ANALYTICAL CHEMISTRY, VOL. 50, NO. 14, DECEMBER 1978
2147
Comment on the Ability of the Representation Space Transformation to Preserve Data Structure Sir: Lin and Chen have recently presented a new algorithm for displaying multivariate chemical information on a three-dimensional coordinate system, which they call Representation Space Transformation ( I ) . They claim that this method of nonlinear mapping would fulfill the criterion of preserving t h e proximity relationship between information points and each of three pairs of reference information. But this assertion, which is formally expressed by Equation 4,is in contradiction t o t h e definition of t h e representation coordinates expressed in Equation 6. This fact is easily perceived by calculating the distances from an arbitrary information point to one pair of reference information points, e.g., X-and X,:
where h , = y12+ z , and ~
Equation 3 is also in error as the distances of X-to Y+and Y_ for example are not equal in general, and hence t h e condition for the vanishing of the >-component of the representation point of X according to Equation 4 is not fulfilled. Consequently the bounds of the three axis of t h e representation space are not identical with the representation points corresponding to the reference information! These facts do not mean that the proposed algorithm has to be rejected, but its ability to preserve data structure has to be interpreted in a slightly different way. As Equation 4 is correct for h, = 0 only, one may state that the distance ratio presenation criterion is fulfilled by the points ( ( P R I )defined ), by the individual components of the representation point vectors along the three axis (e.g. ((Px,)) = ((x,,O,O))), with regard to pairs of reference information marked by the same letter R. Equation 4 of course has to be reformulated in this sense. A mapping method meeting criterion 4 would consist in calculating the intersection of three ellipsoids. It may easily be shown that there does not have to exist a real solution and if one exists it is not unique. Even under the above restriction the Representation Space Transformation has proved to be useful according t o our experience
LITERATURE CITED
because
(1) Chi-Hsiung Lin and Hwa-Fu Chen, Anal Chem 49 1357 (1977)
Helmut Drack Institut fur Anal? tische Chemie und Mikrochemie der Technischen Universitat Wien Getreidemarkt 9 A-1060 Vienna. Austria for h, # 0. Equation 4 does not hold. The same result is valid for the other pairs of reference information and an arbitrary choice of distant exponent 1.1.
RECEIVED for review April 17. 1978. Accepted September 5, 1978.
Breakdown of Organomercurials Sir: The recent paper by Agemian and Chau ( 1 ) concerning total mercury determination has prompted us to draw attention t o the bromate-bromide technique (2) for breaking down organomercurials in water. Here, the oxidation of bromide by acid bromate produces bromine in the sample. T h e reaction is unaffected by waters of high chloride content since t h e Br2/Br- couple has a half cell oxidation potential of 1.087 V which is lower than that of the C12/Cl couple (1.358 VI. Residual bromine is removed prior to the cold vapor determination with 1-2 drops of hydroxylamine reagent. We tested the method on seawater samples (19000 mg/L C1-1 from the outer Thames Estuary which were spiked to 8.3 pg/L with mercury as methylmercuric chloride. T h e bromination treatment and recovery experiments were performed as described previously (2) and mercury signals were compared with a standard calibration line produced by the addition of inorganic mercury standards to seawater. As a result, employing 0003-270017810350-2147$01 0010
a 1-min bromination time and 2 ml, of bromate-bromide reagent, recoveries of organically bound mercury in excess of 96% were obtained. CVe infer from this that the bromination pretreatment could be used as an alternative method to the UY oxidation procedure of Agemian and Chau. In addition. with the bromate-bromide technique, it is possible to brominate samples at the time of sampling. Preliminary results suggest that the acid bromate-bromide reagent will preserve the inorganic mercury formed in solution. We found that samples of distilled water, seawater. and final sewage effluent. spiked to 2 pg/L with inorganic mercury in glass flasks and treated with 2 mL of the brominating reagent, showed no significant loss of mercury after 30 days' standing. Finally, similar to the UV oxidation procedure, the bromination pretreatment removes the sulfide interference from the cold vapor mercury signal. Following bromination with c 1978 American Chemical Society
