IhDUSTRl21, 2 h D ESGINEEKIAG CHEhlISTRf
108
TABLE
A.
Iv.
EXPERIVEKT.tL
RESULTS
Degree of Vulcanization of Rubber Sulfur k
h
kh 1 24 1.14
1.00 0.i9
B
I l i r t u r e s of Rubber a n d Ileoprene NeoRubber prene k
+
Rubber Xeoprene 100 Sulfur 3 Zinc oxide 3 Ljght rnagncsiuni carbonate 5 gtearic acid 2 Nonox 1 Mercaptobenzothiazole 1 C
+
33
33 0
67 100
'
j
100 , 90 ; 75 60 , 25 ~
5s
0.40 0 26
no
1 .OO 0.52
0.86
0.34 0 23
1
n o
n
10 ''5 30 i.5
1.00 0 83 o 70 0.54 0.32
89 89
1, 1
oo
0 Q5 0.91 0.80 0.69
Ruhhei C o m p o u n d e d n i t h 3Iineral H a r r t e s Barytes k h
I00 Rubber Sulfur Zinc o u d ? Stearic acid 2 Nonox 1 Xlercapt obenzuttiiazole 1
:
E Kubbei Sulfur Zinc oside Stearic acid
I 00
o
Mixtures of Rubber a n d Perbuiiaii PerbuRubber nan h
Rubber Perbunan 100 Sulfur a Zinc oxide 3 Stearic acid 2 Nonox I .\lercaptobenzothiazolr 1 D
o
1 10067
kh
h
0 ,
+!I 150
250
1 00 0.91 0.81 0.80
Rubber ('urnpounded with Diatomite Diatomite k
100 3
(I .i ) 2 0 2
F.
hh
Summary and Conclusions
h
/.I,
1.0u
1 00
0.83 0.81
0 8.5 0 74 0 63
1.0u 0 71 0 60 0 4; 0 34 0 2ii
I.
I>
vti
0.il
Iiorosealb
1 .O(I
tioroseal a b
..
0.16
0.42
If .4 = 100 sq, rni,, L = 0.1 I'III., ( p . - 711) = T6 rni. of mercury, and t = 1 hour, then Q = -0.29 r r , a t normal temperature and pressure. The negative ate< that the gas passe from the high- to the Ion--pre
0.79 0.63 0.43 0 22
/: h
i.no
0.iO
j
The product k h , 1.46 X loF6 X 7.15 X = 1.03 X is directly proportional to the permeability of a standard sheet under standard conditions. For a comparison of the permeability of the material of this test piece to nitrogen xith that of a second material, this value is referred directly to the corresponding value for the second material. If it is desired to interpret the result directly in terms of permeahilit!-, the values of kh and of the chosen conditions may h r inswted in F:quation 3 :
Tahle IT aiitl Figiii,es 18 tcl I T give t u i ~ h e rexperimental result? ol~tainedwith the iamc appii'atii\ iititlei, similar condi tion::. I n these experiments, tlie ga. usetl was commercial nitrogen, tlie temperature was 30" C., antl the trqt pieces n-ere unco.i-ered square roils 0.4 x 0.4 x 15.0 cin. In the mixes t'he proportions are given as parts hy weight. Yulcanization was 1 hoiir a t 150" c'. The results are given as relative valiiea.
1 00 0.86 0.66 0 31i
1 00 0.94 0.82
VOI,. 12. NO. 2
0 0;
Coinmercial grade G. Goodrich plasticized polyvinyl chloride.
The rate at which a gas passe. throupli a sheet of ruhherlike niat,erial and the rate a t n-hich a gas is ahmrhed 11y a Iilock of tlie material are l)ot,li rlepetitlrnt upon the same fa(*tors, solubility and tliffusioii constant. The niagnit,ude of these factors can I)e measiiretl 1)y aiworption esperiments carried out under specifietl contiitions and the results can ess the perniealility of tlie material in sheet form. Experimental metliod. antl sui1 ahle apparatus are r1escril)eil for following absorption atid t he maniier of interpreting tlie results iii terms of pernieatdity is given. Resides such advantages as accurate tmiperatiirct cont,rol. convenient size arid ease of handling of the apparatits, t,he m a l l size of the test piece. anti t'lie elimination of the difficulty of producing iiiiiforni thin sheets free froin ~~inlioles, the inetliotl lias the advantage that I)ot,Ii factors. wlitl~ility and dilfusion constant, caii lie awessecl ititlepeiitlently; this is not normally possible lvit,li cliiwt periiieatioii mensrirement~. Some experimental results are talxilateti.
