T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
,282
Vol.:1:2, No. 3 a t
THE MACMICHAEL TORSIONAL VISCOSIMETER' By Winslow H. Herschel OIL
LABORATORY, BUREAUO F
STANDARDS, WASHINGTON, D. C. Received August 26, 1919
I iYT R OD LTCTI 0 N
A torsional viscosimeter is a n instrument for de-
r*
termining t h e viscosity of a liquid by a torsional balance, usually c o n s i s t i n g m w o concentric cylinders, one of which has a n angular motion about their common axis. One of t h e cylinders is suspended by a fine wire, t h u s forming a torsional pendulum. I n some instruments, as for example the Doolittle,2 readings are made of t h e retarding effect of t h e liquid when t h e pendulum is allowed t o oscillate. I n other instruments, of which t h e .MacMichae13 is an example, t h e outer cylinder is revolved a t constant speed. The inner cylinder rotates until t h e torsional force in t h e suspending wire balances t h e viscous resistance, and then remains in a fixed position so t h a t a reading may be taken. I n t h e most accurate, so-called absolute, instruments, care is taken t o avoid end effects, so t h a t t h e instrumental constants necessary in calculating viscosity from t h e readings may be calculated from t h e dimension^.^ With commercial instruments, such as the MacMichael, t h e construction may be simplified by permitting end effects. Instruments of this latter class must be calibrated by t h e use of liquids whose viscosity has been determined b y absolute instruments of t h e torsional or other types. DESCRIPTION O F MACMICHAEL VISCOSIMETER
The essential parts of the MacMichael viscosimeter are a motor-driven oil cup and a torsional pendulum suspended above t h e center of t h e cup by a fine piano wire. The pendulum consists of a tube enclosing t h e wire and carrying a disc a t its lower end and a dial near the point of support. The disc is 60 mm. (2"/,6 in.) in diameter and j mm. ("16 in.) thick, and is immersed in t h e oil or other liquid t o be tested. As t h e inside diameter of t h e cup is 7 0 mm. (213/16 in.) there is ample clearance between t h e cup a n d t h e disc, and accurate centering of t h e pendulum in the cup is not required. The dial is fastened t o t h e tube by a tapered fit, a n d is graduated from o t o 300 for reading t h e angular deflection of t h e pendulum. The zero setting is made roughly by turning t h e dial on the tube, and more accurately b y movement of t h e pointer attached t o t h e support of the pendulum. Since i t is stated t h a t t h e pendulum should not be allowed t o make more t h a n two revolutions, so as not t o overstrain the torsion wire, t h e maximum reading is 600' M (MacMichael degrees). The wires are about 254 mm. (IO in.) long and of three sizes, t h e speed being adjusted so t h a t t h e smallest gives a deflection of 100' M , t h e second gives 10' &/I, and t h e third gives I O M with I I O cc. Published by permission of the Director of the Bureau of Standards. J . A m . Chem. SOC.,15 (1893), 173, 454. 3 THISJOURNAL, 7 (1915), 961. 4 M. Couette, A n n . chim. phys., 21 (1890). 433; E. I ,. Harrington, Phys. Rev., 8 (1916), 738; A. V. Bleininger and H. H Clark, Trans A m . Ceram. SOC.,12 (1910), 383; M. D . Hersey, J . W a s h . Acad. S c i , 6 (1916), 5 2 5 , E. R. Drew, Phys. Rev., 12 (1901), 114. 1
2
of water at 20' C. (68" F.) in t h e cup. I g t h e tests which are t o be described, Instrument 6 wag used with the medium-sized wire, 0.266 mm. (0.0105in.) iameter, and i t was found t h a t a speed of 114 revolutions per minute was necessary t o get t h e above deflection. The speed control is of t h e phonograph t y p e and adjustments are easily made by a t h u m b screw.' POSSIBLE SOURCES O F ERROR
