306 EDMUNDSON CALIBRATION OF A FISHER AIR-PERMEABILITY [Analyst, VOl. 91 Calibration of a Fisher Air-permeability Apparatus for Determining Specific Surf ace BY I. C. EDMUNDSON (Glaxo Laboratories Ltd., Green ford, Middlesex) Calibrating the Fisher sub-sieve sizer at a single particle-size level does not ensure accuracy a t other levels unless several variables are controlled. Instrument modifications that give better control of the several variables, and a calibration method that ensures accurate air-flow measurement without depending on a particle-size standard, are described. The modified instrument has good precision over the range 2 to 4 0 ~ . A method for extending this range is given. THE air-permeability apparatus of Gooden and Smith,l available commercially as the Fisher sub-sieve sizer (Fisher Scientific Company, Pittsburg, Pa., U.S.A. ; Kek Ltd., Ancoats, Manchester 12), is widely recognised as a convenient means of determining specific surface.Its advantages include an automatic calculator and the ability to give readings on a single sample compressed to successively lower porosities. We found considerable variation in the results for identical samples tested on different instruments. Some of the variation arises from fundamental errors in the usual method of calibrating and using the Fisher instrument. An alternative calibration method described by Dubrow2 is indirect, and takes no account of some important factors. The Fisher instrument, like other types of air-permeability a p p a r a t u ~ ~ ~ ~ ~ ~ ~ ~ is a means of measuring flow-rate of air through a powder sample.In this paper it is shown how So modif!, and calibrate the instrument so as to ensure accurate flow-rate measurement. The instrument (Fig. 1) consists of an air-supply section, a sample tube and a flow-meter. The water manometer, P, is not part of the standard instrument, but was added for the investigation and is now retained by us because it increases the instrument's accuracy and precision. The flow-meter consists of a capillary resistance, a water manometer, F, and a chart. A second flow-meter resistance can be opened to double the range. D/' A''' . P' I I t + I -TL E H a \ K \ J '\ M A = Pump B = Air filter C = Pressure control D = Standpipe P = Water manometer E = Drying tube G = Sample tube H = Flow-meter resistances F = Flow-meter manometer J = Zero control K = Chart M = Sample-height line Fig.1. Modified Fisher sub-sieve sizerMay, 19661 APPARATUS FOR DETERMINING SPECIFIC SURFACE 307 ’IVhen the sample is compressed, a pointer indicates the sample height, L , and the corresponding bed porosity, E, on the chart. After the sample tube is inserted in the air line, the water in one arm of the F manometer (a) rises to a level (&F) that depends on the flowrate. This level is read directly as average particle diameter (dvs) on the chart, which is mounted behind the manometer arm and on which there is a series of curves relating $F and E to dvs. A rack-and-pinion device for compressing the sample and indicating L and &F on the chart is not shown in Fig.1. THE INSTRUMENT EQUATIONS The Fisher instrument is based on the equation1- where d , , is the volume-surface mean diameter in p (specific surface in sq. cm per cc = 60,000/dV,), 7 is the viscosity of air in poises, C is the conductance of the flow-meter resistance in cc per second unit pressure per drop, p is the sample density, L is the sample height in cm, , ! ! is the sample weight in g, A is the cross-sectional area of the sample tube in sq. cm, P is the air pressure entering the sample and I; is the pressure drop across the flow-meter resistance, all pressures being expressed as centimetres of water. Therefore, The sample weight is standardised at a value numerically equal to p. equation (1) can be simp1 where c is an instrument - - fied to the form- constant that combines factors from equation (1)- c = L .. . 6o 14 Oo0 JZ (3) I f the flow-meter resistance is a capillary tube of suitable dimensions, C is given by the simple form of Poiseuille’s equation- where Y is the radius and I the length of the capillary, g is the gravitational constant and 7 is the viscosity of air. CONSTRUCTION OF THE CHART The base-line of the chart is graduated in values of E from 0-80 to 0.40. The L ordinates (cm) of the sample-height line are given by- .. .. .. . . 0.7893 L = - l - A ( l - € ) 1--E where A has the nominal value 1-267 sq. cm. The equation for the d,, ordinates, which are equal to $F cm, is obtained by combining equations (2) and ( 5 ) , and substituting the nominal values of c = 3.SO and P = 50.0 cm- ACCURACY OF THE INSTRUMENT All the factors of equations (1) and (2) are possible sources of systematic error.It is apparent from the form of dj77-T) in equation (2) that small errors in P or F can result in large errors in dvs, especially when P and F are nearly equal. It will be shown also that c is not independent of P and F when the instrument is calibrated in the usual way. The remaining factors ( A , L , ,!W, 7 and p ) are less important. The effect of error in measuring or standardising these factors on the apparent particle size indicated by the chart, dvs’, can be calculated after appropriate substitution in equations (1) or (2).308 EDMUNDSON : CALIBRATION OF A FISHER AIK-PERMEABILITY [AlZa&St, VOl. 91 THE INSTRUMENT CONSTANT- The flow-meter resistance in Fisher instruments is either a capillary tube whose resistance can be varied by a sliding wire in its lumen, or an adjustable needle-valve.Either type is usually calibrated against an artificial standard sample supplied with the instrument. This calibrator is a small ruby orifice-plate mounted in a sample tube. I t is inserted in place of the normal sample, and the flow-meter resistance is then adjusted until the chart d,, reading equals the value stamped on the calibrator; the instrument constant is then, nominally, equal to 3.80. The ruby's labelled value is usually about 5.8 p at porosity 0.75, corresponding to about 15 p at porosity 0.5. Porosity has no real meaning in reference to an orifice; essentially, the ruby produces a constant I; value on the flow-meter manometer when other factors are constant.This F value corresponds to different d,, values, which depend merely on the porosity setting of the chart. If the accuracy of this calibration is in doubt, a direct check of the ruby's nominal value is difficult. Since the orifice length-to-diameter ratio is small and the air flow turbulent, the flow-rate and its equivalent d,, cannot be related to the orifice dimensions by any simple equation. However, an accurate and constant value of c can be achieved by replacing the variable resistances with simple capillary tubes of dimensions calculated to give the required con- ductance. Substituting6 q = 0.000183 poise at 25" C and c = 3-80 in equation (3) gives the normal-range conductance, C = 0.004298 cc per second per cm pressure drop at 25" C.The conductance of the double-range capillary is three times that of the normal-range. Sub- stituting in equation (4) gives the required length and radius. Accurate resistances can be made from precision-bore tubing after selecting for uniformity of bore and determining the average radius by filling with mercury. Suitable nominal bore- diameters are 0.03 cm and 0.04 cm for the normal-range and double-range capillaries, respec- tively, with corresponding lengths of about 25 cm and 26 cm. Errors due to turbulence, molecular flow and end effects are negligible with these dimensions at the maximum pressure involved. Mounted vertically in the instrument, the capillaries are protected from chance contamination by dust and have maintained their constants during continual use for sevei a1 years.AIR PRESSURE- The Fisher instrument's constant-pressure device consists of a control valve and a standpipe filled with water. In use, the valve is adjusted until a regular stream of bubbles rises through the water. Since the air pressure depends on the height of water (approxi- mately 50 cm) and on the bubble rate, the standpipe is engraved with a water-level line by the manufacturer, and the bubble rate is directed to be adjusted to between 2 and 3 per second. The reliability of this system was checked by means of the P manometer specially fitted for this purpose, as shown in Fig. 1. The P manometer is made from precision-bore tubing, with a narrow-bore section (1-5 mm), to damp oscillations caused by the pump, and two expansion bulbs to accommodate the initial surge before the standpipe begins to bubble.When the bubble rate was adjusted to 2.5 per second by careful timing with a stopwatch, the manometer gave a steady reading of 50.0 cm. But when different operators attempted to produce a steady bubble rate of 2 to 3 per second by unaided visual judgment, the reading varied between 49.5 and 51-0 cm. It is preferable, therefore, to standardise P by ignoring the bubble rate and adjusting the pressure control valve to give a manometer reading of 50.0 cm during each determination of particle size. Gooden and Smith' adopted the standpipe from an earlier design by Traxler and 1Ba~m.