262 
surface-features and types of scenery. My work is not confined, 
as your reviewer asserts, to a defence of marine denudation, for 
more than a third of it is devoted to the consideration of the 
real or assumed effects of atmospheric agents ; and instead of 
being put forward in a self-confident spirit, as your reviewer 
would likewise lead the reader to suppose, I have stated in the 
Preface that ‘‘my object will be gained if I have said enough 
to stimulate the geologist and intelligent tourist to further 
observation.” D. MACKINTOSH 
“Correlation of Colour and Music.” 
ANALOGIES between tone and tint are a tempting subject; 
and sound and light have enough admittedly in common to make 
it rash to say that the connection may not extend to their effects 
on the ear and eye ; but that your correspondents (Jan. 13th and 
2oth) are seeking for unity in a direction in which it is not to be 
found, seems to me to be rendered pretty certain by the very 
evidence to which one of them, Dr. de Chaumont, appeals 
(Jan. 20th); I mean by that of ‘‘the researches of Helmholtz 
and others.” 
I have often wondered at the small attention paid to the 
general law which these researches have established. Even 
M. Jamin, in his Cozrs de Physique, dismisses Newton’s theory 
of compound colours as ‘‘empirical,’ and apparently of no 
significance. It is as much and as little empirical as the New- 
tonian astronomy; both consist of general laws applied by means 
of particular constants: the evidence for the laws is in both cases 
equally inductive, and the determination of the constants equally 
empirical. 
Stated without reference to the geometrical and dynamical 
analogies which I suspect have had something to do with ob- 
scuring its significance and tainting it with ‘‘ empiricism,” the 
fundamental law of composition of colour is this :— 
Of any four colours whatever, either there is one which may be 
matched by a compound of the other three, or there are two which 
may be compounded so as to match a compound of the other two. 
It is obvious that if negative values of an ingredient can be 
admitted, these alternative cases are the same; and the geome- 
trical and dynamical analogies depend on the fact that, if 
addition of vectors 1s substituted for composition of colours, the 
proposition remains true, becoming in fact a very elementary 
one. And it follows that all colours may be co-ordinated, by 
means of three independent variables, with reference to any 
three colours whatever. 
Accordingly, when differently coloured lights reach the eye 
together, the combination produces a single resultant colour 
varying according to the proportions of the ingredients, and 
completely superseding them; whereas, when two sounds of 
different pitch are sounded together, we still hear both : and, 
though we hear certain other tones besides, these other tones 
have each a pitch determined by the pitches, but independent of 
the intensities, of the original sounds. 
The truth is, that the ear and eye deal with impressions in 
totally different manners. The ear deals with a complex musical 
sound exactly as a system of resonators does ; it sensibly de- 
composes the sound into certain simple tones, just as the complex 
harmonic motion which produced the sound is theoretically 
decomposed by Fourier’s theorem into the simple harmonic 
motions which would produce the simple tones. In order to 
understand the manner in which the eye deals with a compound 
colour, we must turn our attention to that particular unidimen- 
sional series of colours which constitutes the spectrum. As this is 
what your correspondents have done, the issue will be all the 
closer. 
By the law above stated, all the colours of the spectrum might 
be co-ordinated with reference to any three colours chosen in the 
spectrum or out of it. But it has been ascertained by Mr. Max- 
well* (to whose labours we are chiefly indebted in England for 
what we know of the composition of colours) that there are three 
colours in the spectrum to which all the rest stand in relations 
giving these the character of ‘‘ primary” colours. They are the 
articular red, green, and blue, whose wave-lengths are, in Fraun- 
hofer’s measure, respectively 2328, 1914, 1717: and they 
divide the spectrum into three parts, in each of which every 
colour, it appears, may be matched by a compound of the two 
(out of these three) between which it lies. This is very accu- 
rately the case between 2328 and 1914 and between 1914 and 
1717 : it is much less accurately the case on the red side of 2328 
* Phil. Trans. 1860, pp. 57—84. On the theory of compound colours and 
the relations of the colours of the spectrum. 
