Determination of Resin Content of Glass Fiber-Polyester Laminates

Determination of Resin Content of Glass Fiber-Polyester Laminates Containing Calcium Carbonate Filler. S. D. Toner. Anal. Chem. , 1956, 28 (7), pp 110...
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Determination of Resin Content of Glass Fiber-Polyester laminates Containing Calcium Carbonate Filler S.

D. TONER

N a t i o n a l Bureau o f Standards, Washington 25,

D. C.

A reasonably accurate determination of the resin content of glass fiberpol! ester laminates containing calcium carbonate filler nia? be made by following the normal procedure for resin content. The values obtained upon ignition are then corrected b> treating the ignited residue with aninioniuni carbonate to coil\ ert any reduced calcium ovide back to the carbonate. i quantitati\ e measurement of calciuni carbonate cannot he made bj treatment of the ignited residue with h?drochloric acid because cerlaiii constituents of the glass are dissolved by the acid.

I

S C R T fillers are often used in the production of polyester laniiiiates reinforced with unoriented glass fiber. The most widely used inert filler for this application is precipitated calcium carbonate. Previous work has indicated that the presence of this specific filler introduces appreciable errors in the results obtained by the currently accepted method of determining resin content (3). Because the strength properties are, to a certain extent, a function of the resin content, which map vary because of fabrication techniques, the quantitative measurement of the components of plastic laminates reinforced with glass fiber is often necessary to determine whether the materials conform to a specification. Consequently. a modification of the method of test was developed to correct for errors introduced by the calcium carbonate filler. This report describes a reasonably accurate, rapid method for determining the resin content of laminates containing polyester resin, urioriented glass mat, and calcium carbonate filler.

qiieritly, nhen the temperature is raised above this point, as ia required in the method for resin content determination, the cnrtion dioside is evolved into the space immediately above the coustituents, calcium carbonate and calcium oxide. If air iy allowed to pass over the specimen, as in a ventilated muffle fiirnace, some of the carbon dioxide xi11 be d r a x n out of the crucible and the system of calcium carbonate, calcium oxide, and carbon dioxide will no longer be in equilibrium. More c:ii bon dioxide must be evolved from the calcium carbonate to regain the partial pressure necessary for an equilibrium state. A continuous flon- of air. then, results in a continuous evolution of carbon tiioxide. The amount of carbon dioxide lost during t'he period of ignition is dependent not only upon the temperature used but also upon the length of time required to burn the resin. T o regain the weight lost through dissociation of the calciiini c:u.l)oriate, the ignited residue may be treated in some manner to ronvert the calcium oxide back to calcium carbonate without the formation of other constituents. This conversion may be obtained quantitatively by treating the oxide with an excess of concentrated ammonium carbonate solution. The excess unreacted ammonium carbonate, which dissociates into ammonia, carbon dioxide, and water a t 58' C. ( 2 ) ,is then removed by evaporating the solution to dryness. An increase in residual weight obtained with the ammonium carbonate treatment represents quantitatively the amount of carbon dioxide lost on ignition. Subt'racting this increase in weight of the ignited residue and the loss in weight arising from the destruction of the fiber finish from the original loss in weight should give a correct value for the original resin content of the plastic. laminate. PREPARATION OF SPECIXIENS

GENERAL C O \ S I D E R i T I O h S

The resin content of a glass fiber-polyester laminate that does not contain a filler is normall) obtained by igniting a specimen to a weight equilibrium in a muffle furnace a t 538" t o 593" C. and measuring the loss in weight of the specimen This loss of weight on ignition is then corrected for the loss in weight caused by volatilization or decomposition of the fiber finish, previouslv determined on samples of the glass fiber, to give the resin content (3). K h e n specimens containing calcium carbonate filler are used, the loss of weight on ignition in the muffle furnace is considerably greater than the sum of resin content plus fiber finish. The excess loss represents carbon dioxide evolved from the filler a t temperatures above 525' C. ( 1 ) . T h e amount of dissociation of calcium carbonate is dependent upon the temperature and the partial pressure of the carbon dioxide in the furnace atmosphere, and may also be affected by the pyrolysis of the organic matter piesent in the resin and fiber finish. The dissociation of calcium carbonate into calcium ovide and carbon dioxide is a three-phase, two-component equiV = C 2, librium system. Application of the phase rule, P indicates 1 degree of freedom-that is, either temperature or 111essure, if arbitrarily fixed, will define the state of equilibrium. Ikcause the normal partial pressure of carbon dioxide in the atmosphere is 0.24 mm., the carbon dioxide contained in the v q t e m will be evolved when its partial pressure exceeds that of the carbon dioxide in the atmosphere. This pressure is initially iwched a t a temperature of approximately 525' C. Con-e-

