452 
disposal of former generations of pupils, and which are probably 
as completely satisfactory as the present state of science will 
admit. It is pleasant to record that these text-books 
are the work of distinguished men who have always 
taken a prominent part in the proceedings of this sec- 
tion. We have Deschanel’s Physics, edited, or rather re- 
written, by Prof. Everett, a book remarkable alike for the 
clearness of its explanations and for the beauty of the engravings 
with which it is illustrated ; and passing to works intended for 
students somewhat further advanced, we have the treatises of Prof. 
Balfour Stewart on Heat, of Prof. Clerk Maxwell on the Theory 
of Heat, of Prof. Fleeming Jenkin on Electricity, and we expect 
a similar treatise on Light from another of our most distin- 
guished members. 
These works breathe the very spirit ot the method which 
sould guide both research and education in physics. They 
express the most profound and far-reaching generalisations of 
science in the simplest language, and yet with the utmost 
precision. With the most sparing use of mathematical 
technicalities, they are a perfect storehouse of mathema- 
tical ideas and mathematical reasonings, An old French geometer 
used to say thata mathematical theory was never to be considered 
complete till you had made it so clear that you could explain it 
to the first man you met in the street. This is of course a bril- 
liant exaggeration, but it is no exaggeration to say that the 
eminent writers to whom I have referred have given something 
of this clearness and completeness to such abstract mathematical 
theories as those of the electrical potential, the action of capil- 
lary forces, and the definition of absolute temperature. A great 
object will have been attained when an education in physical 
science on the basis laid down in these treatises has become | 
generally accepted in our schools, 
I do not wish to close this address without adverting, though 
only for one moment, to a question which occupies the minds 
of many of the friends of science at the present time, the question 
what should be the functions of the State in supporting, or in orga- 
uising, scientific inquiry. I do not mean to touch on any of the 
cificulties which attend this question, or to express any opinion as 
to the controversies to which it has given rise. But I do not 
think it can be out of place for the President of this section to 
call your attention to the inequality with which, as between 
different branches of science, the aid of Government is afforded. 
National observatories for astronomical purposes are maintained 
by this, as by every civilised country. Large sums of money are 
yearly expended, and most rightly expended, by the Govern- 
ment for the maintenance of museums, and collections of 
mineralogy, botany, and zoology; at avery recent period an 
extensive chemical laboratory with abundant appliances for re- 
search as well as for instruction has been opened at South Ken- 
singion. But for the physical sciences—such sciences as those 
of heat, light, and electricity—nothing has been done; and I 
confess I do not think that any new principle would be intro- 
duced, or any great burden incurred, capable of causing alarm | 
to the most sensitive Chancellor of the Exchequer, if it should 
be determined to establish, at the national cost, institutions for 
the prosecution of these branches of knowledge, so vitally im- 
portant to the progress of science as a whole. Perhaps also, 
upon this general ground of fairness, even the pure mathemati- 
cians might prefer a modest claim to be assisted in the calculation 
and printing of a certain number of Tables, of which even the 
physical applications of their science are beginning to feel the 
pressing need. 
One word further on this subject of State assistance to Science, 
and Ihave done. It is no doubt true that for a great, perhaps 
an increasing, number of purposes, Science requires the assistance 
of the State, but is it not nearer to truth to say that the State 
requires the assistance of Science? Itis my conviction that if the 
true relations between Science and the State are not recognised, it 
is the State, rather than Science, that will be the great loser, 
Without Science the State may builda ship that cannot swim, and 
may waste a million or two on experiments, the futile result of 
which Science could have foreseen. But without the State, Science 
has done very well in the past, and may dovery well in timetocome. 
