servation from a multivariate population. To discover the generic relationship between two geographical locations, replicate samples a t each location should be taken. Then the problem becomes one of the statistical classification analyses. More specifically, it is the subject clustering (not attribute clustering) as described by Green, Frank, and Robinson (2). An excellent review article of classification is by Cormack ( 3 ) .It seems worthwhile to mention that one of the techniques is to apply factor analysis on subjects (locations). Factor analysis on attributes have been used by several chemists ( 4 ) .
..
= ( p z / p x ) ( l + d z ) ( l - dx + (dx)' + .) Taking expectation and retaining only the first and second moments, we have Cov(Y/X, Z/X) = E ( Y / X . Z/X) - E(Y/X)E(Z/X)
APPEND I X Let X, Y , and 2 be three uncorrelated random variables with means p x , w,, wz and variances crx2, cry2, uZ2.We shall show the following theorem. Theorem. Correlation between two ratios Y I X and Z l X is given by
[(P,2U,2
+
li,2(Jy2)(liz2(Jx2 + l i x2 (Jz2
)I 112
Proof: Let dx = (x - w x ) / p x and similarly defined for dy and dz. Then Y/X = (Py/Px)(l
+
dY)/(l + b)
= (P,,/P~)(~ + d y ) ( l - dx Similarly,
+
(dx)2 +
. .. )
(2) 8 . E . Green. R. E. Frank, and P. J. Robinson, Management Sci., 13, 387 (1967). (3) R. M. Cormack, Roy. Stat. SOC.A, 134, 321 (1971). (4) P. H. Weiner and J. F. Parcher. Anal. Chem., 45, 302 (1973).
Mathematics Department University of Maine at Orono Orono, Me. 04473 RECEIVEDfor review January 21, 1974. Accepted July 8, 1974.
I AIDS FOR ANALYTICAL CHEMISTS
I
Simple Device for Improving the Production of Coiled Glass Capillary Columns Eugene Reiner and James W. Weaver Center for Disease Control, Public Health Service, U.S. Department of Health, Education, and Welfare, Atlanta, Ga. 30333
A t present, the use of glass capillary columns in gas chromatography is increasing because of the many advantages of this material over metal (1-3). Since the cost of commercially available uncoated glass columns is high, most workers elect to make their own, either with home-built or commercially constructed glass-drawing machines ( 4 ) . In using a capillary glass-drawing device, troubles are usually encountered when the initial straight portion of capillary tubing (Figure l,A) passes through the rollers (Figure 1,B) and on through the heated coiling tube (Figure 1,C). Some of these troubles can be traced to inefficient lubrication of the heated coiling tube (graphite is the commonly used lubricant). Either too much or too little graph(1) M. Novotny and A. Zlatkis, Chromatogr. Rev., 14, 1 (1971). (2) M. d'Aubigne. C. Landault, and G. Guiochon. Chromatographia, 4, 309 (197 1). (3) A. L. German and E. C. Homing. J. Chromatogr. Sci., 11, 76 (1973). (4) D. H. Desty, J. N. Haresnape, and B. H. F. Whyman, Anal. Chem., 32, 302 (1960).
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Figure 1. Glass capillary coiling device
ite can cause bits of glass to break off in the heated coilforming tube. As a result, the tube clogs, and the entire op-
A N A L Y T I C A L CHEMISTRY, VOL. 46, NO. 12, OCTOBER 1 9 7 4
eration comes to a halt. The accumulated glass fragments and graphite must then be removed. A simple expedient, which we have used advantageously, consists of placing a trough (Figure 1,D) filled with graphite immediately in front of the coiling tube. As the straight portion of capillary burrows through the trough, small portions of graphite cling to the glass, thus assuring constant, adequate lubrication. To avoid getting graphite inside the glass tubing, the first few coils should be severed. For glass drawing machines operating in the vertical mode, a small cylinder with slots cut into the side from top to bottom and filled with graphite, should serve the same purpose. The trough (Figure l , D insert) consists of a block of aluminum (4.5 X 4.0 X 1.3 cm), with a slot milled 3 mm wide and 6 mm deep. The block is supported by a small laboratory jack (Figure 1,E).
