The examination which takes place prior to their leaving the School of Application, is entirely conducted by a board of six officers, under the presidency of a general officer alternately of the artillery or engineers, the remaining members of the board consisting of a general officer of each corps and three field officers of these corps; the last three being specially charged with the duty of examining. It takes place in a room set apart for the purpose, with a small interior room in connection with it, into which the members of the board retire to deliberate at the end of each student’s examination. The jury assembles each year at the period fixed by the minister of war.
The three examining members conduct the examination of the students in three different branches of study; the first more particularly relating to artillery science, the second to engineering science, and the third to mechanical science in its connection with the art of war. The whole of the students who are to leave the school are first examined in such one or other of these branches of study as may be determined on.
The student under examination is specially questioned by the examining officer in his subject, and occasionally by the president or any other member of the board that may wish to do so, for three-quarters of an hour. As soon as the examination of the student has been concluded, the board retire to the adjoining room and compare their notes of the credits they have severally awarded to the student under examination, and they also examine his drawings, sketches, and memoirs relating to the subjects on which he has been questioned, and prepared during his two years of residence in the school. They severally note the credits to which they consider him to be entitled for them, and adopt the general mean.
As soon as the examination of the whole of the students in this particular study has been finished, the examination in the next branch is commenced, so that five or six days elapse between the first and second examinations of the same student; and the same interval of time occurs between the second and third examinations.
The credit allotted to each student by the board of examiners represents, on the scale of 0 to 20, the manner in which he has replied to the questions, or executed the drawings, sketches, memoirs, &c., belonging to each course. The importance attached to each particular branch of study is estimated very nearly by the amount of time allowed for its execution divided by 20; and the definitive marks which each student obtains for that branch of study is obtained from the products of the numbers respectively representingthe credit for answering, and that for the importance of the subjects on which he has been examined.
The final classification of the order of merit, in each arm of the service, is arranged after a comparison of the total of the marks obtained by each student. This total is the sum of the definitive marks gained by each student in the sciences bearing on artillery, engineering, and mechanics in connection with the art of war, for the talent displayed in drawing, sketching, and writing memoirs, and for skill in practical exercises, as determined by the results of the examination conducted by the jury of examiners, added to the marks due to the previous classification in the school, with the weight or influence equal to one-third of that allowed for the examination by the jury.
The co-efficients of influence for the present year are—
So that the examination conducted by the jury of examiners exercises an influence on the position of the students very nearly approaching to two-thirds of the whole amount.
It is this final classification which determines their seniority in the respective services. We were permitted to be present during the examination, which was entirely oral, of two of thesous-lieutenants, before the jury of examiners.
The questions were replied to with great fluency and readiness, but it seemed to us that the examination was somewhat limited for the object in view, viz., that of awarding a credit representing the progress which each student had made in the particular science on which he had been questioned, especially as that credit would have very great weight in determining the candidate’s future position.14
On quitting the School of Application at Metz, the sub-lieutenants of artillery and engineers respectively join the regiments, to which they are then definitely assigned as second lieutenants, and continue to be employed in doing duty, and in receiving practical instruction with them, until they are promoted.
The lieutenants of the artillery are employed on all duties that will tend to make them efficient artillery officers, and fully acquainted with all details connected with the drill, practice, and manœuvres of the artillery, and also with the interior economy and discipline of a regiment of artillery.
After the officers of artillery are promoted to the rank of second captain, but not before, they are detached from their regiments and successively sent into the various arsenals, cannon foundries, powder mills, and small arm manufactories, pyrotechnic establishments, and workshops, in order that they may become practically acquainted with the whole of the processes connected with the manufacture and supply of artillery, rockets, small arms, powder, material of all kinds, tools, &c., and also with the construction and repair of the buildings and factories required for these purposes. Sometimes they are employed as assistants in these establishments. The inspectors of the arms of regiments are selected from among those who have become acquainted with the manufacture of small arms.
When promoted to first captains they again rejoin their regiments, so that they may not lose the qualifications and knowledge required from a good practical artillery officer.
Field-officers of artillery are employed as superintendents and directors, and captains as sub-directors, of the important works intrusted to their arm.
