May, 1 9 1 i
T H E J O U R N A L OF I N D U S T R I A L i l N D ENGINEERING C H E M I S T R Y
DIRECTIONS FOR AwaLYsIs-The specific gravity of t h e ether is determined a t 2 j o / 2 5 O . From I O O t o zoo cc. are then placed in a flask, 30-50 g. KzCO8 added and the sample allowed t o stand 2 4 hrs., shaking occasionally. The specific gravity is then determined as before. This latter value, referred t o t h e lowest curve in Fig. 11, gives t h e per cent of alcohol in t h e dehydrated ether, which is very close t o t h a t in t h e original sample.' The intersection of a vertical line through this point with the horizontal line representing t h e specific gravity of t h e original sample corresponds t o t h e amount 1 A correction could be made for the amount of water removed, but since this correction would always be less than 0.05 per cent, i t will probably not usually he required.
I
523
of water in the ether. If this point falls on a curve, the per cent is known from the fact t h a t it is on t h a t particular curve. If it falls between two curves, the per cent is obtained by interpolation of t h e vertical distance between them. The amount of water can also be determined by use of Fig. I. Starting with t h e specific gravity of t h e dehydrated mixture, on the Y axis, an imaginary curve is drawn parallel t o the nearest curve until i t intersects t h e horizontal line representing t h e specific gravity of the original sample. These intermediate curves could, of course, be actually drawn, using values read from the curves in Fig. 11. 751 HAMILTON AVENUE, DETROIT, MICHIGAN
LABORATORY AND PLANT THE MEASUREMENT OF THE ABSOLUTE VISCOSITY OF VERY VISCOUS MEDIA By S. E. SHEPPARD
Received November 4, 1916
The determination of the viscosity, specific or absolute, of extremely viscous fluids, e . g., rubber, cements, nitrocellulose solutions, etc., is a matter of some difficulty. The usual transpiration (tube) viscosimeters are not suitable, and shearing viscosimeters of t h e Couette t y p e are only beginning t o be developed sufficiently in this direction, while t h e various commercial or industrial viscosimeters introduced in t h e oil industry have, perhaps happily, not been applied t o any considerable extent. T h e methods actually employed are mostly based either on t h e fall of a suitable heavier body (plummet) through t h e liquid or t h e rise of a suitable lighter body, e. g., oil, globule or air-bubble (Cochius). The values obtained have usually been taken as arbitrary .empirical standards, and little d a t a exist on t h e tech-
I
nical application of these methods, either for relative (specific) or absolute measurements of t h e viscosity coefficients. None the less, t h e fall of a n accurately spherical body of suitable density and size depending upon t h e absolute viscosity offers, by way of Stokes' law for t h e terminal velocity of fall of such a spherical body, a ready and fairly precise method for absolute measurement. The ground for this was broken in t h e investigation of Stokes on fluid motion. I n t h e case of a sphere falling under gravity in a viscous liquid, Stokes showed t h a t t h e terminal or steady velocity when t h e viscous resistance just balances t h e force of gravity depends only on the buoyancy and radius of t h e sphere and t h e inner friction or viscosity of the fluid. If X be t h e force acting on t h e sphere, and just balancing t h e resistance in t h e steady state
X = 6nKRV (1) where K = Coefficient of Viscosity, R = Radius of Sphere, and V = Velocity of Fall.
