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Fifth. There should be symmetrical culture of the body, both muscle 
and skill and perceptive capacity, no less than training of the mind. 
How capable soever the mind may be as a tool, the handle by which it is 
directed by the will must yet remain the body and its ability to carry out 
she directions which the intelligence gives. 
Finally, if it be the object of education to lead out and develop the 
Jod-given capacities of a man, to give him a kit of sharpened tools 
and a trained capacity to use them to make him more the master of 
unfriendly environment, to make him more capable of lending a hand to 
help upward those about him less favored than he, to teach him the basis 
on which to decide between that which is wise and unwise, between right 
and wrong, then the contention of this paper is that there is no training 
n education superior to engineering, when properly carried out, to pro- 
duce self-reliant, independent, creative thinkers—to produce God-like 
men. 
DISCUSSION. 
Proressor ROBERT H. TrURstoN, of Sibley College, Ithaca, N. Y.: The edu- 
cational value of applied mathematics and of engineering has, I think, always been 
nore or less recognized from the earliest times. The fact has been that applied mathe- 
natics have not, until these later days, been looked upon as of sufficient importance, 
educationally, to secure for them a very important place in the curricula of the schools. 
The only university giving instruction in all the literatures, arts, and sciences of its 
time was that of Alexandria, the home of Euclid ; and Hero the Younger, Archimedes, 
and their kind were teachers of applied mathematics, even though they, like all Greeks 
and all learned men of every nationality of that time, took no great interest in their 
practical employment. But their value as a discipline was recognized and utilized. 
~ During the succeeding centuries, up to recent times, the arts progressed and science 
made great strides, and, more important than all, science found application in the arts; 
but for a thousand years the schools remained under the influence and direction of the 
cloisters, and only literature had real interest for them. The natural sciences made 
slow progress ; mathematics gained little until the times of Newton and Descartes ; and 
applied science, of whatever department, remained unrecognized by the schoolmen. 
To-day for the first time, and in the United States mainly, we find this attempt made 
deliberately and earnestly—usually by the State governments of the West and of the 
Middle States ; while the independent schools, having for their main purpose the pro- 
motion of professional training in the constructive arts—in engineering, as we have come 
to call them—are taking a more complete form as educational institutions than the 
older schools ever approached. It is these schools which have done most to illustrate 
che educational value of the applied sciences, and especially of applied mathematics. 
These studies, given as a matter of business and for a business purpose, have shown 
shemselves to have extraordinary educational value in ways which make them helpful 
.n every department of a ‘complete and perfect education.” 
The peculiar discipline afforded by the mathematics, pure or applied, is that of the 
seasoning and logical faculties. The study of pure mathematics gives power of starting 
{rom precisely defined premises. with quantities of exactly measured value, and of pro- 
ceeding step by step, with absolute accuracy and quantitatively precise measures. to a 
result which is as exact and certain as the premises upon which it is based. Precision 
of definition and measure, accuracy of process, and exactness of each operation become, 
under this drill, intuitive and habitual. No qualities of mind are of greater importance, 
either to the development of character or to the acquirement of those qualities which 
give life success and value. 
Engineering and the applied mathematics do still more. Engineering consists in the 
application of all available scientific knowledge, of applied science in every field, to the 
arts of construction. The purpose and outcome of the education given by these profes-