Spectrophotometry in the λλ3400-7400 range is presented for 13 areas of the brightest H II region in the SMC: NGC 346. The observations were obtained at CTIO with the 4 m telescope. Based on these observations, its chemical composition is derived. The helium and oxygen abundances by mass are given by Y(SMC) = 0.2405 ± 0.0018 and O(SMC) = 0.00171 ± 0.00025. From models and observations of irregular and blue compact galaxies it is found that ΔY/ΔO = 3.5 ± 0.9 and, consequently, that the primordial helium abundance by mass is given by Yp = 0.2345 ± 0.0026 (1 σ). This result is compared with values derived from big bang nucleosynthesis and with other determinations of Yp.
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