~ Although the latter claimed that such a pressure regulator is highly accurate, they included a manometer in the system and used its readings in their calculations.The real function of the standpipe is to reduce pulsation in the air flow by allowing a bubble to escape at each stroke of the pump, Since the stroke rate is usually about 4.5 per second, a steadier flow is obtained if the water level in the standpipe is lowered by about 0-5 cm, or until one bubble is given for each stroke while the manometer is at 50-0 cm. The upper curve in Fig. 2 shows the error in indicated diameter at porosity 0-5 when P' = 51 cm instead of the standard 50.0 cm used to calculate the chart ordinates. The usual method of calibrating the variable flow-meter resistance against a standard sampleMay, 19661 APPARATUS FOK DETERMINING SPECIFIC SURFACE 309 Fig. 2. Error of indicated particle size a t porosity 0.5 due to error in air pressure (P’ = 51 cm) or to inequality of flowmeter manometer arm radii ( Y ~ / Y ~ = 0.98): curve A, error uncompensated ; curve B, error partially compensated by calibrating with a 15-p standard compensates the error in P’ by introducing an equal and opposite error in the instrument constant, c.But the compensation is complete only at the chart level corresponding to the standard sample. The lower curve in Fig. 2 shows a residual error varying from -56 per cent. to +9.3 per cent. at other diameters when the original error is compensated with a standard equivalent to 15 p at porosity 0.5. Thus a subtle disadvantage of the usual cali- bration method, when either the ruby standard or an actual fine-particle standard is used, is that it is a one-point calibration and gives the operator a false sense of accuracy.ERROR IN MEASLTIIING FLOW-METER PRESSURE DROP- Maizometev error-The Fisher method for determining 4F by observing the rise in one manometer arm, while ignoring the fall in the other arm, leads to error if the two arms are of unequal internal radius. Nanometer-arm inequality has the same effect as error in standardis- ing P’. Hence Fig. 2 also shows the effect of the manometer error when the arms have a radius ratio (ra/~b) of 0.98, corresponding to a maximum difference of 1 cm between the rise and fall in the two arms. Inequality of Ya and Yb may be detected by fitting millimetre scales to both arms of the manometer. In this way, errors of more than 1 and 2 cm in F were found in two of the instru- ments mentioned in paragraph 1 above.I t was not known whether the faulty tubes were original fittings, though the instruction manual refers to the need to use matched pairs. Since the relationship of d,, to F varies with E according to equation (6), Fig. 2 is valid for any porosity if values of F corresponding to E = 0.5 are substituted for dvS‘ in the abscissa. Chart ervor-The accuracy of the drawing and reproduction of the principal d,, curves on the chart was checked by measuring the ordinates with a travelling microscope and com- paring them with the \dues given by equation (6). The ordinates of the principal curves were found to have consistently 99-2 per cent. of the theoretical values at all porosities. The effect of this error on dvs’ at E = 0-5 is shown in Fig.3. As before, partial compensation occurs if the flow-meter resistance is calibrated against a standard sample. JTalues of F may be substituted for dvS’ in the abscissae as in Fig. 2. Some of the intermediate d,, curves on the chart are less precisely drawn, in particular those from 3.1 to 3-3 p at E = 0.47. Drainage error-Drainage error in setting the manometer zero and in taking the sample reading is difficult to differentiate from error due to manometer-tube radius. However, these errors are eliminated simultaneously if manometer tubing is selected so that a rise in one arm is equalled by a fall in the other under standard drainage conditions. In this way, and by applying corrections for measured chart errors, good accuracy is achieved for routine work.Compensation occurs in the same way as for P’.310 EDMUNDSON : CALIBRATION OF A FISHER AIR-PERMEABILITY [A ?Za/$St, 1'01. 