On account of this difficulty, the atomic weights published by Dalton, and the more accurate ones of Berzelius, were not always identical with the values now accepted, but were often simple multiples or submultiples of these.
In addition to these wave-lengths there are other groups centred round the wave-lengths which are submultiples of the principal one - the overlapping spectra of the second and higher orders.
We may therefore put y=a sin -T (x - e) +b sin (x - f)+c sin 6 (x - g) +&c. (21) where the terms may be infinite in number, but always have wavelengths submultiples of the original or fundamental wave-length A.
It follows from this that any periodic disturbance in air can be resolved into a definite series of simple harmonic disturbances of wave-lengths equal to the original wave-length and its successive submultiples, and each of these would separately give the sensation of a pure tone.