568 INTERNATIONAL CONGRESS OF EDUCATION. 
In plotting results we have, for instance, Thurston’s triangle of the 
sopper-zinc-tin alloys, combined with their tensible strength, showing at 
a glance where the highest and where the lowest result is to be found, with 
the percentage compositions thereof. In slag calculation we have the five- 
line problem, designed by myself, of solving at a glance the computation 
for mixing two compounds in such a proportion as to produce a desired 
sompound. 
When a young man reaches the point that he asks for paper and pencil 
1 order to answer your question, then you may know he is going to give 
you some real information and is not going to talk generalities. Need I 
say anything more in favor of drawing ? I think not. 
How, then, are we to get this result? We must teach him drawing— 
(ree-hand drawing, mechanical drawing, projections, descriptive geom- 
stry—so that he may draw the rear side of a cube or any regular solid 
without going round to see it, so that his imagination carries him through 
she solution of intricate problems in points, lines, planes, surfaces, and 
solids. These studies will be found to greatly help his analytical studies, 
sxplaining and clearing them up at every point. 
So far I have only spoken of drawing. Now I will speak of shop-work, 
and will begin by saying that just as drawing is a means of explaining 
and clearing the intricate parts of mathematics, of analytical and applied 
mechanics, and of the study and design of structure and of machinery, 
just so also is shop-work upon the use of materials. No engineering 
course can afford the time for a great deal of shop-work. The time 
required to make elaborate work is quite foreign to a school of engineering. 
But a course should be given of sufficient length that the student shall 
teel at home in the use of wood, cast-iron, wrought-iron, and steel ; and 
he should reach the point where he would feel as great a shock to see a 
material misused—for instance, cast-iron used as a tie-rod—as he would if 
2e saw a horse harnessed up with his face toward the cart. 
I have now mentioned drawing and shop-work independently ; it remains 
tor me to speak of them in their relation to each other. Mechanical 
drawing and shop-work are each independent forms of language. Drawing 
is an expression of thought upon a flat surface. Shop-work is an 
axpression of thought occupying space. The making of a drawing from 
am object is a good mental exercise, as is also the making of an object 
rom a drawing. But when a student has made a drawing from an 
object, and, without further reference to the object, has made a repro- 
Juction of it from his own drawing, he has felt and underctood that 
most useful of modern appliances—the working drawing. 
Now, am I taking too radical a position if I—after lamenting, as we have 
all lamented, our inability to take from the brain of the departing octo- 
genarian something which can be mechanically given to the rising youth, 
whereby he may start in life with a distinct advantage over what we had