10 
US 
A - 
~~ oma 
RK 
n 
3S 
+t 
ie 
y 
Me 
1) 
,e 
im 
le 
iN 
nN 
Vv. 
‘n 
18 
nl 
30 
A 
1e 
3 
se 
1t 
1b 
2S 
T'HE EDUCATIONAL VALUE OF APPLIED MATHEMATICS. 561 
which have been provided by a wise and loving Creator for the progress of 
the race onward and upward, then it is Impossible to lay too much stress 
upon this solid groundwork of scientific principles and laws. These prin- 
ciples, in themselves, are valuable as means of education where they are 
derived either by deduction from accepted axioms, or from foundation 
principles intuitively apprehended, as well as by induction from the obser- 
vation of phenomena. 
The educational value of this class of instruction is even most consider- 
able in the domains of mathematics and what is called natural science. 
in these we get that mental training which comes from deduction and 
Induction in their most rigid and exacting forms. After a certain point, 
however, it becomes rarely possible to take the time to com pel each student 
to convince himself of the existence of a particular law or principle, and 
the instruction takes the form of the predication of law and principle by 
authority, and the familiarity of the student with the law becomes a ques- 
sion of his exact memory of what he has read or heard. While it is of 
course helpful and convincing to know that a certain theorem is accepted 
as true because it has been proved to be so by some one whom the student 
respects, yet is it not possible for a man with a good memory to pass suc- 
cessfully through the requirements of this part of his course in a condition 
of mental Nirvana, where he is satisfied with the exalted plane of achieve- 
ment in the text-book or lecture-room atmosphere, while the other facul- 
bies of his mind, which education must bring out and strengthen, lie com- 
fortably and lazily undisturbed so far as the course of study is concerned ? 
The second starting point in technical instruction is that from which 
she paths lead to the application of these scientific principles and natural 
laws to the problems of civilization and industry as they come to the 
angineer. This is instruction in applied mathematics, applied physics, 
or applied chemistry, as distinguished from the study of these as pure 
sciences, and is an instruction which is deemed of paramount importance. 
It begins, perhaps, at the middle of the school life of the student, but it 
ends only with the end of his natural or active life. It forms that part of 
a man’s education which is never completed, and possibly does not stop 
with the end of existence upon this planet. It is difference in ability to 
apply successfully his knowledge of principles in the conduct of prac- 
tical affairs, which differentiates the successful practitioner of engineering 
(rom him who is professionally but a cumberer of the ground, for whom 
20 one has any use. 
This instruction in applied science or engineering will, of necessity, be 
given along two lines. Every formula of practical value must have its 
theoretical expression which is deduced a priori, modified by coefficients 
of experience and practice, which shall take account of variable conditions 
or factors which the exact theoretical formula cannot, from the nature of 
the case, embrace. The two lines of instruction in this field will there- 
a