The administration has dono wcll in giving the depredations along the Texas border tho consideration that their extent demanda, and the whole country ■will learn wiíh gratification that it lias been procticaUy decided to adopt a more vigorous policy in the treatment of the banditti who have been invading the United States territory f rom the Mexicau nido of the Rio Grande river. These depredations have been going on for years ; the iulmbitants of Texas, New Mexieo, and Lower Ciilifomift have been plundered incessantly, and the United States Government has expended millions of dollars in supporting troops along the border, who have inelTeetually endeavored to check the invasions nuu punish the brigands. It has long been evident that doublé the nuniber of troops employed will bc of.no avail in protecting the property of the Americans so long as they refrain from following tlie marauders across the river into Mexican territory. The Mexicau bandits are experienced seoundrels, and kiiow the country and the river so wel] that they are always able to escape to Mexican territory, where, undei the policy that has prevailed lieretofore, they are safe from pursnit. They thus escape witli their stolen property and their lives, only to renew their raids as they can dispose of their spoils and cxhaust the money io debauch. The Eio Grande border extends nearly 1,000 miles, so that it is out of all question to supposc it can bc eff'eetively policed on the American side while the Mexican Government is either favoiviblo to the bandits or too weak to lend any assistiince to punish them. Tliis is, lias been, and will probable continue to bo, the case. Thero is the strongest presumption that tho Mexicans encourage tl iis outliuvry. The policy which it is proposed to adopt is to notify the Mexiean Government that these raids must be stopped, and, if they are not immcdiately suspended, to authorizo the United Stfites troops ia follow tlie bandits across the river wherever they are encountered, attack them on Mexican territory, recover the property, and bring back such priflonors as they can takc for military trial on tlie American side.