Sept. 10, 1885 | 
NATURE 
447 
the continual increase of those who have received higher educa™ 
tion of some kind or other, and whose daily occupations give 
them an interest, direct or indirect, in one or more branches of 
science. 
It may not be amiss to insist for a little on the advantages to 
science of a great body of men unofficially engaged in scientific 
research, in writing regarding science, or even in merely turning 
scientific matter over in their minds. It will not have escaped 
the notice of those among you who have studied the history of 
science, that few scientific ideas spring up suddenly without 
previous trace or history. It is perfectly true that in many cases 
some mind of unwonted breadth and firmness is required to 
formulate the new doctrine, and carry it to manifold fruition ; 
but a close examination always shows that the sprite was in the 
air before the Prospero came to catch him. It is very striking to 
notice, in the history of Algebra for instance, long periods in 
which great improvements were effected in the science, which 
cannot be traced to any individual, but seem to have been due 
merely to the working of the minds of scientific men generally 
upon the matter, one giving it this little turn, another that, in the 
main always for the better. Like every other thing that has the 
virtue of truth in it, science grows as it goes, not like the idle 
gossiping tale by the casual accretion of heterogeneous matter, 
but by the chemical combination of pure element with pure 
élement in reasonable proportion. 
I know of no greater advantage for science than the existence 
of an army of independent workers sufficiently enlightened for 
self-criticism, who shall test the results and theories of their day. 
Great-and indispensable as are the uses of professional schools 
of scientific workmen, they are open to one great and insidious 
danger. The temptation there to swear by the word of the 
master is often irresistible. Not to speak of its being often the 
readiest avenue to fame and profit, it is the perfectly natural 
consequence of the contact of smaller mind with greater. 
There are few things where the want of an enlightened 
scientific public strikes an expert more than the matter of scientific 
text-books. If the British public were educated as it ought to 
be, publishers would not be able to palm off upon them in this 
guise the ill-paid work of fifth-rate workmea so often as they do; 
nor would the scientific articles and reviews in popular journals 
and magazines so often be writt2n by men so palpably ignorant 
of their subject. 
We all have a great respect for the integrity of our British 
legislators, whatever doubts may haunt us occasionally as to their 
capacity in practical affairs. The ignorance of many of them 
regarding some of the most elementary facts that bear on every- 
day life is very surprising. Scientifically speaking, uneducated 
themselves, they seem to think that they will catch the echo of 
a fact or the solution of an arithmetical problem by putting their 
ears to the sounding-shell of uneducated public opinion. When 
I observe the process which many such people employ for arriving 
at what they consider truth, I often think of a story I once heard 
of an eccentric German student of chemistry. This gentleman 
was idle, but, like all his nation, systematic. When he had a 
precipitate to weigh, instead of resorting to his balance, he would 
go the round of the laboratory, hold up the test-tube before each 
of his fellow-students in turn, and ask him to guess the weight. 
He then set down all the replies, took the average, and entered 
the result in his analysis. 
I will not take up your time in insisting upon the necessity of 
the diffusion of science among that large portion of the public 
who are, or ought to be, appliers of scientific knowledge to prac- 
tical life. That part of my theme is so obvious, and has been of 
late so much dwelt upon, that I may pass it by, and draw your 
attention to another place in which the shoe pinches. All of you 
who have taken any practical interest in the organisation of our 
educational institutions must be aware of the great difficulty in 
securing the services of non-professional men of sufficient scien- 
tific knowledge to act on School Boards, and undertake the 
direction of our higher schools. It is no secret among those who 
carefully watch the course of the times in these matters that our 
present organisation is utterly insufficient ; that it has not solved, 
and shows every day less likelihood of solving, the problems of 
higher education. This arises, to a great extent, from the fact 
that a scientifically educated public of the extent presupposed by 
the organisation really does not at present exist. 
If the existence of a great scientific public be as important as 
I think I have shown it to be, it must be worth while to devote 
a few moments to the consideration of the means we adopt to 
produce it both in the rising and in the risen generation. 
