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Phasmid

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  1. Hi, I'm currently reading through Universal: A Guide to the Cosmos by Brian Cox and Jeff Forshaw and have a question related to one of the calculations detailed therein. The calculation specifically is to do with the use of isochron plots for dating rock samples using the decay of 87Rb into 87Sr. An example of this kind of isochron is attached. Now the passage in the text says that if g = the fraction of 87Rb that has decayed since the rock was formed, then the tangent of the tilt of the line is given by g/(1-g). The text then goes on to determine the value of g by determining the slope, which in this particular example is given by (0.7325-0.699)/0.5 = delta-y/delta-x = 0.067. Note that this does not correspond to the graph attached, the attachment is simply to show how the axes are labelled and what a typical isochron plot consists of. Now that we have the slope of 0.067 using the deta-y and delta-x of the plot, the text goes on to state that this value of 0.067 implies a value for g of 0.063. Plugging 0.063 into the g/(1-g) provides a value of 0.067, so the numbers all work out. The (0.7325-0.699)/0.5 = delta-y/delta-x calculation is used for determining the slope of the graph but so too is the g/(1-g) calculation as both give the same answer of 0.067. Now where I'm getting lost is the step used to determine the value for g of 0.063. Is there a way of manipulating g/(1-g) to give an answer in the form g = 0.063? If not then how is this value determined? It surely cannot be a case of trial and error. I anticipate having missed something obvious and would be most appreciative of someone pointing it out to me. Of course if the information I've provided is too sparse I'm happy to provide any further details. If any of you own the book the specific section is at the bottom of page 30. Kind regards, Phasmid
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