THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES u NOV 7 1957 INTERNATIONAL CHEMICAL SERIES H. P. TALBOT, PH.D., Sc.D., CONSULTING EDITOR FLUIDITY AND PLASTICITY PUBLISHERS OF BOOKS FOIO Electrical \Xbrld v Engineering News -Record Power v Engineering and Mining Journal-Press Chemical and Metallurgical Engineering Electric Railway Journal v Coal Age American Machinist v Ingenieria International Electrical Merchandising v BusTransportation Journal of Electricity and Western Industry Industrial Engineer (Frontispiece). FLUIDITY AND PLASTICITY BY EUGENE C. BINGHAM, PH.D. PROFESSOR OF CHEMISTRY AT LAFAYETTE COLLEGE, EASTO-V, PENNSYLVANIA FIRST EDITION SECOND IMPRESSION McGRAW-HILL BOOK COMPANY, INC. NEW YORK: 370 SEVENTH AVENUE LONDON: 6 & 8 BOUVERIE ST., E. C. 4 1922 COPYRIGHT, 1922, BY THE MCGRAW-HILL BOOK COMPANY, INC. PRINTED IN THE UNITED STATES OF AMERICA All translation rights reserved Physics Library qc ni To my sister 919548 PREFACE Our knowledge of the flow of electrical energy long ago de- veloped into the science of Electricity but our knowledge of the flow of mailer has even yet not developed into a coordinate science. In this respect the outcome of the labors of the hydro- dynamicians has been disappointing. The names of Newton, Navier, Poisson, Graham, Maxwell, Stokes and Helmholtz with a thousand others testify that this field has been well and com- petently tilled. Even from the first the flow of liquids has been a subject of practical importance, yet the subject of Hydraulics has never become more than an empirical subject of interest merely to the engineer. Unfortunately the theory is complicated in that the flow of matter may be hydraulic (turbulent), viscous (linear), or plastic, dependent upon the conditions. It was in 1842 that viscous flow was first differentiated from hydraulic flow, and only now are we coming to realize the important distinction between vis- cous and plastic deformation. Considering the confusion which has existed in regard to the character of flow, it is not surprising that there has been uncertainty in regard to precise methods of measurement and that exact methods have been discovered, only to be forgotten, and rediscovered independently later. As a result, the amount of really trustworthy data in the literature on the flow of matter under reproducible conditions is limited, often to an embarrassing extent. If we are to have a theory of flow in general, we must consider matter in its three states. No such general theory has appeared, although one is manifestly needed to give the breath of life to the dead facts about flow. The author offers the theory given in the following pages with the utmost trepidation. Although he has given several years to the pleasant task of supporting its most important conclusions, a lifetime would be far too short to complete the work unaided. The author makes no apology for any lack of finality. Parts of the theory which have already x PREFACE found their way into print have awakened a vigorous discussion which is still in progress. This is well, for our science thrives on criticism and through the collaboration of many minds the final theory of flow will be evolved. Without going considerably beyond the limits which we have placed upon ourselves, it is impossible to refer even briefly to all of the important papers on the subject. References given in the order that they come up in the discussion are not the best suited for later reference. The novel plan has been tried of placing nearly all of our references in a separate appendix which is also an author index and is, therefore, arranged alphabetically under the authors' names. In the text the name of the author and the year of publication of the monograph is usually sufficient for our purpose, but sometimes the page is also added. The titles of the monographs are usually given in the hope that this bibli- ography may be of considerable service to investigators who are looking up a particular line of work connected with this general subject. It is a pleasure to thank Dr. R. E. Wilson of the Massachusetts Institute of Technology and Dr. Hamilton Bradshaw of the E. I. bu Pont de Nemours & Company for reading over the manu- script and Dr. James Kendall for examining the proof. Profes- sor Brander Matthews of Columbia University, Professor James Tupper and Professor James Hopkins of Lafayette College have assisted in important details. The author gladly acknowledges the valuable assistance of his colleagues and co-workers, Dr. George F. White, Dr. J. Peachy Harrison, Dr. Henry S. Van Klooster, Mr. Walter G. Kleinspehn, Mr. Henry Green, Mr. William L. Hyden, Mr. Landon A. Sarver, Mr. Delbert F. Brown, Mr. Wilfred F. Temple, Mr. Herbert D. Bruce, and others. The author is especially indebted to the University of Rich- mond for the leisure which made possible a considerable portion of this work. EUGENE C. BINGHAM. EASTON, PA. Feb. 11, 1922. CONTENTS PAGE PREFACE vii Part I. Viscometry , CHAPTER I. PRELIMINARY. METHODS OP MEASUREMENT 1 II. THE LAW OP POISEUILLE 8 III. THE AMPLIFICATION OP THE LAW OF POISEUILLE 17 IV. Is THE VISCOSITY A DEFINITE PHYSICAL QUANTITY? 58 V. THE VISCOMETER 62 Part II. Fluidity and Plasticity and Other Physical and Chemical Properties I. VISCOSITY and FLUIDITY 81 II. FLUIDITY AND THE CHEMICAL COMPOSITION AND CONSTITUTION OF PURE LIQUIDS 106 III. FLUIDITY AND TEMPERATURE, VOLUME, PRESSURE. COLLI- SIONAL AND DlFFUSIONAti VISCOSITY 127 IV. FLUIDITY AND VAPOR PRESSURE 155 V. THE FLUIDITY OF SOLUTIONS 160 VI. FLUIDITY AND DIFFUSION 188 VII. COLLOIDAL SOLUTIONS 198 VIII. THE PLASTICITY OF SOLIDS 215 IX. THE VISCOSITY OF GASES 241 X. SUPERFICIAL FLUIDITY 254 XI. LUBRICATION 261 XII. FURTHER APPLICATIONS OP THE VISCOMETRIC METHOD 279 APPENDIX A. PRACTICAL VISCOMETRY 296 APPENDIX B. PRACTICAL PLASTOMETRY 320 APPENDIX C. TECHNICAL VISCOMETERS 324 APPENDIX D. MEASUREMENTS OF POISEUILLE 331 VISCOSITIES AND FLUIDITIES OF WATER FLUIDITIES OF ETHYL ALCO- HOL AND SUCROSE SOLUTIONS 341 RECIPROCALS >342 FOUR-PLACE LOGARITHMS 345 BIBLIOGRAPHY AND AUTHOR INDEX 347 SUBJECT INDEX. . 431 FLUIDITY AND PLASTICITY PART I VISCOMETRY CHAPTER I PRELIMINARY. METHODS OF MEASUREMENT Introductory. What one may be pleased to call "dominant ideas" have so stimulated the work on viscosity, that it would be entirely possible to treat the subject of viscosity by consider- ing in turn these dominant ideas. Practically no measurements from which viscosities may be calculated were made prior to 1842, yet very important work was being done in Hydrodynamics, and the fundamental laws of motion were established during this preliminary period. To this group of investigations belong the classical researches of Bernouilli (1726), Euler (1756), Prony (1804), Navier (1823), and Poisson (1831). In the development of Hydrodynamics much experimental work was done upon the flow of water in pipes of large bore by Couplet (1732), Bossut (1775), Dubuat (1786), Gerstner (1800), Girard (1813), Darcy (1858), but this work could not lead to the elucidation of the theory of viscosity as we shall see. Important work belonging to this preliminary period was also done by Mariotte (1700), Galileo (1817), S'Grave- sande (1719), Newton (1729), D'Alembert (1770), Boscovich (1785), Coulomb (1801), Eytelwein, (1814). It is to Poiseuille (1842) that we owe our knowledge of the simple nature of flow in capillary spaces, which is in contrast with the complex condition of flow in wide tubes, heretofore used. He wished to understand the nature of the flow of the blood in the capillaries, being interested in internal friction from the physiological point of view. He made a great many meas- 1 2 FLUIDITY AND PLASTICITY urements of the rates of flow of liquids through capillary tubes, which are still perhaps unsurpassed. They lead directly to the laws of viscous resistance and they will be described in detail in a later chapter. The theoretical basis for these laws and a definition of viscosity were supplied by the labors of Hagen (1854), G. Wiedemann (1856), Hagenbach (1860), Helmholtz (I860), Maxwell (1860). Since the velocity of flow through the capillary may be considerable, a correction is generally necessary for this kinetic energy, which is transformed into heat. Hagen- bach was the first to attempt to make this correction but Neumann (1858) and Jacobson (1860) were the first to put the correction into satisfactory form. Thus both the method of measurement and the formula used in calculation of absolute vis- cosities were practically the same by 1860 that they are today. Unfortunately, these important researches have not been suffi- ciently well-known, hence their results have been repeatedly rediscovered, and there is an evident confusion in the minds of many as to the conditions necessary for exact measurement. The so-called "transpiration" or Poiseuille method was not the only one which was worked out during this period of perfecting the methods of measurement. The pendulum method was developed by Moritz (1847), Stokes (1849), O. E. Meyer (1860), Helmholtz (1860) and Maxwell (1860). The well-known method of the falling sphere was worked out by Stokes (1849). During the period to which we have just referred, Graham (1846-1862) had been doing his important work on gases, but the development of the kinetic theory gave a great impetus to the study of the viscosity of gases; and at the hands of Maxwell, O. E. Meyer and others, viscosity in turn gave the most striking confirmation to the kinetic theory. The work on the viscosity of gases has continued on until the present, being done almost exclusively by physicists. To chemists, on the other hand, impressed by the relations between physical properties and chemical composition, so forcibly brought to their attention by the work of Kopp, the viscosity of liquids has been an interesting subject of study. To this group belong the researches of Graham (1861), Rellstab (1868), Guerout (1875), Pribram and Handl (1878), Gartenmeister (1890), Thorpe and Rodger (1893) and many others. METHODS OF MEASUREMENT 3 The rise of modern physical chemistry resulted in an awaken- ing of interest in all of the properties of aqueous solutions. Along with other properties, viscosity received attention from a great number of physical chemists, among whom we may cite Arrhenius (1887), Wm. Ostwald (1893), J. Wagner (1883-90), Reyher (1888), Miitzel (1891). It must be admitted that our knowledge of viscosity has not played an important part in the development of modern physical chemistry. It is doubtless for this reason that the subject of viscosity is left unconsidered in most textbooks of physical chemistry. It is certainly not be- cause viscosity does not play an important role in solutions, but rather that the variables in the problem have not been properly estimated. That with the physical chemist viscosity has so long remained in the background, makes it all the more promis- ing as a subject of study, particularly since it is becoming more and more nearly certain that viscosity is intimately related to many very diverse properties such as diffusion, migration of ions, conductivity, volume, vapor-pressure, rate of solution and of crystallization, as well as chemical composition and consti- tution, including association and hydration. It seems probable that the work in this field is going to expand rapidly, for it is becoming imperative that the exact relation between viscosity and conductivity, for example, should be clearly demonstrated. With the recent advances in our knowledge of the nature of colloids, there was certain to be an extended study of the vis- cosity of these substances, because no property of colloids is so significant as the viscosity. This in turn has again stimulated interest in viscosity on the part of the physiologist, so that the viscosity of blood, milk, and other body fluids have been repeatedly investigated under the most varied conditions during the past few years. The use of viscosity measurements for testing oils, paints, and various substances of technical interest has given rise to a series of investigations, that of Engler (1885) being among the earliest and most important in this group. These researches have been devoted largely to devising of instruments and to -a comparison of the results obtained. Quite unrelated to the above groups for the most part, are the investigations which have undertaken to study the viscosity 4 FLUIDITY AND PLASTICITY of solids. The study of elasticity has been the dominant idea in this group of researches. Very little work has been done upon the viscosity of matter in the different states of aggregation taken as a whole. If it has been shown that our knowledge of viscosity consists of somewhat unrelated groups, it is equally apparent that such a separation is artificial and that nothing could be more important for our complete understanding of viscosity, than to bring these groups together into an inter-related whole. We shall therefore not make an attempt to follow the chronological method, where it interferes with the consideration of the subject as a whole. Nevertheless the groups of researches to which we have alluded stand out rather clearly. The methods of measurement in use will be first considered, after which we shall study the viscosities of liquids, solutions, solids, and gases respectively. Elastic Deformation, Plastic, Viscous, and Turbulent Flow. If a perfectly elastic solid be subjected to a shearing stress a certain strain is developed which entirely disappears when the stress is removed. The total work done is zero, the process is reversible, and viscosity can play no part in the movement. This is not a case of flow but of elastic deformation. If a body which is imperfectly elastic as regards its form be subjected to shearing stress, it will be found that a part, at least, of the deformation will remain long after the stress is removed. In this case work has been done in overcoming some kind of internal friction. We may distinguish the kinds of flow under three regimes. It is characteristic of viscous or linear flow that the amount of deformation is directly proportional to the deforming force, and the ratio of the latter to the former gives a measure of viscosity. It has been questioned at times whether this ratio is truly constant, but it appears that only one qualification is necessary. In very viscous substances time may be necessary for the flow to reach a steady state, aside from any period of acceleration, because with substances like pitch the viscous resistance develops slowly, so that the above ratio gradually increases when the load is first put on, but even in this case the ratio finally reaches a value which is independent of the amount of the