6l6 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



prevent the divergence of the impression, and in light there is little or no tendency 

 to diverge; and indeed, in the case of a resonant passage, the air is not prevented 

 from becoming sonorous by the liberty of lateral motion. It would seem, that 

 the determination of a portion of the track of a ray of light through any homo- 

 geneous stratum of ether, is sufficient to establish a length as a basis for colorific 

 vibrations. In inflections, the length of the track of a ray of light through the 

 inflecting atmosphere may determine its vibrations: but, in this case, as it is 

 probable that there is a reflection from every part of the surface of the surround- 

 ing atmosphere, contributing to the appearance of the white line in every direction, 

 in the experiments already mentioned, so it is possible that there may be some 2d 

 reflection at the immediate surface of the body itself, and that, by mutual reflec- 

 tions between these 2 surfaces, something like the anguiform motion suspected by 

 Newton may really take place ; and then the analogy to the colours of thin plates 

 will be still stronger. A mixture of vibrations, of all possible frequencies, may 

 easily destroy the peculiar nature of each, and concur in a general effect of white 

 light. The greatest difficulty in this system is, to explain the different degree of 

 refraction of differently coloured light, and the^separation of white light in refrac- 

 tion: yet, considering how imperfect the theory of elastic fluids still remains, it 

 cannot be expected that every circumstance should at once be clearly elucidated. 

 It may hereafter be considered how far the excellent experiments of Count Rum- 

 ford, which tend very greatly to weaken the evidence of the modern doctrine of 

 heat, may be more or less favourable to one or the other system of light and co- 

 lours. It does not appear that any comparative experiments have been made on the 

 inflection of light by substances possessed of different refractive powers; undoubt- 

 edly some very interesting conclusions might be expected from the inquiry. 



II. On the Coalescence of Musical Sounds. — It is surprizing that so great a ma- 

 thematician as Dr. Smith could have entertained for a moment, an idea that the 

 vibrations constituting different sounds should be able to cross each other in all 

 directions, without affecting the same individual particles of air by their joint forces: 

 undoubtedly they cross, without disturbing each other's progress; but this can be 

 no otherwise affected than by each particle's partaking of both motions. If this 

 assertion stood in need of any proof, it might be amply furnished by the pheno- 

 mena of beats, and of the grave harmonics observed by Romieu and Tartini; which 

 M. De la Grange has already considered in the same point of view. In the first 

 place, to simplify the statement, let us suppose, what probably never precisely 

 happens, that the particles of air, in transmitting the pulses, proceed and return 

 with uniform motions ; and, in order to represent their position to the eye, let the 

 uniform progress of time be represented by the increase of the absciss, and the 

 distance of the particle from its original position, by the ordinate, fig. 33 to 38. 

 Then, by supposing any 2 or more vibrations in the same direction to be com- 

 bined, the joint motion will be represented by the sum or difference of the ordi- 

 nates. When 2 sounds are of equal strength, and nearly of the same pitch, as 



