FEsRuary 24, 1923] 
NATURE 
271 

or Cape whiting, both of which have their centres of 
intensity at 150 fathoms, or even deeper. There is 
also the kingklip (in appearance like a ling), the 
dogfish, various soles and other flatfish, but the 
variety of economically valuable trawl fish so far 
obtained is not great. New fishing areas were 
discovered off Durban and off the Umvoti River, 
. but neither of these are of sufficient size for steam 
trawlers. However, crayfish up to 12 inches occurred 
in immense numbers, a commercial trawler subse- 
uently, in a haul of 1} hours, taking more than 10,000. 
e results of the investigation indicate an abundance 
of life on all this eastern ground, and it must carry 
its due proportion of fish. Many small areas suitable 
for trawling appear likely to be disclosed by further 
survey, but it is not an area for steam trawlers, 
though, like the west coast of France, it should 
develop in time a considerable population of “‘ long- 
shore ’’ men. 
Turning to the south and west the reports give 
indications here of the possible development of an 
immense fishery. The Pickle demonstrated to the 
local trawlers the potentialities of deep-sea fishing, 
and new areas were found within a few hours’ 
_ steaming of Cape Town. The most northerly trawlings 
were off Luderitz Bay, and it would seem probable 
that there is good ground right down to Cape Town ; 
we should also expect similar ground further north 
as far as Union territory extends. Before such 
ground can be exploited commercially it must be 
surveyed, so that trawlers may avoid rough patches. 
To know the depth and nature of the bottom is 
not enough, and trawling tests are essential. 
Doubtless the fish migrate at different seasons, so 
that the latter tests will have to be undertaken at 
least twice over. It is an expensive business, of 
course—the running expenses of a trawler would be 
about rooo/. per month—but the encouragement of 
food production is a vital necessity to all States, 
while fish-meal is a bye-product of high value. In 
any event it is clear that South Africa has to the 
south and west an area more than capable of supplying 
all the fish that can at present be consumed; the 
western grounds alone may well prove as rich as 
those to the south of Ireland of about the same 
area, which in 1910 produced 1-35 million cwts. 
With these potentialities in mind it is extra- 
ordinary to find that the fishery vessel is to be 
given up. In substitution a survey vessel, Crozier, 
is to be used at intervals for fisheries work. To 
employ a twin-screw vessel with a complement of 
80 hands for such work is wretched economy, work 
which can be better done with a trawler and a 
crew. of 14. The phase of using such Admiralty 
vessels for fishery work is one which nearly every 
country of Western Europe has passed through 
and abandoned ; surely South Africa would be well 
advised to learn by their experiences. In any 
event we trust that the series of special reports on 
the fauna obtained by the Pickle, commenced in 
report 2, will be proceeded with; they are of high 
scientific value. 
The Teaching of Elementary Geometry. 
op HE Assistant Masters’ Association recently ap- 
‘pointed a committee to consider the teaching 
of elementary geometry ; the report of this committee, 
backed by the authority of the Executive Committee 
of the Association itself, that of the Assistant Mis- 
tresses’ Association, and that of the Educational 
Institute of Scotland, has now been published. The 
outstanding fact, and one of no little importance, is 
that the committee was appointed to produce an 
agreed sequence of propositions and has not done so. 
The terms of reference were : 
(a) To examine the case for an agreed sequence ; 
(b) To suggest the best means of attaining the 
general adoption of the sequence agreed upon. 
The most definite conclusions are : 
VII. The committee does not feel that it is either 
desirable or rad at present to stereotype a 
sequence ; an 
I. No formal proofs should be required of Euclid I. 
13, 14, 15, 4, 8, 26, 27, 28, 29. . . . The teaching of 
formal geometry should be based upon the quasi- 
axiomatic acceptance of these results. 
The committee is unquestionably right in its belief 
“that the main difficulties due to variety of sequence 
will be removed if the first of its recommendations 
[i.e. I. just quoted] is generally accepted,’’ and possibly 
the most valuable feature of the report is the extended 
currency it will give to this principle. 
For the rest, the committee is concerned not so 
much with principles as with giving what help it 
can to the “‘ very large number of teachers who do 
not claim to be experts in geometry ”’ and who need 
“ suidance amid the welter of sequences and methods 
published during the last twenty years.”’ From 
this modest and reasonable point of view little fault 
will be found with the detailed recommendations, 
though, as is freely admitted, there is room for 
1 The Teaching of Elementary Geometry: Being the Report of a Special 
Committee appointed by the Incorporated Association of Assistant Masters 
in Secondary Schools. Pp. 15. (London: Oxford University Press, 1923.) 
Is. net. 
NO. 2782, VOL. III] 
—————EEEE——— SS ee ee ee ee 
difference of opinion on many points. A teacher 
who followed their scheme exactly would come to 
no harm. 
The committee follows in the main the “‘ Cambridge 
Schedule,’ with some expansions (which some will 
not think improvements) apparently designed to show 
exactly how it intends the propositions to be dealt 
with. For example, the section on areas begins with 
the rule for measuring the area of a rectangle and the 
section is more detailed than in the Schedule, clearly 
indicating a treatment different from Euclid’s. It 
is pointed out at the end of Section VI. that Pytha- 
goras’s proposition and Euclid III. 35, 36 should be 
dealt with by the use of similarity as well as by 
Euclid’s method. The report contains a needed 
warning (Recommendation IV.) against the slovenly 
use of the “method of limits”’ in dealing with 
tangency ; and another (Recommendation V.) against 
ignoring the existence of incommensurables; “‘ at the 
proper stage,”’ the committee says, “the attention of 
the pupil should be called to the fact that the proofs 
given do not cover all cases.” 
A very important feature of-the report is that 
certain propositions are marked with an asterisk, 
indicating that formal proofs of them should not be 
required in examinations. Some are marked also 
with a (f), indicating that no formal proof should be 
attempted in the class-room. 
On this point the practice of Examining Bodies 
differs ; most of them asterisk propositions, but some 
more, some less. It would undoubtedly be of great 
assistance to the schools if uniformity could be 
reached, and for this purpose the selection made by 
the committee might well be taken as the standard. 
Altogether, the committee may be congratulated 
on its work; it has not set up obstacles to further 
progress, as with its terms of reference it easily might 
have done; on the other hand, the report will probably 
reach many teachers who need help and will give 
them much of the assistance they need. 
