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where $R_{47}^{wrg}$ is the 47/44 ratio of the working reference gas (wrg) and is determined as:  \[R_{47}^{wrg} = 2 \cdot R_{13}^{wrg} \cdot R_{18}^{wrg} + 2 \cdot R_{18}^{wrg} \cdot R_{17}^{wrg} + R_{13}^{wrg} \cdot {(R_{17}^{wrg})^2}\]   Note that implicit in this treatment is an assumption that the mass spectrometer working reference gas has a stochastic distribution of isotopes. It is self evident that this is incorrect since the working reference gas has been equilibrated with water at the laboratory temperature. However, since the $\Delta$ values are <1‰ we can make this assumption and carry out a later linear transformation of the data to take account of the actual reference gas $R^{47}$ value without introducing any significant errors. The ratios R13, R17 and R18 are determined from the δ13CVPDB, δ17OVSMOW and δ18OVSMOW values of the working reference gas:   (4)  and similar equations for R17 and R18. The reference gas ratios are R13VPDB = 0.0112372 (reference), R17VSMOW = 0.0004023261 (reference) and R18VSMOW = 0.0020052 (reference).