Although the spectra of the sun and of the nebulae exhibit the same pattern of absorption lines, there is one remarkable difference. The lines in the nebular spectra, in general, are not in their normal positions; they are displaced towards the red end of the spectrum to positions representing wave-lengths somewhat longer than normal. The entire pattern of absorption lines, all details in a spectrum, appear to have been shifted towards the red. These displacements are commonly known as red-shifts. They are characteristic features in the spectra of all nebulae except a few that are in the immediate neighbourhood of our own stellar system.
Each line in a given spectrum is shifted by a certain constant fraction of its normal wave-length . The linear shifts vary with, the wave-lengths, but the fractional shift, d / , remains constant. Therefore, the red-shift in a particular nebula is specified by d / , and it is d / which varies from nebula to nebula.
The study of many nebulae has shown that, on the average, the red-shifts increase with the apparent faintness of the nebulae in which they are measured. Therefore, we conclude that, on the average, red-shifts increase with distance. Extensive investigations have demonstrated that the relation is approximately linear,
This relation is called the law of red-shifts.