+

+

Specimens of known composition were prepared using the following materials: Resin. Selectron 5003, an unsaturated polyester resin; Pittsburgh Plate Glass Co. Glass Fiber. Unoriented, mechanically bonded glass mat, 2 ounces per square foot, with a chrome size; Bigelow Glass Fiber Division of the Bigelow-Sanford Carpet Co. Filler. Precipitated calcium carbonate, assay 99.96%; Merck & c o . , Inc. Catalyst. Luperco ,4TC, 5070 benzoyl peroxide and 50% tricresyl phosphate; Lucidol Division, Wallace and Tiernan, Inc., Belleville, S . J. T h e composition of the specimens is given in Table 1,and duplicates the general range found in some commercial items. The specimens were prepared by adding a predetermined amount of each component t o a weighed porcelain crucible to give a total weight of about 3 gramfi. This weight is approximately that of a glass fiber-polyester laminate specimen 1 by 1 by 1/8 inch. Quantities of components used were as follows: resin, 50.0%; glass m a t (as received), 37.5%; and filler, 12.5% (25.0y0based on weight of resin used). T h e glass fiber used in this work was obtained from a single piece of mat measuring 2 feet square. The 18 specimens used for the determination of fiber finish content measured approximately 1 by 5 inches; the specimens used in the resin content determination measured approximately 1 by 4 inches for group I and 1 by 3 inches for groups I1 and 111. T h e average value of l.5yo fiher finish content based on the total weight of glass mat was taken to apply to all of the specimens in the three test groups. PROCEDURE

T h e glass m a t and calcium carbonate filler were dried a t 110' C. for 1 hour to eliminate any traces of moisture, and cooled t o 1109

ANALYTICAL CHEMISTRY

1110 23" C. in a desiccator charged with calcium chloride. The resin was catalyzed with Luperco ATC, 2% b y weight of the resin. The components were separately weighed into a porcelain crucible on an analytical balance. T h e resin was cured a t 110' C. for 25 minutes and cooled to room temperature. T h e specimen was then placed in a muffle furnace a t 538' to 593' C. and ignited to constant weight, which required about 1.5 hours. Higher temperatures were avoided to prevent fusion of the glass and the resultant entrapment of unburned carbon particles. Upon removal from the furnace, the specimen was cooled to room temperature in a desiccator and reweighed on an analytical balance. T h e weight loss on ignition is equal t o the weight of the resin, the volatilized or decomposed part of the fiber finish, and any carbon dioxide evolved from the dissociation of the calcium carbonate filler. The residual material remaining in the crucible was reacted

with an excess of a concentrated solution of ammonium carbonate. The specimen was evaporated to dryness a t 80" C. t o drive off the excess ammonium salt, then heated a t 110" C. to constant weight. The specimen was again weighed after cooling in a desiccator to room temperature. The increase in weight obtained from treatment with ammonium carbonate is the weight of the carbon dioxide absorbed by the ignited filler and is equal to the carbon dioxide evolved from the filler during ignition in the furnace. The resin content in weight per cent is:

x

R= or

R =

w 1

- WP @?I

- rv, x

100

100

where

W1= original weight of specimen, prior to curing Table I.

Specimen

Composition of Specimens for Resin Content Determination Original Composition, Weight %" Resina

Calcium carbonate filler

Glass fiber, a s received

Volatile fiber finish0

Glass fiberd

50.02 49.96

None h'one h-one None Kone h-one

Group I 50.03 49.98 50.05 49.90 49.98 50.04

0.75 0.75 0.75 0.76 0.75 0.75

49.28 49.23 49.30 49.15 49.23 49.29

11 12

50.37 49.97 49.86 50.00 50.03 50.19

12,45 12.58 12.48 12.49 12.50 12.50

Group I 1 37.18 37.45 37.66 37.51 37.47 37.31

0.56 0.56 0.56 0.56 0.56 0.56

36.62 36.89 37.10 36.95 36.91 36.74

13 14 15 16 17 18

50.06 50.04 50.13 50.14 49.88 50.22

12.52 12.54 12.43 12.50 12.63 12.46

Group I11 37.42 37.42 37.44 37.36 37.49 37.32

0.56 0.56 0.56 0.56 0.56 0.56

36.86 36.86 36.88 36.80 36.93 36.76

1 2 3 4 5 6

49.96 50.02 49.95

7 8 9 10

50.10

W z = weight of fiber finish W 3 = weight after ignition ?V4 = weight after ammonium carbonate treatment

