M a r . , 1913
T H E J O r R S A L O F I L V D U S T R I A L AL%-DE L V G I S E E R I S G C H E ; I I I S T R Y
A NEW VISCOMETER FOR GENERAL SCIENTIFIC AND
TECHNICAL PURPOSES1 By I:UGE\L C B I s G H 4 v Keceiied S o ~ e r n h e r2 5 , 1913
Bingham a n d TThite2 have already published a description of a viscometer mTith which absolute viscosities can be measured v i t h very great certainty. This form of a p p a r a t u s is easily made, b u t since t h e dimensions of t h c apparatus must be accurately knorx-n f o r absolute measurements, t h e time consumed in t h e calibration is considerable. So for general purposes i t is preferable t o calculate t h e a b s o l u t e z'lscosifies f r o m w?casureiizeizfs which are only relatiee. :By this procedure not only is t h e calibration simplified b u t t h e a p p a r a t u s itself m a y be made simpler a n d less delicate t o handle. It will be urged t h a t viscometers in great number have already been devised for relative measurements. W h y another one? T h e answer is t h a t relative measurements are comparatively valueless unless t h e results can be calculated t o absolute units. I t has been supposed t h a t t h e relative measurements obtained b y t h e use of instruments of t h e Ostwald t y p e might be calculated t o absolute units without difficulty. This is not generally t r u e a n d t h e reason is not f a r t o seek. I n t h e viscosity formula for calculating absolute viscosities" _ 71 -_ -st 710
sot0
which seems t o be almost universally used, no account is made of t h e loss of t h e kinetic energy of t h e liquid within t h e capillary, this energy disappearing outside of t h e capillary without helping t o overcome viscous resistance within t h e capillary. Furthermore, it can be shown4 t h a t this correction does not come into t h e calculation in such a way t h a t i t m a y be made t o disappear. 1-iscometers of t h e ordinary t y p e are deficient because t h e pressure producing t h e floIv through the capillary is not variable at will. The result is t h a t with s-ery fluid substances t h e kinetic energy correction becomes large unavoidably, a n d with rather x-iscous substances t h e t i m e of flom becomes intolerably long, necessitating t h e use of several instruments. Ivith il very lollg period of flom the difficulties due t o clogging with dust particles become very great. Applebeyj h a d shol17n that mith rarying pressures, formula, for a particular t h e sTalues of st in t h e liquid, are only constant the tilne of flon7 is rather great-for his particular instrument of the Ostx%.valdtype, a t least sis minutes, But \\,ith such sluggish flow he found t h a t "in spite of all precautions, the tubes frequently became contaminated J\.ith dust,,, specific T h e necessity o f t h e knolr-ledge of t h e gravity of the liquid at each temperature a viscosity measurement is desired lessens t h e convebearing on this subject, cf, Physical Twentieth ~ e ~ i35e (~i 9 1, 2 ) , 4 0 i . I b i d . . K. S. 36 (1913). ~ 6 z. ; p h y ~ i k .Chem., 83 (19131, 641;J . Chcm. .Soc., 103 (1913), 959; J . P h y s i c a l C h e w Feb. (1914). 2 Z.p h y s i k . Chem., SO (1912), 670. 3 so, and t o represent t h e viscosity, density a n d time of eRlux of t h e liquid which is taken as standard: ?, s, a n d t are t h e corresponding quantities for t h e liquid to be measured. 4 J . Chem. Soc., 103 (1913), 959 5 I b i d . , 97 (1910), 2000.
