This falls out naturally if you do the algebra from isotopic ratios 
(THEN convert to deltas) since the denominators (references) are not 
the same...deltas are not linear except over a narrow range


  At 12:00 PM 6/12/2008, you wrote:
>Hi all,
>
>An equation for converting from a working standard scale to an 
>international reference material scale is:
>
>d sa/st = d sa/ws + d ws/st + 10^-3(d sa/ws * d ws/st)
>
>where d is the delta, sa is a sample, st is the international 
>reference material, ws is the working standard, and sa/ws is a 
>sample relative to a working standard. This equation is found many 
>places (e.g. W.A Brand's chapter 38 (p855) in Handbook of Stable 
>Isotope Analytical Techniques (ed. P.A. de Groot)). My question is, 
>what is the derivation of the final term:
>
>10^-3(d sa/ws * d ws/st)
>
>The term clearly deals with those samples and standards that are 
>very different from one another, as it is larger the more disparate 
>samples and standards are. Searching the IsoGeoChem archives shows 
>that many folks leave off this term. Thank you all for your help.
>
>andy
>
>
>
>  Andrew Schauer
>ISOLAB
>Department of Earth and Space Sciences
>University of Washington
>Seattle, WA 98195
>
>
>206.543.6327
>[log in to unmask]

Greg Michalski, Assistant Professor
http://www.purdue.edu/eas/michalski/
Department of Earth and Atmospheric Sciences
Purdue University
550 Stadium Mall Dr.
Lafayette IN.47907