534 
NATURE 
[SEPTEMBER 25, 1902 
paper ; and he will have no fear of the symbols of the infin- 
itesimal calculus. When I insist that a boy ought to be able to 
compute, this is the sort of computation that I mean. Five 
years hence it will be called ‘‘ elementary mathematics.” Four 
years ago it was an unorthodox subject called ‘‘ practical mathe- 
matics,” but it is establishing itself in every polytechnic and 
technical college and evening or day science school in the 
country. Several times I have been informed that on starting 
an evening class, when plans have been made for a possible 
attendance of ten or twenty students, the actual attendance has 
been 200 to 300. Pupils may come for one or two nights toa 
class on academic mathematics, but then stay away for ever; a 
class in practical mathematics maintains its large numbers to 
the end of the winter.! 
Hitherto the average boy has been taught mathematics and 
mechanics as if he were going to be a Newton or a Laplace ; he 
learnt nothing and became stupid. I am sorry to say that the 
teaching of mechanics and mechanical engineering through 
experiment is comparatively unknown. Cambridge writers and 
other writers of books on experimental mechanics are unfor- 
tunately ignorant of engineering. University courses on engineer- 
ing—with one splendid exception, under Prof. Ewing at Cam- 
bridge—assume that undergraduates are taught their mechanics 
as a logical development of one or two axioms; whereas in 
many technical schools under the Science and Art Department, 
apprentices go through a wonderfully good laboratory course in 
mechanical engineering. We really want to give only a few 
fundamental ideas about momentum and the transformations of 
energy and the properties of materials, and to give them from 
so many points of view that they become part of a student’s 
mental machinery, so that he uses them continually. Instead 
of giving a hundred labour-saving rules which must be forgotten, 
we ought to give the one or two ideas which a man’s common- 
sense will enable him to apply to any problem whatsoever and 
which cannot be forgotten. A boy of good mathematical attain- 
ments may build on this experimental knowledge afterwards a 
superstructure more elaborate than Rankine or Kelvin or Max- 
well ever dreamt of as being possible. Every boy will build 
some superstructure of his own. 
I must not dwell any longer on the three essential parts of a 
good general education which lead to the three powers which all 
boys of fifteen ought to possess ; power to use books and to en- 
joy reading ; power to use mathematics and to enjoy its use ; 
power to study Nature sympathetically. English Board School 
boys who go to evening classes in many technical schools after 
they become apprentices are really obtaining this kind of educa- 
tion. The Scotch Education Board is trying to give it to all 
boys in primary and secondary schools. It will, I fear, be some 
time before the sons of well-to-do parents in England have a 
chance of obtaining it. 
When a boy or man of any age or any kind of experience 
enters an engineering college and wishes to learn the scientific 
principles underlying a trade or profession, how ought we to 
teach him? Here is the reasonable general principle which 
Profs. Ayrton and Armstrong and I have acted upon, and which 
has so far led us to much success. Whether he comes from a 
bad or a good school, whether he is an old or young boy or man, 
approach his intelligence through the knowledge and experience 
he already possesses. This principle involves that we shall 
compel the teacher to take the pupil’s point of view? rather than 
the pupil the teacher’s; give the student a choice of many 
directions in which he may study ; let lectures be rather to in- 
struct the student how to teach himself than to teach him ; show 
the student how to learn through experiment and how to use 
books, and, except for suggestion and help when asked for, leave 
him greatly to himself. If a teacher understands the principle 
he will have no difficulty in carrying it out with any class of 
students. I myself prefer to have students of very different 
qualifications and experience in one class because of the educa- 
tion that each gives to the others. Usually, however, except 
in evening classes, one has a set of boys coming from much the 
1 To many men it will seem absurd that a real working knowledge of what 
is usually called higher mathematics, accompanied by mental training, can 
be given to the average boy. In the same way it seemed absurd 500 years 
ago that power toread and write and cipher could be given to everybody. 
These general beliefs of ours are very wonderful. 
2 Usually it is assumed that there is only one line of study. In mathe- 
matics it is assumed that a boy has the knowledge and power and past 
experience and leisure of an Alexandrian philosopher. In mechanics we 
assume the boy to be fond of abstract reasoning, that he is a good 
geometrician who can do the most complex things in geometrical conics, 
but cannot possibly take in the simplestidea of the calculus. 
NO. 1717, VOL. 66] 
same kind of school, and, although perhaps differing considerably 
as to the places they might take inan ordinary examination, really 
all of much the same average intelligence. Perhaps I had better 
describe how the principle is carried out in one case—the sons 
of well-to-do parents such as now leave English schools at about 
fifteen years of age. 