233
nience of this t y p e of instrument. Both t h e unreliability a n d t h e inconvenience of these instruments m a y be avoided b y using- variable aressure. T H E P R O P E R D I 1 \ I E K S I O S S O F Ah- .APPARATUS F O R J I E A S U R I N G VISCOSITY
T h e question of t h e proper dimensions of t h e apparatus should merit more attention t h a n is usually gil-en t o this subject. X s t u d y of t h e best viscosity d a t a leads one t o believe t h a t a n accuracy of one-tenth of one per cent can readily be attained. If one desires values r i t h a smaller limit of error t h a n one-tenth of one per cent he should undoubtedly make absolute a n d not relative measurements. There does not exist t h e necessary experimental d a t a for standardizing a n d testing a relative instrument for such a high degree of precision. We, therefore, assume t h a t a relatii-e instrument m a y be depended upon only t o one-tenth of one per cent a n d t h a t until our d a t a are amplified, t h e absolute method must be used for measurements of higher precision. ST-ith a stop-lvatch reading t o 0.2 see. t h e time, of flo~x-m a y be made as small as 2 0 0 set. The ~ - 0 l u m e small f o r t h e folloiving reasons: of f l o l ~ should (I) T h e \-elocity of t h e liquid lyithin t h e capillary should be 1 0 1 ~in order t h a t t h e kinetic energy correction m a y be kept f r o m beconling inconveniently large. ( 2 ) T h e time of flow should be small in order t o economize time, a n d in order t h a t t h e temperature may be t h e more easily kept constant during t h e time of flow. (3) Smalf masses of liquid come t o t h e temperature of t h e b a t h more quickly. ( 3 ) There is also a n economy of material. The minimum volume of flow is determined b y our ability t o read t h e volume with t h e desired accuracy. This in t u r n is determined b y t h e diameter of t h e constricted portions of t h e apparatus above a n d below t h e measured volume. If, however, bore, the the constricted parts have x-ery of capillary action becomes disturbing. I n particular, very riscous liquids do not drain o u t of t h e Capillary. a meniscus is formed bridging across t h e capillary a n d Opposed to that causing the a pressure is set a n d t h e results of t h e measurement are t h e n quitc d u e l e s s . T h e troubles due t o bad drainage may be minimized by having t h e drainage surfaces everywhere as nearly vertical as possible. I n other m r d s t h e change f r o m the constricted tube to t h e tube Of larger diameter should be made gradually. A constricted p a r t with a bore of 0.2: cm. would have a volume of nearly 0 . 0 : cc. per centimeter of length. L q ~ ~ ~ l m i ~ l : : t h a t as t h e meniscus passes t h e marks. i t can he rend t o 0.01 cm. i t is only necessary t o have a 1-olume of 0 . 5 cc. b u t in order t o provide a margin Of safety in t h e construction a n d use of t h e apparatus, we have Of "K' chosen 3 cc' as t h e Testing for a n y error due t o f a u l t y drainage is easily accomplished. It is only necessary t o test t h e f l o ~ ~ of t h e most yiscous liquid t o be measured, using J7ery different rates Of transpiration. Lack Of perfect drainage - will shovi itself b y t h e substance appearing t o be more viscous a t t h e lower r a t e of flow. Generally t h e more viscous liquids must be allovied t o flow
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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
slowly enough so t h a t t h e drainage will be complete. I n t h e test here given, t h e drainage may conceivably appear t o be perfect or even ultra-perfect. B u t this can be t h e case only when t h e flow begins with t h e meniscus of t h e liquid considerably above t h e upper mark, in which case t h e transpiration volume will be increased b y a certain amount caused b y drainage f r o m t h e surfaces above t h e mark. This gain in volume will t e n d t o offset t h e loss of a p a r t of t h e transpiration volume which fails t o pass through t h e capillary during t h e determination. Hence, i t is highly advantageous t o have t h e shape of t h e apparatus above t h e upper mark similar t o t h a t above t h e lower mark so t h a t these effects may as nearly neutralize each other as possible. T h e ends of t h e capillary are made trumpet-shaped in order t o aid t h e drainage by avoiding horizontal surfaces a n d also in order t o avoid t h e sharp corners on which filter shreds might get hung, causing clogging. I n making absolute measurements, i t is customary t o use a horizontal capillary. T h e theory for an inclined capillary is somewhat more complicated, b u t for relative measurements there appears t o t h e author no reason against