.4cknowledgmenI. The other experimental details were
Po p
2 . 2 cm. ot Iiiercury 205.7 cm. of mercury (barometric pressui'e, it;,?:e's( pressure, 129.5) r0 = 2.40 em. (scale divisions \yere centimeters) r , = 9.14 cm. (scale division- n-ere centimeters) rr = 3.00 c m (scale divisions were centimeters) T' = 2.80 cc. b = 6.23 X I O F 3 < < I , ~ I I I . I', = 2.34 cv. o = 0.40 ~ 1 1 1 . ( = 30.0 * 0.1 C ' . = =
These values, inserted i n Equation 15. give h = 7.15 X IO-', where concentration is measured in cubic centimeters of gas at normal temperature and pressure per rubic centimeter, :ind pas pressure i.5 measured in centimeters of mercury. The averagr value of u is used to calculate the diffusion constant from the relationship k = sq. cni. per second, where 4.63 x 10-3 ?)O( p = 0,514, Substituting these values, k = 0.514 sq. cm. per second = 1.46 X eq. cm. per second. Correction may be made for small variations in the dimensions of the test pieces by substituting for the value of u2 the true cross-sectional area. For example, if the cross-sectional dimensions of the test piece had been 0.395 and 0.403 cm., the value 0.39.5 X 0.403 n-ould have been naed in place of (0.4)*.
I: (Y
Grateful acknon-ledgment is made to the l)unlop Rublwr Co.. Ltd., for periiiissiori t o pulhlish this inrre.;tigation.
Literature Cited (1) Dayilea, H. .I., Proc. Roy. .Yoc., A97, 286 1:1920). Kaq-ser, Ann. P h y s i k , 43, 544 (1891). Morgan, L. B., and Naiintrin, \Y.J . 5 . . P J V CRubber . Tech. Conf., p. 599, London, 1938. (4) Morris and Street, IKD. Eso. ( ' H E M . , 21, 1215 (1929). (5) Reychler, J . chim. p h y s . , 8, 617 (1910). CHEM.,30,409 (1938). (6) Taylor, R. L., and Kemp, A . R (7) Yenable and Fuwa. [ h i d . , 14, (2) (3)
.
PREaENrED before t h e Division o f Rubber Ctieiiii.tri. a t the 98th Meeting of t h e American Chemical Society, Boston, \Iaqa.
i:::l 2 0.4
,
,
yiy;;i\1:
,
0 0
i
2 3 SULFUR
4
FIGURE 13. DEGREE OF VULCASIZATIOS OF RUBBER (TABLE IV, A)
5
100 80 60 40 20 0 RUBBER 0 20 40 60 80 100 NEOPRENE
FIGURE14.
MIXRUBBER XEOPRENE (TABLEIV, B)
TURES .4 S D
OF
100 80 60 40 20 0 RUBBER 0 20 40 60 80 100 PERBUNAN
DIATOMITE
.iSD
XIINERAL
C’OMPOUNDED
WITH
COMPOUSDED
BARYTES ( T ~ B LIV, E D)
PERBUNAN
(TABLEIV, C)
p - initial equilibrium pressure, cm. of mercury P = pressure in outer vessel at commencement of euperiment, em. of mercury ro = initial scale reading, cm. r m = final scale reading, em. rz = height of scale zero above level of mercury in outer vessel, cm. b = bore of capillary, cc. per em. = initial internal volume of tube containing specimen t = temperature, “C. and T’, = volume of specimen, cc.
WITH
DI~TOVITE (TABLE IV, E)
K h e n the shape of the specimen is such that diffusion of dissolved gas takes place in one direct’iononly, the absorption curve is a parabola up to a fractional saturation of about 0.60. Hence, if attention is confined to this initial part of the curve, it can be show1 that
”
1 = 7( T m
16
0 20 40 60 80 100
FILL-RE 18. RUBBER FIGURE 17. RUBBER
If
h
10.2 - 0 0 50 100 150200 250 BARYTES
FIGURE15. MISTURES O F RUBBER
The small degree of this inaccuracy justifies the use of this very convenient form of apparatus. The Henry’s law constant can be calculated without error.
