102 
This question of the reason of symmetrical organs having 
different functions might perhaps be elucidated by astudy of the 
conditions under which deviation from bilateral symmetry occurs 
in the séructures of animal life, even among the highest arthro- 
pods and vertebrates. POS. 
May 23 
The ‘‘Chromatic Octave” 
RENEWED attention to the “chromatic octave”. tempts me to 
suggest an experiment. ‘There used to be a gentleman, Smith, I 
believe, by name, who refuted the undulatory theory by means 
of a disc, divided into black and white sections, which he whirled 
with very high velocities, producing colours (so the Zimes posi- 
tively stated) varying according to the velocities. It is plain 
that such a result might on the contrary confirm the theory, if, 
for instance, the disc were divided into 400 black and 400 white 
sectors, and whirled at the rate of one or two million million 
times a second. Itis also plain that Mr. Smith, in the words of 
an authority who has been quoted in your columns for weightier 
judgments, would have blown his disc into smoke first. But 
once a second is only 40 octaves below a million million times ; 
and it is just possible that something practicable between the two 
might throw light on the “ chromatic octave,” among other things. 
There are some obyious objections : the question is, whether they 
make it worth while to repeat Mr. Smith’s experiments. 
I have just received the number of Poggendorff (Oct. 1867, 
CXXXI.) containing Professor Listing’s paper (p. 564), referred to 
by Mr. Barrett in Narure for Jan. 13 and March 31. _I did 
not expect it would support Mr. Barrett, but I was surprised to 
find how directly it contradicts him. “Listing,” he says, ‘‘ con- 
cludes that, although physiologically and psychologically there 
may be differences, yet there 1s an indisputable physical basis 
for the analogy between tones and colours.” I had myself, at 
the end of my remarks in NatuRE for Feb. 3, admitted the 
“physical basis” in that sense “fof the word physical which 
excludes biological relations,” and the remark is too trivial to 
have formed Listing’s corclusion. It forms part of a sentence in 
the first page of the paper. ‘‘The analogy between tones and 
colours, which has often been pursued with excessive predilection, 
and which certainly has an indisputable physical basis, has against 
it numerous points of disagreement (Déscongruenzen), even now 
not in general sufficiently attended to, which depend rather on 
the physiological and psychological aspect of the phenomena.” 
In the same page of the number it clearly appears how much is 
meant by the physical basis. ‘‘ Physically,” he says, ‘it is the 
period of vibration that determines both tone and colour 3 but 
the physiological effects stand in very different relations to the 
common element in the two cases.” He proceeds to show, as 
correctly explained by Mr. Barrett, that the several colours 
divide the spectrum in an arithmetical progression of their 
rapidities of vibration ; and at the end of the paper, contrasting 
this phenomenon with the geometrical progression of a uniform 
series of tones, he says : ‘‘ This point of disagreement, a very vital 
one in my opinion, between the scales of tone and colour, may 
be briefly stated thus: 2 the musical scale (chromatic and with 
equal temperament”) ¢he logarithms of the tones are in arithmetical 
progression, in the scale of colour the colours themselves.” That 
this should mean what Mr. Barrett understands it to mean, you 
must read agreement for disagreement. 
Of the reality of Listing’s result, I suppose there can hardly be 
any doubt ; and I am glad that Mr. Barrett has corrected my 
suggestion that it probably represented a conventional demarca- 
tion. ‘There does seem something arbitrary in the number of 
divisions made, but their positions represent a mean among the 
impressions of different observers as to the boundaries between 
colours answering to the names assigned ; and the accuracy of 
these determinations may be fairly estimated by likening them to 
the case of a person who, having to divide a space of nine inches 
into nine equal parts, should be correct as offen as not within 
one 24th of aninch, But the most important point is this, that 
the observers would not be aided, but must rather have been 
distracted, by the spaces actually occupied by the colours in the 
spectrum. For the observations were made on two different 
spectra, the irregular one obtained from the prism, and the 
diffraction spectrum in which the colours proceed uniformly by 
wave-lengths ; and the result was a division into equal spaces, 
not oneither of these visible spectra, but on the ideal spectrum, 
which should proceed uniformly by rapidities of vibration. It 
* If this is what is meant by ‘‘chromatischen gleichschwebenden.” 