In time of war, the officers of artillery have the construction of their own batteries, and the direction of the ordnance in battles and sieges, together with the formation of movable bridges and passages by boats.
It must be noticed, in contradistinction to the practice which prevails in England, that the artillery and engineer services manufacture their own tools.
The young engineer officers are employed with the men of their regiments, and with them pass through courses of practical instruction in the field, in sapping, mining, field fortification, sham-sieges,bridges, and castrametation. During this practical instruction one of the lieutenants belonging to each company is always present, and the captain of the company visits the work once in the course of the day.
The duties of the officers of engineers in time of peace are the construction, preservation, and repairs of fortresses and military buildings, and the command and instruction of the engineer soldiers.
In time of war, the officers of engineers are intrusted with the construction of works of permanent fortification, of the general works in the attack and defense of fortresses, and the reconnaissance connected therewith.
Theymayalso be charged—
With the construction of such works of field fortifications as the commander-in-chief or the generals of division consider necessary; such asépaulments, trenches, redoubts, forts, blockhouses, bridgeheads, intrenched camps, as well as the opening of communications, the establishment of bridges resting on fixed supports, and the formation and destruction of roads.
After the officers of engineers have been promoted to the rank of second captain, and not before, they are mostly employed apart from their regiments, on theétat majorof the engineers in fortified towns and places, either in charge of the existing military buildings and fortifications, or with the duty of carrying on, or assisting to carry on, such new works as are in course of construction from time to time.
We have already stated that by the law in France one-third of the officers of the army is obtained from the military schools; one-third from the non-commissioned officers who have been raised to that grade from the ranks; while the remaining third is placed at the disposal of the supreme executive power. As regards the artillery and engineers this last third is in actual practice obtained, like the first third part, from the Polytechnic School, so that only one-third of the officers of those arms are promoted from among the non-commissioned officers, and these seldom rise above the rank of captain. Much attention is, however, paid to the improvement of the education of these latter officers, and we found thatfourofficers of engineers andoneofficer of artillery so promoted were, by order of the minister of war, on the recommendation of the inspectors-general, passing through the School of Application at Metz, the course of instruction for them being modified on their account. And it was confidently expected that a large number of those officers whohad been promoted in this way during the war would be ordered to the School of Application at Metz.
We should not omit to mention that occasional exchanges of service take place, during the first year of residence at Metz, among the pupils destined for the artillery, and those destined for the engineers.
The pay of officers of the artillery and of the engineers is the same. A small additional allowance is granted to officers of artillery when mounted.
ARTILLERY REGIMENTAL SCHOOLS.
There are ten regimental artillery schools established in places or towns that are usually garrisoned by the troops of this arm, and one of these schools exists at Metz.
ENGINEER REGIMENTAL SCHOOLS.
The soldiers of the engineers appear to be very well taught in their regimental schools, of which there are three, one for each regiment, established at Metz, Arras, and Montpellier, where the regiments are usually in garrison. The strength of each regiment is 4,500 men.
The instruction given in these schools has for its object to afford, to its full extent, to the officers,sous-officiers, and soldiers of the engineers, the requisite theoretical and practical knowledge to enable them satisfactorily to fulfill the duties of their various ranks, and to qualify them for promotion to higher rank.
It is so regulated that at the end of the first year the men have learnt the nature of the service and duties of a soldier; and that at the close of the second year, the practiced sapper is cognizant of mining, and the practical miner is acquainted with sapping.
In the lowest classes the men begin with learning to read and write; this if followed by arithmetic, grammar, writing from dictation, and composition. The next subjects are special mathematics, landscape, plan, topographical and architectural drawing. We attended a class in which a corporal of sappers was explaining to the mathematical teacher (a civilian) the theory of the inclined plane, and we saw a large number of their drawings, topographical and architectural, many of which were very well executed.
The theoretical instruction is given between the months of November and March, the practical instruction in the field, (already noticed) occupies the rest of the year. The combined courses are completed in two years.
(Abridged.)
