The chi’s are then computed from Equation 5 , and are given in Table 111. The C-matrix is then inverted-the abbreviated Doolittle method ( I ) can k he used to good advantage here, or, if 1 the probleni is sufficiently complicated, 2 a high-speed computer may be used and 3 the element’s of the inverse matrix 4 t’abulated (see Table IV). The quantities S I and s are t,hen computed: SI = 82
Table IV.
Elements of the M a t r i x
C-’
i 1
2
3
4
2.21047 - 1,34243 0.00048 -0.00033
- 1.34243 4.07616 - 4.41768 0.00392
0.00048 - 4.41768 23.9121 - 13.5172
- 0.00033 0.00392 - 13,5172 15.2730
The fact t h a t x z i ti 100% is due to
0.86819
= -1,68003
ss = s4 =
s =
a
rounding-off errors in t’he calculations. This general approach has been applied to a \vide variety of problems ( 2 , 3).
5.97770 1.75939 6.92525
The &’E are computed from Equation 5: dl = 32,764 dz = 35.377 da = 17.048
&
(i I3
z
x is computed from Equation 8
( I ) Anderson, R. L., Bancroft, T. .4., “Statistical Theorv in Research.” 1st ed., chap. 15, McGraw-Hill, New Tork, 1952. (2) Burnham, H. I]., Jones, L C., AISAL. CHEM.29, 82i-34 (1957). ( 3 ) Ijeniirig, JV. L , “Statistical Adjuutment of Data,” chap. 4 et sey., Riley, Sew >-ark, 1913.
= 16.782, -
2 = -0 0642
) and lastly, the
coinpiited fiom k?qiiation 7 :
I , ’ S :LIT
24.880% = 25.080~0 = 24.15670 26.052oj,
ZI = .CP
LITERATURE CITED
=_
-
100.16370
1
Micro-Parr Bomb Assembly Suitable for Microdetermination of Fluorine in Organic Compounds AI Steyermark and Frank P. Biava, Hoffmann-La Roche Inc., Roche Park, Nutley 10,
microdetermination of fluorine in organic compounds, a number of inrestigators (2-8, 10, 11) recommended iiision with metallic potassium or -odium in a sealed microbomb a t ele\-ated temperatures (up to ’700” C.) for periods as great as 2 hours. Belcher and Tatlow (6, 12) described a special nickel bomb that could be used, but the regulation micro-Parr bomb as-embly ( 1 , 3 ) (Parr Instrument Co.. Moline, Ill., Series 2300, KO. AlMB) 15 not suitable, even when the lead gasket is replaced by a copper one (3-5, ‘7, a), because of breakdown of the clamping device u-hich holds together the parts of the bomb (cup and cover head of 98% nickel). This device was not designed for prolonged heating a t such elevated temperatures. The one described here is suitable, and, when a soft copper gasket is used between cup coyer, the assembly may he treated as above nithout loss of the fusion mixture. Thew units hold iip under continued UT. TOR
Figure 1 shows the details of construction of the nut and bolt clamping device (which should be machined from Type 303 free machining stainless steel), rlimmsions of the copper gaskets, and the assembly showing a micro-Parr bomb ( 1 , 9 ) in position. A stainless steel block may be drilled out as a support for the assembly. For a tight seal, before use, the gaskets should be
HEXAGON HEAD
9/32 DlA D R I L L THRY CHAMFER 1/32 X 4 5
,/
I 1/4 A C R O S S FLAT,;
N. J.
,
A
5/8 --1-14
_ -.
1
MACHINE
‘-CC’SINK
FLAT+
,-
,
HEXAGON NUTI 1/4 ACROSS FLATS
NF-2
6 F U L L THDS
/
x
I / B DP
600
.~ ASSEMBLY
- I - 14NF-2 4 FULL THDS
- 1
5/8
t
~
1/8-L
ic
-I
1
1/16 DIA
Figure 1. Details o f construction of clamping device for micro-Parr bomb All dimensions in inches. Use Type 303 free machining stainless steel
:iiinealed a t 700” C. (preferably in an atmosphere of carbon dioxide or nitrogen), and any oxide coating removed with dilute nitric acid. Annealed coppc’r gaskets of the correct dimensions arc’ commercially available (Parr Instrument Co., Moline, Ill., KO, 73IR copper, or Arthur H. Thomas Co.. Philadelphia, Pa., No. 2196-E). Figurib 1 shows the dimension of both the hexagon head and hexagon nut to be 1’ inches across the flats. For greatw durability this may be increased t o l 1
inches, all other dimensions being left a. qhown. To prevent leakage around the gasket during fusion, the cup and cover should be cleaned after each determination n ith fine emery cloth, while being turned in a lathe. For closing, the nut portion of the unit should be held in a vise while the bolt portion is tightened using a long-handled (20 inches or more) socket wench. After fusion the cup and lid may be separated by holding the former in a vise xhile VOL. 30,
NO. 9, SEPTEMBER 1958
1579
tapping the edge of the latter with hammor and chisel. Since this assembly has been used, hundreds of fusions have been made without leakage and the original nllt and bolt units are still functioning. ACKNOWLEDGMENT
The authors are indebted to dohn A. Stephens for assistance in preparing Figure 1.