its use. There are some i m p o r t a n t advantages t o be gained b y t h e use of a vertical capillary. I n t h e first place it is desirable t o use a long capillary in order t h a t t h e radius of t h e capillary may be relatively large a n d t h e kinetic energy correction relatively small a n d t h a t a n y possible effects of t h e ends of t h e capillary may be negligible. T h u s only with a vertical capillary may t h e limbs be kept close together, so t h a t a n y small error in keeping t h e limbs exactly vertical will not so seriously affect t h e hydrostatic level in t h e instrument. Furthermore, t h e apparatus may be made stronger a n d more convenient t o handle, a n d a smaller b a t h is required t o hold it. It is not desirable t o use a bent capillary, not only because of t h e unknown effect of t h e centrifugal forces b u t because of t h e danger of constrictions in t h e capillary a t t h e bend. Since t h e velocity of flow varies a s t h e fourth power of t h e radius, i t will be greatly increased by a small constriction, a n d eddy currents will be formed a t a relatively low r a t e of transpiration. T h e kinetic energy correction will also be correspondingly increased. E d d y currents cannot be tolerated even in a relative instrument a n d t h e kinetic energy correction should be kept low. T h e pressure should be variable a t will so t h a t t h e time of flow may be kept reasonably constant. There need be no upper limit t o t h e pressure, since liquids are practically incompressible. A pressure of jo grams per sq. cm. can easily be read t o 0.1per cent on a water manometer, hence this m a y be t a k e n as t h e lower limit. AS already pointed out, a long capillary is desirable, b u t since it is difficult t o get a capillary of a n exactly specified bore, it is best t o pick a capillary of approximately t h e desired radius a n d then t o cut t h e length t o fit t h e other dimensions. Assuming t h a t 2 0 cm. is a convenient length, Fig. I is given t o show just what lengths should be taken from capillaries of differe n t radius, t h e values being calculated by means of
Vol. 6 , No. 3
equation ( I ) , using t h e above dimensions t = 2 0 0 sec., p = 5 0 grams per sq. cm., a n d V = 3 . 0 cc. o n t h e assumption t h a t t h e highest fluidity t o be measured is 500. There is no object in following t h e current custom of using a variety of viscometers in measuring liquids of considerably different fluidity. All t h a t is necessary is t o have a sufficient range of pressures a t one’s disposal. Of course, if one is not going t o measure t h e viscosity of very fluid substances like ether
erm. ‘i.0
30
4 $20 Q-3
F J
IO
4 0
.os
.lo
FIG. 1.
.rR
, I + .16 RodLUS
.18
-20
Lengths required from a capillary of given radius, assuming the minimum values o !=ZOO, $=SO, and V = 3 , (A), when the maximum fluidity to be measured is 500, and (B), when the maximum fluidity to be measured is only 125.
a n d hexane i t may be best t o construct a n instrument which will require lower pressures, near t h e minimum of 50 grams given above, b u t this is purely a matter of convenience. I n curve B of Fig. I we give t h e lengths required with capillaries of different radii on t h e assumption t h a t t h e highest fluidity t o be measured will be only 1 2 5 absolute units. T H E C O N S T R U C T I O N OF THE A P P A R A T U S
T h e appearance of t h e viscometer is shown in Fig. 2 as drawn t o scale. T h e capillary is made in two p a r t s E F a n d G H , from non-soluble glass. T h e transpiration volume is contained between t h e t w o marks B a n d D. I n constructing t h e a p p a r a t u s i t is very important t h a t t h e volume of C should be similar in shape, equal in volume t o t h e volume K , a n d moreover, i t is important t h a t their centers of mass be a s nearly a s possible a t t h e same elevation. This is done in order t h a t t h e average resultant hydrostatic head of liquid within t h e instrument during t h e time of flow may be as nearly negligible a s possible. It is also important t h a t t h e volume A B should be equal t o t h e volume H J . As t h e viscometer is made of t h i n glass in order t o facilitate t h e passage of heat a brace is p u t in between t h e right a n d left limbs of t h e instrument in order t o strengthen it. This viscometer m a y be obtained from Eimer a n d Amend of New York. A diagrammatic arrangement of t h e apparatus is shown in Fig. 3. The viscometer V is shown in a b a t h which also contains a thermometer, stirrer, etc. At M a n d N are two three-way cocks for connecting one limb of t h e viscometer t o t h e pressure while t h e other is turned t o air. After a measurement, t h e position of t h e cocks is reversed a n d a duplicate observation is made or both cocks may be turned t o air. A drying device is shown a t D, and a reser-
