In the London Gazette is published, under Whitehall, September 23d 1760, the copy of a letter from Colonel Eyre Coote, who commands his Majesty's forces in the East Indies, to the Right Hon. Mr. Secretary Pitt, dated at Arcot Village, the 13th of February, giving an account of the situation of our affairs on the coast of Coromandel since his arrival, and of our happy success. A summary of which is as follows, viz. That on the 25th of Nov. 1759, he took the field, and on the 27th invested Wandiwash, and erected batteries, and having made a breach on the 30th, took the place and made the garrison (which consisted of 5 subaltern officers, 63 private men, and 800 seapoys) prisoners of war: There were in the garrison 49 pieces of cannon, and a great quantity of ammunition. That on the 3d of December he invested Carangoly, and on the 10th being near the glacis, and having dismounted all their guns but four, Col. O'Kennelly, who commanded, sent out a flag of truce; and on account of his gallant defence, Col. Coote granted him the following terms, * That the Europeans should have leave to march out with their arms, two rounds per man, drums beating, and 6 days provision; the Seapoys to be disarmed and turned about their business.' The garrison consisted of 100 Europeans, (officers included) 200 Seapoys and 9 guns. On the 27th Lieut. General Lally arrived at Arcot, and took the command; and on the 9th of January the enemy were all in motion: on the 10th General Lally marched with all his army towards Wandiwash; and Col. Coote thereupon moved with our army along the banks of the river, in order to observe their motions, and cover our own country: That after several skirmishes and cannonading each other, till the 22d, about one o'clock, when a hot shot striking one of the enemy's tumbrils, it blew up, and about two their whole army gave way, and ran towards their own camp; but finding our army pursuing them, quitted it, and left us entire masters of the field, together with all their cannon, except 3 small pieces which they carried off. The number of cannon taken is as follows; One 32, one 24, three 20, two 18, one 14, two 3, and two 2 pounders, iron; three 6, four 4, one 3 and two 2 pounders, brass; in all 22 pieces: round shot, 3204, grape 110; besides tumbrils, and all other implements belonging to the train. Brigadier-General Busfy, Le Chevalier Godrille, quarter master general, and a number of other officers, were taken prisoners, most of whom were wounded. The French reckon they had 800 killed and wounded, 200 of which our people buried in the field; and have taken above 200 wounded prisoners, besides 40 not wounded. The loss on our side is 5 officers and 48 privates killed; and 8 officers and 41 privates wounded; and among our black troops, about 70 killed and wounded. The enemy's army commanded by Lieut. General Lally consisted of 2200 Europeans, including artillery and cavalry, 400 Cofferies, and between 9 and 10,000 black troops; 20 pieces of cannon in the field and 5 on their batteries against the fort where they blew up a large magazine of powder upon their retreat. Our army amounted to 1300 Europeans, including artillery and cavalry; 3000 black troops; 13 pieces of cannon and howitz. That during the whole engagement the officers and men have shown the greatest spirit. That the next day Col. Coote sent a detachment of cavalry to harass the enemy-- and January 26, finding that General Lally had retired with his broken troops to Pondicherry, he sent Capt. de Caen with 1000 horse, and 300 seapoys towards Pondicherry to destroy the French country, and marched the army to besiege Chettiput. The next day after, making a breach, Le Chevalier de Tilly, with his garrison, surrendered prisoners of war, consisting of 14 officers, 54 private and 300 Seapoys, with 73 Europeans wounded; 9 guns and a good quantity of ammunition. That Capt. Smith had taken a party he was sent after, of 10 Europeans, 50 Seapoys and 2 brass 8 pounders, a captain and 3 French commissaries. That on Feb. 2d, the army marched and encamped within two miles of Arcot-- and the garrison of Timmery surrendered prisoners of war; there were in it 6 guns, 1 sergeant, and 30 men. That on the 5th of February, Col. Coote having opened 2 batteries against the fort of Arcot, and on the 10th got within 60 yards of the glacis, the garrison surrendered prisoners of war: It consisted of 8 captains, 8 subalterns, 236 privates, and between 2 and 300 Seapoys: There were in it 4 mortars, 22 pieces of cannon, and a great quantity of all kinds of military stores. We had during the siege 7 non commissioned and private, killed; an Ensign and 16 wounded.