We are left without precise news from the seat of the war which Ibrahim Pasha, the son of Mohammed Aly, conducts in the Hedjaz against the Wahabi. Until within the last two months, he had not pushed on farther than Hanakye, a station three days journeys in advance of Medina, towards the interior of the Wahabi country. He is reported to have obtained several advantages over small corps of the enemy, and to have defeated them even in a more important battle, but his success appears not to have been decisive, as he has not advanced. Meantime reinforcements are continually sent to Arabia. Three Frenchmen who are in the suite of Ibrahim Pasha, have written lamentable letters to Cairo, stating that they were one night robbed of their whole baggage, and left in their shirts, while sleeping in a tent adjoining to that of the Pasha, whose military chest was carried off on the same occasion. A frigate is building at this moment at Bombay, for Mohammed Aly, with which he intends to harass his enemy in the Persian gulf; and to protect his commerce in the Red Sea which he daily extends, and from which he will succeed to shut out in a short time all private adventurers from Egypt and the Hedjaz. _5th of June._ I have sent off by this opportunity, a packet to Mr. Hamilton, containing a collection of popular sayings of the Arabs of Cairo, written in the vulgar dialect of the city. Captain Gambier, of the Myrmidon, who has come here for a few days, and who departs immediately for Malta, has promised to forward both packets from thence. I hope that within a few weeks, the colossal head will also be embarked at Alexandria.