April 19, 1883} 
NATURE 
581 
College, on January 17, the following statements of work | 
done by the Committees were presented. In Sold 
Geometry no progress had been made in consequence of 
the serious illness of the secretary (Mr. Merrifield), but 
the President in his subsequent address remarked that it 
was hoped that the Committee would meet at an early 
date and work out, upon the basis of what Mr. Merrifield 
had done, a syllabus of propositions corresponding to the 
11th and 12th Books of Euclid and the simpler geometry 
of the sphere. In Azgher Plane Geometry the Committee 
had revised about half of the syllabus issued in 1879 and 
nad added chapters on the geometry of the triangle and 
on geometrical maxima and minima (copies were distri- 
buted amongst the members present, and have been 
subsequently circulated). In Geometrical Comics the 
former syllabus had also been revised and continued to 
the end of the hyperbola (this syllabus is also in the 
hands of members). In Elementary Plane Geometry the 
proofs of Book I. ot the Sy//abws had been revised, the 
proofs of Book II. drawn up,and a collection of Exercises 
on Books I. and lI. had been added (the motion in con- 
nection with the adoption of these proofs, which was 
down in the President’s name, had to be postponed in 
consequence of copies not having been circulated before 
the meeting). Gratifying testimony to the success of the 
Association’s efforts was afforded by the fact recorded in 
the Council's Report that the copies of the syllabus were 
all disposed of, and that it was in contemplation to bring 
out at once a revised edition of the work in accordance 
with the changes made in the books of proofs. 
In addition to the ust.al routine business, the President 
closed the morning sitting with some remarks on the 
teaching of arithmetic. This is a subject the claims of 
which upon teachers he has at many previous meetings 
pressed vpon his hearers, it being his desire that the 
teaching should be put upon a sounder footing than it at 
present in most cases occupies. A true disciple of his old 
master, De Morgan, he insisted strongly upon the more 
frequent appeal to reason than to rule. “It seemed to him 
to be the wrong order to give first the rule and then the 
reason. Teachers should take particular examples, and 
work them out with reasons for every step. They should 
lead up to a rule by a series of examples worked out from 
common sense, and only when these have been thoroughly 
grasped should the rule be introduced as a convenient 
embodiment and summing up of the results attained by 
the application of reason and common sense.” A 
common habit with boys is to ask, ‘‘ How am I to do 
this?” “In his own practice he never answered that ques- 
tion, but he said, ‘What does it mean? If you will only 
find out what it means, then you will know how to do it.’” 
Another principle he advocated was “‘that all arithmetical 
processes should follow the order of thought, according 
to which numbers are grouped in language... .. The 
order of thought in the expression of numbers was from 
the higher group to the lower, hundreds to tens, tens to 
units, &c.” In this connection he referred to a lecture by 
the late Mr. Bidder. A reform on the principles he (the 
President) advocated would, he believed, be very valuable 
in teaching and in the practical operations of a:ithmetic. 
In the natural sciences arithmetic is applied to cases 
where approximate data only are employed. “ Hence it 
was becoming more and more important that methods of 
approximation should be carefully and distinctly taught.” 
This led him to enter a protest against the practice, fre- 
quent amongst University examiners, of setting in papers 
for schoolboys, ‘‘ among the questions on decimal frac- 
tions, some examples to be done only by reducing recur- 
ring decimals to vulgar fractions, and then working out 
the result by vulgar fractions. To give prominence to 
such examples was simply to destroy the notion which a 
* A special meeting for the purpose of considering the postponed motion 
was held at University College on the evening of March 20, at which the 
“* proofs’” were adopted and their publication sanctioned. 
\ 
good teacher would have been endeavouring to instil into 
a boy’s mind, that decimal fractions are useful only in 
general for approximate results. He did not wish to say 
anything against recurring decimals rightly used and in 
their proper place.” A final point was that he would sub- 
stitute Horners process for the extraction of any roots 
for “the awkward and almost useless special piocesses 
usually given for extracting square and cube roots. 
This he would teach simply as a process; but of course 
with fair warning to the boy by telling him that he was 
for once giving him a process which would lead to the 
desired result, an 1 that it would be a reward of his future 
mathematical attainments if he could get to the reason of 
it. 
The novel feature, however, in this year’s proceedings 
was the holding of an afternoon sitting, which was‘wholly 
devoted to the consideration of the subject of elementary 
mechanics. This meeting was the outcome of the recent 
extension of the Association’s sphere vf action, and proved 
to demonstration that the said extension had met with 
the approval of many of our most able physicists. The 
papers rcad were three in number: (1) The Teaching of 
Elementary Mechanics, by Mr. W. H. Besant, F.R.S. ; 
(2) Notes on the Teaching of Elementary Dynamics, by 
Prof. G. M. Minchin ; (3) The Basis of Statics, by Prof. 
H. Lamb of the University of Adelaide. (1) is remark- 
able as proceeding from a successful Cambridge “ coach,” 
_who finds it difficult to emancipate himself “ from the ideas 
and prejudices which are the natural results of an adher- 
ence for many years to a special set of books and to a 
special system of teaching. The fact constantly before 
us in Cambridge, that mechanics are being studied witha 
view to success in examinations, tends to make us forget 
the importance of the practical application to daily 
life of a knowledge of mechanics, and the tempta- 
tion is to luxuriate in the flowery and ornamen- 
tal prcblems which sometimes form the staple of 
examination questions,” whereas ‘‘millions of people 
must acquire a knowledge of the laws of mechanics, 
practical or theoretical, or both, who are not going to be 
tested by a Cambridge examination.” It however goes 
without saying that at present Cambridge methods do 
exercise a very large influence on the teaching of me- 
chanics throughout the country. In the case of young 
students and beginners, Mr. Besant censiders that the 
first requisite for a class-room is a set of models and a 
quantity of machinery (segnius irritant animos, &c.). 
“The handling of systems of pulleys, and experiments 
with levers and screws, will guide the student, almost 
unconsciously, to the ideas of the transmission of 
motions, and of the transmission and multiplication of 
force. . . . Then, again, experiments with falling bodies, 
and with an Attwood’s machine, will illustrate the ideas 
of uniform motion and of accelerated motion, and gene- 
rally of the action of gravity. ... For many students 
this kind of experimental teaching will probably be suffi- 
cient for the work of their lives, and it will be certainly 
educationally useful.” The Cambridge practice has 
been to treat the subjects of statics and dynamics sepa- 
rately, and to take statics first ; and the teaching is so 
limited that the ordinary Bachelor of Arts, whose reading 
has been limited to statics alone, “is sent out into the 
world without any perception of the laws of motion, anc 
without any knowledge of the elementary deductions 
from those laws, which are necessary requisites for a true 
appreciation of a vast range of natural phenomena.” 
Passing next in review the change of nomenclature anc 
of treatment inaugurated by Professors Thomson ana 
Tait, and the late Prof. Clerk Maxwell, Mr. Besant 
records his opinion that Duchayla’s proof is “forced and 
unnatural,” and causes a considerable waste of time. His 
wish is that the examiners should have greater freedom 
of action. He would, following the lead of the above- 
named eminent physicists, commence with a study of the 
