Gosport:Printed by E. Groves, 31, High Street.
By John Denis Macdonald, M.D., F. R. S.,
London:Longmans, Green, Reader, and Dyer.
Gosport:Groves, High Street 1869.
Introductory Remarks, and exposition of the ratios of Musical Vibration.
The phenomena of Light and Sound mutually illustrate each other, and the more they are studied and compared, the more it becomes manifest that both are obedient to the same essential laws and governing principles, though the vibrations of the one may be represented as almost infinitely more minute and subtle than those of the other. A great interval, therefore, may be said to exist between the smallest sonorous and the largest colorific vibration;Moreover, the vibrations of the colorific scale are within very narrow limits, embracing but a single octave, whilst musical vibrations, extending over numerous octaves, take a much wider range. Nevertheless, the internal constitution of the eight intervals of a diatonic musical scale, founded upon any note, will be seen, on close investigation to be represented in striking analogy by the prismatic series.
Admitting the application of the undulatory theory to both Light and Sound, the broad principle has long been admitted, that the undulations of the colours of the iris increase in number and diminish in size, as they ascend from the base red to the violet, just as happens in the musical scale, in passing from the graver to the more acute sounds. But the precise relationships existing between the two scales have never been satisfactorily worked out, which, if it could be done, would elevate painting to the status of a science, based like Music, upon mathematical principles.
Pythagoras, on his death bed, is said to have recommended the monochord as the only test of Musical perfection;and certainly, the facility with which the several intervals of the diatonic scale can be measured and determined by its use, gives it an importance that can scarcely be attached to any means of answering a similar purpose. The practical utility of such measurements is to afford a precise idea of the relation borne by the different notes of the scale, both to the key note and to each other, as also to make the nature of consonance and dissonance intelligible, in connection with the law of interference. Eeferring to the annexed table, if we assume for illustration merely, that the whole string vibrates once in a second, so that if audible it would give the note C, many octaves below that of 32 feet organ pipe, 8/9ths of the string, with a complement of 1/9th, will yield 1 and 1/8th vibrations in a second, producing D, the next note, and so of the rest. With reference to the third column, it may be noticed in explanation, that 1/8th of 8/9ths, or, of the whole length required to make D, being equivalent to the complement, 1/9th of the whole string has been added to express the fractional part of the second vibration, and so of the other fractions following.
The ratios of Colorific miration, and their comparison with those of the Musical Scale.
From the measurements of Newton, Sir John Herschell was enabled to calculate tables of the vibrations of coloured light, shewing their relative rapidity and minuteness, founded upon the estimated velocity ot light, and the assumed distance of the earth from the sun.
A superficial inspection of table 2, selected for reference, would afford but little hope of reconciling the musical with the colorific ratios of vibration, but we find that extreme and intermediate tints have been calculated, without any apparent reference to the constitution of the Musical scale. Yet the great latitude of vibration permitted both in and between the intermediate and principal colours, indicate the possibility of making a right selection of the exceedingly limited spaces within which indubitable ratios may be found. It will be seen, however, that by adding the complements of the musical ratios, (Table I, column 2) instead of the ratios themselves (column 1) to the number of vibrations for the principal colours, a close approximation will result. But this approximation will be still more remarkable on adopting the number 467, (minus the cyphers) instead of 477, the number for Eed, which may well be admitted by the wide range existing between the extreme Ked and the intermediate Orange. (See Table III).
A cursory glance at the following table will suffice to show that there must be something more than simple coincidence in the near resemblance of the two columns of figures, inspiring a hope that all existing doubt of the truth of the analogy may yet be removed by well directed experiment. The employment of the musical ratios themselves would overshoot the mark, but however, this is to be accounted for, they may be more satisfactorily applied to the numbers given by Ganot, expressing in corresponding parts of an inch, the relative size of the undulations taken at the principal dark lines of the
* Elementary Treatise on Physics, Coloured Plata I. (Atkinson's translation.)To Professor Granot's diagram of the spectrum,* I have added:first, his measurements of the undulations occurring at the principal dark lines seriatim, secondly, Sir J. Herschell's more extended series on the same scale, and thirdly, the Musical ratios applied to the principal colours, assuming 300 to represent the base red.