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
524
Now, X, t h e force acting on t h e sphere, = 4/3~R3( ~ s’)g (2) where s = Density of Sphere, s’ = Density of Liquid, and g = Gravitational Constant. 2gR2(s- s’) Substituting in ( I ) K = (3 1 9v
Stokes’ theoretical work was done in 1840-j, b u t t h e first experimental discussion of Formula (3) of any value appears t o have been made by H. S. Allen‘ in I 900. An extensive theoretical and experimental investigation on Stokes’ law was made by R . Ladenburg12 with results which will be noted immediately. H. D. Arnold3 has made a valuable investigation of t h e same problem, which is best discussed in connection with Ladenburg’s work. I have been unable t o obtain access t o a paper b y Flower.4 Arnold points out in t h e paper cited t h a t in t h e mathematical deduction of t h e original formula certain assumptions are made, notably: ( I ) T h a t the discontinuities of t h e fluid are small compared with t h e size of t h e sphere. ( 2 ) T h a t t h e fluid is infinite in extent. (3) T h a t t h e sphere is smooth and rigid. (4) T h a t there is no slip a t t h e surface between sphere a n d fluid. (5) T h a t t h e velocity of t h e sphere is small. As regards t h e first assumption, Cunningham6 has investigated theoretically a n d Millikan6 experimentally t h e effects of a violation. They have shown t h a t in t h e case of a very small sphere, falling in a gas, there is a considerable departure from t h e value by t h e simple formula. Arnold, working only with fairly simple liquids (oils of low viscosity) and comparatively large spheres, considered t h a t for his work t h e assumption was sufficiently justified. I n t h e case, however, of complex fluid media, of colloidal nature, such as those referred to, starch sols, gelatine and other albuminoid solutions, t h e industrial chemist frequently requires a fairly accurate mean value of t h e viscosity for solutions which may readily have internal discontinuities of considerable magnitude. If spheres very much larger t h a n these discontinuities are used, he may yet not have such ample quantities of t h e material a t his disposal as t o be able t o approach, with these larger spheres, fulfillment of t h e second assumption either in t h e absolute limit proper t o t h e simple Stokes’ law, or in t h e restricted form obtained by Ladenburg. The latter found7 t h a t if t h e liquid is contained in a cylinder of circular cross-section of radius R’ a n d of length L. t h a t t h e following modified form held u p t o a certain limit.
K
=
9
R2. g
V’
S ’= Length of Fall in Steady State T = Time of Fall of Length S 1
2 3 4
8 6
Phrl. Mag., 1900, 323. A N N . phys., 2a (1907). 2 8 7 ; a3 (igoi), 447 Phil. Mag., 22 (1911). 7 5 5 . Pvoc. A . S. T . M . , Part 11, 14 (1914). 591. Proc. R o y . Soc., ( A ) 8s (1910), 357. Phys. Reo., A p r i l , 1911.
7 L O G . C7l.
R/R’
=
R/L
=
V O ~9. , NO.5
Radius of Sphere Diameter of Sphere __ - __ _ _ _ ~ Radius of Cylinder Diameter of Cylinder _ _ Radius _ _ of _ Sphere _ _ _ _ _ ~ . Height of Liquid Column
Using this corrected form he obtained for t h e viscosity of Venice turpentine, with a series of steel spheres, t h e value K = 1343, whereas t h e value by Poiseuille’s law and t h e capillary t u b e method at t h e same temperature was K = 132j. This appears t o have been t h e first direct comparison of these t w o methods, a n d t h e agreement t o within 1.3 per cent shows, Arnold points out, t h e validity of t h e correctecl formula in t h e case of liquids of high viscosity. We shall return t o Ladenburg’s formula immediately. With regard t o surface slip, t h e position is as follows. Following Arnold, we may modify Stokes’ law by a n expression for t h e coefficient of sliding function, when \>.e have for t h e terminal velocity ‘I‘ ’I’=2gR2(s- SO QK ’
K I
+@R
+
2 K
which for @ = 03 reduces t o the original form, b u t for @ = o gives a value jo per cent higher. Experimentally, t o test this factor, it is necessary t o use a sphere of sufficiently small radius in a liquid of high viscosity. The simplification of t h e mathematical analysis, allowing t e r h s of t h e order of t h e square of t h e velocity (so-called inertia terms) t o be neglected, is only permissible when assumption (5) is obeyed. This can be shown t o hold only when t h e velocity i s small compared with
v
-.K
sR
The value of R for which
is called t h e critical radius a n d may be sR designated R,. Various observers have assumed t h a t t h e upper limit of radius for which t h e simple formula may be used is of t h e order =
R R, (Ladenburg) to -L (Zeleny).
-~
IO
4IO
E XP E RI M E I i T A L
The experimental results detailed in t h e following were not made with a view t o precision determination of t h e validity of Stokes’ law. simple or corrected, b u t t o find under what conditions it could be used for approximate determinations of t h e absolute viscosity of t h e very viscous media referred to. I t may be pointed out t h a t t h e determination of a n absolute value involves in itself no greater precisian t h a n t h a t of a specific or relative value of a physical constant. The essential point is t h a t t h e value is obtained directly from a function of t h e variables and in terms of absolute units, as ( h l ) , ( L ) , (T) = grams : centimeters; seconds. T h e requirements as t o precision depend upon t h e purpose of t h e determination, a n d may be less t h a n , equal to, or greater t h a n , those for a determination of a specific or relative value of a constant according t o t h e requirements in view. As readily obtainable rigid spheres of considerable precision of figure, steel ball bearings were used. Their dimensions were as follows:
T H E J O C R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
May, 1917
Weight Grams 1,0472 3.4754 8.3170
Diameter Diameter Precision Inches Mm. Per cent 6.35 10.04 . , l/g 9.525 10.03 2 ....... . . J i g +0.02 3 ...,.. I//* 12.70
NO.