load. As, however, the deforming force is steadily in- creased, a point may be reached where the above ratio suddenly METHODS OF MEASUREMENT 5 decreases. At this point the regime of turbulent or hydraulic flow begins. This will be studied in detail at a later point in the development of the subject. There are substances, on the other hand, for which the value of the above ratio increases indefinitely as soon as the deforming force falls below a certain minimum. These substances are said to be plastic. In plastic flow it is generally understood that a definite shearing force is required before any deformation takes place. But whether this is strictly true or not has not been established. The Coefficient of Viscosity. Consider two parallel planes A and B, s being their distance apart. If a shearing force F per unit area give the plane A a velocity v in reference to B, the velocity of each stratum, between A and B, as was first pointed out by Newton, will be proportional to its distance from B. The rate of shear dv/ds is therefore constant throughout a homogeneous fluid under the above conditions. The possibility that it may not be constant near a boundary surface will be considered later. Since the force F is required to maintain a uniform velocity, this force must be opposed by another which is equal in amount due to the internal friction. The ratio of this force to the rate of shear is called the coefficient of viscosity and is usually denoted by the symbol 17 Fs *- (1) The dimensions of viscosity are [ML- 1 T~ 1 ]. The definition of viscosity due to Maxwell may be stated as follows: The vis- cosity of a substance is measured by the tangential force on a unit area of either of two horizontal planes at a unit distance apart required to move one plane with unit velocity in reference to the other plane, the space between being filled with the viscous substance. The coefficient of fluidity is the reciprocal of the coefficient of viscosity, so that if the former is denoted by we have = -. The coefficient of fluidity may be independently defined as the velocity given to either of two horizontal planes in respect to the other by a unit tangential force per unit area, when the planes are a unit distance apart and the space between them is filled with the viscous substance. 6 FLUIDITY AND PLASTICITY Methods of Measurement. Almost numberless instruments have been devised for the measurement of viscosity, but the greater part of these are suitable for giving relative values only. There are, however, several quite distinct methods which are susceptible of mathematical treatment so that absolute viscosities may be obtained. The possible methods for measuring viscosity may be classified under three heads as follows: 1. The measurement of the resistance offered to a moving body (usually a solid) in contact with the viscous fluid. 2. The measurement of the rate of flow of a viscous fluid. 3. Methods in which neither the flow nor the resistance to flow are measured. 1. The various methods for measuring viscosity while maintaining the fluid in a nearly fixed position, together with the names of investigators who have developed the method are as follows: (a) A horizontal disk supported at its middle point by a wire and oscil- lating around the wire as an axis. Coulomb (1801), Moritz (1847), Stokes (1850), Meyer (1865), Maxwell (1866), Grotrian (1876), Oberbeck (1880), Th. Schmidt (1882), Stables and Wilson (1883), Fawsitt (1908). (6) A sphere filled with liquid and oscillating around its vertical axis. Helmholtz and Piotrowski (1868), Ladenburg (1908). (c) A cylinder filled with liquid and oscillating around its vertical axis. Mutzel (1891). (d) Concentric cylinders. The outside one is rotated at constant velocity and the torque, exerted upon the inner coaxial cylinder which is immersed in the viscous fluid, is measured. Stokes (1845), de St. Venant (1847), Boussinesq (1877), Couette (1888), Mallock (1888), Perry (1893). (e) An oscillating solid sphere immersed in the viscous substance and supported by bifilar suspension was used by Konig (1885). (/) A body moving freely under the action of gravity, e.g., falling sphere of platinum, mercury, or water, a falling body of other shape than a sphere, a rising bubble of air. Stokes (1845), Pisati (1877), Schottner (1879), de Keen (1889), O. Jones (1894), Duff (1896), J. Thomson (1898), Tammann (1898), Schaum (1899), Allen (1900), Ladenburg (1906), Valenta (1906), Arndt (1907). 2. The methods for measuring the rate of flow of a viscous fluid: (a) Efflux through horizontal tubes of small diameter. Gerstner (1798), Girard (1816), Poiseuille (1842), G. Wiedemann (1856), Rellstab (1868), Sprung (1876), Rosencranz (1877), Grotrian (1877), Prlbram and Handl (1878), Slotte (1881), Stephan (1882), Foussereau (1885), Couette (1890), Bruckner (1891), Thorpe and Rodger (1893), Hosking (1900), Bingham and White (1912). (6) Efflux through a vertical tube of small diameter. Stephan (1882), METHODS OF MEASUREMENT 7 Englcr (1885), Arrhenius (1887), Ostwald (1893), Gartenmeister (1890), Heydweiller (1895), Friedlander (1901), Mclntosh and Steele (1906), Rankine (1910). (c) Efflux through a bent capillary. Griineisen (1905). (d) Bending of beams and torsion of rods of viscous substance. Trouton (1906), Trouton and Andrews (1904). (e) Rate at which one substance penetrates another under the influence of capillary action, diffusion, or solution tension. 3. Other methods for measuring viscosity: (a) Decay of oscillations of a liquid in U-shaped tubes. Lambert (1784). (b) Decay of waves upon a free surface. Stokes (1851), Watson (1902). (c) Decay of vibrations in a viscous substance. Guye and Mintz (1908). (d) Rate of crystallization. Wilson (1900). Nomenclature. A great variety of names have been given to instruments devised for measuring viscosity, among which we may cite viscometer, viscosimeter, glischrometer, microrheom- eter, stalagnometer, and viscostagnometer. All but the first two are but little used and their introduction seems an unneces- sary complication. Viscometer and viscosimeter are about equally used in England and America, but such a standard work as Watt's Dictionary uses only viscometer. Viscosimeter in its German equivalent Viskosimeter is entirely satisfactory, but in English viscosimeter is apt to be mispronounced viscos- imeter. Furthermore viscosimeter does not so easily relate itself in one's mind to viscometry which is the only word recog- nized in the standard dictionaries to denote the measurement of viscosity. Professor Brander Matthews kindly informs me that the formation of the word viscometer is quite as free from objection as that of viscosimeter, and viscometer is in harmony with modern spelling reform. Hence viscometer should be adopted as the name for all instruments used for measuring vis- cosity. The different forms are distinguished by the names of their inventors. CHAPTER II THE LAW OF POISEUILLE Experimental Verification. Prior to 1842 it had not been established as a fact that the movement of the blood through the capillaries has its origin solely in the contractions of the heart. There were theories current that the capillaries themselves caused the flow of blood or that the corpuscles were instrumental in producing it. Poiseuille reasoned that if the lengths and diameters of the capillaries are different in the various warm- blooded animals and if the pressure and temperature of the blood vary in different parts of the body, light might be thrown upon the problem by investigating the effects upon the rate of flow in capillary tubes of changes in (1) pressure, (2) length of capil- lary, (3) diameter of capillary, and (4) temperature. The results of Poiseuille's experiments were of a more funda- mental character than he anticipated for they proved that the conditions of capillary flow are much simpler than those in the wide tubes which had previously been employed, and by his experiments the laws of viscous flow became established. Not only did Poiseuille perform experiments which resulted in the law which bears his name, and therefore have affected all subse- quent work, but he measured the efflux times of water by the absolute method taking elaborate precautions to insure accuracy, and using capillaries of various lengths and diameters which are equivalent to separate instruments in all over forty in number. Thus one is justified in studying his work in considerable detail, not only for its historic interest, but on account of its bearing upon questions which will arise later. In the Appendix his measurements are reproduced in full. In Fig. 1 is shown the most essential part of the apparatus of Poiseuille. It consists of a horizontal glass capillary d joined to the bulb, whose volume between the marks c and e was accu- rately determined. The bulb is connected above with a tube which leads to (1) a 60-1 reservoir for keeping the pressure of the air within the apparatus constant, (2) a manometer, filled with THE LAW OF PO I SEVILLE 9 water or mercury, and (3) a pump which is used for giving the desired pressure. The capillary opens into the distilled water of the bath in which the bulb and capillary are immersed. After the dimensions of the bulb and capillary have been found, it is only necessary, in making a viscosity determination at any given temperature, to observe the time necessary for a volume of liquid equal to that contained in the bulb to flow through the capillary under a determined pressure. Without going into detail at this point, it need be merely stated here that due means were taken for getting the true dimensions of the capillary and bulb, for filling the apparatus with clean pure liquid, and for estimating the mean effective pres- sure, which consists of the pressure obtained from the manometer plus the hydrostatic pressure from the FlG - 1. Poiseuiile's viscome- bottom of the falling meniscus in the bulb to the level of the capillary, minus the hydrostatic pres- sure from the level of the capillary to the surface of the bath, minus a correction for the capillary action in the bulb, and two corrections for the pressure of the atmosphere, which may be either positive or negative. One of these last corrections is due to the air within the apparatus being more dense than that outside, the other is due to the difference of pressure of the atmo- sphere upon the liquid surfaces in the upper arm of the manom- eter and in the bath, unless they happen to be at the same level. Law of Pressures. In obtaining this law all of the experi- ments were made at a temperature of 10C. For a capillary of given length and diameter, the time of transpiration was meas- ured for various pressures. For example, one capillary was 75.8 mm long, the major and minor axes of the end of the capillary nearer the bulb were 0.1405 and 0.1430 mm and those of the open end 0.1400 and 0.1420 mm respectively. The pressures used are given in the first column of Table I and the times of transpiration in column 2. One of these values is then employed to calculate the others on the assumption that the times of tran- spiration are inversely proportional to the pressures, as given in column 3. 10 FLUIDITY AND PLASTICITY TABLE I. CAPILLARY A' Pressure in Observed time millimeters of mercury at 10C for transpiration of 13. 34085 cc of water Calculated time Per cent difference 97.764 10,361.0 147 . 832 6,851.0 6,851.91 0.01 193 . 632 5,233.0 5,231.22 0.03 337.675 2,612.5 2,612.84 0.01 738.715 1,372.5 1,371.20 0.09 774 . 676 1,308.0 1,307.55 0.04 In the above case it is certainly true that the rate of flow is proportional to the pressure, but it is equally certain that this relation no longer holds when the capillary becomes sufficiently shortened. Thus when the length of the tube used above is shortened to 15.75 mm, the values given in Table II are obtained. TABLE II. CAPILLARY A Pressure in Observed time millimeters of ! for transpiration Calculated Per cent mercury at of 13 . 34085 cc time difference 10C of water 24.661 8,646 49.591 4,355 4,299 - 1 . 29 98.233 2,194 2,170 -1.09 148.233 1,455 1,438 -1.17 194.257 1,116 1,097 -1.63 388.000 571 549 -3.85 775.160 298 275 -7.72 Not only is there a marked deviation from the assumed law of pressures as soon as the capillary is sufficiently shortened, but the percentage difference between the observed and calculated values increases quite regularly as the pressure increases. But in either case, whether the capillary is shortened or the pressure increased, we note that the velocity is decreased. Whether the irregularity here observed is due to the use of some of the avail- able work in imparting kinetic energy to the liquid, or it is due THE LAW OF PO1 SEVILLE 11 to eddy currents which appear under conditions of hydraulic flow, we will reserve for later discussion. This question was not considered by Poiseuille, yet with a great variety of tables show- ing an agreement like that in Table I above, Poiseuille was fully justified in concluding that for tubes of very small diameters and of sufficient length, the quantity of liquid which transpires in a given time and at a given temperature is directly proportional to the pressure, or V = Kp, where K is a constant, V the volume, and p the pressure head, causing the flow through the tube. Law of Lengths. Poiseuille next studied the effect of the length of the tube upon the rate of flow, but this problem pre- sented exceptional difficulty owing to the fact that tubes are never of uniform cross-section. With the camera lucida he ex- amined and measured each section of the tubes, which had been carefully selected from a large number, and finally corrections were made for the small changes in diameter, assuming the law of diameters to be given later. This seems justified since the corrections were very small. In Table III the results are given which Poiseuille obtained with capillary "B." The lengths of the capillary are given in column 1, the major and minor axes of the free end in column 2, the time required for the transpiration TABLE III. CAPILLARY B Length of tube in millimeters Major and minor axes of free end Time of transpiration of 6.4482 cc Time calculated Per cent, difference 100.050 f 0.1135 (0.1117 2,052.98 75.050 0.1140 0.1120 1,526.20 1,539.0 0.85 49.375 0.1142 0.1122 998.74 ! 1,004.0 0.53 23 . 575 0.1145\ \ 0.1123] 475 . 