About a year and a half since, Lord Hastings wrote to Sir John Doyle a private letter, in which he complained bitterly of the conduct of the Board of Directors, saying as he had lost their confidence, he should remain in India no longer. Doyle showed this letter, and had authority from the Directors to say that so far from Lord Hastings having lost their confidence, they entertained the highest opinion of him, and should be extremely sorry if he returned. In answer to this, Lord Hastings writes to Doyle to say he is glad to find the Directors are satisfied with his conduct, but that he should return to England, as he found his health and spirits give way, and he was anxious to return. Upon the strength of this letter the Ministers thought proper to act, and notified their intention of naming Canning for his successor, transmitting the letter of Lord Hastings to Sir John Doyle to the Court of Directors as their grounds for appointing him a successor. The Court return the letter, saying they could not receive a private letter to a private friend as a ground for such an appointment, and on this objection it was decided to write to Lord Hastings to know decidedly his wishes on the subject of return. This letter was prepared by the Court of Directors, and ended in leaving it entirely at his option to remain or come home; and being sent to the Board of Control for approbation, B. Bathurst scratched out the latter paragraph, and left it with the intention of naming him a successor, in compliance with the wish expressed by him to Sir John Doyle. This letter went the 15th of last month, so that no answer can be had for ten months to come; and I have no doubt Canning will wait till that time under an assurance of supporting Government, unless anything turns up in the meantime to make it worth his while to take another position.