Pare, 
TRANSACTIONS OF SECTION A. 891 
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 by 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 practical 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 atten- 
tion 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 
scientific 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 considera- 
tion of the means we adopt to produce it both in the rising and in the risen gene- 
ration, 
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 exercise 
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 ends in themselves. Granting that it 
isimpossible 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 scientific 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 to the most elementary of all the 
exact sciences, viz., geometry and algebra. These two, although among the oldest, 
are, as Professor Cayley very justly reminded the Association not long ago, 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, 
Lobatschewsky, and Riemann, and of Poncelet, Mobius, Steiner, Chasles, and Von 
Staudt, in geometry, and the labours of De Morgan, Hamilton, and Grassmann,. 
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 antiquity 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- 
