100 Colours and their Relations. [January, 



Looking to the general character of the relations exhi- 

 bited in the table, they do not appear to encourage the 

 supposition of their indicating that the lines thus connected 

 correspond to rates of vibration, having their origin har- 

 monically in one common vibration. The most obvious 

 and simple interpretation of them is, that the ratios are 

 those of the respective amounts of vis inertia possessed by 

 the vibrating atoms which originate the lines ; while their 

 arithmetical coincidence with certain musical intervals is 

 merely accidental, and such as might be expected, accord- 

 ing to the law of probabilities, where so large a number of 

 lines are concerned. 



If diverse rates of vibration, having their origin harmo- 

 nically in a common rate of vibration, might be looked for 

 anywhere, it is in the lines produced by the same element. 

 Yet such lines are not, as a general rule, thus harmonically 

 related. The principal fixed lines E and G are both iron 

 lines ; but there is no harmonic connection between them, 

 although E appears to be harmonically related to another 

 iron line in the indigo, and G to another in the green. But 

 the number of iron lines is so great that these may well be 

 mere arithmetical coincidences. If we take another ex- 

 ample, such as magnesium, in which the lines are few and 

 conspicuous, we shall find that their ratios do not corres- 

 pond to any musical interval. These magnesium lines are 

 four in number, and their wave-lengths, according to 

 Angstrom's scale, are 5527*54 in the yellow, 5183*10, 5172*16, 

 and 5166*88 — all three in the green. The ratios subsisting 

 between any two of these are too small to be harmonic. 

 The ratio between the first and last, though greater than a 

 semitone, is less than a tone. Between the first and third 

 the ratio approaches near to that of do to reb in the Pytha- 

 gorean scale ; but this interval is highly discordant. 



On the whole, therefore, whether we take the mean 

 colours of the spectrum, the principal fixed lines, or the 

 lines produced by any single substance, it cannot be affirmed 

 that there is between colours and musical tones any ana- 

 logy, beyond that of their being both produced by vibra- 

 tions ; while the relations of those vibrations are in each 

 case governed by mathematical laws. But these laws are 

 in the case of colours much more simple and regular than 

 in the case of musical sounds, in which they are discon- 

 tinuous, irregular, and complex. 



The points of diversity between the two sorts of vibrations 

 are also very marked. The normal eye can judge much 

 more promptly and correctly of a simple colour than can 



