560 INTERNATIONAL CONGRESS OF EDUCATION. 
laws and doctrines of modern physical science, I need hardly add that 
students of science must make themselves familiar with the instruments 
and methods used in exact measurements, to have an intelligent apprecia- 
‘ion of modern science and to have confidence in the truth of its state- 
ments, which, without that knowledge, are to manv ‘a stumbling-block 
and foolishness.” 
Now, it seems to me that the study and use of the instruments used in 
exact measurements, and of the methods used in combining these measures 
to arrive at the most exact measure possible, are, from an educational point 
of view, highly important. The student thus has his mind opened to the 
view of things and the workings of nature where the minutia, generally 
disregarded as unimportant, appears of the greatest importance in the 
correct interpretation of nature. 
Working with the instruments used in exact measurements gives, in an 
cminent degree, control of the hand, and training of the eye to minute 
and careful vision ; and after the measures are made, the plotting of them 
in a curve in which the correctness or incorrectness of the measures made 
is shown to the eye at a glance, cannot fail to further the appreciation 
of careful and exact work on which often denends success in the practice 
of a profession or of an art. 
THE EDUCATIONAL VALUE OF APPLIED MATHEMATICS, 
INCLUDING ENGINEERING. 
BY F. R. HUTTON, C.E., PH.D., PROFESSOR OF MECHANICAL ENGINEERING, 
SCHOOL OF MINES. COLUMBIA. 
THE committee on programme for the Department Ccngress of Tech- 
nological Instruction has requested the writer, through Commissioner W. 
T. Harris, to prepare a brief paper on the above subject in order to open 
the debate upon it. The compliment is accepted in the hope that, while 
securing agreement in the main, there may yet be additional light and 
confirmation thrown upon the subject by those who will participate in the 
liscussion. 
Assuming at the outset that the important work of the lower and pre- 
paratory schools is well done, to fit the student for his technical course of 
training, there would appear to lie behind the course of instruction in the 
technical schools two fundamental starting points. The first of these is 
that which has for its object the familiarizing of the student with those 
principles of pure science and knowledge which the engineering student 
must have as the foundation of all his later work. If we receive that 
definition of engineering which represents it as aiming to bring to human- 
ity, for the progress of civilization, the utilization of those laws and forces