18 476.8 0.34 9.000 3.900 f 0.1144\ J0.1124/ j 0.1145 \ \ 0.1125/ 199.39 110.20 181.4 86.4 -9.05 -21.64 12 FLUIDITY AND PLASTICITY of the 6.4482 cc of water at 10C contained in the bulb at a constant pressure of 775 mm of mercury are given in column 3. Assuming that the time of flow is directly proportional to the length of the tube, Poiseuille used the time of one experiment to calculate the one immediately succeeding, and thus are ob- tained the values given in column 4. It is evident that the last two lengths are too short, but the others fairly substantiate the law. The agreement is still better when corrections are made for the varying diameters of the tube. This correction is espe- cially important since, as will be shown, the efflux rate varies as the fourth power of the diameter. From results like those exhibited in Table III Poiseuille concluded that the quantity of liquid passing through a tube of very small diameter at a given temperature and pressure varies inversely as the length, and we have that V = K"p/l where I represents the length. But the last two observations show that this law has its limitations. Law of Diameters. To discover the relation between the diameter of the capillary and the rate of flow, Poiseuille calculated the quantity of water which would flow through 25 mm of the different tubes at 10C under a pressure of 775 mm of mercury in 500 seconds, obtaining the values given in Table IV. TABLE IV Designation of tube Mean diameter ' of tube in centimeters Volume efflux in 500 sec. from observations Volume calculated ' Per cent, difference M 0.0013949 0.0014648 0.001465 +0.02 E 0.0029380 0.0288260 ! 0.028808 -0.07 D 0.0043738 0.1415002 : 0.141630 +0.10 C 0.0085492 2.0673912 i 2.066930 -0.02 B 0.0113400 6.3982933 ! 6.389240 -0.14 A 0.0141600 15.5328451 j 15.547100 +0.10 F 0.0652170 6,995.8702463 The volumes calculated in the fourth column are obtained by comparing each tube with the one following on the assumption that the quantity traversing the tube is proportional to the fourth power of the diameter, thus 0.002938 4 : 0.0013949 4 = 0.028826: x, or x = 0.001465. The agreement is very satisfactory, hence the THE LAW OF POISE UILLE 13 pd* formula becomes V = K ~j- For water at 10C he found the value of K to be quite exactly 2,495,224, p being expressed in millimeters of mercury at 10 and I and d in centimeters. He experimented with alcohol and mixtures of alcohol and water and for these we obtain different values of K. Poiseuille did not use the terms viscosity or fluidity, nevertheless these values of K are proportional to the fluidity. The Effect of Temperature on the Rate of Flow. Girard had given a formula to represent the flow of water in a pipe as a function of the temperature, but the constants had to be deter- mined for each pipe. Poiseuille gave a formula for capillary tubes which was independent of the instrument used, Q = 1,836,724,000(1 + 0.03367937 7 + 0.00022099367 72 )^ where Q represents the weight of water traversing the capillary in a unit of time. The adequacy of this formula to reproduce the observed values is shown in Table V. TABLE V. CAPILLARY A I = 10.05 cm d = 0.0141125 cm p = 776 mm of mercury. Time of flow 1,000 sec. WEIGHT OF EFFLUX WEIGHT OF EFFLUX CALCULATED BY TEMPERATURE OBSERVED FORMULA 0.6 5.74376 5.73955 5.0 6.60962 6.60381 10.0 7.64649 7.64435 15.0 8.74996 8.74705 20.0 9.91530 9.91191 25.0 11.14584 11.13892 30.1 12.45631 12.45423 35.1 13.80695 13.80710 40.1 15.21866 15.22184 45.0 16.67396 16.66860 Since the values calculated are weights and not volumes, the values of Q are not proportional to the fluidity. This formula pd* remains empirical, but the expression V = K , can be readily derived from the fundamental laws of motion. Theoretical Derivation of the Law. Hagenbach (1860) appears to have been the first to give a definition of viscosity. He made 14 FLUIDITY AND PLASTICITY a very careful study of the earlier work on viscosity and gave a theoretical derivation of the law of Poiseuille, which has had very great effect upon the succeeding history of this subject. Neumann gave the deduction of the Law of Poiseuille in his lectures on Hydrodynamics in 1858, and thus prior to the publi- cation of Hagenbach's paper in March, 1860. This deduction was first published by Jacobson early in 1860 and the lectures were published in full in 1883. In April, 1860 Helmholtz pub- lished the derivation of the law from the equations of motion. J. Stephan (1862) and Mathieu (1863) gave independent deriva- tions of the law. Reference should also be made to the treat- ment of the flow in long narrow tubes by Stokes (1849). Imagine a horizontal capillary whose bore is a true cylinder to connect two reservoirs L (left) and R (right) there being a differ- ence of pressure between the two reservoirs, at the level of the capillary, amounting to p grams per square centimeter. If the pres- sure in L is the greater the direction of flow through the capillary will be from left to right. The total effective pressure p is used up in doing various forms of work, several of which can be differ- entiated with a resultant gain in clearness of understanding of the conditions of flow. 1. Near the entrance to the capillary the particles of fluid undergo a rapid acceleration; this absorption of kinetic energy causes a fall in the pressure amounting to pk. 2. Within the capillary, there may be a finite movement of the fluid over the walls of the tube, due to slipping. Unless the external friction is zero or infinity, work will be done and there will be a fall of pressure p s . 3. Unless the external friction is zero, the layers of fluid nearer the walls of the tube will move more slowly than the layers nearer the axis of the tube, and an absorption of pressure due to this internal friction will result. Let this be p v . 4. If the path of the particles through the capillary is not perfectly linear, the additional distance travelled in the eddies, will give rise to a further drop in the pressure amounting to p e . This turbulent flow is certain to occur when the velocity of flow becomes sufficiently high. 5. But even before the velocity becomes turbulent it seems possible that the stream lines at the extremities of the tube may THE LAW OF POI SEVILLE 15 be somewhat distorted, in which case there must be a drop in pressure p e . 6. Heat is produced as the fluid passes through the tube and therefore the temperature may be different at different points of the tube and since the temperature greatly affects the viscosity of most substances, this may affect the amount of work done in the passage through the tube. If the fluid is incompressible it will have the same mean velocity through each cross-section of the capillary, and the pressure must fall in a linear manner at least so long as the flow is linear. If on the other hand the substance is compressible, the velocity must increase as the fluid passes through the tube, because of the expansion which results from the decrease of pressure. With the expansion there is a lowering of the temperature. Let the resultant effect of these changes in the temperature upon the effective pressure be p T . It may be either positive or negative. At the exit of the capillary the fluid has no effective pressure but it still possesses all of its kinetic energy which causes the fluid to go for a considerable distance out into the reservoir R, dragging some of the fluid in R with it and producing eddies, so that the kinetic energy is finally dissipated in overcoming viscous resistance outside of the capillary, and not in adding to the effec- tive pressure, as Applebey (1910) has supposed. The sum of these possible losses of effective pressure is then p = p k + p s + Pv + p e + p s + PT (2) We shall consider first the case where p = p v , supposing that the fluid is incompressible, as is nearly the case in liquids. Let the radius of the capillary be R and the radius of a hollow cylinder coaxial with the capillary be r. It is evident from the symmetrical arrangement that at every point in such a cylinder, the velocity must be identical. Let this velocity be v. The dv rate of deformation must be -r; and the tangential force due to dv the viscous resistance, acting from right to left, will be 77 -3- (cf. Eq. (1)). Over the whole surface of the cylinder whose length is /, this force must amount to dv 16 FLUIDITY AND PLASTICITY But the force due to the frictional resistance on the outside of the cylinder must be exactly balanced by a force due to the pres- sure and this is - irr 2 pg where p is the pressure in grams per square centimeter and g is the acceleration due to gravity. The negative sign is used because this force acts from left to right. We have then that but v = when r = R, therefore the constant of integration K can be evaluated JT R * /Y A j 4/77 ,-J*(.-0 (3) From Eq. (3) we may obtain the velocity in centimeters per second at any point in the capillary. It follows that the liquid flowing through the capillary in a given time has the volume of a paraboloid of revolution. If the volume per second is U, then = which is the Law of Poiseuille. If V is the total volume of efflux in the time t, the formula becomes r - (v Sir, The mean velocity of the fluid, in cubic centimeters per second passing through the tube, /, is '-^-f Summary. The simple law of Poiseuille was first discovered experimentally, after which its theoretical deduction was quickly made. There is, however, a considerable amount of data for which the simple law is not sufficient. The law may be given far greater usefulness by adding certain correction terms, which are the subject of discussion in the following chapter. CHAPTER III THE AMPLIFICATION OF THE LAW OF POISEUILLE The Kinetic Energy Correction. In deriving the law in the preceding chapter, we limited ourselves to the simplest case, where all of the energy is employed in overcoming viscous resis- tance within the fluid, or p = p v . It is desirable however that the law be given a wider application, and that the law be tested under the most varied conditions. In the experiments which Poiseuille used to verify his law, the kinetic energy correction was negligible, but the time necessary for a single determination was often excessive, consuming several hours. It is to be recalled at this point that in some of his experiments, in which the rate of flow was higher than in the others, the law was not verified. Poise- uille and others have been greatly troubled in their viscosity de- terminations by dust particles becoming lodged in the capillary. If it were possible therefore to employ higher speeds, not only would there be an economy in time but the dust particles would be much' more likely to be swept out from the tube. However in using these higher velocities a correction for the loss in kinetic energy must be applied. Hagenbach (1860) is the first one to attempt to make this correction, the results of whose work became generally known, although it appears that Neumann prior to 1860 had made the correction in nearly its present form. The work of Neumann was reported by Jacobson in 1860 but his work has also remained but little known to workers in this field. Gartenmeister (1890) reported that Finkener had arrived at a correction which differed from that of Hagenbach, but Finkener seems not to have pub- lished any monograph on the subject stating why he considered his correction superior. However Couette in the same year (1890) published a very important paper in which he arrived independently at the same correction as that given by Neumann and Finkener, and a year later Wilberforce (1891) independently attacked the same subject and showed that there is a slip in the 2 17 18 FLUIDITY AND PLASTICITY reasoning of Hagenbach. He showed that Hagenbach should have reached a value which is identical with that given by the others. The correction may be simply deduced as follows: The kinetic energy of the fluid passing any cross-section of a cylindrical tube per unit of time is where p is the density of the fluid. Since the volume of fluid passing any cross-section per unit of time is TrR 2 I, the energy sup- plied in producing the flow is irR 2 Ipg, hence, the energy converted into heat within the tube must be irR 2 I(pg p/ 2 ). From Eqs. (2) and (6) we have P) Thus taking into account the loss in kinetic energy, the formula of Poiseuille becomes mpV SVl ftrft in which m is a constant which according to the above derivation is equal to unity. The formula of Hagenbach differed only in that the constant m is equal to 2 ~^ or 0.7938. It is of historical interest in this connection to note that Ber- nouilli's assumption that all of the particles flowing through a pipe have the same velocity, leads one to the conclusion that the kinetic energy of the fluid passing any cross-section per unit of irR 2 ! 3 time is exactly one-half of that given above or ^ ' an< ^ the value of m in that case would be only 0.50. This value was actu- ally suggested by Reynolds (1883) when the openings of the tubes were rounded or trumpet-shaped, but m = 0.752 when the ends are cylindrical. It may be added that Hagenbach compared his value of 0.7938 with the observed values obtained by various hydraulicians working with wide tubes, Hagen 0.76, Weisbach 0.815, Zeuner 0.80885, Morin 0.82, and Bossut 0.807, and he found that his value was near the mean. But account should have been taken of the fact that their results apply to the tur- bulent regime, but not necessarily to the regime of linear flow. Boussinesq (1891) while admitting the correctness of the AMPLIFICATION OF THE LAW OF POI SEVILLE 19 method used by Couette and as we have seen, also by Neumann, Finkener, and Wilberforce as a first approximation, gives a more rigorous treatment of the subject on the basis of the kinetic theory by which he finds m = 1.12. Knibbs (1895) in a valuable discussion of the viscosity of water by the efflux method has studied carefully the data of Poiseuille and Jacobson in the effort to find the value of m which would most nearly accord with the experimental results. Throwing Eq. (8) in the form 8?; VI mpV 2 /r . N Pi = fT^ 1 O T1AA ' (9) TfgK ir^gK t we observe that since for a given tube and liquid only p and t 15 ^ ^ 14 ^ k> 13 ^ *" tf % q n Q. o . ' 3& g r*B >n c^. J x g -cT- ^ -t- ^i jy *^ ^ ^ *" s ^ J S 1 1 ) 11 FIG. 2. Finding the value of m for the kinetic energy correction. vary, this is the equation of a straight line and may be written, (9a) where a and 6 are constants. Plotting the values of 1/t as abscis- sas and of pt as ordinates Knibbs obtained the curves shown in Fig. 2, using the data for Poiseuille's tubes A v , A vn , B v , and C v . When t becomes very great the corrective term vanishes and pt = a. The values of a are given by the intercepts of the curves with the axis of ordinates. The tangent of the angle which a line makes with the axis of abscissas gives the value of b, from which the value of m is obtained, since 20 FLUIDITY AND PLASTICITY Using a combination of numerical and graphical methods the following values were obtained. TABLE VI. VALUES OF ra DEDUCED BY KNIBBS FROM POISEUILLE'S EXPERIMENTS Tube Length in centi- meters Mean radius in centimeters Values of m A 111 2 55 00708 04 A 1 57 0.00708 .02 A v 95 00708 15 A VI 68 00708 08 A vn 10 00708 12 B B IV B v C v F 1 10.00 0.90 0.39 0.60 20.00 0.00567 0.00567 0.00567 0.00427 0.03267 .23 .14 .03 .87* .08 F" 9 97 03267 33 F 111 F F v 5.04 2.60 1.07 0.03267 0.03267 0.03267 1.16 0.82* 0.82* The mean is 1.14 or rejecting the values for C v , F IV , and F v , 1.13. Certain of the tubes, viz., A, A 1 , A 11 , B 1 , B", B 111 , C, C 1 , C", C 111 , C IV , D, D 1 , D u , D ni , D IV , E, E 1 , E", and F give no satisfactory indication of the value of m. Knibbs deduced the value of m from 34 series of experiments made by Jacobson and obtained an average value of 1 . 