It was for such boys that the courses of instruction at the 
Finsbury Technical College (the City and Guilds of London 
Institute) were arranged twenty-two years ago. It wasattempted 
to supply that kind of training which ought already to have been 
given at school, together with so much technical training as 
might enable a boy at the end of a two years’ course to enter 
any kind of factory where applied science was important, with 
an observing eye, an understanding brain and a fairly skilful 
hand. The system, in so far as it applies to various kinds of 
mechanical engineering, will be found described in one of a 
small collection of essays called ‘* England’s Neglect of Science,” 
pp. 57-67.1_ I am sure that any engineer who reads that 
description will feel satisfied that it was the very best course 
imaginable for the average boy of the present time. A boy was 
taught how he must teach himself after he entered works. If 
after two or three years in the works he cared to go for a year 
or so to one of the greater colleges, or did not so care, it was 
assumed that he had had such a training as would enable him to 
choose the course which was really the best for him, 
Old Finsbury students are to be found everywhere in im- 
portant posts. The experiment has proved so successful that 
every London Polytechnic, every Municipal Technical School 
in the country has adopted the system, and in the present state 
of our schools I feel sure that all important colleges ought to 
adopt the Finsbury system. It hardly seems appropriate to apply 
the word ‘‘system’’ to what was so plastic and uncrystallised 
and had nothing to do with any kind of ritual. 
The Professors were given a free hand at Finsbury, and there 
were no outside examiners. I need not dwell upon the courses 
in Chemistry and Physics ; some critics might call the subjects 
Rational Chemistry and Applied Physics ; they were as different 
from all other courses of study in these subjects as the courses 
on Rational Mathematics and Mechanics differed from all 
courses elsewhere. The course on Mechanics was really one on 
Mechanical Engineering. There were workshops in wood and 
iron, not to teach trades, but rather to teach boys the properties 
of materials. There were a steam-engine and a gas-engine, 
and shafting and gearing of many kinds, and dynamos which 
advanced students in turn were allowed to look after under 
competent men. There was no machine which might not be 
experimented with occasionally. Elementary and advanced 
courses of lectures were given ; there was an elaborate system 
of tutorial classes, where numerical and squared paper exercise 
work was done ; there were classes in experimental plane and 
solid geometry, including much graphical calculation ; boys 
were taught to make drawing-office drawings in pencil only, and 
tracings and blue prints, such as would be respected in the 
workshop, and not the ordinary drawing-class drawings, which 
cannot be respected anywhere ; but the most important part of 
the training was in the Laboratory, in which every student 
worked, making quantitative experiments. An offer of a 100-ton 
testing-machine for that laboratory was made, but refused ; the 
advanced students usually had one opportunity given them of 
testing with a large machine, but not in their own laboratory. 
I consider that there is very little educational value in such a 
machine ; the student thinks of the great machine,” and not of 
1 The ideas in this Address have been put forward many times by Profs 
Ayrton and myself. See the following, among other publications :— 
“Pngland’s Neglect of Science” (Fisher Unwin); ‘* Practical Mechanics,” 
188r (Cassell); ‘‘ Applied Mechanics,’’ 1897 (Cassell); ‘The Steam En- 
gine, &c.," 1898 (Macmillan); ‘‘The- Calculus for Engineers,” 1897 
(Arnold) ; Recent Syllabuses and Examination Papers of the Science and 
Art Department in Subjects I., VII., VA, and XXII. ; Summary of 
Lectures on Practical Mathematics (Board of Education); ‘he Work of the 
City and Guilds Central Technical College (Journal of the Society of Arts, 
July 9, 1897); Inaugural Lecture at Finsbury, 1879 ; Address at the Coventry 
Technical Institute, February, 1898; ‘‘ Education of an Electrical En- 
gineer ” (Jouonad of the Society of Telegraph Engineers and of Electricians, 
September, 1882); Presidential Address, Institution of Electrical Engineers, 
January, 1892; ‘‘The Best Education for an Engineer” (NATURE), 
Uctober 12, 1899 ; Address at a Drawing-room Meeting, March, 1887- 
2 These great testing-machines, so common in the larger colleges, seem to 
have destroyed all idea of scientific experiment. There is so much that the 
engineer wants to know, and yet laboratory people are persistently and 
lazily repeating old work suggested and begun by engineers of sixty years 
ago. For example, men like Fairbairn and Robert Napier would long ago 
have found out the behaviour of materials under combined stresses. We do 
not even know the condition of strength of iron or steel in a twisted shaft 
which isalsoa beam, The theory of strength ofa gun or thick tube under 
