TRANSACTIONS OF SECTION A. 397 
standing however on a far higher level, multiplies both decimals out in the proper 
fashion, but to eight places, and cuts off four places at the end. No wonder that 
the public at large will hear nothing of the decimal system of weights and measures 
if the very essence of the decimal system of numbers is so little understood by the 
men who have to train the minds of the young generation ! 
I need scarcely say that I do not mean to blame the Science and Art Department, 
far less the teachers who have simply to follow suit. They act up to their light, 
and cannot be expected to introduce methods which are practically unknown at 
Cambridge, and of which the only good text-books are in foreign languages ; books 
which are probably not at all suitable for introduction into our schools without 
considerable change. 
It is satisfactory to learn that an association has recently been formed under 
the presidency of Professor Huxley ‘to effect the general advancement of the 
profession of science and art teaching by securing improvements in the schemes of 
study, and the establishment of satisfactory relations between teachers and the 
Science and Art Department, the City and Guilds of London Institute, and other 
public authorities.’ 
The good wishes of all who have the cause of sound education at heart must go 
with such an undertaking, one of the principal aims of which seems to be to save 
teaching from being any longer enslaved by examinations, and to promote greater 
accord between the teacher and the examiner. It is to be hoped that this associa- 
tion will consider geometry as one of the subjects included under the designation of 
science. 
It is by the neglect of pure geometry and its applications to geometrical 
drawing that Cambridge has lost, or rather has never had, contact with the 
practical needs of the nation. All the marvels of modern engineering have sprung 
into existence without its help. The great engineers have had to depend to a 
degree, now unheard of, upon costly experiments, until they themselves gradually 
discovered mathematical methods adapted to their purposes. 
Only the electrical engineer found ready to his hands a complete theory of 
which the mathematical part has been to a very great extent developed at Cam- 
bridge, or by men who have had their mathematical training there. This theory 
is, however, in its very nature less geometrical. One at least of the great men 
to whom the present theory of electricity is due, the late Clerk Maxwell, had the 
keenest appreciation of the value of modern geometry. I remember a characteristic 
letter of his being read to the Council of the London Mathematical Society, in which 
the writer, forgetting the subject of his letter, burst out into an enthusiastic praise 
of a German text-book, the ‘Geometrie der Lage, by Reye, through which Maxwell 
evidently, for the first time, got any idea of this subject. 
The engineer will always prefer geometrical methods to analysis, and has 
invented for himself a great variety of them. Originally these are disjointed, 
being invented for special purposes. It is the business of the mathematician after- 
wards to connect, simplify, and extend them, as has been done to a great extent 
by Culmann in Ziirich, or by Cremona at the Polytechnic School at Rome. 
Of these methods a few may be mentioned. First of all the geographical 
determination of stresses in certain girders invented both by mathematicians and 
by engineers. Its application is so simple that no engineer will ever use any other 
method if once he knows this one. It is so well adapted to its purpose, that I 
venture to say that a simpler method is impossible, being fully aware how 
dangerous such a statement is. Nay, if I were asked to give the formule to 
obtain the stresses by calculation, I should write these down from a sketch of the 
diagram, this being the simplest way of obtaining them. 
Another problem which recurs again and again is the determination of the 
area of a figure representing perhaps a plot of land or the section of a beam. 
Here also the advantage is altogether on the side of the graphical method. 
It is unnecessary to multiply these examples. But to make full use of graphical 
methods the draughtsman ought to have a thoroughly geometrical education. For 
instance, the real nature of the reciprocal diagrams already mentioned is only 
understood by aid of a peculiar reciprocal relation between points and planes in 
