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\[{R_{47}} = \left( {\frac{{\delta _{sam - wrg}^{47}}}{{1000}} - 1} \right) \times R_{47}^{wrg}\]     where R^{47}_{wrg} $R_{47}^{wrg}$  is the 47/44 ratio of the working reference gas (wrg) and is determined as:  (3)  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 Δ 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 R47 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: