Standard Reference Material 2881 - National Institute of Standards ...

Then taking the ratio of equations [6.6] and [6.7], we obtain:expn∑M /∑= miSiSi[6.9]with the result that:oexp o⎧(1+ ( Q / k − ⎫o)(MwMo)Mn= Mn ⎨o ⎬[6.10]⎩(1+ ( Q / ko)(Mn− Mo)⎭where M n exp is the experimentally-measured M n .For use later in this paper we obtain by the same algebra:expw∑M /∑= 2miSimiSi[6.11]with the result that:oexp o⎧(1+ ( Q / k − ⎫o)(MzMo))Mw= Mw⎨o ⎬[6.12]⎩(1+ ( Q / ko)(Mw− Mo))⎭All higher moments may be obtained in a similar way and have a similar form.This then gives by simple division:which yields:o0 exp⎧(1+ ( Q / k − ⎫o)(MwMo))Mw= Mw ⎨o ⎬[6.13]⎩(1+ ( Q / ko)(Mz− Mo))⎭o0 exp⎧( Q / k − ⎫o)Mw(PDw1)Mw= Mw ⎨1−o ⎬[6.14]⎩ 1+( Q / ko)(Mz− Mo)⎭17