Went to see Bagatelle yesterday with the Duchesse de G----. Here the Duc de Bordeaux and Mademoiselle, his sister, pass much of their time. It is a very pleasant villa, and contains many proofs of the taste and industry of these very interesting children, who are greatly beloved by those who have access to them. Various stories were related to us illustrative of their goodness of heart and considerate kindness for those around them; and, making all due allowance for the partiality of the narrators, they went far to prove that these scions of royalty are more amiable and unspoilt than are most children of their age, and of even far less elevated rank. "Born in sorrow, and nursed in tears," the Duc de Bordeaux's early infancy has not passed under bright auspices; and those are not wanting who prophesy that he may hereafter look back to the days passed at Bagatelle as the happiest of his life. It requires little of the prescience of a soothsayer to make this prediction, when we reflect that the lives of even the most popular of those born to the dangerous inheritance of a crown must ever be more exposed to the cares that weigh so heavily, and the responsibility that presses so continually on them, than are those who, exempt from the splendour of sovereignty, escape also its toils. "Oh happy they, the happiest of their kind," who enjoy, in the peace and repose of a private station, a competency, good health, a love of, and power of indulging in, study; an unreproaching conscience, and a cheerful mind! With such blessings they may contemplate, without a feeling of envy, the more brilliant but less fortunate lots of those great ones of the earth, whose elevation but too often serves to render them the target at which Fortune loves aim her most envenomed darts. Passed the greater part of the morning in the house in the Rue de Matignon, superintending the alterations and improvements to be carried into execution there. It has been found necessary to build an additional room, which the proprietor pledges himself can be ready for occupation in six weeks, and already have its walls reached nearly to their intended height. The builders seem to be as expeditious as the upholsterers at Paris, and adding a room or two to a mansion appears to be as easily accomplished as adding some extra furniture. One is made to pay dearly, however, for this facility and expedition; for rents are extravagantly high at Paris, as are also the prices of furniture. Already does the terrace begin to assume the appearance of a garden. Deep beds of earth inclosed in green cases line the sides, and an abundance of orange-trees, flowering shrubs, plants, and flowers, are placed in them.