504 
tongue and pen, shows himself able to hold 
his position as the peer of other great 
organizers of our industrial life. The 
highest success is to be quickly reached as 
a rule only by those engineers who have 
had adequate preliminary education in cul- 
ture studies, which is another name for the 
liberal arts. Such culture is now most 
readily and suitably attained by pursuing 
some part, more or less complete, of a reg- 
ular college course. This will come to be 
regarded more and more as the best prepa- 
ration for a professional course in engineer- 
ing, as it is now for a professional course in 
law and medicine. 
Following the consideration of the cul- 
ture studies comes that of the indirectly 
technical studies, such as mathematics, me- 
chanics, physics, chemistry and drawing, 
which at the present time occupy between 
one-third and one-fourth of the time of the 
average engineering course. These studies 
rightfully have place in the course, but the 
question whether the amount and quality of 
the work at present accomplished is entirely 
satisfactory is one which has been much de- 
bated. It may be said fairly, I think, that 
the standard of work in mathematics, me- 
chanics and physics has been gradually but 
surely advancing in all the engineering 
colleges, against the opposition of a large 
part of those engaged in engineering prac- 
tice, who have been largely opposed to 
teaching more mathematics, etc., than they 
themselves were taught, saying that they 
have had no use for much of that which 
was taught them. This argument has 
seemed perfectly conclusive to those who 
have advanced it, and also to the student, 
who naturally finds such studies hard, and 
(as he thinks) much in the way of his 
rapidly advancing to purely technical study. 
This view has also often met acceptance 
with the technical professors, who are 
largely in sympathy with those engaged in 
practice. But the argument is fallacious, 
SCIENCE. 
[N. S. Von. VI. No. 144. 
as I am convinced. The contrary view 
has prevailed in the papers before this So- 
ciety. We are to look upon this gradual 
advance of the standard in mathematics, 
etc., as a movement which has not as yet 
ceased, but one still in progress. 
Perhaps the point of greatest difficulty, 
so far as mathematics is concerned, has been 
to have the differential and integral caleulus 
so incorporated into the engineering courses 
as to really become part of the working 
equipment of the student. That may not 
have been completely accomplished as yet, 
but that is the standard now regarded as 
essential, and one which is more and more 
nearly attained year by year. It is my 
opinion that it will not be satisfactorily 
reached until the course in calculus includes 
the treatment of differential equations. 
This conclusion is forced upon me, not 
merely by the abstract consideration that 
physical and mechanical questions find their 
expression best by the use of differential 
equations ; but the problems arising just 
now in the theory of alternating currents 
must evidently be treated on the basis of 
their differential equations. Heretofore it 
has been possible to satisfy the student as 
to the treatment and solution of the me- 
chanical and physical problems in his 
course without special study of differential 
equations, though he was likely to meet a 
number of points that were puzzling and 
unsatisfactory by reason of his ignorance of 
that subject. But now the matter can no 
longer be avoided, I think, as no other 
treatment can give the necessary insight 
into the complicated phenomena which 
must be fully mastered to-day by the stu- 
dent in electricity. 
Mechanics, too, and physics have taken 
on a larger and larger significance. The 
principles of mechanics underlie all phys- 
ical phenomena and all engineering pro- 
cesses. Their formal study has been found 
to be of increasing importance in under- 