-
0.4
0.2
0
m
0.4
3 0.2 $
107
ANALYTICAL EDITION
FEBRUARY 15,1940
-
TO)[TT
+ b(P -
i’,
-
Ti)]
x
1 1 x - (273273+ t ) (15) (7 - P o - r x - r.) x -V, This value for h may be regarded as the change of concentration, measured in cubic centimeters of gai at normal temperature and presbure, per cubic centimeter of absorbent, for a change of gas pressure of 1 cm. of mercury a t the temperature of the experiment. I n many of the experiments which n-ere carried out with nitrogen, the nitrogen used was the commercial gas produced by the fractional distillation of liquid air. This contains about 2 per cent of oxygen and during the experiments this was sufficient to bring about an appreciable steady fall of ~ definite pressure due to oxidation of the specimens. T l i no final pressure was reached. The difficulty was oyercome by continuing the experiments for a longer period than v a s necessary for saturation with nitrogen. The later “oxidation” parts of the curves (Figure 12) were straight lines (S), which when extrapolated to zero time gave the required scale readings. The experimental points of the “absorption” parts of the curves were corrected for oxidation on the assumption that oxidation proceeded at the same rate during the period of rapid absorption of nitrogen (3). I n some of the experimental procedures which h a r e been outlined, the design of the apparatus renders it impossible to make direct observation of the scale readings at zero time, mainly because of the impossibility of applying an instantaneous isothermal increase in the gas pressure. These zero readings can, however, be calculated from the readings taken during the absorption and from the shape of the absorption curves (Equations 11, 12, and 13).
To = 1‘2 - 21.1 = scale reading at zero time T I = scale reading at time tl TP = scale reading at, time La xvhere tl and tn are arbitrarily chosen so
\There and
1.0
that
t y = 4tl
It is desirable to use ieveral such corresponding values of tl and tP and to average the values of Q to obtain a trustn-orthy value for m e in the suhseqnent calciilations. K h e n the shape of the specimen is such that diffusion of dissolved gas takes place in more than one direction] use niay be made of the relationships and tieduced fioni Equations 12, 13, and 14. to show that (again confining attention to the initial parts of the curves) 7,-
1’0
=
[“t’,,,-
1’2
-
z/T,
-
?.,I2
and I.,
-
I.o =
[ z,+’,,~ - r2 -
4~~ -~,]3
fa tn o-directional diffusion (up to a fractional saturation of 0.84) and for three-directional diffusion (up to a fractional saturation of 0.96),respectively. The value of r m is already knonm, and hence r0 can be determined. Experimental Results A typical calculation from a set of observations obtained with the apparatus shown in Figure 10, using as specimen a square-sectioned rod of soft rubber, covered only on its square faces, and commercial nitrogen, is given in Table 111. The specimen was made from the rubber mix Rubber Sulfur Zinc oxide Stearic acid Nonox hleroaptobenzothiaeule
100
I
1
1 1
vulcanized in the form of a square rod 0.4 X 0.4 X 14.6 cm. by heating for 60 minutes at 150” C. The square ends only were covered v-ith tinfoil applied by means of a suitable adhesive.
VOL. 12, NO. 2
INDUSTRIAL AKD ENGINEERING CHEMISTRY
106
r
AT CONSTANT PRESSURE PI
AT A PRESSURE FALLING FROM P I TO Pp DURING THE ABSORPTION W
TIME
I
FIGERE11. ABSORPTIOXOF GAS Broken line applies t o pressure falling f r o m PIt o
Pz during the absorption.
TIME
FIGURE 12. ABSORPTION ASI)
OXID,4TIOX
The fractional error arising from the second source can be shown to 13e The total movement of the mercury level in the capillary,
bx
Plb
There b
= = =
x T'
P I - Ps, was 5.6 cm. TI-e assess the error halfway through the absorption-that is, when x = 2.8 cm. It is found t h a t
+ V - bx
bore of the capillary movement of the mercury level in the capillary initial free rolume in the tube containing thtx specimen
The following values, taken from a typical experiment on the absorption of nitrogen bv soft rubber, may he quoted t o asqess the order of the error:
Po = PI = P? = b = T'
=
and
1.8 mi. of mercury 204.6 cm. of mercury 199.0 cm. of mercury .5.03 X cc. per cni. 2.87 CC.