Thechief Regulations for the Police of the Establishment are as follows:—
I.Barracks.—The Students are lodged in Barracks in the School, under the command of a Captain of the Staff, with the title of Commandant of the Quarter. They take their meals, however, out of the Barracks, in the town. They are allowed free egress and ingress from and to their Barracks, from the call at 6 in the morning to 10 at night, excepting during the hours devoted to lectures and the studies in the rooms. During these hours they must give special notice o£ their times of going out and coming in.
II.Organization into Brigades and Sections.—Each Division is arranged in Brigades of thirty Students at the utmost, and each Brigade in two s. The Students of Artillery and those of the Engineers constitute, as far as possible, separate Brigades. A Captain of the Staff is attached to each Brigade for its superintendence. The students in these Brigades and Sections are arranged in the order of merit which they held on entrance, and the first Student on the list of each Brigade and of each of a Brigade is called its Chief. This arrangement is preserved at their messes, which are held at the Restaurateurs’, each of fifteen having its own table, and its chief being the head of the mess. Private bills or private additions to the mess are forbidden, the maximum price for the daily fare being fixed by the Commandant of the School.
III.Conduct of the Students.—All games of chance are forbidden; and any debts discovered are punished. If a Student continues long without paying such, he is reported to the Minister of War.
IV.Inspection of Work Done Within the House.—No work or drawing may be done out of the rooms of study, except in cases of illness.
All works to be executed by the Students are considered as service ordered to be done, which must be completed at the hours and within the period fixed in the order of the day. Students who are in arrears of work at the end of their first year are required to finish them during the time of vacation.
V.Superintendence of out-of-door Work.—After describing facilities afforded to the Students for working in the country, and stating minutely the method to be followed, the directions add that “on bringing back their plans, Students must present their sketches, and all the notes taken by them, in their rough state, to the Officer of the Staff intrusted to inspect them. They can not begin to put their work into shape till this Officer’s visa has been affixed to the sketches, notes,” &c.
VI.Vacation.—There is one vacation at the end of the first year. Any class, or any single student, under punishment, may be deprived of this. Any work to which the Professor gives a mark below 7, must be considered incomplete, and to be done again. Students are kept up in vacation to finish their work; but if it is done within fifteen days, and marked by the Professor’s visa, they are allowed to go away for the rest of the vacation.
Young Officers, after their final examination, are subject to all the Regulations of the School, down to the moment of their leaving the town.
The time devoted to each of the courses in the School, to the works of every kind which belong to it, to the exercises, drill, theoretical instructions, &c., is fixed in accordance with programmes approved by the Minister of War; and the Table similar to that given at pages 180–181, exhibiting the employment, is each year submitted for his approbation by the Superior Council of the School.
Every kind of work, such as the out-door operations, sketches, drawings, memoirs, calculations, interrogations, manipulations, manœuvres, drill, &c., is valued by the Professor or Officer of the Staff charged with its direction, by the product of two numbers, one representing the merit of its execution, and the other the importance of the work.
The numbers representing the merit of the execution or instruction are regulated by the scale of 0 to 20, as at the Polytechnic School.
The co-efficient of importance is found by dividing the number representing the maximum value allowed for the execution of any work by 20, the maximum credit for merit; and the number representing the maximum value, allowed for the execution of any work has reference to all the circumstances bearing upon its execution. It is regulated by the number of hours appropriated to its execution; and in estimating this number of hours, regard is had, not only to the time occupied in making the drawing, but also to that which is necessary for the calculations, essays, and sketches indispensable to its execution. The lectures are reckoned at one and a half hours, and the sittings in the Halls of Study at four and a half hours.
The number of hours inserted in the Table giving the distribution of the time employed, being insufficient for the composition of the memoirs, specifications, estimates, &c., the value given for this kind of work, of which a great part is performed out of the Halls of Study, is fixed at twice the number of hours inserted in the Table showing the distribution of the time employed.
The interrogations are the subject of a special credit, the maximum being equal to the number of hours devoted to the lectures, multiplied by one and a half hour, the length of each lecture.
The credit given for a work performed outside the school is divided into two parts: one, equal to one-third of the total credit, is in the hands of the Officer charged with the superintendence of the work, who estimates the zeal and aptitude of the student; the other, equal to two-thirds, is applied by the Professor, and given according to the merit of the work.
