The firing is no sooner heard by gen. Philips, than he makes his way, with a part of the artillery, through the wood, and renders essential service. Each commander supports, reinforces, and orders different regiments to engage; and the battle is hot and obstinate on both sides till about half past two o’clock, when it ceases for half an hour. The American and British line, being fully formed, the action is renewed and becomes general at three. Both armies appear determined to conquer or die. There is one continual blaze of fire for three hours without intermission. The report of the muskets resembles an incessant roll beating on a number of drums. The Americans and British alternately drive and are driven by each other. Three British regiments, the 20th, the 21st, and the 62d, are in constant and close fire for near four hours. All suffer considerable loss; the 62d, which was 500 strong when it left Canada, is reduced to less than 60 men, and to 4 or 5 officers. The 24th regiment, belonging to Frazer’s brigade, with the grenadiers and a part of the light-infantry are brought into action. Breyman’s riflemen, and some other parts of his corps, are also of service; but only act occasionally. The American troops in action, are those under Morgan and Durbin; the first, second and third New-Hampshire regiments; the eighth, ninth and tenth Massachusetts; the second and third New-York; and a Connecticut regiment of militia. The ninth Massachusetts regiment, col. Wesson’s, is warmly engaged, and greatly distinguishes itself. Col. Scammell, of the first New-Hampshire regiment, is peculiarly active, enterprising and brave; and leads on his men close to the enemy with great undauntedness, before he suffers them to fire. Capt. Jones, with his brigade of British artillery, behaves with the utmost intrepidity. His four cannon are repeatedly taken and retaken. He is killed; other officers are wounded; and thirty-six out of forty-eight of the matrosses, are killed or wounded. Few actions have been characterized by more obstinacy in attack or defence, than is the present. The British bayonet is repeatedly tried without effect. During the engagement many Americans place themselves in high trees in the rear of their own line; and there is seldom a minute’s interval of smoke in any part of the British line, without officers being taken off by a single shot. One is aimed at Burgoyne, but passes through the arm of captain Green, aid-de-camp to Philips, while delivering a message. The British commander’s escape is owing to the captain’s having a laced furniture to his saddle, which occasions his being mistaken for the general. Toward the close of the day, gen. Gates orders out of camp to the field of battle the 10th Massachusetts regiment under col.