deletions | additions       diff --git a/methods.tex b/methods.tex  index 6f6db9b..2c90726 100644  --- a/methods.tex  +++ b/methods.tex 
...
\subsection{Sample preparation and mass spectrometry}  Two sections of the vein were cut parallel to the main growth axis and, using a Dremel drill with a dental bit, samples for isotopic analysis drilled at 5mm intervals in the direction of growth, Figure 2. Care was taken to avoid using undue pressure so as to minimize any frictional heating of the sample. Analyte CO_{2} CO$_{2}$  is produced by reacting 6-8mg of sample powder with 102\% ortho-phosphoric acid in vacuo at 25$^{\circ}$C and for a period of 12 hours. The evolved CO_{2} is then dried, collected by cryo-distillation into a calibrated volume manometer to check reaction yields and then stripped of potential hydrocarbon contaminants before collection in a Louwers-Hapert valved glass gas tube. The drying stage involves freezing the CO_{2} into a glass spiral trap at liquid nitrogen temperatures before sublimation at -120$^{\circ}$C, passing the gas through a second trap at -120$^{\circ}$C whilst freezing with liquid nitrogen into the manometer. We strip any potential hydrocarbon contaminants from the CO_{2} by cryo-distillation into the valved gas tube via a 20cm x 4mm i.d. glass tube packed with porapak Q ion exchange resin and held at a temperature of -20$^{\circ}$C. The sample gases were analysed for their clumped isotope values, $\delta$^{45} $\delta^{45}$  - $\delta$^{49} $\delta^{49}$  on the UEA MIRA dual-inlet isotope ratio mass spectrometer (Dennis, 2015). All analyses are made at a major beam (m/z=44) intensity of 7.5×10^{-8}A with simultaneous data acquisition for each cardinal mass of the CO_{2} molecule (m/z = 44 - 49). Each measurement consists of 4 acquisitions, each of 20 reference-sample gas pairs. Before analysis and between each acquisition the sample and reference gas volumes and signal strengths are balanced to within 1\%. A sample or reference cycle consists of a 10s ‘dead time’ after switching of the changeover valve followed by a 20s integration period. The total measurement time, including sample and reference gas balancing is approximately 90 minutes. The integration time is 1600s each for the sample and reference gas. Internal precisions ($\pm$1$\sigma$σ) for $\delta$^{45} $\delta^{45}$  and $\delta$^{46} $\delta^{46}$  are better than 0.001‰, for $\delta$^{47} $\delta^{47}$  better than 0.008‰, for $\delta$^{48} $\delta^{48}$  better than 0.03‰ and for $\delta$^{49} $\delta^{49}$  better than 10‰. The reference gas used in MIRA is CO_{2} CO$_{2}$  produced by reaction of BDH marble chips with 85\% ortho-phosphoric acid and subsequently equilibrated with water at 20$^{\circ}$C for a period of 1 month. This is to ensure that the $\Delta$_{47} $\Delta_{47}$  value of the reference gas is in equilibrium at the laboratory temperature. The nominal composition of the reference gas is: $\delta$^{13}C $\delta^{13}$C  = 2.007‰_{VPDB}; $\delta$^{18}O $\delta^{18}$O  = 34.899‰_{VSMOW}, and $\Delta$_{47} $\Delta_{47}$  = 0.94‰_{URF}. 0.94‰$_{URF}$.  To ensure a robust calibration of scale compression and transfer function between the local reference frame for $\Delta$_{47} $\Delta_{47}$  and the universal reference frame (URF) both 1000$^{\circ}$C heated and 20$^{\circ}$C water equilibrated reference gas samples are measured on a daily basis (Dennis et al., 2011). Data quality and long term stability of measured values is monitored by daily measurement of two laboratory standards that bracket the range of $\Delta$_{47} $\Delta_{47}$  values for samples in this study: UEACMST ($\Delta$_{47} ($\Delta_{47}$  = 0.384±0.013‰, n= ) and UEAHTC ($\Delta$_{47} ($\Delta_{47}$  = 0.562±0.014‰, n=). Based on the analyses of standards our best estimate of the external precision for sample analysis is $\pm$0.014‰. The MIRA response is flat with respect to the calculated $\Delta$_{47} $\Delta_{47}$  and $\Delta$_{48} $\Delta_{48}$  values of samples as a function of their bulk isotopic composition as represented by their $\delta$^{47} $\delta^{47}$  and $\delta$^{48} $\delta^{48}$  values \citep{Huntington:2009to}. Not-with-standing this we regularly check for linearity by measurement of 1000$^{\circ}$C heated cylinder CO_{2} CO$_{2}$  (BOC) that is depleted in $\delta$^{47} $\delta^{47}$  with respect to the reference gas by approximately 65‰. \subsection{Data handling and calculation of $\Delta$ values} 
...
\[{\Delta _i} = \left( {\frac{{{R_i}}}{{R_i^*}} - 1} \right) \times 1000\]     where $R_{i}$ is the measured ratio of isotopologue i to the non-isotopically substituted isotopologue and $R_{i}^{*}$ is the expected ratio assuming a stochastic distribution of all isotopes over all possible sites in the lattice (reference). For CO_{2} CO$_{2}$  we are largely concerned with the isotopologue ^{13}C^{18}O^{16}O $^{13}$C$^{18}$O$^{16}$O  (i = 47) but also determine $\Delta$ values for ^{13}C^{18}O^{17}O $^{13}$C$^{18}$O$^{17}$O  (i = 48) and ^{13}C^{18}O^{18}O $^{13}$C$^{18}$O$^{18}$O  (i = 49). The ratios $R_{i}$ and $R_{i}^{*}$ are determined from the measured $\delta^{i}$, $\delta^{13}C$ and $\delta^{18}O$ values of the sample CO_{2}. For $R^{47}$: 
...
\subsection{Temperature estimation using $\Delta_{47}$}  Using the clumped isotope composition of carbonate minerals as a geothermometer is a young and developing technique. Critical to it's successful application is a robust calibration between $\Delta_{47}$ and temperature. At present there exist several different calibrations (references). These are illustrated in Figure 4. There is a range in both the temperature sensitivity (gradient) and offset of the different calibrations. The differences between calibrations are laboratory dependent and measurements of samples when converted to temperature only make geological sense when the local $\Delta$_{47} $\Delta_{47}$  - T relationship is used. For this study we have used the temperature calibration determined at UEA using biogenic carbonates (bivalves and foraminifera) and travertine samples collected from sites with well characterized temperatures: \[{\Delta _{47}} = \frac{{0.0389 \times {{10}^6}}}{{{T^2}}} + 0.2139\]