1..,.. , ,
...
Volume Cu. in. 0.13406 0,45246 1,07249
525
Density 18O, 18’ 7.811 7.681 7.754
The specific gravity of hardened steel is stated t o be 7.6-7.8. 4 s corroborating t h e t r u t h of t h e spherical figure, t h e average deviation in weight of 6 balls of each size was determined. T h e results showed t h a t while t h e mean deviation was nearly constant, the per cent deviation was as follows: 3 ) 8 in. 1 2 in. Diameter., . . , , . . . . . , . . . . 1 in. ‘4
Per cent Deviation., , . . . . 1 0 .7 2
10.23
+O.OY
t h a t is, t h e deviation increases as t h e radius diminishes. Remembering t h e note on t h e increment of importance of rotational movements with other t h a n true spheres, i t will be el-ident t h a t diminution in radius may be pushed too far, in t h a t sphericity is liable t o become steadily diminished with decreasing radius, as well as less amenable t o direct determination. ~ E T H O DO F E X P E R I D T E X T
I n all t h e experiments t h e liquid, a very \-iscous solution of nitrocellulose, was contained in a graduated cylinder of some 40 cm. height, standing in a water jacket a t z o o C. T 0.2. The spheres were allowed t o drop asially, a variety of releases being employed as, e. g., iris diaphragms, etc., but these were found t o be without influence on t h e time of fall in t h e liquid. Time was recorded with a stop-watch reading t o sec. and checked on a standard chronometer. Parallax in observing t h e transit of t h e sphere past t h e selected upper and lower graduation marks on t h e cylinder was avoided b y having fore- a n d hindsight-lines outside t h e cylinder aligned in the same planes with t h e marks in question. I X F L U E X C E O F T H E DIAMETER
T h e next factor investigated was t h e influence of t h e cylinder wall or boundary, upon t h e time of fall, other things being equal, or more exactly, t h e influence of t h e ratio, diameter of cylinder t o diameter of falling sphere, upon t h e experimentally obtained “time of fall” through a fixed measured height, i. e., upon t h e steady velocity. It was soon apparent t h a t this influence is very considerable, only becoming negligible when t h e ratio in question becomes very large, or approaches infinity. This is shown in fact by t h e following figures for a 1 , ’ 4 in. sphere a n d 1 9 . j cm. “fall” distance. Ratio . . . . . 1.810 2 . 2 3 5 3.670 5.245 5.672 7.875 9.340 12.51 Time (sec.) 270.0
162.7
81.7
62.6
58.0
51.0
50.0
48.3
It will be evident t h a t as R’/R = ratio of cylinder diameter (or radius) t o sphere diameter (or radius) increases, t h a t t h e “time of fall” or the “velocity value” tends t o approach a constant value. Compare t h e curves for t h e three spheres of different diameters. As already stated, Ladenburg’ has introduced a correction t e r m for t h e influence of this factor, into t h e Stokes equation, which makes this become: K = 2RZ(s- s’)T
+ 2.47r) ~
~ s ( I 1 LOC.
Lit.
