10. The Regimental Schools (_Ecoles Régimentaires_.) The military schools are under the charge of the minister of war, with whom the authorities of the schools are in direct communication. The expenses to the state of the military schools, including the pay of the military men who are employed in connection with them, for the year 1851, are as follows:-- For Polytechnic School at Paris, _fr._ 554,911. 91 “ Artillery and Engineers School at Metz, 187,352. 06 “ Infantry and Cavalry School at St. Cyr, 682,187. 35 “ Cavalry School at Saumur, 196,170. 27 “ Staff School at Paris, 145,349. 96 “ Gymnastic School of Musketry at Vincennes, 33,211. 33 “ Regimental Schools, 108,911½,30 From this sum, 2,224,542_fr._, should be deducted 421,372_fr._ secured from paying pupils, leaving the total cost to the state to be 1,803,308_fr._, or about $360,000, for about 2,100 pupils. The cost to the state for training an officer of Artillery and Engineers is about $1,500, and that of an officer of the Staff is about $1,400. SUBJECTS AND METHODS OF INSTRUCTION IN MATHEMATICS AS PRESCRIBED FOR ADMISSION TO THE POLYTECHNIC SCHOOL OF FRANCE. “L’ÉCOLE POLYTECHNIQUE” is too well known, by name at least, to need eulogy in this journal. Its course of instruction has long been famed for its completeness, precision, and adaptation to its intended objects. But this course had gradually lost somewhat of its symmetrical proportions by the introduction of some new subjects and the excessive development of others. The same defects had crept into the programme of the subjects of examination for admission to the school. Influenced by these considerations, the Legislative Assembly of France, by the law of June 5th, 1850, appointed a “_Commission_” to revise the programmes of admission and of internal instruction. The President of the Commission was THENARD, its “Reporter” was LE VERRIER, and the other nine members were worthy to be their colleagues. They were charged to avoid the error of giving to young students, subjects and methods of instruction “too elevated, too abstract, and above their comprehension;” to see that the course prescribed should be “adapted, not merely to a few select spirits, but to average intelligences;” and to correct “the excessive development of the preparatory studies, which had gone far beyond the end desired.”