Since i t is not necessary with a torsional viscosimeter t o maintain a constant temperature over a considerable period of time, these instruments have a great advantage in speed of operation as compared with an efflux viscosimeter. This is especially noteworthy when i t is desired t o obtain a temperatureviscosity curve, i t being necessary only t o heat the oil t o a maximum desired temperature, and t o t a k e t h e readings of temperature and of viscosity as i t cools off. Even t h e labor of taking readings may be avoided aking t h e record autographic, as in t h e Hayes by ewis viscosimeter.2 There is, however, considerand able question as t o t h e correct method of calibrating a torsional viscosimeter so t h a t its readings may be converted into absolute viscosities, or poises, for comparison with other instruments. Among t h e possible sources of error are turbulence, centrifugal force, and t h e effect of temperature in changing t h e length and diameter of t h e torsional wire, and thus changing t h e clearance between t h e disc and t h e bottom of t h e cup. To estimate t h e error due t o elongation of t h e wire, a rise of temperature of 80' C. (144' F.) was assumed. The elongation was found t o be about 0 . 2 4 mm. (o.oogj in.) or only 4.8 per cent of t h e total clearance of 5 mm. ( 3 / / 1 6 in.) between t h e bottom of t h e disc and t h e bottom of t h e cup. It will be shown later t h a t only one-third of t h e deflection of t h e pendulum is due t o viscous resistance below t h e disc and when this is taken into consideration t h e estimated error due t o elongation of t h e wire would be reduced t o 1.6per cent. The actual error would be considerably less because only one-fifth of t h e length of t h e wire is exposed t o t h e temperature of t h e oiL3 This question could not be investigated experimentally because t h e instrument a t hand was not supplied with an electric heating coil, so t h a t i t was impracticable t o work at temperatures above jjo C. (131OF.). According t o Hayes," in t h e MachIichael instrument, "the lines of flow above and below t h e disc are spirals a n d not circles. This is due t o t h e centrifugal action of t h e rotating liquid, a n d as a result a n error is introduced due t o t h e fact t h a t t h e liquid undergoes acceleration. This error is not large." T h a t spiral flow takes place is admitted b y MacMichael who does not attempt t o calculate viscosity from t h e dimensions of his instrument. He realized also t h a t i t was desirable t o reduce t h e turbulence by "reducing t h e
'2
1 For further details of the construction of the instrument see U. S. Patent 1,281,042, Oct. 8, 1918 2 J . A m . SOC.Mech Eng., 38 (1916), 626, 1002, 1003. 3 Compare "A Method for Measuring the Viscosity of Blast Furnace Slag at High Temperatures," A. I,.Feild, U S. Bureau of Mines, Technical Paper 157 (1916), 12.
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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 ENGINEERING C H E M I S T R Y
Mar., 1920
speed, reducing t h e dimensions of parts or increasr.ing t h e viscosity of t h e fluid," and says: "For a standard testing fluid, a high grade neutral mineral oil of high viscosity, such as some of t h e medicinal oils now on t h e market, is suggested, this oil t o he supplied in metal containers b y t h e U. S. Bureau of Standards, or some other recognized authority." He also suggests t h e use of a cane-sugar solution of 7 parts by weight of sugar t o 4 parts of cold water, but fails t o state what deflection should he obtained with this liquid. Eimer and Amend have published in Bulletin 2 1 1 comparative tests of t h e hIacMichae1 and Saybolt Universal Viscosimeters which were made a t t h e laboratory of the Standard Oil Company of California. Table I is calculated from t h e d a t a there given, with t h e addition of t h e specific gravities of t h e oils which were kindly furnished b y t h e Standard Oil Company.
>-.
TABLEI-COMPARISON
OF READINOS OF MACMICHAEI, AND SAYBOLT UNIVERSAL VISCOSIMETERS, A ~ C O R D I NTO G MACMICHAEL 3 4 5 6 1 2 Sample N u m b e r 21.3 20.6 21f5 21.4 20.1 19.7 Baume 0.930 0,924 0.925 0.926 0 . 9 3 3 . 0.936 Specific G r a v i t y
TEMPERAT~RE ' F. C. 60
15.6
.. ..