’
Where Y = R’/R, ratio of cylinder t o sphere diameters, and t h e other symbols have t h e significance already defined. This expression was found satisfactory b y both Ladenburg and A4rnold within t h e limits of Y which they employed. I n t h e present case, t h e expression was found t o have only a very limited range of validity, as will be seen from t h e following data: 3/s I N . DIAMETER ‘ 1 2 Ih.. DIAMETER I N - . DIAMETER K, Reciprocal K‘ Reciprocal K‘ Reciprocal of 7 (Ladenburg) of 7 (Ladenburg) of I (Ladenburg) 0.0798 311 0.1198 276.7Mean 0,1597 264.1 0.107 305 M e y 0.1198 281.5 K’ 0.2141 281.5 0.127 300 K 0,1905 282.1 0.254 301.5 0.1762 312 0.2645 311.0 0.3535 397.0 0.1922 328 0.286 330.5 0.381 422.5 0.2723 378.5 0.408 419.5 0.545 705.0 0.4465 603 0.670 1068.0
The only factor varied in each set being r , t h e variation of K’, t h e viscosity constant must be attributed t o t h e insufficiency of Ladenburg’s correction for anything b u t a limited upper range of values of r approaching ; actually in all Ladenburg’s experiments r was greater t h a n IO. Further, i t will be seen t h a t his expression will not satisfy the condition t h a t T’ (corrected time of fall) becomes infinite for r = R ’ / R = I , but instead, as T’ (Ladenburg) = T / I 2.4,~ approaches a constant fixed value T/3.4 which is entirely incorrect, a n d gives real 7-alues for r = R ’ / R > I , which is absurd. While then his formula is satisfactory under t h e condition employed both b y him and by Arnold, i t does not appear so for t h e wider range used in t h e present experiments. A further correction worked out b y Ladenburg, for t h e influence of t h e total height of liquid in t h e cylinder, will be dealt with subsequently; it is independent of t h e factor and d a t a first discussed. The d a t a obtained with t h e three spheres a n d a considerable range of cylinders of t h e same height b u t varying diameter, were plotted as graphs with T = time of fall as ordinate, r = R’,’R as abscissa. Since t h e values for each sphere fall on a smooth curve, a n d
+
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
526
-
= IN. 6.35MM. Fall length S 19.5 cm. Corrected Time of Fall over Length S Tm = T - 268 L 45 (, 1) P. 2R’ Viscosity Coefficient = K -(s--s’).g 9s
S E R I E S I-DIAM. OF SPHERE
- (I=id C
No. - .
Ratio r
1
2.
2
3.
3
4.
4
5.
5
6.
6
7.
7
8.
TIMEIN
SECONDS T Found Calc. Secs.
K
AK Per AK cent
’
8
9.
9
10.
10
11.
11
12.
12
13. ..............
.
2 0.4 20.50 .........
-2.0
T=T,
where T,
+
( Y - I)” = constant value of
T for
Y
=
00
= R’/R (ratio of diameters)
C and 1z are constants Taking t h e exponent 1z as I , 2 , 3, etc., in t u r n , t h e formula reduces t o a 2-constant interpolation formula, easily tested by trial. Actually, with a value ~t= 2, t h e expression T = Too C / ( Y- 1)2 was found t o represent t h e results very satisfactorily, as will be seen from t h e accompanying tables and the curves given. The three correction equations for t h e time of fall are:
+
(I)
T
(2)
T = 20.03
(3) T
= 46.19
+
268.45 for (Y
in. sphere
- I)2
+ 72.28 for = 10.685 + 45*86 for (r - I)2
8/8
(Y
I)2
in. sphere in. sphere
T h e constant C of t h e correction equation may be conveniently termed the “lag.” As will be seen, it diminishes as t h e diameter of t h e sphere increases, a n d in fact, within t h e range investigated, appears roughly t o approach inverse proportionality to t h e mass of t h e sphere. Diameter
.............. 9.525 6.35 mm. .............. mm. ............ 12.70,mm.
1 2 3..
AK
AK Per cent
332
-7.0
-2
-3
-0.9
327
-12
-3
316
-23
-6
338
-1
4 . 3
342
$3
10.9
Wt. in grams 1.0472 3.4754 8.3170
0
C 268.45 72.28 45.86
C X Weight 281 252 380
-
TIMEIN
SECONDS T Found Calc. Secs.
16.2
15.78
13.1
13.55
12.0
12.52
11.9
11.96
11.6
11.41
11.4
11.25
11.3
11.15
11.2
11.07
11.1
11.01
.. -
0
339 0 0 -20.03 339.1 - 9 . 3 -2.7
-
..
-
-
( --
-
Mean value of Tm = 20.03 secs. 9. Mean value of K = 339
t h e curves are quite similar for t h e three spheres, i t appeared possible t h a t a n empirical formula for t h e function T = f(R’/R) might be obtained, giving a satisfactory expression for t h e influence of t h e cylinder wall upon t h e terminal velocity. It is evident from inspection of t h e curves and consideration of limiting conditions, t h a t t h e function sdught must s a t i s f y T approaches 03 for R’/R = Y = I T approaches constant for R’/R = r = 00 These conditions would be satisfied by a function of t h e type: C
No.
