Note 1 — PART I MILITARY SYSTEM AND SCHOOLS IN FRANCE.

It will be admitted, as a postulate, that only one parallel to a given right line can pass through a given point.

2 The volume of the cone is derived from that of the pyramid; and it is to be noted that the demonstration applies to the cone with closed base, whatever the figure of that base.

3 Numerical examples on the areas and volumes of the round bodies, including the area of a spherical triangle, will be required by the examiners. The calculations will be made by logarithms.

4 The true distinction between Algebra and Arithmetic is so commonly overlooked that it maybe well to present it here, in the words of Comte. “The complete solution of every question of calculation is necessarily composed of two successive parts, which have essentially distinct natures. In the first, the object is to transform the proposed equations, so as to make apparent the manner in which the unknown quantities are formed by the known ones; it is this which constitutes the Algebraic question. In the second, our object is to find the value of the formulas thus obtained; that is, to determine directly the values of the numbers sought, which are already represented by certain explicit functions of given numbers; this is the Arithmetical question. Thus the stopping-point of the algebraic part of the solution becomes the starting-point of the arithmetical part.

“Algebra may therefore be defined as having for its object the resolution of equations; taking this expression in its full logical meaning, which signifies the transformation of implicit functions into equivalent explicit ones. In the same way Arithmetic may be defined as intended for the determination of the values of functions. Henceforth, therefore, we may call Algebra the Calculus of Functions, and Arithmetic the Calculus of Values.”

5 The students will apply these reductions to a numerical equation of the second degree, and will determine the situation of the new axes with respect to the original axes, by means of trigonometrical tables. They will show to the examiner the complete calculations of this reduction and the trace of the two systems of axes and of the curves.

6 They will be deduced from the property, previously demonstrated, of the derivative of the ordinate with respect to the abscissa.

7 The method of the change of the planes of projection will be used for the resolution of these problems.

8 Compiled from “Report and Appendix of English Commissioners on Military Education.” 1857.

9 In an Analysis of the Report of this Commission, see page 97.

10 The influence exercised in the various branches of study, and consequently in the position of the students in the list classified according to merit, by the professors and répétiteurs on the one hand, and by the examiners on the other, as in the table above.

11 The students are selected, by a competitive examination, out of a very large number of candidates, as will be seen from the following table, extracted from the yearly calendars:—

Year. Candidates who inscribed their Names. Candidates examined. Candidates admitted to the Polytechnic.

1832 567 468 183

1833 367 304 110

1834 627 541 150

1835 729 633 154

1837 629 508 137

1838 533 410 131

1839 530 531 135

1842 709 559 137

1843 802 559 166

1844 746 531 143

1845 780 559 136

Giving an average of one student for four candidates examined, so that it is impossible to imagine that there is any lack of ability in those selected.

A similar result appears to follow from some other more recent statistics.

Year. Number of Candidates who inscribed their Names. Number declared admissible to the Second Examination. Number admitted.

1852 510 216 202

1853 494 222 217

1854 519 238 170

1855 544 232 170

In judging, however, of these numbers, it should be borne in mind that, a very large number of the candidates who succeed have tried more than once; the successful of this year have been among the unsuccessful of last year, so that the proportion of individuals who succeed to individuals who fail, is, of course, considerably larger than one to four. Of the 170 candidates admitted in November, 1855, 117 had put down their names for the examination of 1854, and 53 only had not been previously inscribed. Of the 117 who put down their names, 19 had withdrawn without being examined at all, 71 had been rejected on the preliminary examination, 27 had been unsuccessful at that of the second degree; 98 of the 170 came up for the second time to the examination.

12 In 1856 there were only 15 professors; there are now two additional professors for history, the study of which has been recently introduced at the school.

13 Formerly two professors of the school were also members of the Council of Discipline, but the professors have now no voice in matters of discipline.

14 The examination chamber is a small room in the school buildings, near the library, ornamented with portraits of Vauban, and of D’Argenson, under whose ministry the original schools at La Fère and Mézières were founded. At a large table under these portraits, and extending across the room, General Morin, President, and four officers, members of the jury, were seated. The sixth member sat at a small table in front, near the blackboard, at which the student stood. The Commandant, the Director of Studies, and the other officers of the school were seated also in this part of the room.

The student who was first examined was questioned partly by the examiner, partly by the president, and gave his answers, working problems and drawing illustrations on the board as he went on. He was asked questions as to the details of the steam-engine, and as to the method of casting cannon. The German teacher of the School put him on to construe from a German book, and tried him in speaking; he succeeded just passably in both. The whole occupied about three-quarters of an hour.

The second student, after answering similar scientific questions, had opportunity given him to show his knowledge, which was considerable, of the geology of the neighborhood; and having lived in foreign countries, he was able to make a very good display of his knowledge of German, Spanish, Italian, and English.

After each examination the jury retired into the inner cabinet, by a door opening to it from behind their seats.

15 Founded the Ecole Royale Militaire, 1751. Junior pupils transferred to La Flèche, 1764.

Suppression of the Ecole Royale Militaire and establishment of ten Colleges, 1776.

New Ecole Royale Militaire, for the best pupils of the Colleges, 1777.

Suppression of the Colleges and of the Ecole Royale Militaire, 1787.

Foundation of the Ecole de Mars, May 1794.

Foundation of the Prytanée Français at Paris, Versailles, St. Germain, Fontainebleau, 1800.

Foundation of the Ecole Spéciale Militaire at Fountainebleau, 1803.

The four Schools of the Prytanée Français are converted into the Prytanée Militaire, 1806; and are transferred to La Flèche, 1808.

The Ecole Spéciale Militaire is transferred to St. Cyr, also in 1808.

16 About twenty-five are sent every year from La Flèche. The admissions from the army (i.e., of soldiers between twenty and twenty-five years old) do not amount to more than four or at the utmost five per cent. They are very frequently young men who have previously failed for St. Cyr, and who then enter the army as privates, and come in as such. They have to pass the same examination.

17 Few usually present themselves; and these also, it is said, are very generally old élèves of St. Cyr, who had not succeeded in obtaining admission to the Staff School before. They are not examined with the pupils of St. Cyr, but are intercalated in the list according to their merit.

18 The system was, in fact, first tried at St. Cyr, and adopted, on the representation of the Mixed Commission, at the Polytechnic. The previous method, by which different sets of examiners took different districts, had created distrust and dissatisfaction.

19 “Report of Observations in Europe during the Crimean War,” by Major Gen. McClellan.

20 There must be some error in the printed regulations on the subject.