Following the weighing after the ammonium carbonate treatment, each specimen was transferred from the crucible to a beaker to which 90 ml. of 3 S hydrochloric acid was added. The acid was heated to 90" C. for 3 to 5 minutes, or until solvent action ceased, and the glass residue was filtered off and repeatedly washed with boiling distilled water until a silver nitrate test of the filtrate was negative for chlorides. The filter paper containing the acid-insoluble glass fiber residue was placed in a crucible and the filter paper burned off. The specimens were allowed t o cool to room temperature in a desiccator prior to the final weighing. Two methods were used to determine the amount of acid-soluble glass. I n method A , the soluble constituents were calculated from the difference in weight between the original corrected glass fiber content and the acidinsoluble residue. Values for method B were calculated from the difference in weight between the total acid-soluble constituents and the original calcium carbonate filler. RESULTS

The test results obtained with the ammonium carbonate treatr ment are given in Table 11. Of three groups of specimens tested, a Original specimen weights ranged from 2.9974 t o 3.0293 grams. group I contained resin and glass, and groups I1 and 111, resin, b Previously catalyzed y i t h Luperco ATC, 2 % b y weight of resin. glass, and calcium carbonate filler. All of the specimens were c Based on 1.5% of original weight,of glass fiber. d Glass fiber, as received, less volatile fiber finish. treated according to the procedure previously outlined, escept that the ammonium carTable 11. Resin Content Determination" bonate treatment was omitted for group 111. (All results are weight per cent) The control specimens in Loss of Corrected Did. in Ignition Carbon Resin Content, Weight group I had a resin content of on Fiber Weight Dioxide Resin Content Measured less Speciabout 0.017, more than the Loss b AbsorbedC Measuredd Original Original Ignition Finish men original resin content after corGroup I recting the loss on ignition for 0.75 49,93 0.07 49.86 49.96 -0.10 50.68 1 0.76 50.09 0.06 50,03 50.02 0.01 50,84 2 fiber finish content. Subse4 9 , 8 6 0 . 0 7 49.79 50.61 0 . 7 5 49.95 -0.16 3 quent treatment with ammo50.12 0.04 50.08 50.10 50.87 0.75 -0.02 4 50.22 0.12 50.10 50.02 50.97 0.75 0.08 5 nium carbonate gave a meas0.75 49.86 0 . 04 49.82 49.96 -0.14 50.61 6 ured resin content of about 50.76 0.75 50.01 0. 06 49.95 50.00 -0.05 Av. 0.05% less than the original Group I1 resin content based on the orig1.79 50.37 0.56 52.16 50.37 0.00 52.72 7 0.56 52.61 2.73 49.88 49.97 -0.09 53.17 8 inal specimen weight. This 55 IO8 5 . 1 1 49.97 49.86 0 . 1 1 56.64 0 . 5 6 9 indicates that a slight error 54.82 4.78 50.04 50.00 0.04 55.38 0.56 10 0.56 51.26 1.28 49.98 50.03 -0.05 51.82 11 may be introduced by the reten54.96 4.73 50.19 0.04 50.23 55.52 0.56 12 tion of a small amount of un54.04 0.56 53.48 3.40 50.08 50.07 0.01 Av. volatilized ammonium carbonGroup I11 ate or its products, either ad0.56 53.40 53.40 50.07 3.33 53.96 13 55.46 55.46 50.04 5.42 0.56 56.02 14 hering to or reacting with the 52.99 52.99 50.13 2.82 0.56 53.55 15 glass fiber or some of its con54.76 54.76 50.14 0 . 5 6 4.61 55.32 16 51.49 51.49 49,88 1.61 0.56 52.05 17 stituents. The difference be54.86 54.86 50.22 4 . 6 4 0 . 5 6 55.42 18 tween measured and original 0.56 53.83 .. 53.83 50.08 3.75 54.39 Av. resin content results from an 4 All values based on original weight of specimen. b Loss of weight on ignition less fiber finish; results obtained by normal method of determining resin content. average weight increase of c Increase in residual weight after treatment with ammonium carbonate. about 2 mg. after the ammod Corrected ignition weight loss less amount of carbon dioxide absorbed. nium carbonate treatment. I

