A detailed study of the isolated modes due to a variety of defects in one-dimensional two-component vibrating systems is made. A version of an analytic method outlined by Montroll and Potts in 1955 is used to deal with the localized modes associated with the simpler types of defect. More complicated defects can be treated in the same way, but the analysis becomes inconveniently complex, and a numerical approach already extensively used in a similar connection by Dean in 1959 and 1960 is preferred. It is found that a relatively few general rules describe all the results; these rules may be used to obtain much information on the spectra of a wide variety of one-dimensional systems.
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