May 29, 1902] 
From the laws of thermodynamics it can be shown, doubtless, 
that the conservation of weight is absolutely true, but this only 
on the assumption that the conservation of energy is absolutely 
true. Again, granted it can be shown that the conservation of 
weight is true in the same degree as the conservation of energy, 
yet these proofs will remain of strictly mathematical interest 
so long as our knowledge of the conservation of energy remains 
of a lower order of accuracy than that of the conservation of 
weight. 
It seems natural for the human mind to state scientific laws in 
absolute terms. Nevertheless, in most cases it is proved that 
the accuracy of the laws is limited. If a scientific law is believed 
in outside the limits of proof, the law is no longer a matter of 
kaowledge—it has become an article of faith. These are 
platitudes; they have point only because scientific men state 
the laws of conservation in absolute terms, and hold these laws 
as articles of faith. (Are Nese Vic 
University College, Liverpool. 
A Solar Halo, 
Ty a letter to NATURE of May tf (p. 5) a description is given 
of a remarkable lunar halo seen at Yerkes Observatory. A 
solar halo of almost identical character is reported in the 
meteorological returns for April from Sule Skerry Lighthouse 
off the north coast of Scotland. The following note and sketch ! 
are appended by Mr. N. A. Macintosh, the lightkeeper, to his 
report :— 
“A curious phenomenon was observed in the sky on the 28th. 
At 12.30 p.m. there was a perfect ring or halo right round 
Fic. r.—Solar Halo, April 28. 
the top of the sky with the sun in its southern edge. At right 
angles to it, and round the sun, was another ring with two 
‘mock suns’ where it bisected the larger ring. These ‘ mock 
suns’ showed prismatic colours, but about due east on the edge 
of the larger ring there was a ‘mock sun’ pure white. In the 
south-eastern sky there was an indistinct half-circle from the 
horizon up to the horizontal circle which showed prismatic 
colours, whilst the others were colourless. At the time there 
was haze all over the sky, but the sun shone very clearly. It 
lasted till 1.30 p.m.” 
The position of Sule Skerry is lat. 59° 6’ N., long. 4° 20’ 
W., and as the sun is about 14° north of the equator on April 
28, its elevation at local noon, about which time the halo was 
first seen, would be practically 45°. Hence the ‘‘ horizontal 
circle”? the centre of which is at the zenith would have a radius 
of 45°. Evidently, therefore, from Mr. Mackintosh’s sketch the 
“vertical circle’ is the ordinary halo of 22° radius. The 
“horizontal circle” is also well known, though not so often seen 
as the halo ; it is due to the reflection of the sun’s light from 
the vertical faces of the ice-crystals. The coloured mock suns 
where the two halos intersect are also well known, but with the 
sun as high as 45° they would be expected to lie a little outside 
the 22° halo on the white circle. The other mock sun on the 
eastern side of the horizontal white circle is more rare; it may 
coincide with the point where a larger halo cuts the horizontal 
circle, but the laws determining the formation of this halo and 
NO. 1700, vor. 66] 
NATURE 
103 
its exact position are not known, and portions of it have been 
seen on only three or four occasions of which we have any 
record. 
The last item in the sketch, the coloured semicircle rising from 
the south-eastern horizon to almost touch the horizontal circle, 
Iam unable to suggest any explanation for. The sketch is 
evidently reversed, as in it this and the white mock sun are 
shown on the western side. In recording observations of 
coloured halos, mock suns, &c., it would greatly add to their 
values if notes were made of the arrangement of the colours, 
such as “ red inside, blue outside halo,” ‘‘ red next sun, blue 
away from it,” and vce versd. R. T. Omonp. 
Scottish Meteorological Society, Edinburgh, May 17. 
Mathematical Training. 
In view of the great influence which Schopenhauer has 
exerted on German thought, I referred to his chapter on mathe- 
matics, and find that half a century ago he was even more 
sweeping in his condemnation of the methods of Euclid than 
are some of your present correspondents. He mentions that the 
exact sciences are confined to those dealing with time, space 
and causality, or without being too precise as regards names, 
the exact sciences are arithmetic, geometry and logic. Schopen- 
hauer’s view is that each of these sciences is independent of the 
other, and he illustrates this by saying that mathematically it is 
just as self-evident that two parallel lines cannot meet as it is 
logically self-evident that an impossibility is not possible. He 
strongly objects to our aping the Greeks and basing mathe- 
matics on logic, and I feel sure that he would consider that 
mathematics were being degraded by the excuse so often given 
for teaching it at all, that ‘* Euclid is an invaluable logical train- 
ing.” It I understand him correctly, Schopenhauer holds that 
any mathematical proposition is as self-evident as any correct 
logical sequence, and only requires illustrations or explanations 
(not proofs) to make this clear to our somewhat imperfect brain. 
This he might have illustrated by the Pythagorean proposition, 
which can be shown to be correct without the elaborate logical 
scaffolding used by Euclid, provided that one’s mind can grasp 
the proportionality of similar triangles. Let a, 4, ¢ be the 
lengths of the sides of a right-angled triangle, draw a perpen- 
dicular from the apex intersecting the hypothenuse c, and divide 
it into two lengths @and e. We then have three similar right- 
angled triangles and the following two sets of proportions :— 
Cand, Gene 
San Gare 
from which it follows that a? =c.e and 6®*=c.d, andasd + 
é = c, we have a? + B= 2. 
Most other propositions, if not self-evident, might be dealt with 
in the same way; and if we were as gifted as Newton was, we 
would, as he did, wonder why anybody should trouble to de- 
monstrate the, to him, quite self-evident truths in Euclid. 
In our public schools we are taught classics, not because of 
the logic they contain, for it is often wrong, but because they 
exercise our memory (and, I fear, cripple our reasoning powers), 
and we teach mathematics; not to improve our knowledge of 
space, but to improve our logic and sometimes also to improve 
our memory. Naturally our views about space are often hazy, 
and our reasoning powers, which receive no direct training, are 
not infrequently stunted, or rather compelled to work in 
narrow grooves. C. E. STROMEYER. 
Lancefield, West Didsbury, May 12. 
Influence of Light upon Plant Assimilation. 
I HAVE for some time been endeavouring to devise a simple 
and cheap apparatus for demonstrating the effect of red and blue 
light respectively upon the assimilatory power and nyctitropic 
movements of plants. The apparatus usually supplied by the 
dealers for this purpose consists of a double-walled bell-jar into 
which a solution of potassium bichromate or of ammoniacal 
copper sulphate may be poured. This is a rather expensive 
piece of apparatus for school use, especially if a large one is 
required. I have not been able to find a blue or red glass that 
absorbs blue or red light only. I have tried home-made glass 
cells about a foot square and a quarter of an inch internal 
diameter, but could not prevent leakage. Perhaps some reader 
of NarurE could help me. Is there a transparent coloured 
paper or some kind of coloured membrane that would serve the 
purpose ? E. E. HENNESEY. 
Bigods School, Dunmow, Essex, May 19. 