14. This seems like a remark- able justification of the deduction of Boussinesq. But it should be added that the individual values vary from 0.82 to 1.44, yet perhaps this variation in the values of m should not be over- emphasized since in some instances the amounts of the corrections are much smaller than the discrepancies among the observa- tions themselves. Knibbs thinks that the values do vary more than can possibly be accounted for by the experimental error and that possibly the value of m is not a constant for all instruments. It is highly desirable that further experiments be undertaken to determine whether m is a constant and equal to 1.1 2 or if it is not constant, the manner of its variation. AMPLIFICATION OF THE LAW OF POI SEVILLE 21 To the present writer it seems probable that the kinetic energy correction is truly constant for all tubes which are perfect cylin- ders. Irregularities in the bore of the tubes will, however, have very great influence in altering the amount of the correction, since the correction, cf. Equation (7), depends upon the fourth power of the radius of the tube. The shape of the ends of the capillary has already been referred to in this connection, but it seems preferable to consider the effect of the shape of the ends of the tube as quite distinct from the kinetic energy correction. There has been a tendency among many recent experimenters to overlook the kinetic energy correction altogether, which is quite unjustifiable. We have indicated that it is not practicable to make the correction negligible. The only course open seems therefore to be to select a capillary which has as nearly as possi- ble a uniform cylindrical (or elliptical) cross-section, to assume that m for such a tube has the constant value of 1.12, but to arrange the conditions of each experiment so that the kinetic energy correction will not exceed 1 or 2 per cent of the viscosity being measured. In this case an error of several per cent in the value of the constant will not affect the result, unless an accuracy is desired which is higher than has yet been attained. If such an accuracy is desired the value of m should be found for each tube by the method of Knibbs which has been discussed above, or by the method employed by Bingham and White (1912), which will be described below in dis- cussing the alteration in the lines of flow at the ends of the tube. Correction for Phenomena of the Flow Peculiar to the Ends of the Tube. If two tubes of large diameter are connected by a short capillary, the lines of flow will be as represented in Fig. 3, the direction of flow being readily visible in emulsions, suspensions, or when a strongly colored liquid is allowed to flow out from a fine tube in the body of colorless liquid near the entrance to the capillary, as was done by Reynolds (1883). In the reservoir at the entrance A there is apparently no disturbance until the opening of the capillary is FIG. 3. Diagr 22 FLUIDITY AND PLASTICITY almost reached, and there the acceleration is very rapid. Even when the stream lines in the main part of the capillary are linear, it seems theoretically necessary to assume that there is a choking together of the stream lines near the entrance as indicated at c. It has been suggested that this effect might be prevented by using rounded or trumpet-shaped openings as indicated at d. At the exit of the capillary, the stream continues on into the reservoir B for a considerable distance with its diameter apparently unchanged. However the fall in pressure of the liquid passing through the large tube B is negligible, so that the flow observed just beyond the exit takes place at the expense not of pressure but of kinetic energy taken up at the entrance. There is no distortion of the stream lines just within the exit end of the capillary, and it is not clear that any correction at this end is necessary, under the conditions which we have depicted. If the capillary opens into the air, there will naturally be a capil- larity correction and the shape and material of the end of the tube will be of importance cf. Ronceray (1911). That the stream should continue for some distance beyond the exit with apparently constant diameter seems at first sight quite surprising, as one might suppose that the stream would at once drag along the adjacent fluid. The explanation is not far to seek. In the first place one should remember that the velocities even in the capillary are by no means uniform. Equation (3) tells us that particles which at a given moment are in a plane surface mno will after a certain time has elapsed be in a paraboloid surface mpo. The transition from the stationary cylinder of fluid in contact with the wall to the coaxial cylinders having high speed is apparently abrupt. As the exit of the capillary is passed, there is nothing to prevent the larger mass of liquid from being drawn along except its own inertia. But the rate at which the kinetic energy of the inner coaxial cylinders of fluid passes out into the outer cylinders is proportional to the viscosity of the medium and to the area of the cylinder. Thus in a fluid of low viscosity a capillary stream will penetrate for some distance. The stream disappears rather suddenly due probably to the development of eddies. Couette has attempted to evaluate the effects of the ends of the tubes by supposing that they are equivalent to an addition to AMPLIFICATION OF THE LAW OF PO I SEVILLE 23 the actual length of the capillary, which he represents by A. The corrected viscosity 7? c should therefore be calculated by the formula _ _ irgpRH mpV_ (1Q) According to Couette the corrected viscosity is always a little smaller than that calculated by means of Eq. (8) and we obtain the relation 77 _ I +A r, c I Since A may be presumed to be the same for tubes of equal diameter but of unequal lengths I and /', one should obtain different viscosities 17 and 77' by applying Eq. (8) to the same fluid. There would thus be the relation Tic (11) To test out his theory, Couette used experimental results of Poise uille with tubes A and A v which gave poor agreement with the simple law, Eq. (5) cf. Table II, VII and VIII. The efflux times are given in column 1, the viscosities rj p calculated from the simple Poiseuille formula (5), in column 2, the more nearly correct viscosities r? and rj', calculated from Eq. (8) taking m = 1.00, in column 3. TABLE VII. VISCOSITY OF WATER CALCULATED FROM POISEUILLE'S EXPERIMENTS WITH TUBE A" For dimensions cf. Appendix D, Table I, p. 331 Time r, P Eq (5) 77 Eq. (8), m = 1.00 8.646 0.01332 0.01328 4,355 0.01349 0.01339 2,194 0.01347 0.01332 1,455 0.01347 0.01324 1,116 0.01355 0.01325 571 0.01384 0.01325 298 0.01443 0.01330 24 FLUIDITY AND PLASTICITY TABLE VIII. VISCOSITY OF WATER CALCULATED FROM POISEUILLE'S EXPERIMENTS WITH TUBE A" For dimensions cf. Appendix D, Table I, p. 331 Time . (5) ,' Eq. (8), m = 1.00 3,829 0.01383 0.01363 1,924 0.01404 0.01363 994 0.01442 0.01363 682 0.01479 0.01364 537 01512 0.01366 291 0.01651 0.01382 165 0.01863 0.01388 The values of 77 vary but little around the mean 0.01329, while the values of t\ v show a regular progression, thus demonstrating the importance of the kinetic energy correction. The first three values of 77' in Table VIII are constant and equal to 0.01363. The last four values show a steady increase which may be due to turbulent flow at such high velocities. From 17 and 77', which are notably different in value, the corrected viscosity 77 C as well as the value of A may be obtained by the use of Eq. (11). We get 77 C = 0.01303 and A = 0.041 cm. The mean diameter of these tubes was 0.01417 cm hence, the fictitious elongation of the tube is a little less than three times the diameter i^-p = 2.868) Couette also obtained the corrected viscosity directly by experiment, in a very ingenious manner. He employed two capillaries simultaneously, which had the same diameter but different lengths. The arrangement of his apparatus is shown in Fig. 4, where T\ and 7 7 2 are the two capillaries connecting three reservoirs M, N, and P. The pressure in each reservoir is measured on the differential manometer H. Since the volume of efflux through both capillaries is the same and may be calculated from the increase in weight of the liquid in the receiving flask D, we obtain from Eqs. (7) and (9) the relation ZLJB*). V or + A) 8Vr, c (l 2 -A) i - p z r] c - AMPLIFICATION OF THE LAW OF PO I SEVILLE 25 By thus eliminating the correction for the kinetic energy and the ends of the tubes, Couette obtained, for the corrected viscosity (TJ C ) of water at 10, 0.01309 which is in excellent agreement with the value calculated above from Poiseuille's experiments. If, on the other hand, the viscosity (77) is calculated by means of Eq. (8) with m = 1.00 for one of Couette's tubes, the apparent viscosity (77) is 0.01389. From the values of 17 and ?7 C the value of A may be calculated as above. It is 0.32 cm and the diameter FIG. 4. Capillary-tube viscometer. Couette. of the tube is 0.090 cm so that the fictitious length to be added is a little over three times the diameter of the tube. In the experiments used by Couette to calculate the value of A the kinetic energy correction is very large, hence a consider- able error may have been introduced by taking m as equal to 1.00 instead of the more probable 1.12. Furthermore the range of data used in establishing his conclusion is rather limited. Hence, Knibbs has made an extended study of the same subject. If for A we substitute nR, Eq. (9) may be written 26 FLUIDITY AND PLASTICITY but since from Eq. (9a) we have that f mpV 2 \ J> ~ w&> ' = and therefore If values of ~oyj are > 5 FIG. 5. Finding the value of n for the "end correction." This is the equation of a straight line. plotted as ordinates and those of R/l as abscissas, the intercept on the axis of ordinates will give the corrected viscosity, i.e., the value of the viscosity when I = or R = 0; and the tangent of the angle made by the line with the axis of abscissas when divided by the viscosity will give the factor n required. Figure 5, taken from Knibbs' work, illustrates the method as applied to the tubes used by Poi- seuille B to B v and F to F IV . The values of n are found to be 5.2 and + 11.2 respectively. According to Knibbs "these results challenge the propriety of Couette's statement that A may be always regarded as positive and taken as nearly three times the diameter of the tube." In order to adequately test the question Knibbs took the whole series of Poiseuille's experiments at 10 and reduced them rigorously on the basis of Eq. (8) taking into account the peculiarities of the bore of the tubes used by Poiseuille as indicated in his data. Whenever possible the value of pt (cf. Eq. (9)) was obtained by extrapolation since then the correction term vanishes; in the other cases marked with a star, the value of m was taken as 1.12. The results are arranged according to increasing values of R/l, since if n has a positive value there should be a progressive increase in the values of the viscosity. Rejecting the last four values as uncertain, the general mean is 0.013107 which is almost identical with the mean for each group of eight, whereas if n had a constant value there should be a steady progression. On the other hand the values for the vis- cosity for the B series of tubes increase while those for the F series decrease as we go down the Table. It appears therefore that no general value can be assigned to n unless it be zero. AMPLIFICATION OF THE LAW OF PO I SEVILLE 27 TABLE IX. THE VISCOSITY OF WATER AT 10 CALCULATED BY KNIBBS FROM POISETJILLE'S EXPERIMENTS, USING EQ. (8) Tube f X 10S R* X 10 10 i? D 22 0.242840 0.013074* M C D 1 B C 1 E A B 1 F C" D 11 A 1 37 42 44 56 57 64 70 75 85 86 87 93 0.002367 3.250400 0.233770 10.235000 3.265900 0.047160 24.941000 Mean 10.276000 11,207.000000 3 . 298000 0.227870 25 059000 0.013090* 0.013028* 0.013020* 0.013202 0.013071* 0.013242* 0.013145 0.013109 0.013134* 0.013147 0.013151* 0.013078* 013109* En 115 10 303000 013070* A" 139 25 183000 013119* F 1 163 11,187.000000 Mean 0.013065 013109 E 1 C 111 174 175 0.048400 3 339400 0.013588* 013092* D m 219 224400 013045* B in 240 10 331000 013002* A 111 277 25 231000 012946 F n 326 11 233 000000 013249 QIV 421 3 339400 012498* A IV 450 25 231000 013343 Mean 013095 M 1 B iv 558 630 0.002367 10 357000 0.013181* 012742 F" 1 646 11 290 000000 013967 D IV E 1 C v A v A VI jpiv 649 706 709 742 1,046 1 254 0.223310 0.048400 3.339400 25.231000 25.231000 Mean 11 316 000000 0.012652* 0.013222* 0.012015 0.013515 0.013607 0.013113 014891 B v 1 455 10 368000 012193 F v 3 034 11 316 000000 014851 A vn ... 7,088 25.231000 0.016980 28 FLUIDITY AND PLASTICITY Bingham and White (1912) have confirmed the conclusion of Knfbbs by a study of interrupted flow. A capillary I = 9.38 cm R = 0.01378 cm was used to determine the time of flow of a given volume of water at 25 under a determined pressure. The capillary was then broken squarely in two and the parts separated by glass tubing, the whole being afterward covered with stout rubber tubing. The time of flow was again determined under the same conditions as before except that the corrections for kinetic energy and for the effects of the ends of the tubes were doubled by the interruption in the flow. The breaking of the capillary was then repeated until the capillary was in six parts, the corrections necessary being proportional to the number of capillaries. For this case Eq. (10) becomes jrgR*pt mpVb + &A) nt - C' 6A) mb (12) " I + 6A / + 6A where C and C' are constants under the conditions of experiment, and b is the number of capillaries, and A as before is the fictitious length to be added to each capillary. Substituting in Eq. (12) the values of the time of efflux and the pressure when the capillary is unbroken ti and p\ and when broken t 2 and p 2 respectively, we obtain the relation I + 6A Cp 2 t z - hence, I + A A = ti - C'm/ti K - 1 K b - K I. TABLE X. EXPERIMENTS TO DETERMINE THE "FICTITIOUS LENGTH" OF A CAPILLARY UNDER CONDITIONS OF INTERRUPTED FLOW Number of capillaries b Time Pressure in grams per cm 2 Cvt i.iac'6 K A c P t t I 179.7 87.46 0.0836 2 180.2 87.77 0.0837 1.001 0.009 3 182.4 87.32 0.0835 0.999 0.006 4 183.1 87.75 0.0836 1.000 0.000 6 185.0 88 . 