S
..
366 419 517 1016 1.906 1.724 2.085 2.082 .. 70 21.1 S 262 331 357 673 1084 .. R 1.858 1 . 9 9 4 2.111 2.083 2.098 . . 80 26.7 S 191 238 259 467 706 100.5 R 1.818 1.888 1 . 9 6 3 2.140 2.108 2.250 90 32.2 S . 144 177 190 323 484 658 R 1 . 6 9 4 1.808 1.900 2.018 2.122 2.150 S 112 137 143 231 336 4.52 100 37.8 R 1.648 1.7.57 1 . 8 1 1 1.975 2.100 2.142 110 43.3 S 92 108 113 175 254 326 R 1.586 1.636 1.713 1.863 2.049 2.090 S 78 89 92 135 184 240 120 48.9 R 1 . 5 9 2 1.589 1.615 1.777 1.898 2.050 S 67 75 77 109 142 183 130 54.4 R 1.595 1 . 5 6 2 1.604 1.678 1.776 1.927 140 60.0 S 58 64 66 92 113 142 R 1 . 6 1 0 1.561 1.610 1.672 1.713 1.844 S 53 57 58 77 96 112 150 65.6 R 1 . 6 5 6 1.583 1 . 5 6 8 1.638 1.683 1.698 S 49 52 54 67 80 94 160 71.1 R 1 . 6 9 0 1 . 6 2 5 1.635 1.634 1.632 1.678 170 76.7 S 46 48 49 59 69 80 R 1 . 7 6 9 1 . 7 1 3 1.690 1.638 1.605 1.666 S 44 45 46 54 61 68 180 82.2 R 1.833 1.731 1.703 1.687 1.605 1.619 190 87.8 S 42 43 44 50 55 61 R 1.908 1.791 1 . 8 3 3 1.723 1.618 1.648 200 93.3 S 39 42 42 47 51 55 R 1.950 1.909 1.909 1.808 1.700 1.667 S 38 39 40 44 47 50 210 98.9 R 2 . 1 1 1 1.950 2.000 1.833 1.740 1.666 S-Time of flow in seconds, Saybolt Universal Viscosimeter. of time, Saybolt, t o MacMichael degrees, R-Ratio
R
I t will be seen t h a t t h e ratio of time, Saybolt, t o MacMichael degrees decreases with t h e temperature of a given sample, except at high temperatures, and decreases as t h e specific gravity decreases, for a given temperature. I t is, therefore, evident t h a t the conversion factor changes with so many variables t h a t a Mac Michael-Saybolt conversion table is impracticable except for some assumed specific gravity. THE D E T E R M I N A T I O N O F VISCOSITY I N P O I S E S F R O M
h1 A C M I C H A E L D E G R E E S
If t h e effects of turbulence, centrifugal force, and other sources of error are neglected, t h e turning moment due t o t h e viscous resistance of t h e layer of oil underneath t h e disc would be equal t o :
where T
turning moment in kg. cm. viscosity i n kg. sec. per cm2. revolutions per sec. of oil cup D = diameter of disc in cm. h = clearance below disc in cm. = p = n. =
A known turning moment was applied t o t h e torsional pendulum and t h e torsional modulus of elasticity was calculated from the equation 4800Tl
G = -a2d4M
(2)
'where G
= torsional modulus of elasticity, in kg. per cm2. d = diameter of torsional wire in c m . . 1 = length of torsional wire in cm. M = deflection of wire, in MacMichael degrees Using t h e value of G = 880,000, U S f o u n d by test, t h e measured values of d , I , h , and D, a speed of 114 r. p. m.. and an assumed value of 1.4 poises = 0.000001428kg. sec. per cm2, for t h e viscosity,' it was found b y combining Equations I and 2 t h a t t h e theoretical deflection would b e 119.7' M . From Fig. I t h e actual deflection for this speed and viscosity was 3 jo" M , so t h a t t h e calculated deflection is only 0.342 of t h e total. This shows t h e impossibility of calculating t h e deflection from t h e dimensions of t h e instrument. On this account, and also on account of t h e impracticability of manufacturing instruments in which t h e variations i n t h e essential dimensions would be negligible, it is necessary t h a t each operator should be able t o calibrate his own instrument b y t h e use of liquids of known viscosity. TABLS
11-TESTS OF MACMICHAEI. VISCOSIMETER AT 114 REVOLGTIONS PER MINUTE
TEMPERATURE
' C.
