A chronic dispute which has gone on from the very first year of the school’s existence, between the exclusive study of abstract mathematics on the one hand, and their early practical application on the other, was brought to a head (though it has scarcely been set at rest) by this commission. All the alterations effected have been in the direction of eliminating a portion of the pure mathematics, and of reducing abstract study to the limits within which it was believed to be most directly applicable to practice. The results, however, are still a subject of vehement dispute, in which most of the old scientific pupils of the Polytechnic, and many of what may be styled its most practical members, the officers of the artillery and engineers, are ranged on the side of “early and deep scientific study _versus_ early practical applications.” It is, indeed, a question which touches the military pupils nearly, since it is in their case particularly that the proposed abstract studies of the Polytechnic might be thought of the most doubtful advantage. We do not try to solve the problem here, though the facts elsewhere stated will afford some materials for judgment. We incline to the opinion of those who think that the ancient _genius loci_, the traditional teaching of the school, will be too strong for legislative interference, and that, in spite of recent enactments, abstract science and analysis will reign in the lecture-rooms and halls of study of the Polytechnic, now as in the days of Monge. II. AN OUTLINE OF THE MANAGEMENT AND OF THE ESTABLISHMENT OF THE SCHOOL, ETC. The Polytechnic, as we have said, is a preparatory and general scientific school; its studies are not exclusively adapted for any one of the departments to which at the close of its course the scholars will find themselves assigned; and on quitting it they have, before entering on the actual discharge of their duties of whatever kind, to pass through a further term of teaching in some one of the schools of application specially devoted to particular professions. The public services for which it thus gives a general preparation are the following: _Military: Under the Minister at War._ Artillery (_Artillerie de terre_.) Engineers (_Génie_.) The Staff Corps (_Corps d’Etat Major_.) The Department of Powder and Saltpetre (_Poudres et Salpétres_.) _Under the Minister of Marine._ Navy, (_Marine_.) Marine Artillery (_Artillerie de mer_.) Naval Architects (_Génie maritime_.) The Hydrographical Department (_Corps des Ingénieurs Hydrographes_.) _Civil: Under the Minister of Public Works._ The Department of Roads and Bridges (_Ponts-et-chaussées_.) The Department of Mines (_Mines_.) _Under the Minister of the Interior._ The Telegraph Department (_Lignes Télégraphiques_.) _Under the minister of Finance._ The Tobacco Department (_Administration des Tabacs_.)