Mar., 1914
T H E J O U R N A L OF ILVDL;STRIAL A N D ENGINEERING C H E M I S T R Y
voir for keeping t h e pressure constant is indicated at A . F o r this purpose a large glass bottle will serve, b u t particularly for t h e higher pressures a n ordinary gas t a n k , wrapped in felt t o keep t h e temperature steady, is convenient. T h e manometer E is conveniently filled with water b u t at t h e higher pressures mercury is required. I t is best, therefore, t o have t w o manometers, either of which m a y be connected t o t h e pressure a t will, b u t only one is shown in t h e figure. It has been found most convenient t o read t h e manometer on a steel t a p e supported vertically against a By strip of plate glass mirror. bending both limbs of t h e manometer in such a way t h a t t h e upper half of t h e right limb is directly above t h e lower half of t h e left a n d closed limb only one t a p e is required a n d t h e measurement is t h u s simplified. T h e upper p a r t of t h e closed limb is prolonged upward so t h a t all danger is obviated of t h e liquid in t h e manometer being drawn back into A or D when t h e pressure is removed. As shown in t h e figure, t h e pressure is obtained from a t a n k of compressed gas, B , b u t i t m a y be obtained b y means of a n aspirator. a h a n d p u m p , or b y means of a head of water. Generally i t is necessary t o have a check-valve, F , t o hold t h e pressure once obtained. T h e right limb consists of tubing of very small diameter while t h e left limb is of large diameter. A little mercury a t t h e b o t t o m allows t h e easy passage of air t o t h e left b u t n o t toward t h e right. I n making viscosity measurements b y t h e variable pressure method, it is neither necessary nor desirable t o have every possible pressure a t one’s It is better t o have only a few considerably disposal. differing pressures. I t is desirable, therefore t o have a device for giving constant pressures a t t h e desired intervals. Such a n arrangement is shown at G. T h e right limb is of large bore a n d contains a liquid through which t h e excess of gas rises in a fine stream. Other smaller pressures are obtained b y allowing t h e gas t o pass through t h e cocks I, 2, or 3. It is often desired t o measure t h e viscosity of a liquid above its ordinary boiling point in which case t h e cocks M a n d N must n o t open t o air a t P b u t , together with t h e open e n d of t h e manometer, t h e y must lead t o a low pressure reservoir, C. T h e air i n this reservoir is maintained at a constant pressure b y means of t h e second pressure regulator H like t h a t at G. T h e dotted p a r t of t h e a p p a r a t u s is not essential t o t h e manipulation under ordinary conditions. All of t h e p a r t s except t h e viscometer a n d t h e manometer m a y be made of metal so as t o withstand high pres-
235
sures, b u t glass tubing with rubber connections will serve for ordinary conditions. If one is working at other t h a n atmospheric pressure, i t is unnecessary t o a d d t h a t another manometer is essential if t h e pressure within t h e reservoir C must be exactly known. THE M A K I S G O F A V I S C O S I T Y MEASUREMEXT
After thorough cleaning, t h e apparatus is rinsed out with pure, dust-free water. If other liquids t h a n water are t o be introduced, dust- a n d grease-free alcohol a n d ether, a n d dry air which has been passed through cotton m a y be used for drying. Thc: liquids m a y be regarded as satisfactory when dust particles cannot be seen when carefully examined in t h e direct rays of t h e sun. T h e a p p a r a t u s is t h e n partially filled n-ith t h e pure liquid t o be measured, t h e liquid being introduced
.:i./a.,.
3
,,.
nm,.,,,,.rr.,;i:;
.....
3
into t h e right limb. Pressure is now applied t o t h e right limb a n d as t h e liquid passes into t h e left limb care is t a k e n t h a t n o bubbles remain in t h e apparatus. Finally t h e liquid runs over into t h e t r a p a t A . Making sure t h a t t h e temperature is adjusted properly, t h e liquid is allowed t o r u n into t h e t r a p until t h e lower meniscus reaches exactly t o t h e point H , when i h e pressure is removed, t h e cock N being t u r n e d t o air. If much liquid is in t h e t r a p i t m a y be removed. T h e remaining liquid in t h e apparatus is t h e “working volume, ” so-called b y Thorpe a n d Rodger.‘ Keeping t h e temperature constant, t h e left limb is now turned t o pressure a n d while t h e meniscus falls from A t o 1
Phil. Trans., 18SA (1894). 3 9 i .