The total fractional error in the scale readings is therefore
1.74 X 10-2, which corresponds with an error of about 2 to 3 per cent in the deduced value of the diffusion constant.
TABLE 111. TYPICAL CALCULATION Time after Start
Hours 0.0 0.125
Scale Readings
Scale Readings Corrected for Oxidation
2,40d 4.13 4.87
0.3;a 0.5 0.625
4:i3 4.87 5.38 5.76 6.07
0.75 0.873 1.0 1.125 1221.3;a 1.5 1.625 1.75 2.0 2.5
6.36 6.60 6.79 6.98 7.17 7.36 7.48 7.61 7.71 7.97 8.28
6.35 6.59 6.78 6.97 7.16 2.35 ~ 4 7 7.59 z.69 ,,95 8.26
3.0 3.5
8.51
8.48
0.22-
8.72 8.87 8.97 9.06 9.39 9.61 9.82
4.0 4.5 5.0 24.0 48.0 72.0 m
(rm
-
ro)
= 2v-b C
..j ..
5.38
5.76 6.06
8.69 8.83 8.93 9.01
..
rm-,'
Calculation of r m -r
t r m -r
?.'iis
5,'oi 4.27 3.76 3.38 3.08
2.066 1.939
2.79 2.55 2.36 2.17 1.98 1.79 1.67 1.55 1 45 1.19
1.6iO 1.597 1.536 1.473 1.407 1.338 1.292 1.245 1.204 1,091 0,938
0.88
0.66 0.45 0.31 0.21 0.13
1.838
1.755
0.812
0.671 0.557 0.458 0.361
- ro
:
.'ik
4 .'47s 4.132 3.878 3 676 3.510
0 0.25
d.'5
0.375 0.5 0.625
1.5 2.0
2.5
2.572
3.340 3.194 3.072 2,946 2.814 2.676
0.75
3.0 3.5 4.0 4.5
2.528 2.526 2.515 2.488 2.453
2,584
0.875 1.0 1.125 1.25
1.0
5.0
6.'9'ige 6.739 6.687 6.682 6.615
2.'$3'8 2.596 2.586 2.585
0.0 1.73 2.47 2.98 3 36 3.66
0.0 0.257 0.366 0 442 0.498 0.543
,.. ,.. ,.. , . . ,..
A v . 6.74
2.490 2 408
2.182
1.876
0 0 0.138 0 204 0.253 0 291 0.324
4:23 X 10-5 4.62 4.74 4.71 4.67
0.357 0.358 0.408 0 432 0.457 0.484 0,502 0.520 0.536 0.579 0.637
4.i2 4.71 4.63 4.61 4.64 4.73 4.67 4.62 4.56 4.66 4.52
1.624 1,242 1.114 0.916 0.722
..
9:iu 6.74
\G.
Fractional quantities absorbed after times of first column
. ., Fractional quantity a-hich would have been absorbed if diffusion had been allowed t o t a k e place i n one direction only ( = 1
d Deduced from infinity scale reading of third column and the t o t a l movement i n t e n t h column.
-
%/I-).
Approximate average from first few values is 6.7. .Isimple calculation from this approximate value shows t h a t t h ? fractional saturation exceeds 0.84 after a b o u t 2.5hours. I n this experiment scale readings after 2.5 hours can therefore not be used i n these calculations. I Oxidation r a t e 0.96 X 10-2 scale division per hour. IDeduced b y extrapolation of graph of scale readings against time during "oxidation" period. e
FEBRUARY 15, 1940
105
AXALYTICAT. E D I T l O l
gas. The apparatus, although giving satisfactory result', is comparatively inconvenient and is not described here. ~IEASUREMESTS I h T O L V I S G SIMULTINEOUS C H A S G E I X
VOLUMEASD PRESSURE.An experimental method n hich is very conveniently applied in the important cases of gases such aq nitrogen and hydrogen, where the solubility in rubberlike sulxtancer is IOTV, is based on the removal of gaq hy absorption from a reference quantity changing both volume and pressure. T h e specimen, saturated with gas a t a lonpressure is confined over mercury in a quantity of ga. a t a higher pressure. Kith progressive absorption, mercury rises into the enclosed space and simultaneously reduces both volume and pressure. Tlie calculation of the Henry's law constant 1s b e d on tlie final equilibrium pressure and no error is introduced into its calculation by t'he change in pressure during the experiment. Change of pressure, however, dining the absorption affects the progress of ahsorption, and for a strict calculation of the diffusion constant, the experimental remlts cannot he used in Equations 12, 13, and 14. It is shown below, horrever, that if the change i n pressure is not,great, the error is small. A simple form of tlie apparatus is shoxvn in Figure 9. The specimen of square cross dertion is sealed inside a glass tube, onc end of which is fused to a communicating graduated capillary tube of known CAPILLARY bore. The dimensions are so chosen that the internal free space is small. In order to prevent possible harm to the I specimen during the sealing of the tube, it may be convenient to insert a short, well-fitting glass rod (as shon-n) behind the specimen. The loaded tube is suspended from the stopper of the large outer vessel by means of a wire FIGURE 9. APPAsealed into a small piece of sealing u-ax, RATCS F O R h1Eb.Sso that 11-hen the stopper is secured in URING GASABSORPplace n-ith a gas-tight fit, the capillar?. 