Introduction to the theory of sampling
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Introduction to the theory of sampling


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of misleading words such as \u2018homoge- 
neous\u2019 and \u2018homogeneity\u2019 which describe a 
state that can neuer be observed in the physical 
world. 
The \u2018actual sampling variance\u2019 is proportional 
to what we have called the \u2018distribution het- 
erogeneity DH,\u2019 of the batch L. 
The \u2018fundamental variance\u2019, which is the min- 
imum minimorum of the actual sampling var- 
iance, is proportional to what we have called 
the \u2018constitution heterogeneity CH,\u2019 of the 
batch L. The proportionality factor is different 
for this and the preceding statement. 
The two preceding points show the impor- 
tance of a theory of heterogeneity for analyt- 
ical chemists who are interested in the 
importance of sampling as. indeed, they 
should be. 
11. Appendix 1 
11.1. Computation of CH, and HIL set of 
enumerable units 
In order to illustrate for a real example the defi- 
nitions associated with heterogeneity we give in 
Table 1 the contents urn ( CaO %), the masses M,,, 
and the heterogeneities h,, (dimensionless) carried 
by a series of 60 units U,,, which are increments 
extracted from the feed to a cement plant at uniform 
intervals. Together, the 60 increments make up 
what we shall regard as the batch L. The reader can 
check the identity m( h,,) = 0. The constitution het- 
76 
Table 2 
Computation of CH, and HI, 
trends in analytical chemistry, vol. 74, no. 2, 1995 
References 
aL = 39.66254% CaO 
M;=96 655 g 
m( h,) = 0 
C1Y,=~(h,J=2144~10-~ 
ML = CH, M; = 207.7 g 
~(h,)=46.3.10-~ 
erogeneity, CH,, and the heterogeneity invariant 
HZ= have been computed in Table 2. 
Acknowledgements 
The author would like to express his gratitude to 
Professor Dr. E. Pretsch, ETH Zurich, and to the 
TrAC reviewer, for their valuable advice and cor- 
rections. Thanks to them, this article should be 
clearer and easier to read than the original manu- 
script. 
[ 11 P.M. Gy, Sampling of Heterogeneous and Dynamic 
Material Systems, Elsevier, Amsterdam, 1992. 
[ 21 P.M. Gy, He\u2019te\u2019rogdne\u2019itb, Echantillonnage, 
HomogPne\u2019isation, Masson, Paris, 1988. 
[3] R. Kellner, Anal. Chem., 66 (1994) 98A-101A. 
[4] G. Kateman and L. Buydens, Quality Control in 
Analytical Chemistry, John Wiley, New York, pp. 
15-76. 
[5] F.F. Pitard, Pierre Gy\u2019s Sampling Theory and 
Sampling Practice, CRC Press, Boca Raton, FL, 
1989. 
[ 61 K.C. Ng, W.B. Whitten, S. Arnold and J.M. 
Ramsey, Anal. Chem., 64 ( 1992) 2914-2919. 
[7] S.A. Soper, Q.L. Mattingly and P. Vegunta, Anal. 
Chem., 65 (1993) 740-747. 
Dr. Pierre M. Gy is a Sampling Consultant at 14 
Avenue Jean-de-Noailles, 06400 Cannes, France. 
Recent advances in fundamental studies of 
hydride generation 
Qiu De-ren 
Shanghai, China 
Advances in fundamental studies of hydride 
generation (HG) are described under three 
topics. These are a study of non-nascent 
hydrogen mechanism; of the alkaline mode 
of HG; and observation on the course of 
release of hydride and the reaction sequence 
for the hydride-forming elements. 
1. Introduction 
Hydride generation (HG) has shown great pro- 
gress since NaBH4 was introduced as a reducing 
agent and more than 1200 papers, including several 
excellent reviews [l-S] have been published. 
There now seems to be a state of relative stagnancy 
whereas only a few analytical standards have estab- 
lished on the basis of HG, which is still not mature. 
Development of HG demands fundamental studies. 
Wang and Barnes studied the pH dependence of 
HG for As, Se, Sn and Pb, and considered the 
decomposition of the borohydride and hydrolysis 
of the four hydride-forming elements [9]. The 
author\u2019s group is focusing on studies of the follow- 
ing three topics: 
0 the non-nascent hydrogen mechanism; 
0 the exploitation of an alkaline mode of the HG 
reaction; 
0 observation of the reaction sequence and reac- 
tion course for the hydride-forming elements. 
2. Study of the non-nascent hydrogen 
mechanism 
The nascent hydrogen mechanism has been 
accepted as the classical theory for HG for the 
explanation of AsH3 generation over a century. In 
1979, when NaBHa was introduced for HG, Rob- 
bins and Caruso [ 1 ] followed the nascent hydrogen 
theory already available for explanation of the 
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