What is this I hear of a certain Noble Duke, well-known in sporting circles, having accepted a three months' engagement to appear in a "comic character sketch of his own composition," at a long-established East End-Music Hall? If there is any truth in the rumour, I should like to ask _what the Duchess has been about?_ * * * * * A distinguished Oxford Mathematical Professor has, just after prolonged and patient research, established the undoubted certainty of the following interesting facts beyond any possible question or controversy:--That the quantity of Almond Rock Hard Bake, consumed in the United Kingdom in the year terminating on the 15th of May last, amounted to 17 lbs. 9 oz. for each member of the population, including women and children. That if at all the old and discarded Chimney Pot Hats for a like period were collected in a heap, and packed closely together, they would fill a building twice the height of St. Paul's, and three times the length of the Crystal Palace. That winners of the Derby who have become eventually four-wheeler cab-horses are ninety-six in number, but that there is _only one authentic_ instance of a four-wheeler cab-horse having become a Derby winner. * * * * * So great is the craze for the newest idea in locomotion that it is calculated that including Duchesses no less than 1470 _grandes dames_ whose names are well-known in Society, now pass Piccadilly Circus on the outside of the London General Omnibus Company's vehicles, between the hours of 8 A.M. and 10 P.M. daily. * * * * * A PASSPORT TO THE BEST SOCIETY, AND A GUARANTEE FOR RESPECTABILITY, is to be a diligent student of _Mr. Punch's_ works, and to have earned the abuse of the _Pall-Mall Gazette_. * * * * * THE OPERA-GOER'S DIARY.