NATURE 
[ Fune 9, 1870 
would haye been in the spirit of good German precedents if we 
had been given some measure of the variation between different 
observers. 
It must be confessed that all this is damaging to the theory of 
a ‘chromatic octave,” essentially a theory of geometrical pro- 
gression. Still more obviously damaging is the fact that ‘‘ laven- 
der” would be the octave above something so unlike it as 
*“brown,” or ‘‘ brown” and ‘‘ red.” 
Mr. Murphy’s argument (NATuRE, April 28) seems to assume 
that complementary waye-lengths must be in some constant ratio. 
His theory is, at any rate, inconsistent with his author’s ; for 
primary red and blue would be nearly complementary, so that 
‘true white” could not be produced by any mere preponderance 
of blue, and would be white only to the green-blind. 
C. J. Monro 
In Mr. Murphy’s interesting letter in No. 26 of NATURE, 
April 28, 1870, he assumes that the number expressing the 
frequency of vibration producing a colour complementary to 
another, is the geometrical mean between the frequency of 
vibrations corresponding to that other, and its double. By this 
means he does not get colours complementary from sunlight. 
Thus red and bluish green (whose numbers are respectively 36°4, 
48°3) are not complementary on his hypothesis ; which would re- 
quire the number for bluish green to be 51°47. So for yellow and 
indigo, the numbers are 41°4, 54°7, but should be 41°4, 58°4. 
This he attributes to the impurity of the solar spectrum. There 
seems as much reason, however, for taking the Aarmonic mean 
instead of the geometric; and, on this supposition (the har- 
monic mean between two quantities being twice their product 
divided by their sum), the numbers would be red, 36°4 ; bluish- 
green, 48°5; yellow, 4174; indigo, 55:2. The second and 
fourth, 48°5, 55°2, are not very different from 48°3, 54°7. 
Taking then a colour twice over in the spectrum and its inter- 
mediate complementary, the relation between the three would 
be that of a musical note, its fifth and its octave. 
Little Wratting, Suffolk, May 16 
The Colour of the Moon by Day and by Night 
CAN any of your readers give me a full explanation of the 
reason why the moon looks white by day and yellow by night ? 
The light that proceeds from it is of course the same at both 
periods ; whence does the change in appearance arise? Two 
reasons occur at first thought, but they do not completely 
satisfy the many requirements of the problem. ‘The one is, that 
the light, being really somewhat yellow, though less so than it 
often appears to be, passes in daytime through an atmosphere 
made blue by the solar rays, and the blue and yellow neutralising 
each other, the moon looks white. The other reason is, that as 
the evening closes in, the twilight becomes purple, and the moon 
being but moderately yellow in itself, looks more intensely yellow 
by contrast. All this is correct so far as it goes ; but Ido not see 
why the moon should often look extremely yellow in the middle 
of the night after twilight has quite disappeared. Does it show 
that the light, one knows not exactly whence it comes, which is 
found even on clouded and moonless nights, is purple? There 
are some grounds for this hypothesis, because the moon almost 
always, as I have been assured by a practical astronomer, looks 
comparatively white through a telescope, which of course isolates 
the field of vision. Also, it seems to me that the street gaslights 
are just as yellow at midnight as in twilight ; the stars, also, 
commonly look yellow all the night through. It is strange that 
the very frequent and beautiful phenomenon of the white moon 
of the day suddenly turning yellow as the evening closes in, 
should not have long since attracted scientific comment. 
EG: 
M.A. 
What is a Boulder? 
A CORRESPONDENT in your journal of the 26th of May inquires 
about the size of boulders, and states that he cannot find any 
definition of the word -which gives a notion of its size accurate 
enough for scientific purposes. 
There are several definitions of boulder-stones given by 
geologists and others, which determine their size within tolerably 
narrow limits. 
Dr. Page defines boulders as being ‘‘any rounded or water- 
worn dlocks of stone, which would not, from their size, be regarded 