With the former arrangement, starting with borosilicate glass tubing (122 cm long X 0.8-cm 0.d. X 0.3-cm i.d.), wastage is kept to such a minimum that 62-68 meter lengths of coiled capillary tubes (0.95 mm-0.d. X 0.34-mm i.d.) are consistently attained. In addition, since column efficiency increases with column length, longer columns are frequently desirable. By using shrinkable Teflon tubing, capable of operating a t temperatures to 327O, several coiled sections of glass capillaries can be joined together without loss of efficiency.
ACKNOWLEDGMENT Thanks are due to Edgar Biel, Instructional Media Division, CDC, for the drawing which appears in this communication. RECEIVEDfor review June 11, 1974. Accepted July 22, 1974.
Glass-I mmobilized 8-Hydroxyquinoline for Separation of Trace Metals from Base Electrolytes Used for Anodic Stripping Analysis E. D. Moorhead and P. H. Davis Departments o f Chemical Engineering and Chemistry, University ot Kentucky, Lexington, K y . 40506
That anodic stripping voltammetry (ASV) provides a rapid and convenient method for the measurement of trace levels of amalgam-forming heavy metals is well known ( I ) . However, the very high sensitivity of the ASV technique can produce problems arising from the purity of available solvents and reagents when the sample constituents fall into the parts per billion (ppb) or sub-ppb range. This complication is further accentuated if the material to be analyzed contains a mixture of trace metals, since separation of the complex response due to the sample from that produced by contaminants in the base, or supporting, electrolyte is difficult, and substantially compromises analytical speed and convenience. Absolute reagent purity is a virtually unattainable ideal. Even with the purest of available chemicals and conscientious attention to problems of laboratory handling and storage, ad hoc contaminant levels in the ASV test solution may far exceed those in the original sample. A frequently employed, straightforward method of reducing the effect of background interferences involves the use of extremely dilute supporting electrolytes and modern, three-electrode instrumentation with provision for IR compensation. If more concentrated base electrolytes are required for the analysis step, it is customary to clean up such solutions beforehand. using controlled-potential electrolysis at a mercury pool cathode (2). In a recent study of the phase-selective anodic stripping analysis of gallium, we were confronted with the need to substantially reduce trace metal impurities from stock supporting electrolytes 2.OM to 6.0M in NaSCN. Concentrated thiocyanate is required in order to obtain polarographic reversibility of gallium ( 3 ) , which ruled out using a very dilute salt as supporting electrolyte. Purification by (1) E Barendrecht in "Electroanalytical Chemistry-A Series of Advances,'' Vol. 2, A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1967, p 53. (2) J. J. Lingane. "Electroanalytical Chemistry," Interscience, New York, N . Y . . 1958. (31 E 0 . Moorhead, J . Amer. Chem. SOC..87, 2503 (1965).
controlled-potential electrolysis proved to be an unsuitable solution in this case because of the appearance of anode-generated thiocyanate oxidation products. The long electrolysis period required for purification produced yellow oxidation products even when the anode compartment was well isolated using a fine porosity glass frit diaphragm. To circumvent these difficulties, an alternative purification approach was adopted in which the concentrated thiocyanate, contaminated primarily with Zn, Pb, Cd, and Cu, was passed through a 6-mm X 41-mm glass column packed with 7.16 cm3 (wet) of Corning CPG-550 microporous glass beads, the surface area of which contained a coating of immobilized 8-hydroxyquinoline ("oxine") as metal chelating agent (Pierce Chemical Co.). The CPGoxine had a pore diameter, average particle diameter, and surface area of 550 A, 177-840 micrometers, and 70 m2 @-I, respectively; its exchange capacity in milliequivalents of amine per gram was 0.03. As in the case of bulk separations of metals using oxine, retention of metals by immobilized oxine appears to be strongly pH dependent. Following the manufacturer's recommendations, the column packing was first conditioned by elution with 1.OM HC1 in an attempt to displace any residual metal, and then flushed with ca. 50 ml of quadruply-distilled water. In a trial run, a neutral solution 2.OM in NaSCN was passed through the column. Analysis of the effluent using the phase-selective ASV technique ( 4 ) revealed a substantial increase in Cu content, with Pb, Cd, and Zn essentially unchanged. It is the manufacturer's recommendation that alkaline solutions, especially strongly alkaline solutions, should not be employed with the immobilized oxine if quantitative regeneration of separated metal is to be expected. As this was not an important consideration in the present application, it was decided to operate the column at pH > 7 to maximize retention of the trace metal constituents. ( 4 ) E. 0. Moorhead and P. H . Davis, Anal. Chem., 45, 2178 (1973)
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