91 c A Average particle size (dv;),p Fig. 3. Error of indicated particle size a t porosity 0.5 due to - 0.8 per cent. error in the chart d,, ordinates: curve A, error uncompensated; curves B and C, error partially com- pensated by calibrating with 15 and 5.5-p standards, respectively If greater accuracy and precision are required at the expense of convenience, the errors of the Fisher manometer - chart system can be eliminated by calculating d,, via equation (2) from direct F readings on a separate manometer, so fitted that both arms can be read against a single millimetre scale. VISCOSITY OF AIR- If the viscosity of air is assumed to be constant within the range of pressures used, 7 cancels out when equation (4) is substituted in equation (I), and the instrument reading should be unaffected by temperature changes (cf.Lea and Nurse3). This was confirmed experimentally for constant ambient temperatures between 10" and 30" C and for flow-rates within the instrument range. OTHER FACTORS- The form of equation (1) is such that small percentage errors in A , L , -21 or p result in larger percentage errors in the apparent particle size, dvs', indicated by the chart. The dvS' errors are independent of particle size, but increase as porosity is reduced (see Table I). Sample-tube diameter-The nominal cross-sectional area of the sample tube, A = 1.267 sq. cm, corresponds to an internal diameter, D = 1.270 cm.The internal diameters of the effective portions of three sample tubes measured with a travelling microscope were each found to be 0.31 per cent. high. Table I shows the factoIs by which this percentage error must be multiplied to give the corresponding percentage eriors in dvs'. TABLE I EFFECT OF ERROR I N SAMPLE TVBE DIAMETER, SAMPLE HEIGHT ASD SAMPLE UTIGHT ON dvsf AT DIFFERENT POROSITIES Multiply the percentage error in D, L. or ,iM by the factors shown below to obtain the corresponding percentage error in dvS' Porosity 0.80 0.70 0.60 0.50 0.40 D + 3.8 + 4.3 +5.1 $6.1 + 7.6 L + 0.9 + 1.3 + 1.5 + 2.0 + 2.8 M - 1.4 - 1.7 - 2-0 - 2.5 - 3.3 Sample height-The sample height, L, is equal to the ordinate of the sample-height line on the chart, provided that the compression mechanism is properly adjusted in the usual way.The errors in the L-ordinates on a typical Fisher chart were found to vary from +0.2 to -0.7 per cent. over the porosity range 0-50 to 0.80, with a maximum error of - 1.1 per cent. a t porosity 0-40. Table I shows the factors by which these errors must be multiplied to give the corresponding errors in dvs'.May, 19661 APPARATUS FOR DETERMINING SPECIFIC SURFACE 31 1 Sample demity aizd weight-The standard sample weight for the instrument is equal t o the density of the sample material ( M = p). Any systematic error in density, e.g., by round- ing-off, therefore results in a systematic error in sample weight, and the effect on dvS’ is increased by the factors shown in Table I.The factors are negative because an excess sample weight results in a low value of dV8’. THE FLOW-METER RESISTANCE- A normal-range flow-meter resistance was made, as described previously, from selected precision-bore tubing. Substituting the measured radius and length in equation (4) gave the conductance as 0.004299 :c per second per cm pressure drop at 25” C, or 100.1 per cent. of the desired nominal value. The conductance at that temperature was measured by a bubble meter method8 at constant pressures of about 50 cm as indicated on the P manometer. Four replicate determinations ranged from 0-004296 to 0.004320 cc per second per cm, the mean being 100.26 per cent. of the value by equation (4) or 100-33 per cent. of the desired nominal value of 0-004296 cc per second per cm.The same result was obtained for P values down to 5 cm. From equation (l), d,, is proportional to 4 C ; it is therefore probable that the error of the calibration is not more than 0.16 per cent. in terms of d,,. Further confirmation was sought by using the capillary tube to determine the tiYS’ of a standard Portland-cement sample No. 114j from the Xational Bureau of Standards, Washington, D.C., U.S.A. Chart errors were avoided by measuring F and L directly, as described above; the result was calculated from equation (2) after determining c from the measured dimensions of the capillary and gwing A the value found by measuring the sample-tube diameter. Duplicate results were 99.9 and 98-7 per cent. of the value, 5.755 p at E = 0-500, assigned to the sample by the Bureau, or 100.1 and 98.9 per cent.when calculated by the bubble meter calibration factor. The bubble meter and cement results confirm the calibration accuracy within the limits of their respective experimental errors. THE RUBY CALIBRATOR- Substituting measured values of F in equation (2) gave d,, results about 2 per cent. lower than the rubies’ labelled values. I t is possible that this discrepancy is due to the makers’ method of calibrating each production batch of rubies on a standard instrument that has itseli been calibrated against a fresh K.B.S. Portland-cement sample. If the chart d,, ordinates in the standard instrument have the -0.8 per cent. error reported above (Error in Measuring