It would naturally be expected that we should look carefully 
to the scientific education of our youth, to see that the best men 
and the best means that could be had were devoted to it; that 
we should endeavour to make for them a broad straight road to 
the newest and best of our scientific ideas ; that we should exer- 
cise them when young on the best work of the greatest;masters ; 
familiarise them early with the great men and the great feats of 
science, both of the past and of the present ; that we should avoid 
retarding their progress by making the details and illustrations or 
particular rules and methods end in themselves. Granting that 
it is impossible to bring every learner within reach of the fullest 
scientific knowledge of his time, it would surely be reasonable to 
take care that the little way we lead him should not be along 
some devious by-path, but towards some eminence from which 
he might at least see the promised land. The end of all scien- 
tific training of the great public I take to be, to enable each 
member of it to look reason and nature in the face, and judge for 
himself what, considering the circumstances of his day, may be 
known, and not be deceived regarding what must to him remain 
unknown. [If this be so, surely the ideal of scientific education 
which I have sketched is the right one: yet it is most certainly 
not the ideal of our present system of instruction, To attain 
conviction on that head it is sufficient to examine the text-books 
and examination papers of the day. 
Let us confine ourselves for the present tothe most elementary 
of all the exact sciences, viz., geometry andalgebra. These two, 
although among the oldest, are, as Professor Cayley very justly 
reminded the Association last year, perhaps the most progressive 
and promising of all the sciences. Great names of antiquity are 
associated with them, and in modern times an army of men of 
genius have aided their advance. Moreover, it cannot be said 
that this advance concerns the higher parts of these sciences 
alone. On the contrary, the discoveries of Gauss, Lobat- 
schewsky, and Riemann, and of Poncelet, Mobius, Steiner, 
Chasles, and Von Standt, in geometry, and the labours of De 
Morgan, Hamilton, and Grassman, not to mention many others, 
in algebra, have thrown a flood of light on the elements of both 
these subjects. What traces of all this do we find in our school 
books? To be sure azéiguity is stamped upon our geometry, for 
we use the text-book of Euclid, which is some two thousand years 
old ; but where can we point to the influence of modern progress 
in our geometrical teaching? For our teaching of algebra, I am 
afraid, we can claim neither the sanction of antiquity nor the 
light of modern times. Whether we look at the elementary, or 
at what is called the higher teaching of this subject, the result is 
unsatisfactory. With respect to the former, my experience 
justifies the criticism of Professor Henrici ; and I have no doubt 
that the remedy he suggests would be effectual. In the higher 
teaching, which interests me most, I have to complain of the 
utter neglect of the all-important notion of algebraic form. I 
found, when I first tried to teach University students co-ordinate 
geometry, that I had to go back and teach them algebra over 
again. The fundamental idea of an integral function of a cer- 
tain degree, having a certain form and so many coefficients, was 
to them as much an unknown quantity as the proverbial x. I 
found that their notion of higher algebra was the solution of 
harder and harder equations. The curious thing is that many 
examination candidates, who show great facility in reducing ex- 
ceptional equations to quadratics, appear not to have the remotest 
idea beforehand of the number of solutions to be expected ; and 
that they will very often produce for you by some fallacious 
mechanical process a solution which is none at all. In short, 
the logic of the subject, which, both educationally and scienti- 
fically speaking, _is the most important part of it, is wholly 
neglected. The whole training consists in example grinding. 
What should have been merely the help to attain the end has 
become the end itself. The result is that algebra, as we teach 
it, is neither an art nor a science, but an ill-digested farrago of 
rules, whose object is the solution of examination problems. 
The history of this matter of problems, as they are called, 
illustrates in a singularly instructive way the weak point of our 
English system of education. They originated, I fancy, in the 
Cambridge Mathematical Tripos Examination, as a, reaction 
against the abuses of cramming bookwork, and they have spread 
into almost every branch of science teaching—witness test- 
tubing in chemistry. At first they may have been a good thing ; 
at all events the tradition at Cambridge was strong in my day, 
that he that could work the most problems in three or two and a 
half hours was the ablest man, and, be he ever so ignorant of bis 
subject in its width and breadth, could afford to despise those 