,LIQUID
20 per cent sucrose'. . . . , . . . 40 p e r c e n t sucrose.. . . , . , , 60 per c e n t sucrose.. . . . , . Oils, Saybolt viscosimeter..
20 20 20 15 20 25 25 25 25 20 40 55 20 40 55 20 40 55 20 40 55 Oils, Engler viscosimeter.. . . 4 10 15 17 20 25 30 37.8 25 25 20 15 25
.
TIME DENSITY Sec. G. per Cms.
., . .. .. ..
54.3 50.1 48.4 97.3 114.6 171.5 323.4 127.0 79.2 106.6 60.8 48.4 205.4 88.4 61.4 653.0 239.2 133.8 936.3 620.6 468.9 391.0 330.1 238.3 189.7 146.2 142.3 173.4 82.9 88.0 77.3
0.871 0.894
0.829 0.893 0.879 0.870 , 0.877 0.863 0.853 0.897 0.893 0.889 0.889 0.886 0.883
0.879 0,874 0.871 0.894 0.855 0.858 0.852
0.0196 0,0620 0.565 0.0740 0.0634 0.0588 0,1702 0.2111 0,3235 0.615 0.2272 0.1284 0.1855 0.0874 0.0574 0.3955 0.1530 0.0921 1.255 0.447 0.2395 1.228 0.809 0.606 0.502 0.420 0.295 0,228 0.1655 0.1593 0,2087 0.0654 0,0744 0.0555
15 321 157 31 26 23 52 64 86 170 65 50 61 36 27 125 55 40 324 128 75 264 187 142 130 109 86 71 56 52 64 26 31
23
If it is assumed t h a t t h e equation2 1 F o r conversion table of different units of viscosity, see Winslow H . Herschel, Bureau of Standards, Technologic Paper 100 (1917), 5 . 2 Winslow H. Herschel, Bureau of Standards, Technologic P a p e r 112 (1919), 19.
4
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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
Kinematic viscosity =
viscosity in poises _ _ ~ density in g. per cc. 1.80
-
0.00220 t
-
~
t
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-. 24 2 3
(3) 2 2
(in which f is t h e time of discharge in seconds) applies t o the Saybolt viscosimeter used in the tests of Table I, the viscosity of the six samples may be calculated for t h e temperatures given. This equation applies only t o a Saybolt Universal Viscosimeter of standard dimensions, but i t is the best available for t h e present purpose and 1.1s been used in calculating Fig. I. The upper curve is from d a t a of Table I , a n d the lower curve from the results of tests given in Table 11. The difference between the two curves may be attributed t o differences in dimensions of t h e viscosimeters and t o inaccuracies in adjusting t h e speed of t h e MacMichael instruments so as t o give a reading of exactly 10.0’M in water. MacMichael’s method of calibration is t o use “a standard testing sample of known viscosity and t o assume t h a t other readings are directly proportional in value. Through a wide range this does not seem t o introduce serious errors.’’ It is evident from Fig. I t h a t this method would lead t o serious error unless the calibrating liquid and t h e sample t o be tested were not greatly different in viscosity.
Z f 20
19
/ R
I 7 /6
l 5
FIG.2
From Equations 3 a n d 5 and the value of 0.876 for the average density of t h e oils a t the temperature of t h e test, .~.
t = 1.09 (M-17)
( +-\il I
).