LITERATURE CITED
(1) Beamish, F. E., IND. ENG.CHEM., ANAL.SD,5, 348 (1933).
(2) Belcher, R., Caldss, E. F., Clark, S. J., Analyst 77, 602 (1952), (3) Bdcher, K., cddns, E. F., Clark, S. J., Maedonald, A,, Mikroehim. Acta 1953, 283. (4) Belcher, R., Macdonald, A,, I M . , 1956, 899, 1187. (5) Belcher, R., Tatlow, J. C., Analpt 76, 593 (1951).
(6) Kimhall, R. H., Tufts, L. E., ANAL. CHEM.19, 150 (1947).
(7) Ma, T. S., Microehern. J . 2, 91 (1958). (8) Ma, T. S., Gwirtsmsn, J., ANAL. CHEM. 29, 140 (1957). (9) Parr Instrument Co., Moline, Ill,, Manual 121, pp. 3i, 4 i , 1950. ( I O ) Rush, C. A,, Cruikshank, S. S., Rhodes, E. J. E., Mikroehim. Arlo 1956, 858. (11) Schwaftzkopf, O., Sehwarakopf Microanalyticsl Laboratory, 56-1Y 37th Ave., Woodside ii, Pj. Y., privatp
communication.
(12) Stacey. l f . , Tatlow, J. C., Massingham, W. I.;., Brit. Patent Applic:ttion 3631/51 (Feb. 14, 1951).
New Microtechniques Lee Cahn, Cahn Instrument Co., Paramount, Calif., and W. J. Cadmon, Laboratory of Crirninalistics, Sheriffs Office, Orange County, Calif. IYEBALtechniques developed for use %with the Cahn Electrobalanee [R. H. Muller, ANAL. CHEM.29, No. 4, 49A (1957)l appear to be generally useful in microanalysis. Disposable platinum "crucibles" costing about 10 cents each are made by folding squares of platinum foil. There is no cleaning problem. Used crucibles are accumulated and returned for credit on subsequent platinum orders. Platinum foil nominally 0.00025 inch thick feels and handles much like household aluminum foil. I n one method a 12mm. square, weighing ahout 12 mg., is folded as shown in Figure 1 and in Figure 2 (upper left). It is suspended from the beam in a special wire hanger, and weighed relative to a tare. Sample is added, and it is weighed again. The hanger is removed from the balance, and the square is folded as shown. The sample is completely enclosed in metal and may be handled conveniently. If it is to be weighed after ashing, it is again inserted in the hanger. Alternatively, pieces 9 to 10 mm. square, weighing 7 mg., may be weighed on a standard Electrobalance stirrup. The same folding scheme is used. Advantages. Crucible cleaning is eliminated or substantially simplified. Crucibles are small when folded, so more can fit into an oven. Sample is securely enclosed; the crucible can he dropped without losing sample. Liquid samples are weighed eonveniently in glass capillary tubes, suspended from the same wire hangers. T i t h Kimble 34500 Kimax melting point capillary tubes, 1.5 to 2.0 mm. in diameter, the following capacitks arc obtained :
Ranges, Mg.
5-10 20
20-50-lW
Length, Mm.
Volome, MI.
8
0.009 0.014
11 50
0.065
Evaporation errors may he reduced to negligible proportions by a number of 1580
ANALYTICAL CHEMISTRY
Figure 2.
Sequence of folding foil
methods. Water in the Kimble 34500 tubing a t room temperature will lose about 50 y per minute. By holding the ends in a flame for ahout 20 seconds they can be necked down to 0.1 to 0.2 mm. in diameter, reducing the water evaporation rate to about 10 y per minute. To eliminate evamration comnletelv. as for extended storage, both ends nc; be sealed off in a flame before weighing. Alternatively, the interval between balancing the beam and transferring the sample to the next operation may be timed. The Electrobalance beam balances rapidly, so that one may establish a definite weight a t a definite time. It is
not necessary to null the meter and read the m i g h t during this interval. For evaporation rates of the order of magnitude given, this timing need not he very ca.refn1. Micropyenometers may he made of the same tubing, by drawing out the small diameter portion and marking the glass. They are readily calibrated with water or other pure materials. Disposable sample pans may be made of a number of materials. Polyethylene film, nominally 0.002 inch thick, may he cut with a No. 8 cork borer to produce 12-mm. pans, n.hich are rigid under loads of 100 mg. or less. Pans may be cut out of household aluminum foil with a No. 8 cork borer, and out of 0.00025-inch platinum foil with a No. 5 cork borer. Square pans may be cut with scissors. Ma,terial costs are negligible, because SO little material is used. Micro cover elassrs mav be used as disposable pansrup to 18 mm. in diameter in the No. 1 thickness, 0.13 to 0.17 mm. They are suspended on standard stirrups in the Eleetrohalance. Disposable containers can reduce thc labor cost of many laboratory procedures. With micro scale apparatus, the added material cost can he neglim;hl-