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V O L U M E 28, NO. 7, J U L Y 1 9 5 6

1111

After the ammonium carbonate treatment the difference Table 111. Determination of Acid-Soluble Constituents of Glass in Glass FiberPolyester Plastics between the measured resin (All results are weight per cent) cont'ent and original resin conhIethod A" Method B b tent for the specimens in group tilass .IcidAcidAcidAcidAcidAcid-soluble Speci. I 1 was about O.OIc; based on fiber insoluble' soluble soluble soluble soluble glass and Filler men contentese glass* glasse glasse g lad glassf fillere content the original weight of resin. Group I T h e difference in resiii content 1 49.28 f5,ll 4.17 8.47 4.28 Sone 4.28 8.69 in both groups I and I1 appears > 49,23 45.61 3.62 7.35 3.61 3.61 7.33 None 3 49.30 46.43 6.14 to be a measure of the variation 2.87 5.82 3.03 3.03 Sone 4 49.15 43.85 5.38 5.32 Sone 5.30 10.78 10.83 in glass fiber finish content 5 49.23 44.05 5.18 10.51 5.10 5.10 10.37 Sone 4 4 , 97 6 4.32 4.46 49.29 4.46 8.76 9.04 None rather than errore in the resin 4V. 49.25 45.00 4.25 4.30 8.73 8.62 4.30 content determination. These Group I1 values fall within the range t h a t 7 36.82 34.13 2.49 2.48 6.79 6.79 14.93 12.45 could be expected from the data 8 36.89 33,84 3.14 8.28 15.72 12.58 3.05 8.52 37.10 34.57 9 obtained on the fiber finish 2.53 2.43 6.55 6.82 14.91 12.48 10 36.95 32.52 4.43 4.39 11.87 16.88 12.49 11.98 content of the glass fiber. 36.91 34.50 11 2.41 2.46 6.50 14.96 12.50 6.64 36.74 33.26 12 3.48 3.44 9.47 15.94 12.50 9.36 The specimens in group I11 . I Y. 36.87 33.80 3.07 8.31 15.58 12.50 3.06 8.29 were not treated with ammoGroup 111 nium carbonate. The measured 13 36.86 30.50 6.36 17.25 15.54 12.52 3.02 8.21 loss on ignition, after correcting 36.86 29.80 14 7.06 19.16 14.18 12,54 1.64 4.44 36.88 34,48 15 for the fiber finish content, was 2.40 6.51 1 2 . 4 3 0 . 4 7 11.96 -1.27 36.80 28.71 16 8.09 3.47 21.97 15.97 12.50 9.44 36.93 33.03 about 3.75% more than the 17 3.90 10.56 14.92 12.63 2.29 6.22 36.76 33,30 3.46 9.42 11.28 12.46 -1.18 -3.20 original resin content baaed on 18 AV. 31.64 36.85 5.21 14.15 1 3 . 9 8 12.51 1 . 4 7 3 .97 the original specimen weight. a Acid-soluble glass calculated from original corrected glass fiber content less residue insoluble in hydrochloric This error is attributed to the a,+ ---I. 6 Acid-soluble glass calculated from loss of weight on treatment with hydrochloric acid less original filler content. loss in weight of the calcium Original glass content less volatile fiber finish. carbonate filler caused b y d Original calcium carbonate content. e BaGd on original weight of specimen. evolution of carbon dioxide. f Based on weight of glass. The ignited residues of the three groups of specimenq were treated n i t h hot 3.Y hydroTable IT. Volatile Glass-Fiber Finish Content chloric acid. R relatively mild acid treatment that was neither Srea Yo. of Volatile Fiber Finish Content, Wt. yo carried to completion nor intended to indicate the limiting soluSampled Specimens Iv.5 Std. del-. Range bility of glass in hydrochloric acid. This treatment was primarily 1 sq. ft. 8b 2.06 0.11 1 . 9 2 to 2 . 2 3 0.11 1 . 2 8 to 1 . 6 6 4 sq. f t . 18 b 1. 5 l designed to remove the filler quantitatively, thus allowing a quan125-yd. roll 20 b 1.34 0.25 0.79 to 1.94 125-yd. roll 20 1 52 0 . 3 6 0 . 9 3 to 2 . 