In the second division the teacher will not always be able to avoid giving a repetition of the reasons of propositions. This is necessary when he perceives from the work or expressions of the students, that the majority have not perfectly comprehended the proposition. Still the teacher will here content himself with bringing forward the most important points in the chain of deduction. The explanatory problems are solved by the teacher himself, who then sets similar ones for working out by the students at home.
For practical static problems, the teacher can use with great benefit objects often occurring in common life, and yet regarded so little; the numerous applications of the lever, of the inclined plane, &c., by artillerists and engineers, for their works, carriages, draught, &c., furnish sufficient material for such problems; as for instance, determination of the depth of a boat of given length and breadth when after putting into it a piece of ordnance a given height out of water is required; determination of the power requisite to overcome the resistance of a log lying in the track of a vessel; determination of the pressure of a laden beam on two or more supports with reference to the flexibility of the beam; determination of the center of gravity in an excentric hollow shot, both theoretically with given radius and known centers, as well as more practically when the centers and the radius of its interior are unknown, as by dipping the hollow shot into quicksilver; determination of the counterpoise of a drawbridge and examination of the best position for the axle ; investigation of the strength of metal and wood pipes which are to serve as water-pipes at given heights of pressure, &c.
At the same time the teacher ought not to leave unnoticed the advantages which theory can offer to practice when rightly applied, by which is in no way meant that the practical man should enter every time into a prolix and anxious calculation, but from the improvement his mind and capacities have received, he may apply readily what he has learnt to the purposes of common life.
Dynamics and hydraulics will be rather treated in a physical and historical point of view; here, too, the application of known professional results is the principal object.
As the limited time will not allow separate mathematical repetitions, the teacher should therefore be the more careful to make his lectures as much as possible applicatory. To insure progress the students must, besides the usual writing out the lecture, have frequent themes given to them for work at home, and of which their own execution should be secured by proper means.
It is perfectly necessary that a hand-book should form the basis of the instruction, from which the teacher should lecture, and the students make repetitions.
The hand-books are to be proposed by the teacher to the Board of Studies, and must not be changed without permission.
These books, as well as the logarithm tables, every student must have a copy of, as he can not do without them in the school, and may frequently require them in future life.
Models of solids, to illustrate the projection theory, are in the collection of the models of the school.