The sum of the credits, given for work of all kinds in a course of study, forms the maximum credit for the course.
The method of fixing the credit for the execution of works, according to the time devoted to them, is equally applicable to the exercises, practice, and drill.
When the time granted for the execution of any work has expired, the Director of Studies sends this work to the Professor for his examination, who establishes the number or credit, showing its importance, and returns it to the Director of Studies.
Every work which has been finished and examined, is marked by the Professor by a number representing its merit, which number may be fractional.
This is multiplied by the number representing its importance, and the nearest whole number resulting from this product expresses the value of the examined work.
Every unfinished work receives a provisional value, and is then returned to the person executing it, and as soon as it has been completed a second evaluation is made, but only two-thirds of the difference between the first and second evaluations is added to the first; the same principle is applied to the works which have been valued below seven, or to those which have been amended or recommenced.
Every work which has not been executed by the student is marked 0; but the grounds for its non-execution are placed before the Jury of Examination.
In the event of two papers being so similar that it is evident one must have been copied from the other, and that it is not possible to decide which has been copied from the other, both are marked 0.
And on the other hand, if it is proved that there was no complicity between the authors of the two papers, the copied paper is the only one canceled.
At the end of each year’s study, the Council of the School makes a classification of the students of the two divisions.
Each of these classifications is formed of the following elements:—
1st. Notes of conduct given by the General commanding and the Colonel Second in Command.
2nd. Notes of appreciation given by the General Commanding, and the Colonel Second in Command, and by the Officers of the Staff of the School.
3rd. Tables of credits given by two Field Officers of the Artillery and Engineers on the theoretical and practical instruction with which they are charged.
4th. Tables of credits given by each Professor for the works of all kinds, interrogations, &c., of his course.
The classification of the first year comprehends all the works, drill, and practice, executed during the first year, which have been valued, as well as the notes of appreciation and of conduct.
The number appropriated to these notes at the end of the first year is equal to the moiety of the total number allowed for the two years of study.
The classification of the students of the second year presents the reunion of the works executed by them since their entrance into the school.
The maximum number of credits appropriated to all the Officers of the Staff, as a note of appreciation, is equal to one-sixth of the total of all the courses taken together.
The same number, divided into two equal parts, is assigned to the notes of appreciation given by the General commanding and the Second in Command.
Lastly, the notes of conduct given by the General commanding and the Second in Command form one-fiftieth of the total value.
For the classification of each division the Director of Studies abstracts into a Table, for each arm, all the elements which should enter into this classification. Below the name of each student are inserted all the credits which belong to him, and the total, reduced in the ratio of the maximum 20, is the definitive number of the classification of each student.
The Director of Studies appends to these Tables a report containing everything which affords a means of estimating the work, the conduct of eachstudent, the delays, and the causes, &c. In giving the names of the students whose credits are less than 7, he proposes, conformably with the Regulations, the measures that should be taken with regard to them.
The Superior Council of the School being assembled, the different Tables furnished by the Professors and by the Officers of the Staff, as well as those in which they are summed up, are collated, and the list of classifications for each division and for each arm is fixed separately, with the definitive numbers representing the credits.
These classified lists indicate for each arm the new rank of the Students, their rank at admission to the School of Application and of passage to the first division, the sum of the values for the works executed by them, and all the elements which would tend to enable a proper judgment to be formed of their merits and conduct.
The Superior Council adds to it, if there be any necessity for it, notes, exposing the grounds which have contributed to the principal alterations in the relative position of the Student, and points out those whose credit is less than 7, as well as those who by their bad conduct deserve to become the object of exceptional measures.
Examination for Leaving.
Each year the General commanding the School determines by lot, at least one month in advance, the order in which the examinations for the promotions in the Artillery and Engineers are to take place. The Students belonging to the same arm can change among themselves, but eight days after the lots have been drawn the list of the order of examination is definitely closed. The General commanding the School makes known at the same period the order of the examinations and the division of the subjects between these examinations.
The General commanding the School places before the General of Division, President of the Jury of Examination, the following:—
1st. The division of the subjects between the three examinations.
2nd. The order of examination of the Arms, and of the students of each Arm.
3rd. The provisional classification of the students of the first division made by the Superior Council.