Flow-meter Pressure Drop), and that error is compensated at 5-5 p by calibrating the instrument against cement of that value at porosity 0-5, curve C in Fig.3 shows that the labelled value of a ruby, equivalent to 15 p at porosity 0.5, will be 2-15 per cent. high. PRECISION OF THE MODIFIED INSTRUMENT CONFIRMATION OF ACCURACY OF CALIBRATION Several calibrators were checked with the calibrated capillary tube. The over-all precision of d,, determinations depends on the precision of measuring or standardising the factors previously mentioned. In the treatment below, it is assumed that when a quantity is measured to the nearest graduation on a linear scale, the measurement error is distributed rectangularly, and that the standard error is equal to the scale interval multiplied by 41/12 for a single reading, or by d l j 6 for a measurement by difference.CALIBRATION BY THE MERCURY METHOD- The instrument constant, c, depends on the capillary radius and length. The precision of c therefore depends on weight and length measurements. The standard error of the Calibration, in terms of d,,‘, is k0.17 per cent. in the single-range, or +0-08 per cent. in the double-range, if weighings (of mercury) are made to the nearest 0.001 g, and length is measured to the nearest 0-002 cm (by travelling microscope). SAMPLE-TUBE DIAMETER- The error in d,,’, when D differs from its nominal value, can be corrected by applying factors calculated from the measured value of D. The standard error of the corrected dVB’, due to error in measuring D with a travelling microscope graduated to 0.002 cm, ranges from t-0-24 per cent.at porosity 0.80 to $_O-47 per cent. at porosity 0.40.312 EDMUNDSON CALIBRATION O F A FISHER A41R-PERMEARILITY [Analyst, VOl. 91 PRECISION OF dvS‘ DETERMINATION- The precision of d,,’, determined on a single modified instrument, with a singIe sample tube, depends on the precision of five successive operations : weighing the sample, standardising P a t 50.0 cm, setting the pointer to the sample-height line, setting the reference bar of the pointer to the flow-meter meniscus, and reading the dvS’ indicated on the chart by the pointer. Sample weight-Weighing to the nearest 0.001 g gives M a standard error of k0-03 per cent. when 211 = 1.5 g. This is smaller than the errors in other factors, but caution is necessary because this error must be multiplied by the factors given in Table I to obtain the standard error of dvs’, Air firesszrre-Tf the P-manometer levels are set to the nearest 0.1 cm, the standard error of P’ will be k0-04 cm.This error has been used to calculate the d,,’ error shown in Fig. 4, but greater precision can be obtained in practice. Since the manometer has no adjustment for the effective volume of contained water, it is impossible to set the pressure so that both menisci will coincide with scale graduations; if one coincides exactly, the other will fall at random between two graduations. But the 0.04 cm standard error can be reduced to the extent that the operator can judge both menisci to be equally displaced from the appropriate graduations. Sample height-The precision with which twenty operators could set the instrument pointer to the sample-height line was determined with a sensitive clock-gauge.The standard deviation from the mean setting was 0.003 cm, equal to one-fifth of the line thickness, or approximately equivalent to the limit of unaided visual resolutiong at 15 cm. The same error occurs in setting the zero; combining both errors gives the standard error of I , at porosity 0.5 as i 0 - 2 7 per cent. F-manometer settifig-In a similar clock-gauge experiment the standard deviation of the meniscus setting was 0.009 cm. This is larger than that for the sample height, probably because the parallax error is greater. The equivalent standard error of F’ is k0.026 cm. Chart dvS’ readiizg-The spacing between dvs curves on the chart is sufficient to permit visual estimation of the reading to the nearest one-fifth interval between successive curves.If we assume that such interpolation is accurate, the standard error of the reading will be +0.22/1/12 multiplied by the interval, in microns, between successive curves. This is the minimum theoretical error and has been used in the calculations for Fig. 4. After some training in recognising the appearance of the pointer in different positions between the curves, a careful operator can reduce the error to about 1.2 times the theoretical error. The individual and combined effects of these errors on dV,’ at porosity 0.5 are shown in Fig. 4. The P , F and d,, effects depend essentially