(M - 1 7 ) ~
(6)
Equation 6 emphasizes the fact t h a t t h e conversion formula between readings of two viscosimeters may be complex, and i t is preferable t o convert t h e readings of each instrument into poises for comparison. It also shows t h a t a torsional and an efflux instrument cannot be compared unless t h e density is determined by a n auxiliary instrument, since a torsional instrument measures viscosity in poises, a n d a n efflux instrument measures kinematic viscosity. The relation between time, Saybolt a n d MacMichael degrees is shown in Fig. 2, both according t o Table I a n d [to Equation 6. T h e ratio of d/M approaches a value of 2.18 a s . t h e viscosity increases. Figs. I and 2 show t h a t Equation 5 does not apply for viscosities less t h a n about 0.15 poise or go seconds, Saybolt. THE E F F E C T
O F DENSITY
UPON T H E DEBLECTION
According t o Hersey the most general equation for a torsional viscosimeter is
FIG.1
The lower calibration curve of Fig. I is found t o be represented by the equation p = 0.00275
(n1 - 10)1-07
(4)
or, more simply and accurately, if only the straight part of the curve is considered p = 0.0042 (M - 17) (5) where p is the viscosity in poises. Since Equations 4 and 5 contain two instrumental constants, two calibrating liquids (or one liquid a t two temperatures) are necessary as in the case of efflux viscosimeters.
where T = torque exerted on the torsional penduium n = revolutions in unit time Y = radius of inner cylinder g = acceleration of gravity = 981 cm. per sect. p / y = kinematic viscosity f = an unknown function. Of these three special cases considered by Hersey, t h e MacMichael instrument most closely approaches the second, where “ t h e torque is not independent of t h e density of the sample, owing to spiral flow across t h e bottom or t o turbulent end effects, but in which the free surface is level, so t h a t t h e argument containing g in Equation 7 drops out. I n this case the instrument is self-calibrating; by observing with a single liquid what function of speed t h e deflection is, we can a t once infer what function it is of the viscosity.”
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 CHEMISTRY
Mar., 1920
I n t h e MacMichael instrument, however, the free surface of the liquid is perceptibly parabolic, a n d t h e elevation of t h e surface might have a slight effect on t h e deflection on account of t h e viscous drag exerted o n t h e t u b e of t h e pendulum. This tube is only I O mm. (s//8 in.) in diameter where i t emerges from t h e liquid. 30
20
parison, for a given change of speed. An exact proportionality between speed a n d deflection would correspond t o a constant value of t h e ordinate of Fig. 3. I n reality, as shown most clearly from t h e tests with heavy liquids, t h e ordinate increases as t h e speed increases. An extension of Fig. 3 t o include liquids of very low viscosity shows a n approximately parabolic relation between t h e coordinates, t h e curve passing through the point having a n ordinate of 8.73 a n d abscissa of 11,300, obtained from t h e calibration with water. Table I11 was interpolated from Fig. 4 and other tests made with variable speed. Viscosities were calculated from Equation 3. TABLE 111-TESTS
io
Revoluftons . p e r M i n u t e , n r Kinemotrc Vircosity I I I I I
1
I
I
1
71 1 1 I
zoo
/Or)
300
400
~
500
600
700
FIG.3
Disregarding t h e argument containing g in Equation 7 for a given instrument i t may be written
Using t h e d a t a of Table 11, by plotting t h e first term against t h e second in Fig. 3 the equation was obtained,
M
= 2.10 pn
+
0.00150y n 2
or p = 0.0042 (M - 19.5 y ) . (9) Comparing Equations 5 a n d g i t is seen t h a t 17 is a n average value of 19.5 y . TESTS W I T H V A R I A B L E S P E E D