4th. The particular reports relating to each student made by the General commanding the School.
5th. The list of the propositions made by the Superior Council and the proceedings of the sitting at which it was agreed to.
6th. The classification of the Students of the second Division.
7th. Tables of questions established for each course.
8th. The abstracts of the sittings of the Superior Council held since the last examination.
The Student Sub-lieutenants are successively examined in all the branches composing the theoretical and practical instruction of the School. The theoretical knowledge is grouped in three series, each of which is the object of a particular trial.
The drill and practice are executed in the presence of the Jury, who cause the command to be given to the Sub-lieutenant, in order to satisfy themselves of the amount of their instruction, and to assign marks of merit to them individually.
The subjects of the three examinations are divided in the following manner:
First. Examination, made by the Field Officer of Artillery in the—
Course of Military Art.Course of Artillery.Course of Veterinary Art.Sham Siege (part relating to Artillery.)Course of Military Law and Administration.
Course of Military Art.
Course of Artillery.
Course of Veterinary Art.
Sham Siege (part relating to Artillery.)
Course of Military Law and Administration.
Second. Examination, held by the Field Officer of Engineers.
Course of Permanent Fortification and the Attack and Defense of Places.Course of Construction.Sham Siege (part relating to the Engineering.)
Course of Permanent Fortification and the Attack and Defense of Places.
Course of Construction.
Sham Siege (part relating to the Engineering.)
Third. Examination, held by the third Examiner, taken either from the Artillery or Engineers, in the—
Course of Mechanics.Course of Applied Sciences.Course of Topography and Geodesy.German Language.
Course of Mechanics.
Course of Applied Sciences.
Course of Topography and Geodesy.
German Language.
Every Student, on presenting himself before the Examiners, submits for their approbation the drawings and manuscripts relating to the subjects on which the examination is to bear. Independent of the questions which are placed before him by the Examiners, the Student Sub-lieutenant must reply to any objections or questions which the members of the Jury may think fit to address to him.
The German Master directly questions the Students, if the Jury wish it. The Professors or their Assistants must be present at the examinations relating to their course.
As soon as the examination is ended, the members of the Jury retire to an adjoining room with closed doors, to determine on the amount of marks to be given to the Student examined.
When the trials of all kinds are finished, the Jury proceed to the definitive classification of the Students belonging to each arm. In making this classification, regard is had to the following considerations:—
1st. Each examination has a co-efficient of importance equal to the sum of all the different courses which are included in it.
2nd. The co-efficient of importance for drawing is equal to the 1/20 of the sum of the co-efficients of the three examinations.
3rd. The co-efficient of importance of the practice, drill, &c., is, as for the courses, the sum of the co-efficients appropriated to the works taught in the School.
By multiplying the co-efficients of importance by the mean number of marks of merit obtained by the Students in the different examinations, the definitive credit which must be assigned to each Student in the Table of Classification is obtained.
The classification of the School enters into the definitive classification for a value equal to one-third of the total number of the three examinations, without comprising the valuation of the drawings; this value is added to the credits determined above.
The Jury give an account of the proceedings of the examinations in a “procès-verbal” addressed to the Minister by the General acting as President.
Twenty-six Lectures common to Students of both Arms.
First Lecture.—(1.) Definition of the word Artillery. Material, personnel, science. Object and division of the course.
FIRST SECTION.—EFFECTS OF POWDER.
Ideas on the origin of powder and its use in fire-arms; mealed or pulverized powder; powder in grain. General conditions which powder ought to satisfy; action of each of its component parts. Proportion of component parts used in France.Fulmi-ligneux.
Considerations on the physical properties of powder. Size of the grains expressed by the number of grains to the gramme. Density of the grains and specific density of the powder; circumstances causing them to vary. Effects of damp upon powder.
Second Lecture.—(2.) Combustion of powder. Different modes of ignition of powder. Research respecting the laws of its combustion, process of observation employed, laws discovered. Influence of the density, the composition, the mode of manufacture, the damp, the tension and temperature of the surrounding gases.
Combustion of the grains of powder. Calculation applied to the spherical grain. The formula is applicable to the irregular grains of ordinary powder.
