  In the context of the search for triples of relativistic $\alpha$-particles
in the Hoyle state, the analysis of available data on the dissociation of the
nuclei ${}^{12}$C, ${}^{16}$O and ${}^{22}$Ne in the nuclear emulsion was
carried out. The Hoyle state is identified by the invariant mass calculated
from pair angles of expansion in $\alpha$-triples in the approximation of the
conservation of the momentum per nucleon of the parent nucleus. The
contribution of the Hoyle state to the dissociation of ${}^{12}$C $\to$
3$\alpha$ is 11\%. In the case of the coherent dissociation of ${}^{16}$O $\to$
4$\alpha$ it reaches 22\% when the portion of the channel ${}^{16}$O $\to$
2${}^{8}$Be is equal to 5\%.