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
236
B t h e pressure a n d temperature of t h e manometer are read. As t h e meniscus reaches t h e point B t h e time record is begun a n d closed when t h e meniscus reaches t h e point D. T h e pressure a n d temperature are again read after which t h e left limb is immediately turned t o air, before t h e point E is reached. T h e liquid is now in exactly t h e position for a duplicate reading in t h e reverse direction. On account of t h e change in volume on heating, i t is necessary t o adjust t h e working volume after each elevation of temperature. It is evident t h a t t h e duplicating observations in reverse directions will not be identical even if t h e pressure as read on t h e manometer is t h e same, unless t h e effective hydrostatic head within t h e instrument is equal t o zero. In constructing t h e instrument it was intended t o make this as small as possible, a n d b y making a series of observations with a liquid of known specific gravity a t constant pressure a n d t e m perature, it is easily possible as shown later t o calculate t h e correction for a n y failure in t h e construction. Naturally water is t h e liquid which one would select for t h e purposes of calibration. T h e viscosity of water is better known t h a n t h a t of a n y other liquid a n d for convenience t h e values obtained by several observers for t h e fluidity of water have been grouped together in Table I. I t is important t o emphasize TABLE I-THE FLUIDITY OF WATERAT VARIOUS TEMPERATURES AS MEASURED BY DIFFERENT OBSERVERS
Temperature
Fluidity h_
c
55.3 56.2 55.8 55.9 55.9 ... 65.6 65.9 5 65.6 66.2 10 76.1 76.5 76.4 76.9 76.6 ... 87.6 87.7 15 87.4 87.9 20 99.2 99.8 99.1 99.4 99.4 . . . 1 1 1 . 8 111.7 25 111.6 112.0 30 124.5 125.4 124.7 125.0 124.8 . . . 138.3 138.5 35 138.1 138.9 40 152.2 153.2 152.2 152.4 152.5 166.8 166.9 45 166.1 167.4 50 ... 180.8 182.4 180.8 181.8 181.4 ... 1 9 6 . 1 1 9 7 . 8 . . . 1 9 6 . 9 1 9 6 . 9 55 . . . 211.9 213.7 211.9 211.2 212.1 60 228.3 229.5 ... 228.9 228.9 65 ... ... 245.1 246.3 245.7 245.4 235.6 70 ... ... 261.8 263.5 . . . 262.8 262.7 75 ... . . . 279.3 280.5 2 7 9 . 4 280.1 279.8 80 ... . . . 296.7 298.3 ... 298.7 297.9 85 ... ... 314.5 316.8 316.5 318.2 316.5 90 . . . 332.2 335.0 ... 334.0 333.7 95 100 ... 350.9 353.4 350.9 . . . 351.7 a. Mem. prlsent. pars divers Savants cf l'academie Roy. des Sciences de l'lnsl. de France. 9 (1846). 433. Calculation b y Thorpe and Rodger. b. Pogg. Ann., 169 (1876), 1. c. Wied. Ann., 20 (1883). 257. d. LOC. cit. e. Phil. Mag., [6] S (1902), 487. f. L O C . Cil. 0
56.3 66.0 76.3 87.3 99.2 111.5 124.5 138.7 153.1 168.1
...
... ...
...
56.3 66.2 76.9 88.1 99.7 111.6 124.7 138.3 152.2 166.1 180.8
...
...
...
here t h a t t h e testing of a relative instrument with only one liquid a t a single temperature is entirely unsatisfactory. Such a procedure allows all sorts of errors t o creep in without a n y means of detection. It is best t o use several liquids a n d a variety of temperatures in t h e calibration a n d testing. T h e fluidity
Vol. 6, No. 3
of water increases over 500 per cent from o o t o 100'. For very fluid liquids, ether a n d hexane are suggested, a n d for very viscous liquids cane sugar solutions.' Finally, it needs t o be remarked t h a t a correction may be required for errors of thermometer a n d stopwatch. Particular care needs t o be exercised t o see t h a t t h e stop-watch keeps unijovm time. This can be tested b y timing ten-minute intervals on a chronometer. M a n y stop-watches fail in this test a n d must be discarded. Temperatures must be read t o t h e hundredth p a r t of a degree. THE C A L C U L A T I O N O F M E A S U R E M E N T S
The formula for calculating viscosity under t h e above conditions of measurement is r g r 4 t p mnpV
77=gyl--sat1 . . . . . . . . . . . . . . . . . . . . . .