on the F-manometer level. When the instrument is used in the double-range, a sample of given average paficle size produces an F level equivalent to half the average size, and the chart reading must therefore be doubled.Hence the double-range error curve is obtained by doubling the abscissae of the single-range curve. The steps in the d,, curve correspond to changes in the micron intervals between successive chart graduations. The precision for samples over 40 p can be increased, and the instrument range extended somewhat beyond 50 p, by using an over-weight sample in order to obtain a lower F reading and so increase the value of (P - 1;) in equation (2) ; the indicated E and dv,’ can be corrected for the excess weight by means of the equations given in an earlier paper.1° Since the curves intersect at 8 p, it is advantageous to use the double-range for all samples over 8 p at porosity 0.5.The precision of the modified instrument cvas determined experimentally by testing four weighed samples from each of six procaine penicillin batches. The batches were prepared by grinding one lot of crystalline material at different pressures in a fluid-energy mill; they were therefore similar in general characteristics but differed in d,,. Each batch was well blended to ensure uniformity between samples. Each weighed sample was tested at seven porosity levels obtained by compressing the same sample bed to successively lower porosities. The detailed results for one batch are shown in Fig. 5 (a), and are typical of the results for each batch. They show two kinds of random error, an instrument error revealed by the small scatter of the points for a given sample about a smooth curve drawn through them, and a larger error between samples.The results for each batch, expressed as the mean of four samples, are shown in Fig. 5 ( b ) , and show a trend towards a minimum dvs‘ at porosities between 0.56 and 0.48.May, 19661 APPARATUS FOR DETERMINING SPECIFIC SURFACE I I c C a, U L aJ a . > , l o - > -D 0 L L 2 -Y aJ -0 C 0 d": u i L U C (u L aJ a - L n > -3 0 L 0, 7 0) -0 C id CI I/) Single rang I I Double range I I I I I I I I I I 5 10 15 20 25 L-+-Lb+ Average 20 p a r t i c l e size 30 ( dy[, ),p 40 Average p a r i i c i e size (d,,:),~ O ] t Intersection at 8~ 313 Fig. 4. Precision of a single determination a t porosity 0.5 on a single modified instrument with a single sample tube as affected by the determined precision of: M , sample weight; P, air pressure; L , sample height ; F , flow-meter manometer setting; d,, chart reading.The effect of sample variability is not included. (a) Individual effects of the five factors in the single range ( b ) Combined effect (root sum of squares) of the five factors in the single and double range The combined effect of the instrument error and the error between samples is shown by the standard deviations of the sample results from their corresponding batch means, calculated separately for each porosity and expressed as percentages of the over-all batch means- Porosity . . . . . . . . 0.60 0.58 0.56 0.54 0.52 0.50 0.48 Over-all mean db.s' . . . . 7.96 7.80 7.70 7.70 7.71 7-72 7.72 Standard deviation, per cent.. . 4-73 3.13 2.99 2.74 3.17 2.98 3-49 The several sources of variation are isolated by the analysis of variance summarised The analysis is confined to the porosity range, 0.56 to 0.48, within which the in Table 11. porosity effect appears, from Fig. 5 ( b ) , to be negligible. TABLE I1 ANALYSIS OF VARIANCE OF dvs' RESULTS FOR 24 PROCAINE PENICILLIN SAMPLES AT FIVE POROSITY LEVELS (E = 0.56 TO 0.48) Degrees of Mean Significance Source of variation freedom square level Porosity . . . . . . . . 4 0-0023 not 'significant Batches . . . . . . . . 5 25.4231 0.1 per cent. Interaction . . . . . . 20 0.0021 not significant Samples within batches . . . . 18 0.2696 0.1 per cent. Error . . . . . . .. 72 0.0033 Total . . ..119EDMUNDSON : CA4LIBRATION OF A FISHER AIR-PERMEABILITY [Analyst, VOl. 91 I I I I I I I ‘ ?