Marcu 7, 1912] 
the Department of Public Instruction of New South 
Wales, to accompany and explain the programmes 
for the mathematical classes in the high schools 
recently established in this State. Regret is expressed 
by the writer of that article that New South Wales 
**has been frightened by difficulties which were bound 
to arise in a period of transition, into going back 
to the old methods instead of boldly remedying the 
evil by helping all teachers to get the spirit of the 
new methods.” 
The point at issue is the treatment of the funda- 
mental theorems of congruence, parallels, and the 
angle-sum for a triangle, in the course of deductive 
geometry given to pupils in these high schools. In 
the programmes, as issued, the teachers are advised 
to follow Euclid’s method (or something of the same 
nature) in these fundamental theorems. The Board 
of Education circular, from which we have ventured 
to differ in this particular alone, recommends that 
these results be obtained by induction and experiment. 
It seems proper that your readers should be aware 
of the following facts :— 
(i.) The course of geometry in question is not meant 
for children of twelve years of age and under, as the 
writer of your article seems to assume. 
Pupils enter these schools after completing a full 
course of primary education. Their age at entrance 
varies from thirteen to thirteen and a half. 
(ii.) Before entering the high schools they have had 
a full year’s work at geometry. In this preliminary 
study the newer methods are fully employed; the 
results are obtained by induction and experiment, and 
a great part of what the Board of Education circular 
recommends is adopted. However, the box of mathe- 
matical instruments does not hold sway to the entire 
exclusion of theoretical work. 
(iii.) Although it has been thought advisable to asl 
for some uniformity of treatment in these early 
theorems in the deductive course, when this stage is 
past the fullest amount of freedom is granted. 
There is no doubt that experience will show that 
some modifications in the syllabus are necessary. 
Some of the points mentioned in your article had 
already been noted as requiring alteration, and the 
suggestions which it contains will certainly receive 
the careful attention of the proper authorities. But 
the decision with regard to the earlier stages of the 
geometry course was made only after the fullest con- 
sideration. For this reason it is to be regretted that 
it has been, to some extent at least, misunderstood 
by the writer of your article. 
Sydney, January to. H. S. Carstaw. 
In spite of Prof. Carslaw’s assurance that pupils 
on entering secondary schools have reached the age 
of thirteen or thirteen and a half and have had a full 
year’s work at geometry, the writer of your article 
feels most strongly that it is extremely unwise to 
impose on them in their first year at the secondary 
school a logical treatment of the fundamental 
theorems of congruence and parallels. Anyone who 
has had much experience of teaching pupils of that 
age knows how difficult it is to teach this work and 
how little impression it makes except on a very small 
minority; on the other hand, if these theorems are 
frankly assumed (after the pupils thoroughly under- 
stand their meaning) the rest of the geometry usually 
done in secondary schools can be treated logically, and 
the vast majority of pupils will get a proper grasp 
of the ideas of logical geometry. In the latter case 
the foundations are broad and the structure is firm 
at every stage; if the fundamental theorems are 
treated logically, an attempt is made to build on a 
NO. 2210, VOL. 89] 
NATURE - 
narrower base, but in the majority of cases the lower 
stories of the structure are insecure. 
The writer of your article must still regret the atti- 
tude taken up by the New South Wales authorities 
on this point. Re ence 
The Isothermal Layer. 
In reading Dr. Evans’s reply to my letter in 
NatTurE of January 25 with regard to the isothermal 
layer, I was specially interested in his reference to 
radiation of heat from orbital interplanetary matter 
as a probable climatic factor, because in Symon’s 
Meteorological Magazine of February, 1911, I sug- 
gested that the recurrence year after year of warm 
and cold periods, first directed attention to by the late 
Dr. Buchan, may be attributable to modifications in 
a screen of cosmic matter, such, for instance, as that 
from which the zodiacal light and the Gegenschein 
are reflected. 
I mentioned in a later number of that magazine 
that my own observations of the light in tropical 
latitudes, extending over several years, conveyed to 
me the impression of a ring of cosmical bodies 
encircling the earth about the zodiac. 
For evidence of the isothermal layer at the equator 
the report of Prof. Borson on the aérological expedi- 
tion of the Royal Prussian Aéronautical Observatory 
to East Africa in 1908* may be quoted. In this 
report at least two instances are recorded of balloon 
ascents near the equator in which the isothermal was 
reached: on August 30, at a height of 173 km., 
when a temperature of —82'5° C. was registered, and 
slightly lower temperatures at higher elevations; and 
on September 5, at 15°4 km., temperature —70°3° C., 
slight inversions being registered at greater altitudes. 
The greater height of the isothermal in equatorial 
regions may be due to strong convection currents, as 
Mr. W. H. Dines supposes,* even though the origin 
of the layer be attributable to reflected heat from 
interplanetary matter. CampBELL HrEpwortH. 
2 Amherst Road, Ealing, W., February 18. 
St. Elmo’s Fire. 
On Thursday evening, February 22, about 9.20 
p-m., whilst traversing a country road which crosses 
the head of Carr Wood, a well-wooded clough in 
the neighbourhood of Heywood, near Rochdale, I was 
fortunate enough to witness a most unique pheno- 
menon. The road in question skirts a hill on the left- 
hand side, and the opposite side, at this particular 
place, overlooks a small plateau which runs along 
the edge of the clough. 
During the day we had had much rain. The 
atmosphere was now very close and heavy, and every- 
thing was ominously silent, even the usual breeze 
having disappeared. Suddenly, without the slightest 
warning, there appeared an area of faint electric-blue 
light, almost circular in shape and about 70 yards in 
diameter, which covered the plateau. The edge of 
this area was not more than 10 yards from where the 
observations were made. The whole electric field 
seemed to be three or four feet above the ground- 
level, and was in a state of intense agitation. Within 
the general blue ground there appeared flashes of a 
more decided blue, very similar in character to forked 
lightning, but not nearly so distinct. 
1 “ Results of Investigations of the Royal Prussian Aeronautical Observa- 
tory at Lindenburg.”’ Edited by the Director, Doctor Richard Assman. 
2**The Vertical Temperature Distribution in the Atmosphere over 
England, and some remarks on the General and Local Circulation.” By 
W. H. Dines, F.R.S., Phil. Trans. Royal Soc., Series A, 211, page 269. 