1'10s B Y ROD t,iibe does not reach the mercnrv coiit&ed in the outer vessel. The initial ga. pressure is produced in the aisenibled apparatus, using the tap, and is maintained until equilibrium is reached. The pressure is then increavd to the new value, the tap i > closed, and the sealing wax support is joftened by a small flame applied externally, to allov the capillary to descend into the mercury. The pressure inside the specimen-containing tube I originally the same as that in the outer vessel, hut a:: gas I . absorbed by the specimen the pressure falls and mercury ascends the capillary. The position of the mercury meniscus is noted from time to time, The total quantity of gas in the whole apparatus is great compared ii-ith the quantity absorbed, so that the alteration in pressure in the outer vessel due to the absorption is negligible. At equilibrium the final saturation pressure is that of the gas in the outer vessel, less the back preswre due to mercury in the capillary. At the concluRion of the experiment, the free volume of the tube containing the specimen is determined by neighing before and after filling vith n-ater. This volume is required, together with the initial and final equilihrium preasures, in order to calculate the Henr?-'s Ian cowtant. Tlie pressure measurements made during the eour
02
0
04
06
08
IO
12
14
I
(V x n x m )
16
18
20
kt kl
3. \-ARIiTIoS O F FRACTIOSAL qU.INTIT1- O F G A S ROD,ASD CURE ABSORBEDBY SHEET,SQUARE-SECTIOS
I.'IGCHE
~ I T H TIME
1
The series is rapidly convergent and can lie suimned by evaluating the first few terms. Figure 2 , v-hich was derived in this way, slio~vsthe gas concentration a t all points througli a sheet after sereral time intervals. The quantities of gaj absorbed a t any time are obtained from relationships 6, 7 , and 8 by integration (see Equation 5 ) , the results again heing in series form. They may be written
I t is to 1)e iioted that Q l r Q 2 , and Qa are independent of qo, q.. , k , and I and are dependent only upon z, y, x , and the product kt. T h a t is, two identical blocks of materialb in nhich the diffusion constants of the gases are k , arid k p reach the same degree of fractional saturation after times ti and tz which hear the relation t l j f 2 = k,/k,. Relatioiiships 9, 10, and 11 inay be simplified, as may also G , 7 , antl 8, by considering test pieces the dimensions of nhich are equal in the directionb in which diffusion takes place and by choosing units of length such that these dimension, are equal to R units; or, in other words, by considering, for example, (1) a n infinite sheet of thickness R units of length ( X = a); ( 2 ) a n infinite rod of square cross section R x a (units of length)2, ( X = Y = a); and (3) a cube, a x a x R (units of l e i ~ g t h ) (X ~ , = Y = Z = a). Relatioiiships 9, 10, and 11 reduce to Q1 Q2
and
= =
Q3 =
1-8 1 - S2 1 - 83
(12)
(13) (14)
where
where I , m, and n are positive odd integers; qo = quantity of gas in the block a t equilibrium under the original gas pressurei. e., a t zero time-q, = quantity of gas in the block a t equilibrium under the new gas pressure-i. e., after infinite time-and Q1, Q 2 , and Q3 are the fractional increases in the quantities of gas absorbed in cases 1, 2 , and 3, respectively. The summations may be carried out by assuming particular values for the product kt. For example, the fractional increase in the quantity of gas absorbed after a time ti by a
and n is a positive odd integer. Table I gives the values of Q1, Q 2 , and Q 3 for a range of values of lit; it also includes the values of Q 2 for these values
2
of kt. It is seen from the table that, u p to a value of about 0.6
' for Q,, the value of Q -L remains substantially constant. This kt is a purely empirical relationship. Figure 3 gives the values of Table I plotted graphically. This constancy of Q ' in the experimental results of investigations covering only a n initial fraction of the absorption has led to a n erroneous assumption that this law applies over the whole absorption period; the
VOL. 12,
INDUSTRIAL AND ENGINEERING CHEMISTRY
100
The diffusion constant is defined hy the fundamental diffusion relationship dc dQ= - k X B X - X d d t
(2)
dl
where Q = quantity of solute 1 = distance d = cross-section area perpendicular to the direction in which 1 is measured; its dimensions are (1ength)l (time)T h e diffusion constant is characteristic of any pair of substances, solut'e and solvent, and is dependent upon temperature. JUs t if ic a t io n for the assumption of Equations 1 and 2, t'hat tlie diffusion constant is intlepeiidciit of t h e actual concentration, is given Iielon-.