Calculation of the density of the gases of powder in a fixed space, on the hypothesis of a simultaneous ignition of the grains. Discussion of the formula obtained; influence of the density of the grains, of the duration of their combustion and of the space in which the powder is inclosed.
Inquiry into the rapidity of ignition of charges of powder. Experiments made upon trains of powder, and upon gun-barrels filled with powder. Conclusions drawn from the results obtained.
Third Lecture.—(3.) Calculation of the density of the gases of the powder on the hypothesis of successive ignition.
Results of the application of the formula to charges of a spherical and a truncated form.
Tension of the gases of powder. Impossibility of determining it by considerations of a purely theoretical nature. Experimental solution of this question. Experiments by Rumfort; description of his apparatus. Results obtained. Formula representing them. Observations on these results.
Fourth Lecture.—(4.) Effects of powder in a fixed space.
Hollow projectiles. The readiest bursting of a hollow sphere takes place in the direction of the plane of a great circle. Determination of the minimum bursting charge; law by which this charge varies with the thickness of the envelope. Influence of the fuse-hole of hollow projectiles; weakening of the envelope of the shell, diminution of the charge; loss of gas, increase of the charge. Effects of the shock of the exploding gases; means of estimating it. Influence of the vivacity of the powder in burning. Number and rapidity of the explosions.
Hollow cylinders burst more easily longitudinally than transversely. Consequencesof this principle relatively to the employment of a fibrous metal for the manufacture of arms. Thickness necessary to resist bursting.
Fifth Lecture.—(5.) Effects of powder in cannon.
Analytical theory of the effects of powder in cannon.
Equation of the problem. General expressions of the quantity of force exercised by the expansion of the gases,—of the density of the different s of gas and of their tension. Differential equations of the motion of the gases, of the projectile, and of the gun. Equation of condition leading to the establishment of the general formula which determines the position of a stratum of gas in the terms of the function of its original position, and of the other data of the question. General relations between the velocity of the projectile and that of the gun.
Density of the stratum of gas at a given moment. Position of the stratum which has a maximum density.
Sixth Lecture.—(6.) Approximative solution applicable to the cases ordinarily met with in practice. Hypothesis relating to the velocity and the tension of different strata of gas.
Relations between the velocity of the projectile and that of the gun. Approximate expression of the amount of force due to the expansion of the gases; line to be followed in the execution of the arithmetical calculations. Formula serving to determine the velocity of the projectile. General considerations on the state of the gases of powder during the burning of the charge. Influence of the motions of the projectile and of the bottom of the bore on the distribution of the gases at each instant. Influence of the successive generation of the gases combined with the enlargement of the space which incloses them on their density throughout the whole duration of the phenomenon.
Seventh Lecture.—(7.) Influence of the vent and of the windage of the projectile on the effects of powder in cannon.
Determination of the loss of velocity occasioned by the windage of the projectile. Influence of the weight of the piece upon the velocity of the projectile. Influence of the weight of the projectile on tension of the gases and upon the velocities of the two bodies set in motion. Influence of the weight of the charge of powder. Charge giving the maximum of velocity. Influence of the size and density of the grains of the powder as well as other circumstances which cause a variation in the law of generation of the gases. Advantage of very rapid combustion in short pieces and of slower combustion in long ones.
Eighth Lecture.—(8.) Influence of the length of bore; circumstances which modify it; length corresponding to the maximum of velocity. Comparison of the quantities of motion of the projectile and of the gun. Trial of a formula fitted to represent their relation. Determination of this relation with the help of the balistic pendulum.
Mean pressure exercised on the projectile during its passage through the bore. Injuries produced in guns by firing; enlargement of metal and cracks; lodgment and percussion of the projectile.
Different effects of the percussion; means tried to prevent injuries (in general.) Considerations on the metals employed in the manufacture of ordnance. Charging with elongated cartridge; use of wooden bottoms and wads.
Ninth Lecture.—(9.) Examination of the proper means for measuring the effects of powder. Eprouvettes of different sorts. Experimental processesfounded on the measure of the velocity of the projectile. Grobert’s rotatory machine. Process of Colonel Debooz. Process based on the employment of an electric current. Method by ranges (mentioned here by way of note.)
