In quiescent prominences of a different brightness the full intensity ratios of He to H are varied in the different parts of the features. In the outside, more thin, parts of bright prominences or in the faint prominences a helium emission is stronger than hydrogen one. With a brightness increase the full intensity ratio of He to H is decreased. A modern interpretation of this ratio behaviour is connected with a fine filamentary structure of quiescent prominences. In this paper we consider a model filamentary feaaure, with different values fo structure coefficients, which consists of He and H atoms in excited and ionized states. We solve the non-LTE problem for the main transitions, coupled with the statistical equilibrium equations for a set of physical parameters typical for a quiescent prominence. As the result we compute He(3888) to Hα ratios and compare them with observations. We find this ratio to be sensitive to structural parameters, as some other ones.