2 6 titative determination of the glass fiber present. Such a method, if applicable, n-oiild provide a means of obtaining a total analysis Average loss in weight after ignition in muffle furnace. h These specimens obtained iron1 the same 125-yard roll of glass mat. of the material Values obtained from this treatment, however, indicate that a considerable amount of the glass fiber was dissolved b3 the acid along with the calcium carbonate and calcium oxide. This indicates the effect of even mild acid treatment on the glars and of the magnitude of error in this method furnace under the usual conditions is assumed to be the volatile which is now being used by some workers in the field. part of the fiber finish and is reported in Table IV as weight per The amount of acid-soluble glass is reported in Table I11 and cent of the original glass fiber. Results obtained on the 2-ounce was determined by two methods, A and B. I n method A , the mat in this and previous work have indicated a wide variability amount of acid-soluble glass was determined b y the difference in of the amount of finish not only from roll to roll but also from weight of the acld-insoluble residue from the original amount of location to location within a roll. The results given in Table I V glass fiber present. Average values obtained for groups I and I 1 indicate that the variation obtained is high. were 8.6 and 8 . 3 7 acid-soluble glass, respectively. Group 111, The variation in fiber finish may introduce an error in the which was not subjected to the ammonium carbonate treatment, measured resin content, the magnitude of which is dependent had an average loss of 14.2'%. upon the uniformity of the fiber finish and the proportions of The loss in neight determined b y method B mas made on the glass and resin used in the laminate. assumption t h a t all of the original calcium carbonate was present Although this method provides for a quantitative determinaas such in the residue and n a s dissolved by the acid. T h e diftion of the resin content, it does not provide for a quantitative ference between the total weight of acid-soluble material and the determination of the glass fiber and calcium carbonate filler in a amount of calcium carbonate originally present was considered to sample of unknown composition. Because a total analysis of a be the amount of acld-soluble glass. Results obtained for groups specimen is sometimes useful, the following modification of the I and I1 were 8 7 and 8 3V0, respectively, comparing favorably described method is proposed as one that might be used successwith resiilts obtained by method A. T h e average weight loss for fully for the determination of glass fiber and calcium carbonate. group I11 n a s 4.OTc. The difference between this value and the The specimen is ignited a t 538" to 593' C. until the carbonacesimilar one obtained by method A results from the fact that a cerous material resulting from pyrolysis of the resinous materials is tain amount of the calcinm carbonate had been reduced to calremoved. T h e furnace temperature is then raised to 1000° C. cium oxide and use of the original weight of the calcium carto convert all of the calcium carbonate t o calcium oxide. T h e weight increase of the residue after ammonium carbonate treatbonate introduces an error, the magnitude of which is determined ment is a quantitative measurement of the carbon dioxide conby the amount of carbon dioxide evo!ved during ignition. tent of the calcium carbonate. Knowledge of this value permits T h e volatile part of the finish on the glass fiber was obtained calculation of the original amount of calcium carbonate. T h e according to the method used for determination of resin content amount of glass fiber present is then obtained from the difference in weight of the original specimen less the sum of the weights of (3). T h e loss in weight resulting from ignition in a muffle