NATURE 
[#2b. 3, 1870 
and on the violet side of 1717 ; but in this region observation is 
difficult, and various eyes variable ; and it seems probable that, as 
Mr, Maxwell infers, every colour in the spectrum, and therefore 
every colour in nature, is, as felt by us, a compound of three 
elementary sensations of colour excited separately by those 
three rays. 
Now it must be observed that this result does tend to justify 
so much of the anticipations mentioned by Mr. Barrett as Sir 
John Herschel and Mr. Grove had long ago committed them- 
selves to: it shows that the spectrum, like the musical scale, 
does in a manner return into itself. Beyond this the analogy 
fails. 
In the first place there are, in music, no fixed tones with refer- 
ence to which other tones possess any general properties at all ; 
much less the property of being matched by combinations of 
them. In relations of tone, the constant quantities are not 
constant tones, but constant intervals between tones. Still, no 
doubt, if the three primary colours stood (as Dr. de Chaumont 
seems to think they do) in the arithmetical relations of tonic, 
fourth, and fifth, the fact would be as remarkable as two numerical 
coincidences could make it. But the case is not so. The ratio 
2328: 1914 (or 1‘211) corresponds not to the interval of a fourth, 
but to an interval about two-ninths of the way from a minor 
third (6:5 or 1°2) to a major third (5:4 or 1°25); and the ratio 
2328: 1717 corresponds not to the interval of a fifth, but to an 
interval about a third of the way from a natural fourth (4:3 or 
1°333) to a sharp fourth (45:32 or 1°406); intervals which, I 
presume, one can make nothing of. 
Mr. Barrett’s principal argument depends upon Prof. Listing’s 
demarcation of the colours answering to the names red, orange, 
&c.: much too vague a basis, I should have thought, for exact 
inference, even if Mr. Barrett had not been obliged to sacrifice a 
boundary to obtain his most important interval ; moreover the, 
correspondences in Table IV. are somewhat exaggerated for 
orange and yellow by errors of computation. Mr. Barrett does 
certainly get a good fourth, fifth, and sixth ; but these coincidences 
seem to me to offer a simpler and more effectual key than that 
which he has applied to the lock. What this key is will be 
evident on substituting for the numbers in Table I. or IL., the 
reciprocals of the same numbers. Take Table I. and divide ten 
millions by each of the numbers. The results, with a column of 
differences, are as follows : 
1382°3 F 
1545°1 1848 
PT 162°5 
1870°2 162°7 
2032°9 162°5 
2195'4 3625 
23579 : 
2520°8 16219 
I suppose this speaks for itself. Professor Listing has simply 
divided his spectrum into seven equal parts upon some scale 
which varies inversely as the wave-length. Such a scale would 
of course be furnished by comparative rapidities of vibration ; 
but it is no use guessing. Whatever led him to this particular 
measure, it is evident what his measure virtually was, and it 
nearly corresponds with the ratios of the musical scale because 
these approximately form a ‘‘ harmonic” progression. 
The other suggested analogies are less definite. ‘‘ The juxta- 
position of two colours nearly alike is dad,”’ but surely not what 
would be called discordant, except for the sake of finding an 
analogy between colour and music. The fact probably depends 
upon the extreme sensitiveness of the eye to the effect called 
relief ; a sensitiveness shared in a different degree by the ear, 
but shared also by all modes of feeling, even the least material, 
as men count materiality. The best results of juxtaposition are 
generally those given by complementary colours: but the relation 
between complementary colours is one which depends partly on 
relief and partly on the laws of composition above stated, and 
has nothing corresponding to it in music. But indeed I am sur- 
prised that anybody should even look foran analogy between the 
effect of simultaneous sounds and the effect of contiguous, not co- 
incident, colours. 
For these reasons I venture to think it is only by the unphilo- 
sophical restriction of the word physical, which excludes biolo- 
gical relations, that ‘* harmony in colour and music” can be said 
to ‘* have a common physical basis.”’ 
With regard to the coloured bands within the rainbow, it is 
not doubtless without solid reasons that Mr. Grove can have 
decided against identifying the phenomenon he describes with 