“I 0 56 0 52 0 18 Pot-OSl t y 1 I I I I I I 0 60 0 56 0 51 0 48 Porosity Fig. 5. Average particle size, dv8‘, of six pro- caine penicillin batches as determined after com- pression of each weighed sample to successively lower porosities, (a) single determinations on four weighed samples of one batch, showing a small within-samples scatter and a larger between-samples scatter. Similar scatter occurred with the other batches: (b) means of four determinations on each of six batches Instrzcment error-The square root of the error mean square (0.0033) is the standard error of the instrument (and the operator’s ability to read it) after eliminating the sample error and the variation due to porosity, batches and their interaction.Expressed as aper- centage of the over-all mean dvS’ for all batches in the porosity range, 0.56 to 0.48, it is -10.74 per cent., which agrees well with the estimate in Fig. 4 (b) if the small effect of M is neglected. Error betmeen sumpZes-The samples-within-bat ches mean square (0.2696) = 5 x samples variance - error mean square. Hence the samples standard error, excluding all other sources of variation and expressed as a percentage of the over-all mean dvS’ for allbatches in the porosity range 0.56 to 0.48, is 3.0 per cent. This is too large to be explained as weighing error. I t is probably due, not so much to inhomogeneity within batches of powder, as to variation in the uniformity of packing in successive sample beds as suggested by R i g d e ~ ~ The analysis of variance shows that the slight upward trend between porosity 0.56 and 0-48 is not significant.However, when the analysis was repeated over the range 0-60 to 0.48, the porosity effect was significant at the 0.1 per cent. level; the interaction between porosity and batches was also significant at the same level, indicating that the trend of dvS’ with porosity is not constant for all batches. DISCUSSION The calibration method described above is absolute in the sense that it standardises the instrument variables in terms of c.g.s. units, without depending on an external particle- size standard. It therefore permits an accurate measurement of sample permeability. The The porosity efect-Fig. 5 (b) shows that dvs’ varies with porosity.May, 19661 -4PPtlRATUS FOR DETERMINING SPECIFIC SURFACE 315 equation by which the Fisher instrument, like other apparatus such as those of Rigden or Lea and Nurse, relates permeability to mean particle size is adapted from the original Kozeny - Carman equation.ll All such instruments, if properly calibrated, should therefore give the same result for mean particle size. The question of the validity of the Kozeny - Carman relationship between permeability and particle size is not one of instrumental accuracy and is beyond the scope of this paper.In this respect, the X.B.S. Portland-cement sample is to be regarded as a permeability standard rather than a particle-size standard. The modified instrument approaches the standard Lea and Nurse a p p a r a t u ~ ~ 9 ~ in accuracy and precision, provided that the significant variables are standardised or calibrated as described.The ability to compress a single sample to successively lower porosities and obtain corresponding diameter readings is a further advantage of the Fisher instrument. Other workersl0?l2 have observed a variation of apparent diameter with porosity, and it has been suggested that the minimum diameter may have special significance. The effect can be observed more readily with the Fisher apparatus than with apparatus that requires separate sample weighings for each porosity level; with the latter, the combined sampling and instru- mental errors may obscure a trend in apparent diameter. The porosity level, 0.56 to 0-54, at which the apparent particle size is a minimum and the wide range over which the size is almost constant in Fig. 5 ( b ) , are characteristic of the particular batches used in this study; other batches and materials may show their minimum at a different level and over a narrower porosity range.1° I thank Mr. H. Gresley Grey for the analysis of variance, and Mr. J. W. Mitchell of the Fisher Scientific Company for information about their methods of calibrating standpipes and ruby orifices. I t has the additional convenience of permitting direct reading. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. REFERENCES Gooden, E. L., and Smith, C. M., Ind. Engng Chem., Analyt. Edn, 1940, 12, 479. Dubrow, B., Analyt. Chem., 1953, 25, 1242. Lea, F. M., and Nurse, R. W., J . SOC. Chem. Ind., Lond., 1939, 58, 277. Rigden, P. J., Ibid.. 1943, 62, 1 . Dubrow, B., and Nieradka, M., Analyt. Chem., 1955 27, 302. “Portland Cement,” British Standard 12 : 1958. Traxler, R. N., and Baum, L. -4. H., Physics, 1936, 7 , 9. Levy, A., J . Scient. Instrum., 1964, 41, 449. Hooke, Robert, 1674, quoted by Gage, S . H., “The Microscope,’’ Seventeenth Edition, Comstock Edmundson, I. C., and Tootill, J. P. R., Analyst, 1963, 88, 805. Carman, I?. C., J . SOC. Chem. Ind., Lond., 1938, 57, 225. Hutto, F. B., jun., and Davis, D. W., Off. Dig. Fed. Paint Varn. Prod. Clubs, 1959, 31, 429. Publishing Co. Inc., New York, 1943, p. 279. First submitted, March Ist, 1965 Amended, December 22nd, 1965