Balistic pendulum. Pendulum of Robins, of d’Arcy, of Hutton. Improvements introduced in France into the construction of these apparatus. Description of the pendulums in use at the present day; cannon pendulum; musket pendulum.
Tenth Lecture.—(10.) Analytical theory of the balistic pendulum.
1. Receiver pendulum; formula which gives the velocity of the projectile. Determination of the elements which enter into the formula, and the degree of approximation necessary. Simplification of the calculation of the velocities in the case of firing several times consecutively.2. Cannon pendulum. Amount of recoil in the gun. Percussion of the knife-edges of the pendulum. Case where there is none. Means of correcting the position of the center of percussion.
1. Receiver pendulum; formula which gives the velocity of the projectile. Determination of the elements which enter into the formula, and the degree of approximation necessary. Simplification of the calculation of the velocities in the case of firing several times consecutively.
2. Cannon pendulum. Amount of recoil in the gun. Percussion of the knife-edges of the pendulum. Case where there is none. Means of correcting the position of the center of percussion.
Eleventh Lecture.—(11.) Examination of the effects of the recoil upon guns and their carriages. The question may be considered as resolving itself into two others.
1. Percussions of the carriage upon the points supporting it; analytical solution. Determination of the percussions and of the force of the recoil in the case of carriages on wheels, and that of mortar beds. Graphic solution of the same question by an analysis of the force which acts upon the bottom of the bore. Modification of the sketch according to the different cases presented by the direction of fire relatively to the ground.
1. Percussions of the carriage upon the points supporting it; analytical solution. Determination of the percussions and of the force of the recoil in the case of carriages on wheels, and that of mortar beds. Graphic solution of the same question by an analysis of the force which acts upon the bottom of the bore. Modification of the sketch according to the different cases presented by the direction of fire relatively to the ground.
Twelfth Lecture.—(12.) Discussion of points relating to the percussion of the carriage upon its supports, and to the force of the recoil. Influence of the elevation of the line of fire; of the inclination of the ground or of the platform; of the length of the carriage in proportion to its height and of the friction which results from the contact of the trail with the ground. Velocity of recoil of the collective apparatus. Determination of the extent of the recoil on a given ground. Recoil of the different pieces of ordnance in use. Case in which the forepart of the carriage has a tendency to be lifted up; velocity of this motion; determination of the effect resulting from it.
Thirteenth Lecture.—(13.)
2. Percussions produced by the gun upon its carriage. Determination of the amount of percussion of the breech upon the elevating screw, and of that of the trunnions upon the trunnion holes. Discussion of points relative to the effects produced. Influence of the elevation; of the dimensions of the gun, and of the proportion of its weight to that of the entire apparatus.
2. Percussions produced by the gun upon its carriage. Determination of the amount of percussion of the breech upon the elevating screw, and of that of the trunnions upon the trunnion holes. Discussion of points relative to the effects produced. Influence of the elevation; of the dimensions of the gun, and of the proportion of its weight to that of the entire apparatus.
Effect of the elasticity of the different parts of the apparatus. It diminishes the wear of the parts struck, and renders it necessary to take into account the velocity of the parts striking.
Fourteenth Lecture.—(14.) Effects of powder in mines. Historical notices. Dimensions of the boxes containing the powder. Considerations on the effects of the expansion of the gases in an indefinite or limited compressible medium.
Definitions having reference to craters and chambers of mines. Ordinary charge of the chamber. The old rule for miners; its entire alteration. Tablerelating to different kinds of medium. Overcharged chamber. Overcharged chamber or “camouflet.” Limit of the effects of compression which result from the action of the chambers. Use of gun cotton. Considerations on the effects of the petard. Dimensions of the cavity reserved for the powder. Means employed or proposed to diminish the charge of powder proportioned to a given effect.
SECOND SECTION.—MOTION OF PROJECTILES IN SPACE.
Fifteenth Lecture.—(15.) Science of projectiles. Historical notices. Utility of an acquaintance with the laws of the motion of projectiles in a vacuum. Definitions relating to the trajectory. Differential equations of the motion in vacuo. Equation of the trajectory. Inclination of its elements. Velocity of the projectile at any one point. Duration of its passage. Determination of the range and of the angle of greatest range. Relations between the ranges; the initial velocities; and the angles of projection. Examination of the cases where the theory of the parabola is applicable.