'Y
y
F I C ~ R1.E Ur.ocri
Permeation through a t-xiiforin Sheet The niechanisni of permeation liere tlescribed, involving solutioll, tlift'usioli, alld eraporatioll, ila5 l,eeli clearly in~a ~ of a r,ll,l,erlike ~ ~ dicate,j l)y l)aylles ( 2 ) . ~ sul,stalice, of ,uliforlli tllicklleSs, L , allti cros+sectiolLal area, -4, tTyoreservoirs of gas lliaintained at (iiffereilt (-;as tiissolves at tlie surfaces constallt p, ,--iffuaes illto tile interior, so static equilil,riunI call reaclled a5 tile saturation gas concelltratiolls, correspol1clillg Tvith the tn.o gas pressures, are maintained in the respective faces and a constant concentration difference is maintained I,etn-een t~lelll. -1dynamic eq,lilii,riulll 7j-i11, 11ol\-(:yer, be attainetl at n-ilicll tlirougll tile sileet at a c~olistallt rate. K e may asmilie Henr?'.s Ian- and n-rite c = h p , where I , = gas pressure, c = equilibrium gas concentration in the materialh = proportionality i. e., the solubility at, gas pressure -and constant characteristic of the solute and solrent. The simpler diffusion Equation 2 may he applied and used to s l i o ~ v ,first, that c =
c1
+ L-1
(C?
=
Absorption by a Block Considering now t'he change in the total quantity of gas dissolved in a solid block of ruliberlike material, when after attaining equilibriuni in the gas at one pressure, the pressure is instantaneously and isothermally changed and maintained at a new value, the total quantity of gas, p, dissolved at any time is given by q = $$$c
X ds X dy X dz
(5)
n-liere c, the concentration of gas dissolved in the element of volume dx x dy x dz at, thp point 2, y, z, is given by the Fick's l a x relationship, Equation 1. It is possible, under the above conditions of gas pressure, antl limiting consideration to certain geometric ehaI)es for blie block of malaiv equation and evaluate c as terial, to integrate the Fi a function of t'lie product kt arid 2, 21, anti z, and further, to carry out the integrations to tletermine q as a function of kt and of tlie tiinierisions of the hlock of material. The paiticular geometric shape of tlie Iilock which lye coiid e r liere (Figwe 1) i> that of a right-rectangular prism of tlimeii~ionsS, ant1 %, a i d we disciis>~the tliree particular case- i n n-hicli (1) tn-o imirs of 'qqiositc faces are impermeal~le, the pair of faces of (1iiiiensk;iis I-% oi;ly heing periiieahle: (2) oiie pair of opposite fncc-: i. inipernie:ihle, t h e two pair> ( i f faces of tliriieiisions 1-Z aii(l l*Zonly heiiig permealile; aiid (3) d l six faces are P e r ~ ~ ~ e a ~ ~ ~ e ~ The condition of impernical)ility, or negligil>leperineahility, is easily i expcrinientally ~ i realized ~ eitlicr by ~ the obvious niethocl of the application of iiiiperiiiezthle coatings-e. I$., of tinfoil-by nieana of a suitalde atllic+i.:e! or l)y cmployiiig test pieces the (IiineriGxis of xliich we great in certain directions for exanil)le, ca