(1)
where a = 3.1416,g is t h e acceleration due t o gravitation, r is t h e radius of t h e capillary in cm., t t h e time in sec., p t h e pressure in grams per sq. cm., V t h e volume of flow in cc., 1 t h e length of t h e capillary. The second t e r m contains t h e correction for t h e loss of kinetic energy a n d it should always be b u t a small fraction of t h e whole, preferably less t h a n one per cent. T h e number of capillaries is represented by 12, while P is t h e density of t h e liquid under investigation, a n d m is a constant equal t o 1.12. For a given instrument t h e equation (I) becomes 77 =
ctp- C ' p / t . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
Since t h e second t e r m is of comparatively small importance, t h e value of C' = mlzV/8?rl may be obtained b y approximate measurement with sufficient accuracy. Knowing t h e values of p a n d t as well as t h e density a n d viscosity of t h e liquid used in standardization, t h e value of C may be readily calculated. I n obtaining t h e value of t h e pressure several corrections must be made: ( I) T h e pressure in t h e manometer must be calculated in grams per sq. cm. from t h e known height of t h e liquid a n d t h e specific gravity of t h e liquid a t t h e temperature observed; (2) T h i s pressure must be corrected for t h e weight of t h e air displaced b y t h e head of liquid in t h e manometer, a n d if t h e limbs of t h e manometer are very unequal in bore a capillary correction may be required; (3) Unless t h e surface of t h e liquid in t h e lower limb of t h e manometer is a t t h e same height a s t h e average level of t h e liquid in t h e viscometer, a correction must be made for t h e greater density of this enclosed air, which is under pressure, t h a n of t h e outside air; (4) Finally a correction must be made for t h e average resultant hydrostatic head of liquid within t h e viscometer. If t h e two volumes .C a n d K in Fig. z are exactly similar in shape, equal in volume a n d a t t h e same elevation when t h e viscometer is supported 'in its vertical position, it is evident t h a t t h e gain in head during t h e first half of t h e flow will be exactly neutralized b y t h e loss in head during t h e last half of t h e flow. Since this is never exactly t h e case, a correction is made a s follows: Duplicate observations in reverse directions are made upon a liquid of known density a n d viscosity a t a constant pressure a n d tempera1
Cf. Hosking, Phil. Mag., [SI 49 (1900), 274.
T H E J O U R S A L O F I J D C S T R I A L ALVD EXGILVEERING C H E M I S T R Y
M a r . , 1914
237
ture. Let tl be t h e t i m e of transpiration from left t o right a n d fz t h e corresponding time from right t o left. Let P o be t h e pressure, corrected except for t h e average resultant head of liquid in t h e viscometer. Let this head be equal t o x centimeters of liquid as t h e liquid flows from left t o right, so t h a t in this case pz b u t t h e total pressure becomes equal t o $ 0 when the liquid flow from right t o left t h e pressure must be P o - p x . F r o m equation (2) we obtain t h e following equations.
+
Po-px
17 =
+ C/P/t2 Ctz
q
C'p
-Giz+Ctzz
whence
I n obtaining this correction t e r m i t is sufficient t o use t h e approximate value of C obtained b y using equation (2) with $ 0 in place of p . I n subsequent calculations i t is necessary t o know t h e specific gravity of t h e liquid t o be measured in order t o make t h e necessary pressure correction a n d also in order t o make t h e kinetic energy correction, b u t i t is t o be noted t h a t if t h e construction of t h e viscometer a n d t h e measurem e n t has been properly done these correction terms will both be small; hence, t h e specific gravity need be only approximately known, which constitutes a great advantage of this method. If t h e viscometer is constructed of t h e same material throughout, t h e coefficient of expansion of t h e material need n o t be taken into account, as m a y be easily verified b y introducing t h e coefficient of expansion into the dimensions in equation (I). B u t we cannot legitimately assume t h a t t h e same is t r u e of a n y changes in t h e dimensions of t h e a p p a r a t u s due t o t h e solubility of t h e glass. For this reason t h e t i m e of flow of t h e liquids used in calibration should be redetermined occasionally. However, so far as is known t o t h e author, t h e most prolonged use of a given instrument h a s never yet shown a change in t h e time of flow which could be attributed t o this cause. I n conclusion, we believe t h a t this viscometer is capable of a higher degree of precision t h a n t h e forms usually employed a n d t h a t a t t h e same time i t is easily made, convenient t o use, a n d economical of time. T h e corrections which have been discussed are small in this t y p e of apparatus, so t h a t t h e calculation of t h e viscosity b y means of equation ( 2 ) is simple. RICHXONDCOLLEGE,RICHMORD, VA.
MODIFIED HEMPEL PIPETTES By R. P. AXDERSON Received November 7, 1913
T h e chief objection t o t h e present form of t h e Hempel pipettes lies in t h e fact t h a t small drops of t h e reagent collect in t h e capillary while t h e gas is i n t h e pipette a n d are carried over into t h e burette on t h e return of t h e gas. This causes n o appreciable error when water is used as t h e confining liquid, b u t is ob-
For example, let i t be assumed t h a t there is 0.1 cc. of water on t h e mercury in t h e burette a n d t h a t about 0 . 0 1 3 cc. of alkaline pyrogallol is carried into t h e
v