25 . 0838 1.002 0.003 AMPLIFICATION OF THE LAW OF POI SEVILLE 29 Since the values of K are unity within the experimental error the addition to the length is zero. In no single instance does the value of A amount to even one-half the diameter of the tube. If however the value of m had been taken as unity, A would have appeared to have positive value. Had A been found to have a definite value, it would have been necessary to consider the legitimacy of making the correc- tion by means of an addition to the length of the capillary instead of by means of a correction in the pressure as suggested in Eq. (2), but since no definite value can be assigned to this correction, there is no need for raising the question. The shape of the ends of the tube are of considerable impor- tance in determining the development of turbulent flow, under cer- tain conditions. Tubes with trumpet-shaped entrances appear to promote linear flow (cf. Reynolds (1883) and Couette( 1890) p. 486). Slipping. Coulomb (1801) made experiments with an oscillat- ing disk of white metal immersed in water, and he noted that coating the disk with tallow or sprinkling it over with sandstone had no effect upon the vibrations. This seemed to prove that the fluid in contact with the disk moved with it, and that the property being measured was characteristic of the fluid and not of the nature of the surface. These observations were confirmed by O. Meyer in 1861. After the Law of Poiseuille had been experimentally and theoretically established, it was still unsatisfactory that the results of measurements of viscosity by the efflux method did not agree with those by other methods. It was natural to suppose that the discrepancy might be explained by the external friction between the fluid and the solid boundary which had been assumed by Navier (1823), cf. also Margules (1881) and Hada- mard (1903). Helmholtz in his derivation of the Law of Poi- seuille had taken into account the effect of slipping and obtained the formula, which in our notation is where X depends upon the nature of the fluid as well as upon that of the bounding surface. In treatises on hydrodynamics this is usually written F-g 30 FLUIDITY AND PLASTICITY /3 being the coefficient of sliding friction which is the reciprocal of the coefficient of slipping. From the experiments of Piotrowski upon the oscillations of a hollow, polished metal sphere, suspended bifilarly and filled with the viscous liquid, Helmholtz deduced a value for X of 0.23534 for water, but it is worth noting that he deduced a value of the viscosity which was about 40 per cent greater than that obtained by the efflux method. From some efflux experi- ments of Girard (1815) using copper tubes, Helmholtz deduced the value X = 0.03984. More recently Brodman (1892) has experimented with concentric metal spheres and coaxial cylin- ders, the space between being filled with the viscous substance. He thought that he found evidence of slipping. Slipping can be best understood in cases where a liquid does not wet the surface, as is true of mercury moving over a glass surface. If we consider a horizontal glass surface A, Fig. 6, as being moved tangentially toward the right over a surface E, FIG. 6. between which there is a thin layer of mercury C, then we can imagine that the mercury is separated from the glass on either side by thin films B and D of some other medium, usually air. Points in a surface at right angles to the above indicated by abed may at a later time occupy the relative positions a'b'c'd or if the films B and D are more viscous than the mercury the section may be better represented by a"b"c"d. But from Eq. (1) dv a (f>ds so that in any case, the respective contributions to the flow by the inner mercury layer or by the superficial films will depend upon their relative fluidities and their relative thicknesses. Whether the liquid wets the surface or not, anything which affects the AMPLIFICATION OF THE LAW OF POISEUILLE 31 fluidity of the surface film, whether it be surface tension, absolute pressure, positive or negative polarization, static electricity, or magnetism may therefore affect the amount of flow. And these effects when detected experimentally would undoubtedly be attributed to slipping or to the overcoming of external friction. So while we might expect the effect of slipping to be more pro- nounced in cases where the liquid does not wet the surface, it is quite possible that even when the liquid does wet the surface, the fluidity of the liquid near the surface is not identical with that within the body of the liquid. On the other hand, it is important to remember that the thickness of the layer of liquid affected by the forces of adhesion, with which we are here chiefly concerned, is only molecular. Even with mercury in a glass tube, the thickness of the layer of air seems to be of molecular dimensions. One may get an idea of the upper limit to this thickness by the following experiment. A thread of mercury was placed in a narrow capillary so that the air surface would be relatively large. Taking care that no air-bubbles were present, the length of the thread was measured with a dividing engine, in a determined part of the tube. The tube was exhausted from both ends simultaneously and the thread moved back and forth in order to sweep out the supposed layer of air. When the mercury was finally brought back to its former position no decrease in length could be detected. In order to have slipping under ordinary conditions of measurement it would appear that the surface film must be of very much more than molecular thickness or else it must have practically infinite fluidity. In view of the strong adhesion 1 between all liquids and solids it seems improbable that the particular layer of liquid in contact with the solid should show an amount of flow which is comparable in amount with that of all of the other practically infinite layers of liquid. Nevertheless if the value deduced by Helmholtz for water on a metal surface be correct, X = 0.23534, the effect of slipping ought to be readily observed. According to Whetham (1890), if we take R = 0.051, Eq. (12) becomes V = ^ 117.67 X 10~ 6 l Cf. Duclaux, 1872. 32 FLUIDITY AND PLASTICITY whereas if there were no slip and therefore X = we would have F = ^ 7 6.25 X 10- 6 8rjl Thus it would appear that the rate of flow through a polished metal tube should be nearly 20 times more rapid than through a tube in which there is no slip. Since Poiseuille's experiments prove that the viscosity is constant for tubes of very different radius when calculated without regard to slipping, there can be no slipping when water flows through glass tubes. This conclusion is admitted by Helmholtz. Jacobson (1860) criticised Helmholtz's use of Girard's experi- ments in that he failed to apply any correction to the pressure. Jacobson himself experimented with copper tubes as well as glass tubes but found no evidence of slipping. Warburg (1870) investigated the flow of mercury in glass tubes. He found that Poiseuille's law of pressures and his law of diameters were verified, which proved that slipping did not occur. Be"nard as reported by Brillouin (1907) page 152, has repeated the work of Warburg using greater care, and he finds that X cannot have a value greater than 0.00001. Whetham (1890) caused water to flow through a glass tube before and after being silvered, proper corrections being made for changes in temperature and in the radius of the tube, due to the silver layer. Different thicknesses of silver as well as different pressures were used, but the difference in the times of flow between the silvered and unsilvered tubes were all within the limit of experimental error. Copper tubes were also used and the results in all cases were in agreement with Poiseuille's observations. Cleaning the tubes with acids and alkalies, polish- ing with emery powder, coating with a film of oil and amalgamat- ing with mercury were all without effect in producing a deviation which could be detected. Whetham repeated an experiment of Piotrowski with an oscillating glass flask, plain and silvered. Care was taken to make correction for temperature and to prevent changes in the bifilar suspension which seems to have been neglected by Piotrowski. Whetham found the ratio of the friction of water on glass to the friction of water on silver to be 1.0022, which may be taken as unity within the limits of experi- mental error. Couette (1888-1890) attacked the problem AMPLIFICATION OF THE LAW OF PO I SEVILLE 33 independently but along much the same lines. He tried the effect of a layer of grease and of silver on the inside of a tube. He found invariably the same efflux time or even a little greater which was due to the diminution in the radius of the tube. But even this latter effect did not occur when the thickness of the silver layer was a negligible fraction of the radius of the tube. He then used tubes of white metal, copper, and paraffin using rates of efflux close to the critical values, and obtained the following results: TABLE XI. COUETTE'S EXPERIMENTS ON SLIPPING Substance of tube Temperature , 1 T] Calculated from Tj Observed . .,, roiseuille Copper Copper White metal 15.5 17.3 18.2 0.01175 0.01073 0.01037 0.01130 0.01079 0.01055 White metal 18.9 0.01064 0.01037 White metal 18.3 0.01092 0.01052 Paraffin 12.6 0.01241 0.01219 Paraffin 12.9 0.01278 0.01209 Paraffin 12.3 0.01276 0.01228 Couette goes further and gives reasons for the conclusion that slipping does not occur even after the flow becomes turbulent. More recently Ladenburg (1908) has carefully repeated the experiments of Piotrowski under as nearly as possible the same TABLE XII. LADENBURG'S EXPERIMENTS WITH AN OSCILLATING GLASS FLASK, SHOWING ABSENCE OF SLIPPING, AT 19 . Flask Logarithm dec- rement Period of vibration Remark A 0.019570+2 11,9732 Unsilvered A 0.019642+3 12,049+2 Silvered A 0.019620 3 11,990 + 1 Unsilvered j B 0.025026+25 11,716+4 Unsilvered B 0.025011 + 15 11,688+2 Silvered C 0.025162 2 11,8702 Silvered 34 FLUIDITY AND PLASTICITY experimental conditions. He used plain and silvered oscillating glass vessels and a hollow metal sphere. Table XII proves conclusively that slipping was absent in the former case. Using the hollow metal sphere filled with water, Ladenburg obtained values of the viscosity which agree with the values found by other methods, and shown in Table XIII. TABLE XIII. A COMPARISON OF THE VISCOSITY OF WATER AS OBTAINED BY DIFFERENT METHODS (LADENBURG) Method 17 at 17.5 , at 19.2 Observer Efflux glass 0.01076 0.01031 Poiseuille (1846) Efflux glass Efflux glass Efflux glass Oscillating solid sphere Oscillating hollow cylinder. . Oscillating hollow sphere . . . 0.01065 0.01075 0.01067 0.01099 0.01082 0.01065 0.01027 0.01030 0.01025 0.01054 0.01037 0.01032 Sprung (1876) Slotte (1883) Thorpe and Rodger (1894) W. Konig (1887) Mutzel (1891) Ladenburg (1908) Ladenburg indicates how Helmholtz erroneously obtained his large coefficient of slipping by overlooking a point in the theory, and recalculating Piotrowski's data he finds that instead of the viscosity being 40 per cent greater than the generally accepted value, this difference becomes only 3 per cent and the slipping becomes negligible. It was stated above that the verification of the Law of Diameters of Poiseuille is a proof that slipping does not occur between glass and water. Knibbs (1895) has collected an extensive table of observations of the viscosity of water at 10 for tubes of various materials having radii varying from 0.0140 to 0.6350 cm or nearly a thousand-fold, but there is no evidence of progressive deviation as the radius increases. In experimenting on the possible effect of an electrical or magnetic field upon viscosity, W. Konig (1885) obtained a negative result. Duff (1896) seemed to detect an increase in the viscosity of castor oil of 0.5 per cent using the falling drop method and a potential gradient of 27,000 volts per centimeter, but for the most part the results were negative. Quincke (1897) AMPLIFICATION OF THE LAW OF POI SEVILLE 35 found a definite effect on the viscosity in an electrical field, which Schaufelberger (1898) attempted to explain on the basis of hysteresis. However, Pacher and Finazzi (1900) obtained results which were contrary to those of Duff and Quincke finding that insulating liquids under the action of an electrical field do not undergo any sensible change in viscosity. Ercolini (1903) made experiments along the same line and concluded that the effect was less than his experimental error. He used petroleum, benzene, turpentine, olive oil, and vaseline. Carpini (1903) measured the viscosity of magnetic liquids in a magnetic field but found no certain effect. Koch (1911) tried the effect of oxygen or hydrogen polarization at the boundary using a platinum tube and an oscillating copper disk. No change in the viscosity was observed and Koch regards this as strong evidence against slipping. Ronceray (1911) has studied the effect of surface tension. These results seem to make it quite certain that, whether the liquid wets the solid or not, there is no measurable difference between the velocity of the solid and of the liquid immediately in contact with it, at least so long as the flow is linear. The Transition from Linear to Turbulent Flow. It is well known that the formulas which have been discussed do not apply to the ordinary flow of liquids in pipes. Under ordinary conditions we know that the flow is undulatory, instead of being linear as is assumed in the simple laws of motion. It is important that we know under what conditions these sinuous motions appear so that they may be properly taken into account or guarded against. An extended study of the flow of water in pipes having a diameter varying from 0.14 to 50 cm was made by Darcy (1858). He found the hydraulic resistance proportional to I n where n had a value nearly equal to 2 (1.92). He saw more clearly than any of his predecessors that hydraulic flow is very different in character from the viscous flow studied by Poiseuille, since the viscous resistance is proportional to the first power of the mean velocity (/). Darcy paid little attention to the tem- perature at which his experiments were carried out, probably as Reynolds remarks, because "the resistance after eddies have been established is nearly, if not quite, independent of the viscosity." Since Darcy's work was approved by the Academy 36 FLUIDITY AND PLASTICITY in 1845, he is probably the first to distinguish clearly between the two regimes. Hagen (1854) investigated the effect of changes in temperature upon the rate of efflux in tubes of moderate diameters. Figure 7 8.?! NARROW TUBE MEAN TUBE WIDE TUBE III! 0.71 0.98 ~0 5 10 15 ?0 15 10 35 40 , 45 50 55 60 65 10 Temperature Degrees Reaumur FIG. 7. Transition from linear to turbulent flow. The effect of temperature. exhibits the results of his experiments. The abscissas are degrees, Reaumur, the ordinates the volumes in cubic inches ("Rheinland Zollen ") transpiring in a unit of time. The pressure to which each curve corresponds is given at the right of the figure, being expressed in inches of water. Hagen used three tubes of varying width as follows: AMPLIFICATION OF THE LAW OF POI SEVILLE 37 Tube Radius, inches Length, inches Narrow 053844 18 092 Mean. 077394 41 650 Wide 11.391400 39.858 FIG. 8. Apparatus of Reynolds for studying the critical regime. Inspection of the figure shows that with the lowest pressure and the smaller tubes the efflux is a linear function of the temperature except at the highest temperatures. With the wide tube, however, there is a maximum of efflux at about 37 even at the smallest pressure. As the pressure is increased the maximum appears at a 38 FLUIDITY AND PLASTICITY lower and lower temperature and the maximum appears even in the smallest tube used. There is a minimum of efflux after passing the maximum but then the efflux becomes again a linear function of the temperature. Brillouin (1907) page 208, has confirmed the experimental results of Hagen. A clear picture of the phenomena connected with the passage from one regime to the other has been given by Reynolds (1883). One form of apparatus used by him is depicted in Fig. 8. It FIG. 9. Linear flow. consists of a glass tube BC, with a trumpet-shaped mouthpiece AB of wood, which was carefully shaped so that the surfaces would be continuous from the wood to the glass. Connected with the other end is a metal tube CD with a valve at E having an opening of nearly 1 sq. in. The cock was controlled by a long lever so that the observer could stand at the level of the bath, which surrounded the tube BC. The wash-bottle W contained a colored liquid which was led to the inside of the trumpet- shaped opening. The gage G was used for determining the level Fia. 10. The beginning of turbulent flow. of water in the tank. When the valve E was gradually opened and the color was at the same time allowed to flow out slowly, the color was drawn out into a narrow band which was beautifully steady having the appearance shown in Fig. 9. Any consider- able disturbance of the water in the tank would make itself evident by a wavering of the color band in the tube; sometimes it would be driven against the glass tube and would spread out, but without any indication of eddies. As the velocity increased however, suddenly at a point 30 or more times the diameter of the tube from the entrance, the color AMPLIFICATION OF THE LAW OF POISEUILLE 39 band appeared to expand and to fill the remainder of the tube with a colored cloud. When looked at by means of an electric spark in a darkened room, the colored cloud resolved itself into distinct eddies having the appearance shown in Fig. 10. By lowering the velocity ever so slightly, the undulatory movement would disappear, only to reappear as soon as the velocity was increased. If the water in the tank was not steady the eddies appeared at a lower velocity and an obstruction in the tube caused the eddies to be produced at the obstruction at a consider- ably lower velocity than before. "Another phenomenon which was very marked in the smaller tubes was the intermittent char- acter of the disturbance. The disturbance would suddenly come on through a certain length of the tube, pass away, and then come again, giving the appearance of flashes, and these flashes would often commence successively at one point in the pipe." The ap- pearance when the flashes succeeded each other rapidly is shown w FIG. 11. Flashing. in Fig. 11. "This condition of flashing was quite as marked when the water in the tank was very steady, as when somewhat disturbed. Under no circumstances would the disturbance occur nearer the funnel than about 30 diameters in any of the pipes, and the flashes generally, but not always commenced at about this point. In the smaller tubes generally, and with the larger tube in the case of 'ice-cold water at 4, the first evidence of instability was an occasional flash beginning at the usual place and passing out as a disturbed patch 2 or 3 in. long. As the velocity further increased these flashes became more frequent until the disturbance became general." Reynolds further noted that the free surface of a liquid indi- cates the nature of the motion beneath. In linear flow, the sur- face is like that of plate glass, in which objects are reflected without distortion, while in sinuous flow, the surface is like that of sheet glass. A colored liquid flowing out into a vessel of water has the appearance of a stationary glass rod in the first regime, but as the 40 FLUIDITY AND PLASTICITY velocity is increased the surface takes on a sheet glass appearance due to the sinuous motions, and finally the stream breaks into eddies and is lost to view (cf. Collected Papers 2, 158). Reynolds reasoned from the equations of motion that the birth of eddies should depend upon a definite value of where R is a single linear parameter, as the radius of the tube, and / is a single velocity parameter, as the mean velocity of flow along the tube. Reynolds found the value of the constant to be approximately 1,000, hence, the maximum mean velocity in centimeters per second for which we may expect linear flow, may be taken to be / = im (14) In Table XIV we have calculated the value of the product pRI

"i THE LAW OF POI SEVILLE eJ 43 \ \ Log velocities 44 FLUIDITY AND PLASTICITY Number Diameter Temper- ature Surface A 0.0014 0.0270 0.0650 0.615 1.270 1.400 2.700 4.100 2.600 8.260 19.600 28.500 8.190 13.700 18.800 50.000 24 . 320 24.470 4.968 10 10 10 5 5 12 21 21 15 15 Glass 1 Glass ^ Poiseuille Glass j Lead No. 4 \ T j XT f rteyno Lead No. 5 J Lead Lead Lead Varnished Varnished Varnished Varnished Cast iron, new Cast iron, new Cast iron, new Cast iron, new Cast iron, incrusted Cast iron, cleaned Glass ds Darcy B c D E . F G H I J K L M N o p Q R S the oscillations in the mixed regime is entirely characteristic, it seems hardly probable that we can always sharply differentiate the mixed from the hydraulic regime. Indeed Couette (p. 486) Fio. 15. Coaxial cylinder viscometer of Couette. found that with a tapering tube the oscillations do not appear at all. One may draw the conclusion from Reynolds' observations AMPLIFICATION OF THE LAW OF POI SEVILLE 45 that the formula P = KI n may be used in the critical regime. Reynolds has compared the data of Darcy for large tubes, that of Poiseuille for small tubes, with his own, plotting the logarithmic homologues as in Fig. 13. The result is shown in U 9' 3/10 FIG. 16. Detail of coaxial viscometer. Fig. 14. Each line represents the logarithmic homologue for some particular tube, described in the figure. It is at once apparent that, for the most part, experiments have been made well below or else well above the critical values. In the small tubes of Poiseuille the velocities were below the critical values. 46 FLUIDITY AND PLASTICITY The smallest tube with which he experimented, A, gives a curve, only part of which is shown in the figure. It should be Ve 1 o c i 1 1) FIG. 17. The transition from viscous to hydraulic flow with coaxial cylinders. added that Reynolds corrected Poiseuille's data for the loss in kinetic energy. For pipes ranging in diameter from 0.0014 to 500 cm and for pressure gradients ranging from 1 to 700,000, there is not a difference of more than 10 per cent in the experimental and AMPLIFICATION OF THE LAW OF POISEUILLE 47 calculated velocities and, with very few exceptions, the agree- ment is within 2 or 3 per cent, and it does not appear that there is any systematic deviation. Couette (1890) has strongly confirmed the work of Reynolds by his measurements with coaxial cylinders. The external appearance of the apparatus used is shown in Fig. 15 where V is the outer cylinder of brass which can be rotated at a constant velocity by means of an electric motor around its axis of figure T. The inner cylinder is supported by a wire attached at n. A section through a part of the apparatus in Fig. 16, shows the inner cylinder s while g and g' are guard rings to eliminate the effect of the ends of the cylinder. The torque may be measured by the forces exerted on the pulley r which are necessary to hold the cylinder in its zero position. Plotting viscosities as ordinates and the mean velocities as abscissas, he obtained Fig. 17. Curve I represents the results for the coaxial cylinders, curve II represents the same results on five times as large a scale in order to show better the point where the regime changes. Curves III and IV are for two different capillary tubes. It is clear from the figure that the viscosity is quite constant up to the point where the regime changes. The apparent viscosity then increases very rapidly, and finally becomes a linear func- tion of the velocity. The dotted parts of the curves where the viscosity increases most rapidly, represents the region of the mixed regime, and the measurements were very difficult to ob- tain with precision. He proved that pRI

\ \ \ \ \ \ \ \ \ go ^0 \ \ ^" \ \ \ ^ ^ \ \ \ ^ V \ \ \ \ ^ \ \1 \ \ V \ \ v \ \ \ . s\ \ s \ V \ , s\ \ \ ^ A \\ \ ^ \ N N s ^ ^ \ " s ^ ^ \ ^ ^ \ 1 2 3 4 5 9 Observer Transpiration 5,942 Graham (1846) Oscillating disks 5,325 Maxwell (1866) Oscillating disks 5,814 Meyer and Springmuhl (1873) Oscillating disks 5,590 Puluj (1874) Oscillating disks 5,556 Puluj (1874) Transpiration 5,854 Obermayer (1875) Oscillating disks 5,489 Puluj (1876) Transpiration 5,951 Obermayer (1876) Transpiration 5,650 E. Wiedemann (1876) Transpiration 5,988 Obermayer (1876) Transpiration 5,952 Obermayer (1876) Transpiration 5,848 O. Meyer (1877) Transpiration 5,882 O. Meyer (1877) Transpiration 5,747 O. Meyer (1877) Oscillating disk 5,714 Puluj (1878) Transpiration 5,650 Hoffman (1884) Oscillating disk 5,955 Schumann (1884) Oscillating disk 5,838 Schneebeli (1885) Oscillating cylinder. . . . 5,831 Tomlinson (1886) Transpiration 5,770 Breitenbach (1899) Oscillating cylinder .... 5,659 F. Reynolds (1904) Transpiration 5,761 Tanzler (1906) The transpiration method appears to give higher values for the fluidity than are obtained by the other methods but the results are not very consistent among themselves. However the follow- ing table of recent values for the viscosity of air at 15 is very satisfactory. We have the authority of Fisher (1909) page 150, for the state- ment that "No experimenter has made the attempt to apply a correction to his measured pressures to allow for the kinetic energy of the emerging gas." It appears probable that the exist- 60 FLUIDITY AND PLASTICITY TABLE XXI. FLUIDITY OF Am AT 15 Method 7 FIG. 23. Viscometer for absolute measurements. 68 FLUIDITY AND PLASTICITY amount of liquid may flow into V from E after the record of the time has begun, and this will tend to offset the effect of any liquid left in V at the end of the time of flow. To make these amounts as nearly equal as possible, the lower part of E should be exactly similar in shape to the lower part of V. The pressure should be variable at will so that the time of flow may be kept reasonably constant. For gases, high pressures are as unnecessary as they are undesirable. For incompressible fluids, there need be no upper limit set to the pressure. A pres- sure of 50 g per square centimeter can easily be read to 0.1 per cent on a water manometer, and the various pressure correc- tions to be discussed may be ascertained well within this limit, hence this may be taken as a lower limit. The measurement of the radius of the capillary offers the great- est difficulty in viscosity measurement by this method. Since the flow is proportional to the fourth power of the radius, any error in this measurement is multiplied four times. Careful weighing of the quantity of mercury required to fill the tube is perhaps the best means for obtaining the mean radius, R = ^(W/irpl) ; but for a capillary such as that used by Thorpe and Rodger, I = 4.9+ cm R = 0.0082+ cm, the weight of the mer- cury is only about 0.013 g so that the desired accuracy is diffi- cult to obtain with the ordinary balance. If the radius is increased, the time of flow may be kept constant by increasing the length so that the ratio l/R* is constant. Fortunately both of these changes tend to increase the volume of the capillary. At the same time the increase in length diminishes the effect of any possible alteration in the stream lines near the ends; and the increase in the radius diminishes the possible effect of slip- ping and probably also the effect of dust particles. The formula (20) applies only to a capillary which has the form of a true cylinder, but usually the capillary is elliptical and it may at the same time be conical. To determine the conicity, the tube must be calibrated with a mercury thread. To deter- mine the ratio of the axes, the micrometer microscope should be used. In using the micrometer microscope it is somewhat difficult to see the exact circumference to be measured, owing to various causes. Poiseuille found it best to grind off and polish the end of the tube and then attach a cover-slip to this end by THE VISCOMETER 69 means of Canada balsam which is warmed slightly until it fills the end of the capillary. If the capillary is elliptical, R* in Eq. (20) must, according to Riicker (cf. Thorpe and Rodger (1893)), be given the value 2B 3 C S P2 _i_ rz wnere B and C are the major and minor axes of the ellip- .D "~T~ tical cross-section. If the capillary is the frustrum of a circular cone, Knibbs has shown that R* must be replaced by where R and R z are the radii of the two ends. If the capillary is at the same time elliptical, R* becomes 3R 3 S R* S (1 - e 2 ) 3 R 3 2 + R 3 Ri + RS ' 1 + e z where R 3 and # 4 represent the arithmetical means of the major r> _ ri and minor radii at their respective ends, and e = p . n where t> ~\~ B and C represent the mean semi-axes. Knibbs has also con- sidered the corrections necessary for other peculiarities in the bore of the tube which need not be considered here. There is no special advantage in using a variety of viscometers for liquids of not very different fluidity. For liquids below the boiling-point the fluidity never exceeds about 500. Assuming this value as the maximum the lengths necessary for a capillary of a given radius have been calculated by means of Eq. (5) and plotted curve