The purpose of this paper is to present a variational formula of Schläfli type for the volume of a spherically faced simplex in the Euclidean space. It is described in terms of Cayley–Menger determinants and their differentials involved with hypersphere arrangements. We derive it as a limit of fundamental identities for hypergeometric integrals associated with hypersphere arrangements obtained by the authors in the preceding article.
"Generalization of Schläfli formula to the volume of a spherically faced simplex." J. Math. Soc. Japan 72 (1) 213 - 249, January, 2020. https://doi.org/10.2969/jmsj/80238023