I am not sure that we should know more of pure mathematics, 
or of heat, of light, or electricity than we do at this moment if 
we had had the best help of the State all the time. There are, 
however, certain things which the State might do and ought to 
do for Science. It, or corporations created by it, ought to 
undertake the responsibility of carrying on those great systems 
of observation which, haying a secular character, cannot be coms 
NATURE 
a4, 4 
[ Sept. 25, 1873 
pleted within the life-time of a single generation, and cannot 
therefore be safely left to individual energy. One other thing the 
State ought to do for Science. It ought to pay scientific men 
properly for the services which they render directly to the State, 
instead of relying, as at present, on their Jove for their work as a 
means of obtaining, their services on lower terms. If anyone 
doubts the justice of this remark, I would ask him to compare 
the salaries of the officers in thé British Museum with those 
which are paid in other departments of the Civil Service, 
But what the State cannot do for Science is to create the scien- 
tific spirit, or to control it. The spirit of scientific discovery is _ 
essentially voluntary ; voluntary, and even mutinous, it will re- 
main; it will refuse to be bound with red tape, or ridden by ~ 
officials, whether well-meaning or perverse. You cannot have 
an Established Chtrch in Science, and, if you had, I am afraid 
there are many scientific men who would turn scientific noncon- — 
formists. L 
I venture upon these remarks because I cannot help feeling 
that the great desire which is now manifesting itself on the part — 
of some scientific men to obtain for Science the powerful aid of 
the State may perhaps lead some of us to forget that it is self- 
reliance and self-help which haye made Science what it is, and 
that these are qualities the place of which no Government help 
can ever supply. ; 4 
Report of the Committee appointed to consider the possibilisy of 
improving the methods of instruction in Elementary Geometry. 
Until recently the instruction in elementary geometry given 
in this country was exclusively based upon Simson’s modification — 
of the text of Euclid. Of late years, however, attempts have 
been made to introduce other text-books agreeing with the 
ancient Elements in general plan, but differing from it in some 
important details of treatment. And in particular, the Associa- 
tion for the Improvement of Geometrical Teaching, having con- 
sidered the whole question with great labour and deliberation, 
is engaged in the construction of a Syllabus, part of which is 
already completed. The Committee had thus to consider, frst, 
the question of the plurality of text-books ; secowdly, certain 
general principles on which deviation from the ancient standard 
has been recommended; and, /hirdly, the Syllabus of the 
Geometrical Association. ; KF 
1. On the Plurality of Text-Books. 
It has already been found that the practical difficulty of ex-— 
amination stands in the way of allowing to the geometrical 
teacher complete freedom in the methods. of demonstration, and. 
in the order of the propositions. The difficulty of demonstrating” 
a proposition depends upon the number of assumptions which it 
is allowable to start from ; and this depends upon the order in 
which the subject has been presented. When different text-books 
have been used, it thus becomes virtually impossible to set the 
same paper to all the candidates, And in this country at present 
teaching is guided so largely by the requirements of examinations, 
that this circumstance opposes a serious barrier to individual 
attempts at improvement. On the other hand, the Committee think ~ 
that no single text-book which has yet been produced is fit to 
succeed Euclid in the position of authority ; and it does not seem 
probable that a good book could be written by the joint action 
of selected individuals. It therefore seems advisable that the 
requisite uniformity, and no more, should be obtained by the 
publication of an authorised Syllabus, indicating the order of 
the propositions, and in some cases the general character of the 
demonstrations, but leaving the choice of the text-book perfectly © 
free to the teacher. And the Committee believe that the 
authorisation of such a Syllabus might properly come from the 
British Association. : 
2. On some Principles of Improvement, 
The Committee recommend that the teaching of Practical 
Geometry should precede that of Theoretical Geometry, in order, 
that the mind of the learner may first be familiarised with the 
facts of the science, and afterwards led to see their connection. — 
With this end the instruction in practical geometry should be ~ 
| directed as much to the verification of theorems as to the 
solution of problems. " 
It has been proposed to introduce what are called redundant 
axioms ; that is to say, assumptions whose truth is apparently 
obvious, but which are not independent of one another. Such, 
for example, as the two assumptions that two straight lines — 
| cannot enclose a space, and that a straight line is the shortest 
“= 