K
’ 339 46.187 358 - 8 Mean value T m = 46.19 secs. Mean value of K = 358 =f 8.
Y
(
TIME IN SECONDS T Found Calc. Sece.
-
SERIES III-DIAM. OF SPHERE = IN. 9.252 MY. Fall Length S 19.5 cm. Corrected Time of Fall over 45 86 T m = TLength S (r 1)s. 2R* Viscosity Coefficient K = 9s (S d).g T (r 2 1 ) s )
- --
-
-
(T
-
SERIES 11-DIAM, OF SPHERE = IN. = 9.525 MY. F d Len h S = 19.5 cm. Corrected Time of Fapover Length S = 72.28 l ) ~ Viscosity . CoeffiToo = T 2R’ C cient K = -(s-s’).g T-- (r-l)2) 9s
Vol. 9, No. 5
__
K
AK Per
AK
cent
10.18 325 - 5
-1.5
10.05
-7.0
306 -24
11.69
356 +26
+7.0
11.51
350 +20
+6.0
10.70
326 4 -1.3
10.81 329 -1
-0.3
10.75
4 . 5
327 -3
10.61 323 -7
-2.0
-- --
10.085 330 - 9 . 9 - 2 . 8 Mean value of T m = 10.685 secs. Mean value of K = 330.1 T 9.9.
I N P L U E N C E O F T H E T O T A L HEIGHT O F L I Q U I D
T h e values compared for t h e viscosity-coefficient K using Stokes’ formula, with t h e time of fall corrected t o T oo by t h e expression just discussed, i. e., = 2/9R2(S v ”Ig,where Sphere Diam. 1/4 in. */a in. ‘/a
in.
K Abs. viscosity a t 20’ C. 358 4 8 . 0 339 7s 9 . 0 330 9.9
-
V
=
S/T, were: K / k , relative to water a t 20‘ C. 3.58 X 10‘ 3.39 x 104 3.30 X 10‘
It will be seen t h a t t h e values of K although constant in t h e same series for one diameter of sphere and varying cylinder radius, show some tendency t o diminish a s t h e diameter of t h e sphere is increased. Now in all t h e experiments t h e total height of liquid was t h e same, viz., 40 cm., and it appears probable t h a t this falling off may be due t o a similar effect t o t h a t from t h e wall, b u t in this case due t o “reflection” from t h e bottom of the cylinder and t h e surface layer of the liquid. This effect was in fact taken u p by Ladenburg in t h e second of his two papers cited, a n d he applies a second, independent correction term similar in form t o t h e one for t h e cylinder wall: 3.3R/L) V‘ = steady velocity = S(1 T where S = fall length T = time of fall R = radius of sphere L = total height of liquid. The multiplier of t h e term R / L depends considerably upon t h e experimental conditions-in Ladenburg’s case, t h e cylinders were 24 cm. long and t h e fall length was the middle I O cm. I n t h e present investigation, t h e height of liquid was 40 cm., t h e fall length 19.5 cm., in all except certain special experiments a t nearly I O cm. from t o p and bottom of t h e liquid column respectively. The values of R/L for t h e three spheres were:
+
Sphere Diam. 6.35 mm. 9.52.5 mm. 12.70 mm.
R/L 1/126 1/84 1/63
L/R 126 84 63
L
-
40 cm.
May, 1917
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
I n view of t h e order of magnitude of L / R , as compared with t h a t of R’/R in these experiments (see previous section) it appeared probable t h a t a correction of t h e linear form, as used by Ladenburg, would be satisfactory; t h a t is, t h e values of K found are multiplied by t h e terms (I b.R/L) where b is a constant and R / L is t h e particular value of t h e ratio of radius of sphere t o height of liquid column, t o give t h e corrected value K. I n this caqe three equations are obtained, for two unknowns, b a n d K. The mean value of b by solution of these was 11.65, and the corresponding values of K’ were:
+
Sphere Diam. l / k in. ‘ / 8 in. i/a in.