If, as suggested by MacMichael, a more viscous calibrating liquid were used in place of water, the error in adjusting t h e speed might be greatly reduced, but t h e assumption of a straight line relation between MacMichael degrees and viscosities would still cause considerable error a t low viscosities. If, however, the speed were reduced so as t o decrease the disturbing effects of turbulence and centrifugal force, t h e readings would be more nearly proportional t o t h e viscosities, as in t h e ideal instrument. Tests with variable speeds were made after t h e torsional wire had been removed for measurement and replaced. Results are shown in Fig. 4 where t h e numbers on the lines are values of t h e viscosity in poises. The speed may be varied considerably by t h e adjusting screw, and still further by decreasing t h e current t o the motor. With t h e rheos t a t employed, a minimum speed of 7 0 revolutions per minute could be obtained, a n d for t h e few tests a t lower speeds t h e cup was retarded by hand, taking care t o keep t h e deflection as constant as possible. Fig. 4 shows t h a t a t moderate speeds, with oils of not too low viscosity, t h e readings are approximately proportional t o t h e speed, b u t with licluids heavier t h a n water t h e change-in deflection is greater in com~~
285
MACMICHAEL VISCOSIMETER WITH VARIABLESPEED DENSITY AT DEFLECTION M AT SPEEDOF VISCOSITY TEMPERATURE 70 85 100 115 LIQUID Poises O F TEST -Rev. per Mia0.479 1.285 Sucrose. 70 90 109 129 0.603 1.293 87 Sucrose. 111 135 158 0.796 1.303 Sucrose.. 116 147 176 206 Glycerin. . , 0.437 1.207 65 85 103 122 1.298 1.229 Glycerin. . 162 203 243 282 Glycerin.. . 1.698 1.234 237 295 353 410 50 per cent alcohol 0 . 0 2 2 4 0.929 10 12 15 8 Mineral oil. . 2 . 7 10 0.923 383 465 548 630 , 2.621 Mineral oil. 0.915 264 320 375 432 Mineral o i l . . 1.683 0.914 230 279 328 377 0.926 0.897 Mineral o i l . . 151 183 215 247 Mineral oil.. . . . 0.879 0.887 120 145 171 196 Mineral o i l . . . 0.864 0.867 130 158 186 214 Mineral oil.. 0.835 0.897 113 137 161 185 Mineral o i l . . 0.393 0.902 60 73 86 99 Mineral o i l . . . , . 0 . 2 0 3 0.909 38 47 54 62 OF
.. .. .. .. .. .. .. .. .. . .. . . . . . .. .. . .. .. .. .. .. ... . . ... ... .. ... ... .. . . . .. . ........ .. . . . ..
From tests of Table I11 a t 70 revolutions per minute, a new equation was obtained as shown in Fig. 3. This gave M = 1-95p n o.ooo833yn2 (10) or, with a n average density of 1.04 and speed of 70 revolutions per minute, p = 0.0073 (M-4.1 7 ) = 0.0073 (M-4). (11) T h e disagreement between Equations g a n d I O may be due t o t h e neglect of t h e t e r m r n 2 / g in Equation 7 as well as t o the change in conditions due t o removing and replacing t h e torsional wire. T h e method of fastening t h e wire does not permit a n exact adjustment of its length.
+
R e v o / u t i o n s g e r minute
FIQ.4
Fig. 5 shows results of tests with variable speed. I n t h e main figure t h e curves are calculated from Equation I O for t h e average density. I t will be seen t h a t liquids with high density show in general
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
286
higher deflections a t t h e higher speeds t h a n are given by t h e oils or by t h e curves. The curve for highest speed in Fig. j lies between t h e two curves of Fig. I . Equation 11 and t h e deflection for a speed of 7 0 revolutions per minute were used t o determine t h e viscosities a t some of t h e points listed as determined b y equation. These points, therefore, merely show t h e change of deflection with change of speed, and do not help locate t h e position of the curve for lowest speed.
