404 
NATURE 

[Sep¢. 21, 1871 

tematic matters is rather less detailed than in the English 
“ Zoological Record,” the notices of anatomical and phy- 
siological papers are fuller, and the student will always 
find indications of the direction in which to look for in- 
formation on other subjects. The conductors of these use- 
ful Reports havs always been in the habit of delaying their 
publication until the literature of each year could be 
analysed as completely as possible, and in the present 
issue we have only the particulars of the contributions to 
entomological. knowledge published during the years 
1867-68. The Insecta proper are reported upon by M. 
F. Brauer of Vienna, whilst Prof. Gerstacker confines his 
labours to the Myriopoda, Arachnida, and Crustacea. 
W. 5. D: 



LETTERS TO THE EDITOR 
[The Editor does not hold himself responsible for opinions expressed 
by his Correspondents. No notice is taken of anonymous 
communications. | 
The Science and Art Department 
BELIEVING your columns to be at all times open for the dis- 
cussion of matters connected with Science and Art teaching, I 
venture to offer a few remarks on the administration of the above- 
named Department. 
Since tue arrival of the results of the last May examination, 
the teachers have been enabled to make up their claims for pay- 
ment, and there has been a great outcry from all parts of the 
country on account of the serious reduction that has taken place 
in the amounts the teachers are entit'ed to claim for their work. 
This reduction arises from the operation of the Jast alteration by 
the Department of the scale of payments on results, the full effecc 
of which was not felt until this year. 
Many objections were raised at the time the minute was issued 
(in the latter part of 1869), especially to its being introduced 
after the commencement of the work of the session, and in 
deference to these remonstrances it was modified in its applica- 
tion to the May examinations of 1870, and its full operation de- 
ferred till the May just past. When I say just past I am 
speaking after the manner of the Department, for they are so 
far behind that the Annual Report for the session of 1869-70 has 
not yet been received by the committees here. 
Now I venture to submit that this reduction in the scale of 
payments is likely to have a very injurious etfect on the spread 
of education in Science. In many cases, especially in smail 
towns, and where a teacher has a class in only one or two sub- 
jects, the amount of payment to be recrived is so small as t» give 
rise to the apprehension that such classes will be given up, be- 
cause of the utter inadequacy of the payment to remunerate a 
teacher for the time and trouble spent in ihe work of instru ting 
them. To give an illustration, I have just been informed of an 
instance where a teacher has had to proceed fourteen mil-s by 
rail to give his lectures to a class, and the result of the recent 
examin.tion is that he received absolu'ely nothing from the De- 
partment in respect of this cla-s, all those of the students who 
passed being persons of the middle classes. 
When in conjunction with such facts as these we read that the 
payment for instric.ion in Science and Art in 1870 was 17,0cO/. 
less than in the previous year, there seems grea! reason for the 
complaints of the teachers, and one must, I ihink, come to the 
conclusion that the Department has proceeded too far in the 
direction of eccnomy to be conducive to efficiency or to the 
continued spread of scientific instruction. 
If the presen: scale is to be retained, I think the suggestion of 
a writer in the Daly News recentiy, that the system of payment 
by re-ults alone should be modified, is worthy of considera'ion. 
The teacher often has the greatest amount of trouble with those 
students who just miss obtaining a certificate, and in these cases 
the master receives nothing at all for the labours of the session. 
It would be more encouraging to the teacher if a small payment 
was made for those students who have attended the required 
number of class lectures, alihough they may not be able to pass 
the examination for proficiency. Ol! course, there should be 
safeguards provided against the abuse of such a rule, say, by 
excluding from its operation all such as are unable to attempt a 
stated pr: portion of the questions propou: ded. 
Even under the present arrangements I have seen many 

students sit idle the greater part of the evening, or leave the 
examination room as soon as permitted to do so by the regula- 
tions, through not being able to attempt to answer more than two 
or three questions. 
With regard to another matter of which complaint has been 
made, viz., the recent minute of the Department imposing fines 
on Committees who ask for a larger number of papers than they 
require, I must say I cannot see the r asonableness of the com- 
plaint. At the last May examination in Plymouth, one school alone 
(according to the printed list issued by the department) sent up 
a requisition for 714 papers in the various subjects of Art and 
Science, while the total number of papers worked by pupils of 
that school, and by strangers whose papers were asked for 
through its committee, was only 339—less than half. If this. 
case is at all a sample of what was occurring in the country 
generally, and the issue of the minute leads me to think such 
must have been the case, I consider it was quite time for some- 
thing to be done to prevent such wholesale waste. Of course in 
all schools there will be a certain number who will shrink back 
at the Jast moment, after having given in their names for the 
examination, and this being fairly provided for, I do not see 
anything in this regulation that efficient schools and committees 
should complain of. A LocaL COMMITTEEMAN 
Plymouth, Sept. 14 
Elementary Geometry 
I HAVE to thank the Editor of Nature for insertmg my 
letter, and Mr. Wilson for writing so fully. I was not aware 
when I wrote, that Mr. Wilson had himself published an ele- 
mentary book on geometry. He has modestly omitted to refer 
to it; but I have seen it, and it appears to me a suggestive book 
for a teacher. He acknowledges himself unable to recommend 
one suited to. boys, fr laying the foundation of geometry. 
Mr. Wilson’s advice seems rather suited to teachers of geo- 
metrical drawing than of mathematics. Of course it is essential 
that a boy should know what measuring means; but scales of 
measurement have no essential connecion with geometry. 
Nevertheless, I entirely agree with him that much trouble must 
be taken to teach the metrical system, especially as it is not 
likely to be popularly used in England, at least while our 
children are living. To purchase a simple metrical rule is by no 
means an easy task. They are not kept, that I can find, at any 
ordinary instrument makers in London, Oxford, or Cambridge. 
With your permission I wiil say what I think is required in a 
bok for boys. It must, to a certain extent, be suvable for being 
commited to memory, as Euclid is. No child is capabl< of 
taking in a subject, especially if it involves logical thought, 
except by very slow degrees ; and must at the beginning com- 
mit much to memory which he does not comprehend. What 
I write will appear, to those who do not know children, to 
involve a most vicious principle in teaching ; but it is, never- 
theless, a fact. Our new book must, therefore, contain all the 
steps of every proof in ful, and no symbols must be used. 
In the next place, it must not be artificial It seems agreed 
that the use of compasses ought to be of the na-ure «f a pos 
tulate, which would at once get rid of such propositions as 
the second and third of Euclid. There can be no reason for 
excluding the idea of the motion of a point, since in practice 
no figures can be diawn except by moving the pencil's po'nt. 
It appears then that, having once got over the difficulty of 
defining a point, a une should be “the path of a point,” a 
definition which would easily lead on tothe doctrines of curvatuie 
and tangents ; are a staight lne would be that which does not 
alter its direction (virtually Euclid’s definition) ; and, as in Mr. 
Wilson’s book, para lel straight lines, those whose directions are 
the same. 
It seems to me that it would be better to retain Euclid’s 
detnition of proportion, only converting it into a éest uf pro- 
portion ; because the constructions founded upon it are so 
convenient for geometrical purposes; and if it be superseded 
by the algebraical mode of treating the subject, reasoning on 
in commensurable quantities must be introduced. 
In fine, the book which is to supplant Euclid appears to be at 
present a desideratum. When it appears, it probably mst be 
the work of more heads than one, if it is to be generally accepted © 
among teachers. A FATHER 
THE circumstances attending my own introduction to geome'ry 
lead me .o doubt whether a long course of practical geometry is 
