deletions | additions       diff --git a/results2.tex b/results2.tex  index 54c1cdd..0361c9f 100644  --- a/results2.tex  +++ b/results2.tex 
...
Using the measured T($\Delta$_{47}) and $\delta$^{18}O values we have calculated the composition of the fluid that is in isotopic equilibrium with the samples of vein calcite. For this we used the Kim and O'Neill (1996) calibration of the calcite-water fractionation factor. The data plotted in Figure 6(d) show a marked linear covariation that resembles a two end-member mixing line. Data for the two sections DLR7 and DLR7(i) are the same within measurement error. At the high temperature end the calcite is in equilibrium with water at 100-110$^{\circ}$C and with an enriched $\delta$^{18}O value close to +6‰_{VSMOW}. The low temperature end (30-40$^{\circ}$C) is characterized by more negative values of $\delta$^{18}O between -2 and -4‰_{VSMOW}.  It is important to note that T($\Delta$_{47}) and the fluid $\delta$^{18}O plotted in Figure 6(d) are not independent and thus the errors are not orthogonal. We have plotted the 90\% error envelope corresponding to a $\pm$0.014‰ (1$\sigma$) and $\pm$0.1‰ precison for $\Delta$_{47} and $\delta$^{18}O respectively. This was determined using a monte-carlo simulation of 1000 independent $\Delta$_{47} and $\delta$^{18}O pairs. The errors are dominated by the precision at which $\Delta$_{47} can be measured with the first eigen vector of the error ellipse oriented parallel to the isopleths of constant calcite $\delta$^{18}O value. This lends a false sense of precision coherence  to the observed trend. Not-with-standing this observation the trend is real with a gradient greater than the local slope of the calcite $\delta$^{18}O isolpleths. This is revealed in the inverse covariation of T($\Delta$_{47}) and calcite $\delta$^{18}O values plotted in figure 6(c).