558 
NATURE 
‘ B 
It will be noticed also that D, F, A generate 76? oF red, yel- 
low, blue generate indigo-blue. A, C, E generate e or blue, 
violet, orange generate yellow. I need not increase the length of 
my paper by more examples, but leave the field open to all who 
choose to test the above formula as regards its application to 
combinations of colour. 
In conclusion, I wish to make the following suggestion. 
Should it be admitted that the musical scale, in its perfect divi- 
sion into intervals under the law of harmonical progression, finds 
its counterpart in Newton’s rings rather than in the prismatic 
spectrum, would not a spectroscope, constructed so as to give the 
image of these rings, be a more perfect instrument for the com- 
parison of colours than that in present use? We might also 
have a double spectroscope, capable of giving the images of the 
secondary rings produced by the refraction of homogeneous 
light, the cube roots of whose diameters give the series which 
corresponds to that of the musical scale. 
We should in this way be able to know the melody which cor- 
responds to the light of any particular star, provided that the 
light be strong enough to produce the images of the secondary 
rings. W. S. OKELY 
Rome, February 18 
Analogy of Colour and Music 
AT the close of my short article on the Analogy of Colour 
and Music, published in your journal of January 13, I ventured 
to ask for the opinion of physicists on the subject. Accord- 
ingly I, for one, am much indebted to the many able con- 
tributors who thereupon addressed you. The correspondence 
having apparently ceased, I will now ask your permission to 
say a few words, 
Although I do not attach too much importance to the closely 
approximate ratios, given in my paper, between the waye- 
lengths of colour and the notes of the diatonic scale, yet I think 
nothing said by your correspondents seriously affects my main 
argument. 
The most important objection is that urged by Mr. Monro 
(NATURE, No. 14), who regards the correspondence of the two 
ratios as a mere coincidence, depending on the mode by which 
Prof. Listing obtained his scale of wave-lengths of the colours. 
By an ingenious calculation, Mr. Monro shows that Listing most 
probably ‘‘ divided his spectrum into seven equal parts upon some 
scale which varies inversely as the wave-lengths ; . . . so that it 
nearly corresponds with the ratios of the musical scale because 
these approximately form a harmonic progression.” When I 
wrote my article I had not read Listing’s paper, but, as stated, 
quoted his numbers from a recent memoir by Thalen. The 
perusal of his original paper shows me that Listing obtained his 
numbers in the following manner, which I think Mr. Monro will 
see confirms his calculation, but overrides his criticism:— 
Employing pure spectra, and using every precaution, Listing ex- 
perimentally determines the transition places and the central region 
of each colour, Fraunhofer’s lines being used as landmarks. The 
observations are repeated upon the normal spectrum obtained by 
diffraction, and are checked by the independent observations of 
others, and by repetitions at different times. In this way the 
remarkable fact is disclosed that the numbers of vibrations 
at the transition spots form an avithmetical progression throughout 
the entire series of colours, For reasons given he adopts 
the following scale of colours—brown, red, orange, yellow, 
green, cyanogen, indigo, and lavender, and states as a law that 
this series can be physically expressed by an arithmetical pro- 
gression of eight numbers, in which the last is the double of the 
first. He then proceeds to discover the constant factor by which 
this series can be turned into absolute values. After considerable 
care, and upon grounds fully detailed, he selects 48+ billions as 
the number of vibrations per second expressing the range of each 
colour. The possible error he shows to be + 0'038—taking 
billions as unity—and this, though apparently a large error, is 
actually less than 3th of the interval between the two D lines. 