A in Fig. 24. It is not always possible to obtain a capillary of an exactly specified radius, but with one having an approximately satisfactory radius, the necessary length can be read off from the curve. For gases the maximum fluidity must be taken as 10,000. If only very viscous liquids are to be meas- ured the maximum may be taken as less than 500, curve B or C. (cf. also Appendix A, Table IX.) Construction and Calibration of Apparatus. A point of great importance in the construction of the viscometer is to have the volume V (1) as nearly equal to that of V as possible, (2) similar to it in shape, and (3) at the same height from the hori- zontal capillary. This construction greatly facilitates the esti- mation of the correction for hydrostatic pressure, within the 70 FLUIDITY AND PLASTICITY instrument. Finally the small bulbs C, E, 'C', and E f should have nearly the same volume. By having the surfaces nowhere depart greatly from the vertical, the drainage is improved. It is impracticable however to use long, cylindrical bulbs, since then the true average pressure, due to the hydrostatic head within the instrument, becomes awkward to determine. (C/. Appendix A, page 297.) The best form for the bulbs V and V is therefore obtained by making them so that each resembles as much as ,f JS 006 .009 .010 .Oil .012 0.15 0.14 0.15 .016 .017 . .018 .019 .020 .021 Radius in cm. FIG. 24. Chart for use of instrument maker in selecting capillary for vis- cometer, knowing the approximate radius of the capillary and the maximum fluidity to be measured, the length to be used may be read off. V =3ml t =200 sec., p =50 g per cm 2 . possible a pair of hollow cones, placed base to base as shown in Fig. 23. The marks at 1 and 3 are so placed that the volume from 3 to F is exactly equal to that from 1 to 2'. If the two limbs of the apparatus are similar there will be no correction for capillarity. Poiseuille has given a method for estimating this correction when that is necessary. The volumes V and V may be easily deter- mined by the weight of volumes of mercury. The appearance of the complete apparatus used by Thorpe and Rodger is shown in Fig. 25. The viscometer is shown in the bath B which has transparent sides. Water in the vessel R exerts pressure upon the air in the large reservoir L. The gas THE VISCOMETER 71 FIG. 25. Complete viscometer apparatus of Thorpe and Rodger. 72 FLUIDITY AND PLASTICITY is dried by passing over sulfuric acid in a smaller bottle M t whence tubes lead to the three-way stop cocks Z and Z' and thence to the two limbs of the viscometer. The pressure is measured on the water manometer D. The bath is stirred by means of a motor connected with the mechanism shown at E. Since the fluidity of a substance like water changes from 1 to 3 per cent with a change of 1 in the temperature, it is necessary that the temperature be controlled to a few hundredths of a degree. Since they were working over a wide range of temperature, Thorpe and Rodger controlled the temperature by hand. A word may be added here in regard to stop-watches. The com- mon form of stop-watch in which the whole mechanism starts or stops simultaneously with the time record may not give consistent results, even though it appears to neither gain nor lose during a long period of time. This is the fault of the mechanism. The watches whose movements con- tmue, whether the time is being recorded or not, seem to be freer from this defect. The Measurement. In preparing substances for measurement as well as in cleaning and drying the instrument, many investi- gators have strongly emphasized the importance of avoiding the presence of dust particles. Both Poiseuille and Thorpe and Rodger took elaborate precaution in this regard. Figure 26 shows the apparatus used by the latter for distilling pure liquids. It has the advantage of allowing a good determination of the boiling-point to be made while the liquid is being fractionated. To avoid contamination by dust and moisture in filling the vis- cometer, Thorpe and Rodger used a special apparatus, Fig. 27. The liquid was placed in the bottle H and forced over into the right limb of the viscometer M by means of the pressure of a mercury head A. The viscometer was held in a frame and supported on the vertical rod by means of the setscrew N. no. 26.-Ap P aratu 8 of Thorpe and Rodger for obtain- ing dust-free liquid. THE VISCOMETER 73 The left limb of the viscometer was evacuated by means of the mercury head Q in order to draw the liquid through the capillary. Having run in a little more than the required amount of liquid, the viscometer and frame were placed in the bath B of Fig. 25 and the limbs of the viscometer were connected to the pressure outlets on either side. With the temperature main- tained constant at the lowest point at which measurements were desired, the cock Z f (or Z) was turned to air and the cock Z (or Z'} to pressure. As the liquid rose in the left limb, it finally overran into the trap T,' Fig. 22. At the instant that the meniscus in the right limb reached the point k 2 , the cock Z was turned to air. Thus the working volume was adjusted. A measurement of the fluidity is made by turning the cock Z' to pressure and immediately read- ing the pressure on the manom- eter as well as the temperature of the manometer, while the liquid is flowing out of the bulb V. As the meniscus passes the point m' the time recorded is begun. Keeping the temperature constant the time is taken as the meniscus passes the point m 2 . The pres- FIG. 27. Filling device of Thorpe sure is then read as before, and and Rodger. before the meniscus reaches the point k' the left limb is again turned to air. The apparatus is then ready for a duplicate observation in the opposite direction. The Calculation. The corrections to the time and temperature are not peculiar to viscosity measurements and need no special comment. In obtaining the pressure, several corrections must 74 FLUIDITY AND PLASTICITY be made. (1) The pressure on the manometer must be calculated to grams per square centimeter from the known height of the liquid and its specific gravity at the temperature observed. A correction to the observed height of the liquid is avoided by having the long limb of the manometer doubly bent at its middle point so that the upper half is vertical and in the same straight line with the lower limb of the manometer. The levels on both limbs may then be read on the same scale, which may con- veniently consist of a steel tape mounted on a strip of plate-glass mirror placed vertically. Similarly a correction for capillary action may be avoided if the bore of the manometer is large enough so that it may be assumed to be uniform. (2) The pres- sure must be corrected for the weight of the air displaced by the liquid in the manometer. (3) Unless the surface of the liquid in the lower limb of the manometer is at the same height as the average level of the liquid in the viscometer, a correction must be made for the greater density of this enclosed air, than of the outside air which is not under pressure. (4) Finally a correction must be made for the average resultant hydrostatic head of the liquid within the viscometer. If the two volumes V and V in Fig. 23 are exactly equal in volume, similar in shape, and at the same elevation above the capillary, when the viscometer is in position, in the bath, it is evident that the gain in head during the first half of the flow will be exactly neutralized by the loss in head during the last half of the flow. Since this cannot be exactly realized, a correction may be made as follows : Duplicate observations in reverse directions are made upon a liquid of known density and viscosity at a constant temperature and pressure. Let t\ be the time of flow from left to right and t z the corresponding time from right to left. Let p be the pressure as corrected, except for the average resultant head of liquid in the viscometer. Suppose this latter correction to amount to x cm of the liquid as the liquid flows from left to right. In this case the total pressure becomes equal to p + px and when the liquid flows from right to left, it becomes equal to p px. Since Eq. (8) when used for a given viscometer may be written in the form r, = Cpt - C'p/t (22) THE VISCOMETER 75 where C and C' are constants, which can be calculated, we obtain Po + PX= * + whence, Po _ 2C P U Cti r, + C'p/i* Ct z ^.Ti n 2CU 2 * 2 2 J In subsequent calculations it is necessary to know the specific gravity of the liquid whose viscosity is desired, in order to make the necessary pressure correction and in order to make the kinetic energy correction, but it is to be noted that if the instrument has been constructed with that end in view, these corrections will both be small, and there- fore the specific gravity need be only approximately known, which is a great advantage. Relative Viscosity Measurement. On account of the labor involved in obtaining the dimensions of the viscometer, many investigators have followed the example of Pf ibram and Handl in disregarding these dimensions, and calibrating the instrument with some standard liquid. The most important instrument of this class is that of Ostwald, Fig. 28. It "consists essentially of a U-tube with a capillary in the middle of one limb above which is placed a bulb. A given volume of liquid is placed in the instrument and the time measured that is required for the meniscus to pass two marks one above and one below the bulb under the influence of the hydrostatic pressure of the liquid only. If 770 is the viscosity of the standard liquid and 77 that of liquid to be measured, we have from Eq. (22) rj = Cpt - C'p/t and if 77 is very nearly equal to 7/0 or if t and t are very large, this may be written ? = -4, (23) 170 Po*o FIG. 28. The Ostwald viscometer. 76 FLUIDITY AND PLASTICITY FIQ. 29. Viscom- eter suitable for the relative measure- ment of not too viscous liquids. The pressure in this instrument must be proportional to the densities so that which is the formula suggested by Ostvvald. The formula is true for dilute solutions when water is taken as the standard, for 77 is then nearly equal to rj . It is inconvenient to make the time of flow very large both on account of the lack of economy and because of the increased danger of clogging. Unfortunately this formula has been used where neither of the necessary con- ditions was complied with and the results are therefore of uncertain value. It is much better to make the correction for the kinetic energy, in such cases, than to attempt to make the correction negligible. It is a disadvantage of the Ostwald instru- ment that the pressure is not variable at will, because if the time of flow is sufficient in one liquid, in another more viscous liquid the time of flow may be intolerably long, practically necessitating the use of a variety of instru- ments. Furthermore the total pressure is so small that a small error in the working volume may introduce considerable error into the result and the density of the liquid must be known with considerable accuracy. A form of instrument which has the mani- fest advantages of the Ostwald instrument and overcomes the above objections is shown in Fig. 29. The volume K is made as nearly as possible equal in volume, similar in shape, and at the same height as C. The working volume is contained between A and H and the volume of flow between B and D, the measurement being made as the meniscus passes either from B to D or from D to B THE VISCOMETER 77 depending upon the direction of the flow. The corrections are made as for absolute measurements and the viscosity calculated from formula (22). In obtaining the pressure correction due to the average resultant hydrostatic pressure in the viscometer C" can be estimated accurately enough by means of rough measure- ments. The value of C can be obtained accurately enough for the calculation of this correction by assuming p = p. After obtaining the value of the hydrostatic head x in this way, the true value of C may be calculated from an observation upon the time of flow of any liquid whose viscosity is accurately known. In the use of any relative instru- ment, it is important that two stand- ards be employed so as to obtain a check upon the method. For this purpose a single liquid may be used at widely different temperatures or two or more liquids may be used of widely different viscosities. While this test is very simple and its importance is obvious, it does not appear to have been frequently employed. Viscosity Measurements of Liquids above the Boiling-point. If the viscosity of liquids is to be measured above the ordinary boiling temperature, one must work at pressures above the atmospheric pressure. The three-way cocks in Fig. 22 must lead to a low- pressure reservoir, this pressure being measured by a second manometer. The rubber connections must of course be replaced by others capable of withstanding the desired pressure. Viscosity Measurement of Very Viscous Substances. Sub- stances like pitch which are excessively viscous can yet be measured by the efflux method by the use of very great pressure (cf. Barus (1893)). On account of the lack of proper drainage, Section V-Yl FIG. 30. Plastometer. For use with very viscous or with plastic substances. 