Preliminary ideas on the resistance of fluids; difficulties inherent in this question. Approximative formula of the resistance, established by the help of the principle of active forces; circumstances not taken into consideration by it.
Sixteenth Lecture.—(16.) Experiments relating to the determination of the resistance of the air.
1. Case of small velocities. Rotatory apparatus; results furnished by them in the case of thin planes; their essential defect. Apparatus with rectilinear movement. Mean value of the co-efficient of the theoretical resistance in the case of thin planes; modification of this value for the case of spheres, &c.2. Case of great velocities. Direct determination of the resistance of the air by the aid of the balistic pendulum. Experiments of Hutton, their results. Experiments made at Metz in 1839 and 1840. General expression of the resistance based upon the total of the results obtained, and containing a function of the velocity in three terms. Search after a function in two terms fit to replace in each particular case the general expression.
1. Case of small velocities. Rotatory apparatus; results furnished by them in the case of thin planes; their essential defect. Apparatus with rectilinear movement. Mean value of the co-efficient of the theoretical resistance in the case of thin planes; modification of this value for the case of spheres, &c.
2. Case of great velocities. Direct determination of the resistance of the air by the aid of the balistic pendulum. Experiments of Hutton, their results. Experiments made at Metz in 1839 and 1840. General expression of the resistance based upon the total of the results obtained, and containing a function of the velocity in three terms. Search after a function in two terms fit to replace in each particular case the general expression.
Seventeenth Lecture.—(17.) Theory of the motion of projectiles in the air. Differential equations of the motion. Hypothesis on the relation of the element of the trajectory to its projection. Calculations based on this hypothesis, and leading to the final equation of the arc of the trajectory. Inclination of the element of the trajectory. Velocity of the projectile at a given point. Duration of the passage.
Eighteenth Lecture.—(18.) Examination of the functions employed in the formulas of the science of projectiles. Formation of the balistic co-efficient, and the series contained in the functions. Relations of the series and the functions to each other. Arithmetical tables designed to give their values. Determination of the relation of an arc of the trajectory to its projection. Error resulting from the introduction of the constant relation in balistic calculations.
Nineteenth Lecture.—(19.) Application of balistic theories to the movement of projectiles thrown at great angles. Analysis of the trajectory, and determination of all the circumstances of the movement. Trajectory of shells considered as a single arc. Solution of several problems involved in this hypothesis. Determination of the range. Velocity corresponding to a given rangeand angle of projection. Angle of projection corresponding to a known initial velocity and range. Angle of greatest range. Variation of the velocity of the projectile during the whole of its passage. Limit of velocity of projectiles falling vertically in the air.
Twentieth Lecture.—(20.) Application of balistic theories to the motion of projectiles thrown at low angles. Case where the relation of the arc to its projection can be supposed sensibly equal to unity. Problems relative to direct fire; distinction established between the angle of projection and the angle of fire. In ordinary cases in practice the angle of fire is very nearly independent of the height of the object aimed at. Relations between the angle of projection, the angle of elevation of the object aimed at, and the angle of descent. Problems relating to plunging fire. (Ricochet fire.) Determination of the initial velocity and the angle of projection for a projectile which has to pass, firstly, through two given points; secondly, through one given point, the trajectory having at this point a known direction. Case of practical impossibility.
Twenty-first Lecture.—(21.) Relations between the velocities, the spaces traversed, and the durations of passage in the rectilinear movement of projectiles. They are applicable to direct fire, and are independent of the function of the velocity which enters into the expression of the resistance of the air. Case where the resistance of the air can be supposed proportional to the square of the velocity. Establishment of balistic formulas in this hypothesis. Application of the formulas to the resolution of one of the problems connected with a plunging fire. Comparison of the results obtained with those arrived at by the use of general formulas. Indication of methods applicable to the resolution of several questions in projectiles.
Twenty-second Lecture.—(22.) Examination of disturbing causes which influence the motion of projectiles.