K
R/L 1/126 1/84 1/63
358 339 330
K’ 391.2 386.0 392.0
Mean K’
389.7
On t h e other hand, by plotting K (uncorrected for height) as ordinate, R / L as abscissa, and extrapolating t h e closest fitting straight line t o cut t h e K-ordinate, giving t h e value K for R / L = o or L / R = w , t h e value K = 386.5 was obtained. Hence, t h e corrected values are: Ht. correction applied By formula.. . . Graphically.. ,
R
.......... ... .. 389.7 386.5
k (viscosity relative to water at 20’) 3 9 x 10‘ 3 87 X 10‘
The correction for t h e length of height of t h e tube appears rather large, and further work is planned using a wider range of values of L / R , t o test t h e validity of t h e linear correction more precisely, as well as a comparison of t h e method with t h e “shearing” t y p e of viscosimeter. While t h e viscosity found is very high, it is less t h a n t h a t of t h e turpentine solution of colophony used by Ladenburg (K 1343) a n d was shown t o be of t h e right order by a comparison with castor oil, a t the temperature given 2 0 ’ C., which made our medium t o be 3.1 times the viscosity of castor oil which, a t = 10,000K,,,.l
20’
Hence by this t h e viscosity of our medium would be some 31,000 times water. The viscosity of “castor oil” varies considerably b u t t h e comparison shows t h e result is of t h e right order. SUMMARY
I-The application of Stokes’ law t o viscosimetry is discussed, particularly for very viscous media, and with special reference t o t h e influence of t h e wall or boundary of t h e containing vessel. 11-An empirical formula correcting for the influence of t h e wall of a cylinder is obtained which is valid over a wide range. III-uSing this formula and a linear correction for t h e influence of t h e total height of the liquid column, determinations of the absolute viscosity of very viscous n - ~ d i amay be made with relatively simple apparatus, by application of Stokes’ law. T h e author’s thanks are due t o Mr. W. H. Davis for help in t h e experimental work, a n d t o Mr. S. Tompkins for assistance in t h e computations. RESEARCH LABORATORY EASTMAN KOUAKCOMPANY ROCHESTER, NEW YORK 1
Landolt-Bornstein, 4 Auflage, p. 75.
527
A SIMPLE DEVICE FOR THE AUTOMATIC AND INTERMITTENT WASHING OF PRECIPITATES By ELBERTC. LATRROP Received January 31, 1917
The accompanying illustration shows a simple and efficient form of apparatus for t h e automatic, intermittent washing of precipitates. The feature which distinguishes this apparatus from t h e well-known constant level device is t h e capillary tube (represented in t h e figure by heavy black lines), t h e function of which is not only t o permit air t o enter t h e inverted flask, b u t also t o produce a n intermittent flow of solvent from t h e flask. The principle underlying t h e use of t h e capillary tube may perhaps be best explained by a description of the operation of t h e apparatus. Suppose t h a t t h e apparatus is set up as shown, with t h e end of t h e capillary tube, which is full of solvent, just touching t h e surface of t h e solvent in the funnel, and t h e other tube, which in t h e apparatus used has been about 5 mm. in diameter, just touching t h e surface of t h e settled precipitate. As t h e solvent passes through t h e precipitate and out of t h e funnel t h e level of the liquid above t h e precipitate will fall below the end of t h e capillary tube. Air will not pass into t h e inverted flask, however, until t h e level of liquid in t h e t’ a point such that the has differences of hydrostatic pressure in t h e two tubes is sufficient t o overcome t h e force of capillarity, \ which tends t o keep the capillary t u b e filled with water. In the apparatus as drawn, this point lies just above t h e end of t h e large tube, so t h a t t h e precipitate is almost bare of solvent thus permitting each addition of solvent t o drain from t h e precipitate, t h e most efficient method of freeing a precipitate from soluble substances. When this point on t h e large t u b e is reached t h e air rushes into t h e flask through t h e capillary tube, the funnel fills again with solvent, which finally reaches t h e end of t h e capillary t u b e a n d cuts off t h e air supply, the t u b e filling with liquid due t o diminished pressure within t h e flask. The process then repeats itself. Experiment has shown t h a t t h e vertical distance from t h e end of t h e capillary t u b e t o t h e point on t h e other tube, a t which t h e pressure just overbalances t h e capillarity, is just a little greater t h a n t h e height of capillary rise. The pressure required t o pull air through a capillary tube full of liquid depends on t h e size of t h e capillary opening and on t h e nature of t h e liquid. I n practice, t h e author, after allowing the precipitate t o settle on t h e filter, measures t h e vertical distance from t h e lowest point on t h e surface of this precipitate t o t h e t o p of t h e filter paper, and selects - for use a capillary t u b e having a capillary rise for t h e given solvent equal in length t o this distance. T h e total length of t h e capillary t u b e should be a little greater t h a n t h e capillary rise. The author has