The number of vibrations corresponding to the extreme limit 
of colour at the red end, he fixes, upon Helmholtz’s and Ang- 
strom’s authority, at 363-9 billions per second, or a wave-length 
of 819°8 millionths of a millimetre, By adding to the former 
number half the coiour interval—namely, 24} billions—the 
normal centre of the first colour is obtained; 484 billions added 
to that gives the centre of the next colour, and so on, These, 
and also the limits of each colour, are tabulated along with the 
corresponding wave-lengths, 
Listing closes his paper with the statement of a general law, 
that while the successive vibrations of the series of colours in the 
spectrum form an arithmetical progression, the same is also true 
of the logarithms of the vibrations corresponding to each musical 
note in the so-called chromatic scale. Hence he concludes that 
although physiologically and pyschologically there may be 
differences, yet there is an indisputable physical basis for the 
analogy between tones and colours. From this very imperfect 
outline it will be seen that the entire memoir is a remarkable 
one, and I am surprised no translation of it has appeared. It is 
certainly the most important contribution to the analogy that I 
have met with, and renders my little paper on the subject quite 
unnecessary. e 
Mr. Okely, writing to the next number of NATURE, gives some 
additional evidence in favour of the analogy, but thinks my 
process of taking the mean of the limiting wave-lengths of each 
colour, in order to obtain the average wave-length, is ‘*‘ very 
rough,” Mr. Okely does not tell us what he would do in such a | 
case, but turns aside to become the champion of the widths of — 
Newton’s rings, charging me with having treated too summarily 
this old and famous ally of the analogy. But to this, my next 
critic, Mr, Sedley Taylor, replies, although other considerations 
also influenced me in neglecting this analogy. 
Mr, Taylor, however, believes that he has deprived my com- 
parison of any serious importance, for the following reason :— 
In the musical scale, he observes, ‘‘a very slight departure from 
accurate pitch in any concord provokes a harsh dissonance 5” 
but ‘any part of any one colour-division produces an equally 
harmonious effect on the eye,” because ‘‘in the spectrum there is 
very little, if any, change of tint except close to the extremities 
of any one colour.” Whilst it would be certainly unwise to push 
the analogy too far, I think Mr. Taylor is here mistaken, There 
is a very material difference of tint in different parts of any one 
colour in the spectrum. Regarded alone, any region of the 
spectrum, like any single musical note, is, of course, equally 
agreeable ; but it is not the case that an equally harmonious effect 
on the eye is produced by the combination of avy part of any one 
colour-diyision with some other colour, 
Mr. Stuart, in an interesting letter, points out a close relation- 
ship, discovered by Prof. Mossotti, between the intensities of 
the light in different parts of a normal spectrum and the notes of 
the diatonic scale. Finally, Dr. Chaumont, in an early part of 
this discussion, showed, what indeed had been noticed else- 
where, that if the ratios I give be accepted, then the once-called 
primary colours, red, yellow, and blue, correspond to the notes 
of the common chord ; whilst the modern triad, red, green, and 
blue, correspond to the tonic, sub-dominant and dominant, that 
i$ to say, to the three notes which in music constitute the funda- 
mental base of the scale. 
In addition to what has been brought forward in this corre- 
spondence, there are some valuable remarks on the analogy in 
one of Dr. Thomas Young’s mempirs, ‘‘ Philosophical Transac- 
tions, 1802” ; in Chevreul’s work on the ‘‘ Principles of Har- 
mony of Colour” ; in a recent brochure by Dr. Macdonald on 
“ Sound and Colour’? ; and, lastly and chiefly, in §19 of Helm-~ 
holtz’s “ Physiological Optics,” 
authorities who have written on the subject since the time of 
Newton, 
Reviewing what has been done in this matter, there are there- 
fore, I believe, many good grounds for asserting the existence of 
a physical basis for the analogy between colour and tone, 
Opposed, it is true, are many mental differences; such, for 
example, as that of the judgment, which is far more prompt and 
correct in determining a colour than a note; then also colour 
primarily involyes only the conception of sface, music the con- 
ception of “ize, Nevertheless against all this we may place the 
facts that the source of harmony in colour, as in music, is purelya 
question of ve/a¢tive impressions ; and a painting and a melody 
eyoke a succession of ideas that haye a remarkable similarity. 
Woodlands, Isleworth, March 13 W. F. BARRETT 
THE METROPOLITAN MAIN DRAINAGE 
HE magnitude of the underground works of London 
is scarcely understood by the public in general. 
They occasionally hear of this or that sewer or pumping 
station being completed, but as the greater portion of 
[March 31, 1870 . 
In this last a list is given of a 
