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It is shown that the Debye-Waller factor (or Lamb-Mössbauer factor) for a finite one-dimensional lattice is nonzero (it is zero for an infinite one-dimensional lattice) and experimental situations can exist when elastic neutron scattering or recoilless emission or absorption of γ rays may be observed in polymers. Specific heat of finite linear lattices is also worked out. It is found that the conditions under which one may replace the sum over lattice modes by an integration without introducing much error in the calculation of the Debye-Waller factor are entirely different from similar conditions in the case of specific heat.

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