deletions | additions       diff --git a/The_proposed_method_for_determining__.tex b/The_proposed_method_for_determining__.tex  index 5f9acf3..637d76b 100644  --- a/The_proposed_method_for_determining__.tex  +++ b/The_proposed_method_for_determining__.tex 
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The proposed method for determining $c$ depends on calculating $\Delta$, which is defined as the sum of and $\Delta_{JS}\big(\rho $\Delta = \Delta_{JS}\big(dP;(dP_+ - dP_-)\big) + \Delta_{JS}\big(\rho  cdU;(dP_+ - dP_-)\big)$, for different values of $c$ and determining the value of $c$ that minimises $\Delta$. The results of this calculation for the distributions shown in Figure 4 are shown in Figure 5 where the minimum value is indicated by the red circle. We see, as predicted, that $\Delta$ decreases as $c$ increases from zero until it reaches a minimum and then increases as $c$ continues to increase. For this case we have chosen 32 bins and the minimum occurs at $c = 4.5$ m/s. The minimum is reasonably sharp and more accuracy could be obtained by considering small intervals of $c$ in the region of the minimum.