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proportional t o d 4 G with a given speed, deflection, and length of wire. The viscosity of a very viscous liquid may t h u s be calculated from values of d 4 G for t w o wires, using a large wire for t h e liquid t o be tested, a n d calibrating t h e small wire by liquids of known viscosity. The determination of diameter a n d torsional modulus of elasticity with sufficient accuracy is difficult, a n d this method should only be used when sufficiently viscous liquids for direct calibration cannot be obtained. Care should be taken not t o use plastic substances' either as calibrating liquids or as liquids t o be tested. No definite point can be set as t h e minimum viscosity which can be measured with a given wire. It might, however, be pointed out t h a t i t is impracticable t o make readings closer t h a n t o t h e nearest MacMichael degree, and t h a t an error of I ' in a reading of 18' M (the lowest value given in t h e Eimer and A m e n d table) is an error of over 5 per cent. There is some danger of damaging t h e wire when unhooking t h e pendulum t o clean i t , and this furnishes t h e practical limitation t o t h e fineness of wire which can be used. There should be no difficulty in obtaining a suitable calibrating liquid, since water with a viscosity of from 0.01519 poise a t j " C. (41' F.) to o.ooz9gz poise a t 95' C. (203" F.) may be used. CONCLUSIONS
I
I /oo
1 zoo
300
400
500
FIG.5
For tests a t very low viscosities, shown in t h e insert on a n enlarged scale, Equation I O does not apply. a n d t h e curves were calculated from Equation 4, assuming t h e deflection proportional t o t h e speed. UETHODS OF INCREASING RAKGE O F MEASURABLE
VISC 0S I T Y
Since t h e deflection is limited t o 600' M i t may be calculated from Equation 5 t h a t t h e maximum viscosity which can be measured if t h e speed of t h e instrument is adjusted so as t o give a deflection of I O ' R/I with water will be about 2.45 poises. A reduction of speed t o 7 0 revolutions per minute would increase t h e maximum measurable viscosity t o 4.0 poises, and a t t h e same time make t h e deflections a t low viscosities much more nearly proportional t o t h e viscosity. Viscosities up t o any desired magnitude could be measured b y increasing t h e diameter of t h e torsional wire. There is difficulty, however, in obtaining suitable calibrating liquids for heavy wires, since t h e measurement of viscosities above about 20 poises by t h e most accurate capillary t u b e method is open t o considerable question on account of possible drainage errors. If t h e speed is reduced so t h a t t h e deflection is proportional t o t h e viscosity, then t h e viscosity would be
Every Wf acMichae1 instrument should be calibrated b y t h e operator on account of unavoidable differences in dimensions of instruments, especially of t h e torsional wire. Calibration is necessary because t h e relation between instrumental readings a n d viscosity cannot be calculated from t h e dimensions of an instrument. T h e method of calibration suggested b y MacMichael, of adjusting t h e speed until a deflection of I O " M is obtained with water, is inadequate because adjustments cannot be made with sufficient accuracy a n d because there are two instrumental constants. On account of t h e marked effect of differences in density, two liquids (or one liquid at two temperatures) of approximately t h e same density as t h e liquid t o be tested should be used. This would make i t inadvisable t o calibrate with sucrose solutions an instrument intended for use with oils. This Bureau is a t present prepared t o certify t o t h e viscosity of calibrating liquids having a viscosity not exceeding 2 0 poises. It is believed preferable for interested parties t o send samples of, say, IOO cc. (4 02.) t o t h e Bureau for tests, rather t h a n for t h e Bureau t o furnish large samples i n tin containers as suggested by MacMichael. Equations showing t h e relation between MacMichael degrees and poises have been given. These show t h e general form of equation t o be expected, and serve as a guide in calibrating instruments. They are n o t intended for use as standard equations t o be applied t o all MacMichael instruments with medium sized wires. 1 For the distinction between plastic substances and viscous liquids see E C Bingham, Bureau of Standards, Sczentzlic P a p e r 278 (1916), 310.
