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THE EDUCATIONAL VALUE OF APPLIED MATHEMATICS. 5063 
spicuous wight further down the roll. The valedictorian had an excellent 
memory and extensive vocabulary. Down the class, however, were those 
who had more reluctance to yield themselves to the guidance of recorded 
rule, and yet had in compensation the faculty of perception, of wise 
Jeduction, and even of origination. In engineering, when properly 
taught, from the very fact that it is not an exact science, like the pure 
mathematics, there is an opportunity given to bring out this most impor- 
cant principle, that successful mastery over circumstances means success 
and reputation, which these faculties bring, if other things are equal. 
To a pure mathematical problem there is either no solution, the solu- 
sion is indeterminate, or there is a fixed number of solutions. In engi- 
aeering this is not so. He is easily discouraged who says there is no 
solution to a problem in engineering. The whole history of this century 
repeats over and over again the solution of that which was formerly said 
0 be impossible, even by high authority. In engineering, the problem 
cannot be indeterminate when its solution, as in a manufactured article or 
in an achievement, is presented in a concrete form. 
It is a most important consideration of any which can be impressed 
apon a young man, that in engineering problems there are many prac- 
sicable solutions to every one; and (here mark the essential kernel of the 
whole matter) that it is left for him to make the choice of the most suit- 
able solution under the special circumstances in which that particular 
problem comes to him. It is this exercise of a trained, critical, or judicial 
faculty, called by whatever name—common sense, horse sense, shrewdness, 
acumen, or what not—which engineering, more than any of the other 
professions, medicine alone perhaps excepted. demands from its successful 
epresentatives. 
It is to be noted further that the considerations which are to be guiding 
factors in the exercise of this judgment, or critical faculty, or common 
sense, are not to be found in the school text-books nor in the pocket- 
vooks usually, nor from an authority calling down the vista of even an 
honored past. The choice has to be guided from the conditions of the 
lay and the hour. The achievement of to-morrow must be built upon the 
success of to-day, the discovery of the last new combination, and even 
she commercial environment of the district where the solution is to be 
realized. It therefore comes back upon the teacher of engineering so to 
shape his instruction in this field that the men under his instruction shall be 
able to make the most of themselves, he standing by to help all in his power. 
How shall this be done ? 
First. Teachers of engineering should be engineers possessing this ele- 
ment of sense, judgment, and critical faculty, rather than scientists only, 
sompetent authorities in pure science, but nothing more. 
Second. Teachers of engineering should be practitioners in touch with 
the competition of the dav, familiar with achievement of colleacues and