...

C

Q

1112

ANALYTICAL CHEMISTRY

calcium carbonate and resin. The volat’ile fiber finish is included in the values for resin content and could only be estimated. The results preqented (a) indicate the magnitude of the error int,roduced by calcium carbonate decomposition on results obtained using normal analytical ignition procedures for t,he determination of resin content, and ( b ) provide a simple, but preciw, tcchniqrie for correcting the resultant errors. The method described is wefill in t h o x cases n-here resin content is limited by specifiration, and where failure to correct for the loss of carbon dioxide n-orild result in the rejertion of the material for its specified I I Y , :mc1 n-here fairly accurate resin contents are needed.

LITERATURE CITED

(1) Hamilton, L. F., Sinnpson, S.G., “Talbot’s Quantitative Chemical Analysis,” p . 320, Xacmillan, Yew York, 1948. (2) Hodgman. C. D., “Handbook of Chemistry and Physics,” 34th ed., p. 462, Cherniral Rubber Co., Cleveland, Ohio, 1952. (3) XIilitary Specification IIIL-P-8013 (L7.SA.F.), “Plastic AIate-

rials, Glass Fabric Base, Low Pressure Lamimted, Aircraft Structural,” Test lIet,hod 4.2.2.1.2. RECEIVED for review May

4, 1935. Accepted April 19, 1956. The x v r k reported here \vas sponsored by the Materials Laboratory, Directorate of Research, Wright Air Dewlopment Center, V.S.A.F., under Contract No. 33(038)51-4060.

End Point Calculation in Conductometric and Photometric Titrations ERNEST GRUNWALD’ The Weizmann lnstitote o f Science, Rehovoth, lsrael

i11 objeetibe inchhod of end point calculation is described for conducton~r.tricor photometric titration curves which have no sharp end-point indicating change of slope. These include all titrations which Mould be difficnlt or impractical by the potentiometric method. The method makes use of the cur\ed part of the titration cline near the equikalence point and niinimises end point errors due to kariations in the equibalent conductivities, dekiations from Beer’s law, and sj stematic experimental errors. 4n end point accuracy of better than 0 . 5 7 ~is obtained eben in cases where the end point error may be as large as lO7c by other methods of calculation. Yo additional data are required.

procedure has a sound basis i n theory. There is a linear r:ingc\ before the equivalence point where the added titrant reacts quantitatively x i t h the substrate; there is a linear range past the equivalence point \There the added titrant no longer reacts with the substrate, the substrate-titrant reaction being complete; and the intersection of the tn-o straight lines defined in this way occurs at the equivalence point.

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O X D U C T O l I E T R I C and photometric methods of titi,ation can give accurate results in many cases where thp potentiometric method fails because the inflection point on the plot of electroinotive force us. volume of titrant is not clearly dpfinrd. For esaniple, the photometric titration of p-bromophenol i p I i ~ 9.2) with aqueous sodium hydroxide can be accurate to hrtter than lye a t concentrations as low as 0.001M ( 3 , 4). Similarly, 0.001.1f p-nitrophenol (pEi.4 7.0) can be titrated photomrtrically in the presence of 0.001JI m-nit,rophenol (p& 8.3) with an accuracy better than 2Ce ( 3 ) . However, in all cases where the potentiometric method fails, the conductometric and photometric titration curves are also difficult to interpret because there is no sharp change of slope at the equivalence point. The difficulties are illustrated by the titration of 0.01.Y aqueous sodium acetate with 1 S hydrochloric acid, a titration which would be difficult by the potentiometric method, The conductometric titration curve in Fater a t 25” C. is shown in Figure 1. The ordinate, K , is the conductivity, and the abscissa, E, the ratio of the equivalents of titrant to those of substrate. The curve was computed using the h o l m values of the dissociation const,ants and equivalent conductivities a t the ionic strengths existing during the titration ( 7 ) . -4s the figure shows, there is no sharp end-point indicating change of dope at the equivalence point. However, there are trro nearly linear segments, one before and the other past the equivalence point. The end point is usually taken as the intersection of the two straight lines drawn through the points in these linear ranges. Under certain idealized conditions (no changes in the equivalent conductivities and no volume changes during the titration), this 1 Present address, Chernktry Department, Florida State University, Tallahassee, Fla.

.5

c

0I

03

0.5

0.7

0.9

E

1.1

1.3

1.5

1.7

1.9

Figure 1. Conductometric titration of 0.01.V sodium acetate with 11%’ hydrochloric acid in water at 25’ C.

I-nfortunately, it is difficult in practice to recognize these linear ranges. For example, in Figure 1, only the portion of the titration curve between E = 0.9 and E = 1.1has pronounced curvature. Because of experimental error, different portions of the nearly linear remainder will appear to be linear in different titrations, and the end point is sensitive to the €-range selection which is made. -4s shown in Table I, errors of the order of 2y0 may arise from this cause. (This error is, of course, in addition to that causrd by the uncertainty of the experimental data.) Moreover, the actual choice of the linear ranges is subjective. T o make the selection of the linear ranges objective, one poesi-