“Pr, * 
- 

SATURDAY, MARCH 3, 1923. 

CONTENTS. jriteti 
Sequence in School Geometry . ‘ Sf) ary 
The Development of the nee Theory. By Prof. 
H. S. Allen . ; ~ ae 220 
History of Medicine Pe : . 281 
Frontier Tribes of Assam. (dtustrated.) - ‘ P . 282 
Our Bookshelf - : ; ‘ : - 283 
Letters to the Editor :— 
The Function of Mendelian Genes.—Julian S. 
Huxley . 286 
Age and Area ‘and Natural Selection. Say r 
Cunningham . 2 = f287 
The Value of e/m. —Raymond ue 'Birge - 287 
Sir Christopher Wren’s Science Museum. (///us- 
trated.)—R. T. Gunther . 288 
Tesla Spectra of Complex Compounds. —Prof. Victor 
Henri; J. K. Marsh, and Prof. A. W. Stewart 289 
Calendar Reform.—L. C. W. Bonacina or he aD 
Time Relations in a Dream.—H. F. Biggs . 290 
The Ascent of Elvers in Egyptian Waters —G. w. 
Paget . ° 290 
Transcription of Russian Proper Names, —Prof. 
Bohuslav Brauner . 290 
aaa s Artificial Tourmalines.—Dr. M. Nieren- 
291 
The Modiatin of Audition.—Frederick W. Kranz ws 
Spiranthes autumnatis,—E. Philip Smith ; John B. 
Simpson 291 
The Drayson Paradox.—A. H, Barley ; 7 The Writer 
ofthe Note . 291 
The Naming of Elements. — Dr Norman R. 
Campbell : e 75 ab2 
_ Sarsen Stones. —C. Carus-Wilson . 292 
pcre, 20 Illuminating Gas ‘ 293 
Imperial lege of Science and Technology. Open- 
ING OF THE NEW Bovany BUILDING (PLANT TECH- 
NOLOGY). (///ustrated.) . - . 5 ° + 295 
Obituary :— 
Dr. C. P. Goerz. By J. W. F. e 297 
The Hon. R. C. Parsons . : : : 297 
Mr. W.M. Hutchings . . fs 298 
Current Topics and Events . A 2 298 
Our Astronomical Column . 301 
Research Items ° 4 + 302 
The Unit Activity of Animal Organs ; : 304 
Climates of the Past. By G.A.J.C. . = s 304 
Studies on Phytophthoras : = . : e305 
Aeronautical Deseatch Committee . ‘ . . 300 
The Hydrautomat . ; + 306 
University and Educational Intelligence - = : + 306 
Societies and Academies. ° “ E J 42 3308 
Official Publications Received . 2 : ; oe SEE 
: 2 «(gre 
Diary of Societies . F : . 



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NO. 2783, VOL. 111] 
NATURE 277 

Sequence in School Geometry. 
HERE is discontent as to the condition of 
geometry teaching in schools, and in the search 
for remedies the question has been reopened whether 
there should be an “agreed ” sequence. It appears from 
the report summarised in Nature of February 24, 
p. 271, that go per cent. of those members of the Assist- 
ant Masters’ Association who replied to a questionnaire 
voted for such a sequence, but there is the significant 
note, “ The figures cannot be more than approximately 
correct, as some of the replies were difficult to interpret.” 
It may be worth while to consider the question itself : 
for, unless we are 
and dis- 
be wide 
what is meant by a “ sequence” ; 
clear about this, the question is ambiguous, 
cussion, to say nothing about voting, may 
of the mark. 
Fifty, forty, 
through school (and even college) mathematics was 
beset with the notice “ Verboten.” A boy might not 
use algebra in doing arithmetic; analysis was for- 
bidden in geometry papers ; calculus in doing analyti- 
cal geometry or mechanics ; while to mention a sine 
or cosine in the natural philosophy paper of a certain 
examining body would have been to pull the very 
even thirty years ago the pathway 
whiskers of death. 
Such, at least, were the facts as understood by those 
still im statu pupillari and as impressed upon them by 
their immediate teachers, whatever liberty the higher 
powers—the examiners—may have exercised in prac- 
tice. But, above all, there must be no departure from 
the order of Euclid, and to use a later proposition in 
the proof of an earlier was mortal sin. 
Now, here a distinction should be made: in part 
Euclid’s order is essential to his general argument ; 
but in part it is not and is merely matter of chance or 
convenience. For example, I. 16 (that the exterior 
angle of a triangle is greater than either of the interior 
opposite angles) of necessity comes before I. 32 (that 
the exterior angle is equal to the two together) ; and 
to use the latter to prove the former is a real error, 
betraying want of grasp of Euclid’s argument. 
On the other hand, his Sixth Book (on proportion 
and similar figures) does not depend on any proposi- 
tion subsequent to I. 36 and I, 38 (that parallelograms 
and triangles on equal bases and between the same 
parallels are equal). Consequently, to use VI. 8 to 
prove I. 47 would not have been false logic, or an 
essential departure from his system, but merely a 
variation from the particular method he chose to adopt. 
By sequence, then, we may mean either essential 
sequence, departure from which destroys the validity 
of the argument, or merely the arrangement of the 
subject-matter in an order dictated by convenience 
