Russell’s law

Qearly, there are many ways according to which one can express the caUbration factor Ki/j as functions of time and mass. Equation (5.4), for example, is commonly known as the linear correction law, Eq. (5.5) as Russell s law, and Eq. (5.6) as the exponential law. To add flexibility to the fitting function in the mass domain, it has been proposed that a discrimination exponent, n, be introduced into the mass bias correction factor [19] ... 

Russell s law [40], on the other hand, is not equivalent to the exponential mass bias correction model, although these two names are often used interchangeably. However, the difference in the correction factors for the two models is determined solely by the masses of all nuclides involved. Combining Eqs. (5.5) and (5.6) leads to the following ... 

Non-conformity of the mass bias to Russell s law can be demonstrated in a simple experiment. From Russell s law [Eq. (5.5)], it follows that the slope of the linear... 

Figure S.2 Departure from Russell s law of mass bias for isotope amount ratio measurement results using a Neptune MC-ICP-MS instrument. Isotope amount ratios N ° Hg)/N( Hg) and N( ° TI)/N( ° TI) are considered here [Eq. (5.21)]. Agreement with Russell s law would result in/Hg/jfi = l. Uncertainties are quoted with the coverage factor/c=l.

What is more important, this calibration model is not derived from either the exponential or Russell s laws as is commonly perceived (and originally presented) [15, 32], Rather, it only requires the mass spectrometer response be linear [Eqs. (5.27) and (5.28)]. It is the interpretation of the slope and the intercept that can lead to the reliance on the exponential mass bias correction or even erroneous results. Consider, for example, the substitution of Eq. (5.34) in Eq. (5.32) ... 

Table S.2 A gedanken experiment for double-spike calibration of natural lead using NIST equal-atom lead reference material SRM 982. (a) True isotope amount ratios in the sample ( natural lead), calibrator (NIST SRM 982), and their equimolar mixture, (b) Measured" isotope amount ratios subjected to Russell s law of less than 1% bias for the ratio N( ° Pb)/ N( ° Pb). (c) Estimated isotope amount ratios of natural lead using the traditional doublespike equations (assumed linear discrimination), showing a 0.5% bias in N( ° Pb)/N( ° Pb).

Russell et al. (1992) conducted a similar study using the same data set from Hine and Mookeijee (1975). They developed a computer-assisted model based on five molecular descriptors which was related to the compound s bulk, lipophilicity, and polarity. They found that 63 molecular stmctures were highly correlative with the log of Henry s law constants (r = 0.96). 

Russell, C.J., Dixon, S.L., and Jurs, P.C. Computer-assisted study of the relationship between molecular structure and Henry s law constant, Ana/. Chem., 64(13) 1350-1355, 1992. 

Loewer, B. (2007a). Counterfactuals and the Second Law. In H. Price and R. Corry, eds.. Causation, Physics, and the Constitution of Reality Russell s Republic Revisited. Oxford University Press. 

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