The positions occupied by the dark lines only give a rough idea of the true localization of the prismatic colours. But on comparing the 1st and 2nd series with each other, ther would appear to be no valid objection to the possible truth of the 3rd. Thus, the range of measurements embraced by the two former, cannot oppose the provisional selection of 0,0000,300 of an inch, as the length of the wave of the base red, and half that number for its octave, so that all the other colours may have the ratios applied to them in the 3rd series, by the musical analogy. It will be observed that any wide deviation occuring in the 1st series is compensated in the 2nd, and vice versa. The inference is therefore legitimate, that, if the analogy of the musical scale were taken as a guide, the special points of spectrum, whose respective vibrations would compose a well tempered diatonic scale of colour, may be readily chosen. It is probable also, that the musical ratios alone can be the test of the truth of such a scale, for by shifting ever so little above or
below the precise locality required, a difference of millions
of millions of vibrations must result.
The probable nonexistence of a Luminiferous Ether, and the consistency of such a doctrine with the exposition of all the known phenomena of light.
Ganot remarks " that in the case of sound, there is independent evidence of the existence and vibration of the medium (air) which propagates the undulation, whereas, in the case of light, the existence of the medium and its vibrations are assumed, because the supposition connects and explains in the most complete manner, a long series of very various phenomena. There is however, no independent evidence of the existence of the luminiferous ether." And indeed it is just as easy to conceive that common natter may be the subject of luminous vibration, as to assume the necessary existence of a luminiferous ether, in which similar vibration must be excited, in order to induce in us the sensation of vision. Sonorous vibration, obeying precisely the same general laws, has never suggested to the philosopher the presence of any such special medium, apart from common matter. Again, if waves of light are measurable, and we can estimate the rapidity of their sequence, there is still a wide margin for the play of the so called ultimate atoms of even the grossest form of matter. It might be supposed that any change wrought in the component atoms of a body by chemical force would exert some influence upon the ether flowing between them, yet, in ordinary coloured substances, this is not enough to produce luminous vibration in the dark, and can only respond to the impression of common light from some other source. But it would seem much more rational to refer the cause of this reaction, so to speak, to the chemical constitution of the atoms themselves, and their resident chemical forces, than to the. play of any hypothetical medium, which, after all must be the subjective, and not the governing agent, if it exist at all. Setting aside cases of interference, there appears to be as intimate a relation between chemical force and those occult conditions giving rise to colorific vibration in coloured bodies, as there is between mechanical force and the conditions of sonorous vibration.
This view of the case will explain to us why mechanical mixtures of coloured bodies develop intermediate compounds of the original tints, while those of colourless bodies remain colourless. On the other hand, when progressive chemical changes are attended with the evolution of colours, they generally occur in consecutive order, ascending or descending the scale, thus:the green iodide of mercury, which assumes a darker hue on exposure to light, yields a yellow sublimate when gradually heated, and thus, in turn becomes red, either by friction or after cooling;again, while the red iodide of mercury becomes yellow by the application of a gentle heat, at a higher grade, lemon chrome changes to orange chrome, and yellow ochre to light red. Autumnal tints also descending in the scale, admit of the same explanation, and many Other instances might be adduced;indeed, the subject admits of a very wide application, and might be extensively treated.
If we only assume the transmission of force, from atom to atom in ordinary matter with integral vibratory motion, we have a simple principle perfectly analogous to what we know to take place in the production and propagation of sound, superseding the necessity of corpuscular emission, or ethereal undulation, while it is quite as consistent with the exposition of all optical phenomena.
As long as chemical affinity holds the constituent atoms of a substance in union, they may be said to be in a state of tension involving specific vibration, and the persistence of this force is evidenced by their colorific reaction in the presence of common light or achromatic vibration. A musical string of definite diameter and length, in a certain state of tension, or a pipe of the necessary length and calibre will sound C, but a red substance may be divided almost innnitesimally, and all the molocules are red still, so that practically, as well as theoretically, we are obliged to acknowledge that the force in the latter instance is resident in the atomic constitution of the body. Is it not, therefore, more reasonable to look for this exquisitely fine vibration in the atoms themselves than in an interstitial ether, which would appear to carry the mystery one point further than the ultimate fact? A similar theory may yet be found applicable toall the so called imponderabe agents.