78 FLUIDITY AND PLASTICITY the apparatus described above is unsuited. But in this case the- volume may very properly be obtained from the weight of the efflux into air, because the effect of surface tension would be FIG. 31. Viscometer for gases after Schultze. negligible at these high pressures. A viscometer designed for very viscous substances is shown in Fig. 30. The use of this form of apparatus is described in detail in connection with plastic flow (cf. Appendix B, p. 320). The Viscosity Measurement of Gases. A very satisfactory apparatus for the measurement of the viscosity of gases by the THE VISCOMETER 79 efflux method has been worked out through the labors of Graham (1846-1861), 0. E. Meyer (1866-1873), Puluj (1876), E. Wiede- mann (1876), Breitenbach (1899), and Schultze (1901). We may describe briefly the form used by Schultze as illustrating the modifications which are necessary in the apparatus used for liquids. In Fig. 31 the glass capillary, I = 52.54 cm, R = 0.007572 cm, is contained in the upper chamber of the bath /, which is maintained at constant temperature by water, water vapor, or aniline vapor. A condenser is shown at 6 and SS is a shield to protect the rest of the apparatus from the radiation. On either side of the bath the apparatus is exactly similar, so that only the right side is shown in the figure. The gas is contained in the bulbs P and Q (and P' and Q' on the left side) surrounded by a separate bath. The lower bulbs are each connected with two stop cocks B and C (or B' and C") ; from B (or B'} a rubber tube leads to the mercury reservoir G (or G'), and from C (or C') there is a glass tube drawn out into a capillary. Adjacent to both the capillary and the bulbs, considerable lengths of glass tubing are put in connection and immersed in the respective baths in order that the gas in the capillary or bulbs may be at the desired temperature at the time of measurement. In each tube leading from the bulbs to the capillary there is a stop cock A (and A') and a connection with a manometer K (and K'}. By means of stop cocks at E and E' the two manometers may be connected together or gas admitted to the apparatus from outside. Since the presence of water vapor is objectionable and gases are more or less soluble in water, the manometer contains both mer- cury and water, and is calibrated before use. In makin'g a measurement, enough gas is admitted into the evacuated apparatus so that at atmospheric pressure, the surface of the mercury is in the lower part of the bulb Q and in the middle part of the bulb Q' '. The stop cock A is then closed and the mercury reservoirs G and G f raised, but the former enough higher than the latter so that a pressure head is estab- lished which is a few millimeters greater than is desired in the measurement. The mercury fills the two bulbs Q and Q'. When the temperature is constant the stop cock A is opened. The pressure is immediately adjusted and thereafter maintained constant by means of the screws F and F 1 which serve to slowly 80 FLUIDITY AND PLASTICITY raise or lower the mercury reservoirs. When the mercury passes into the bulb P, contact is formed with a platinum point and an electrical signal given. At this moment the chronometer is started. After the elapse of sufficient time, the stop cock B is closed and thus the current is broken between the two platinum electrodes at either side of this stop cock, and a signal is given. The mercury is now allowed to run out through the stop cock C until the signal is given when the mercury loses connection with the platinum point in the bulb P. From the weight of this mercury, the volume of flow is calculated. PART II FLUIDITY AND OTHER PHYSICAL AND CHEMICAL PROPERTIES CHAPTER I VISCOSITY AND FLUIDITY It has been tacitly assumed by the great majority of workers that when two liquids are mixed, the viscosity of the mixture is normally a linear function of the composition. This appeared as early as 1876 in the work of Wijkander. In a great many mixtures, including practically all of those in which water is a component, the viscosity is certainly very far from being a linear function of the composition, there being often a maximum in the viscosity curves. However water mixtures should not be con- sidered as "normal," but since it is difficult to decide what shall be considered normal mixtures, the question whether the viscosities are additive or not is admittedly difficult of solution. Dunstan (1905) classifies as normal those mixtures whose vis- cosity-weight concentration curves do not show a maximum or a minimum. This classification is not satisfactory not only because it lacks a theoretical justification but also because many of the so-defined normal mixtures give curves which depart considerably from the linear, so that the suspicion is aroused that the occurrence of a maximum or minimum may depend upon accidental circumstances such as the nearness to equality of the viscosity of the components. The accidental character of such a classification is very striking in mixtures which fall into the normal class at one temperature but at a slightly different tem- perature must be classified as abnormal. Such light as can be gained from a study of the viscosities of mixtures, seems to lead to the conclusion that viscosities are! not additive, as has been assumed. Thus Dunstan (1904) remarks, "The law of mixtures is never accurately obeyed and 6 81 82 FLUIDITY AND PLASTICITY divergences from it seem to be more clearly marked out in the case of viscosity than with other properties, such as refractive index." Thorpe and Rodger (1897) say, "The observations described in this paper afford additional evidence of the fact indi- cated by Wijkander and supported by Linebarger, that the vis- cosity of a mixture of miscible and chemically indifferent liquids is rarely, if ever, under all conditions, a linear function of the composition. It seldom happens that the liquid in a mixture preserves the particular viscosity it posesses in the unmixed condition. To judge from the instances heretofore studied, the viscosity of the mixture is, as a rule, uniformly lower than the mixture law would indicate, but no simple relation can yet be traced between the viscosity of a mixture and that of its constit- uents." Thorpe and Rodger were so struck by the absence of linearity in the viscosity curves, that they thought that an ex- planation was needed for the fact that the viscosity curves of some mixtures measured by Linebarger (1896) are indeed linear. " The observed viscosities in general are less than those calculated by the mixture rule, except, possibly, in the case of mixtures of benzene and chloroform and mixtures of carbon disulfide with benzene, toluene, ether, and acetic ether, where, possibly, the temperature of observation (25) was too near the boiling-point of the carbon disulfide to make any specific influence, which that liquid might exert at lower temperatures, perceptible." Lees (1900) showed what are the necessary assumptions in regard to the nature of flow in mixtures, so that the viscosities should be additive, but by making a careful study of existing data, he found little justification for these assumptions. Simi- larly Lees tried the assumptions that fluidities or logarithmic viscosities are the characteristic additive property, but he was unable to obtain a satisfactory verification of either from the experimental results. The question before us seems to be: "Is viscosity or fluidity or some function of one of them the characteristic additive prop- erty?" The answer to this question is imperative before we can intelligently discuss the relation of viscosity to other proper- ties. This statement requires no proof in view of the statements which we have quoted to show that in some cases the viscosity concentration curve is linear according to assumption, but in the VISCOSITY AND FLUIDITY 83 great majority of cases it is sagged and there is 110 known law to account for the peculiarity. Surely any discussion of chemical combination or of dissociation on the basis of deviation from the " normal" curve under such conditions would be of very uncertain value. There are numerous reciprocal relations besides viscosity and i fluidity, such as electrical resistance and conductance, or specific/ heat and heat capacity, or specific gravity and specific volume. \ It has been repeatedly pointed out 1 that if one of these is additive, / its reciprocal cannot be. It is singular enough that among all of these reciprocal relations, viscosity is the only one for which the decision has not been reached as to whether viscosity is additive or not, or if it is, under what conditions. In electricity for example we have absolutely no doubt but that resistances are additive under certain conditions, viz., when the conductors are in series, and likewise that conductances are additive under other equally definite conditions, viz., when the conductors are in parallel. It seems probable that the present unsatisfactory condition as regards viscosity has arisen due to the extraordinary sensitiveness of this property to molecular changes in fluids, either combination or dissociation. We shall attempt to reach a solution of the problem from a consideration of the nature of viscous flow and then test this solution by means of the experi- mental facts. After we have reached a conclusion in regard to the true additive property under given conditions, it may well turn out that the present unsatisfactory condition will prove to be a blessing in disguise, for it may then be shown that viscosity is of the greatest importance in physiochemical investigations. The fundamental law of viscous flow dv = F dr rj is the analogue of the well-known electrical law of Ohm. In fact Elie in 1882 suggested a modification of the Wheatstone's bridge method for the measurement of viscous resistance. Case I. Viscosities Additive Emulsions. We will first con- sider the very simple case of a series of vertical lamellae of viscous material arranged alternately, as in Fig. 32, and subjected to a 1 Cf. p. 89. 84 FLUIDITY AND PLASTICITY horizontal shearing stress. For convenience suppose that all of the lamellae of the one substance A have the same thickness si and that the laminae of the substance B have the uniform thickness 82, etc. Let the viscosities of the substances be -n\, 772 ... and the shearing stresses per unit area pi, p% . . . respectively; then if R is the distance between the horizontal planes, the velocity of the moving surface is _ RP _ Rpi _ Rpz V TT a r?i 172' where H is the viscosity of the mixture, and P is the average shearing stress over the entire distance S. '1 | ? y J^r\A.V "J / hence / /'// -XX ' & V . r TT ^ //^l"- i^ /^2"2 T " ~ o \ 5 ~ Fig. 32. Diagram to illus- trate additive viscosities. But since Si/o is the fraction by volume of the substance A present in the mixture, which we may designate a, and similarly s 2 /S = 6, etc., H = a-ni + &T? 2 + . . . (24) This case is of particular interest in connection with emulsions and many other poorly mixed substances. The formula tells us that the viscosity of the mixture is the sum of the partial viscosities of the components, provided that the drops of the emulsion completely fill the capillary space through which the flow is taking place. Case II. Fluidities Additive Fluid Mixtures. If the lamellae are arranged parallel to the direction of shear, as shown in Fig. 33, we have a constant shearing stress, so that p= W = M_ 2= . (24a ) TI r 2 where vi, v z , . . . are the partial velocities as indicated in the figure. There are two different ways of defining the viscosity of a mixture, and it becomes necessary for us to adopt one of these before we proceed further. 1. If we measure viscosity with a viscometer of the Coulomb VISCOSITY AND FLUIDITY 85 or disk type, we actually measure the velocity v, BS in the figure, and we very naturally assume that P = (24b) 2. It is more usual, however, to calculate the viscosity from the volume of flow, as in the Poiseuille type of instrument. Let v r , BS' in the figure, be the effective velocity which the surface BS would have, were the series of lamellae replaced by S' S S" FIG. 33. Diagram to illustrate additive fluidities. a homogeneous fluid having the same volume of flow. The effective velocity is related to the quantity of fluid U passing per second in a stream of unit width, as follows: U = V '^ Let the viscosity as calculated from the flow, as for a homo- geneous fluid, be H', then P = V- = W" (24c) It is to be noted that had the less viscous substance been in contact with the surface AE, the effective velocity of flow would have been represented by the distance BS". We shall take the former of these for our definition of the viscosity of a mixture, 86 FLUIDITY AND PLASTICITY since, as we shall now show, by using it the viscosity is indepen- dent of the number or arrangement of the lamellae. Since v = v\ + v 2 + . . . we obtain from Eqs. (24a) and (24b) that etc. /i K the fluidity of the mixture is . . (25) The fluidities are, according to this definition, strictly additive and entirely independent of the number and arrangement of the layers. Since, however, the viscosities are usually calculated by means of the Poiseuille formula based on the volume of flow, it is important to determine for a given arrangement of lamellse what correction must be made to the effective viscosity, as calcu- lated from the volume of flow, to make it accord with the true viscosity, as defined above and as obtained by the disk or other similar method for the measurement of viscosity. Reverting again to the figure, we find that + Vir 2 + v 2 r 2 + ViTz + -~ If there were n pairs of alternate lamellae of the two substances A and B U = [n%iri + n(n + I>ir 2 + nv\r 2 + n(n - l.W,] (26). D Since n = - , on substituting into Eq. (26) the values of fi T TI Vi and v 2 , we get TT R2p r . a& / U y-^api + 6^2 + ~\Vi and if S> / = Trf we obtain from Eq. (24b) ti V = an + 6^2 + ( V i - vj (27) VISCOSITY AND FLUIDITY and when n = , the fluidity becomes simply 87 and in this case *' - *. (28) In a homogeneous mixture it appears, therefore, that the two definitions lead to the same fluidity, and experimental results lead us to believe that this is the case usually presented in liquid mixtures, since the disk method and the capillary tube method give the same fluidity so far as we > have certain knowledge. If, however, the number of lamella is small, which may well be the case in very imperfect mixtures, or when the flow takes place through very narrow passages, the effective fluidity as calculated from the volume of flow may be either greater or less than the sum of the partial fluidities of the components, FG - necessarily brings about com- p i e te mixing, so that even when th e viscosities were originally depending upon the order of the trate arrangement of the lamella in refer- mixed but miscibie fluids, flow ,i , . c mi. ence to the stationary surface. The amount to be added or subtracted from the effective fluidity in order to obtain the true fluidity is represented cible fluids, the layers A and by the term, corresponding to the L'SSJSSS'l.'SST areas A CD, etc. or AFD, etc., Fig. 33. A combination of the cases I and II would lead to a checker- board arrangement, but it may be shown now that such an arrangement tends to reduce itself to the case II where fluidities are additive. If the arrangement considered in Fig. 32 is subjected to continued shearing stress, the lamellae will tend to become indefinitely elongated as indicated in Fig. 34; and unless the surface tension intervenes, as may be the case in immiscible liquids, the lamellae will approach more and more nearly the horizontal position. Thus, so far as we can determine without going into the complicated problem of the molecular motions, it seems certain that the fluidities will become more and more 88 FLUIDITY AND PLASTICITY nearly additive as the flow progresses and the mixture becomes more and more nearly complete. This result takes place further- more irrespective of the original arrangement of the parts of the mixture. Some one may object that a perfectly homogeneous mixture in itself a contradiction of terms is not made up of layers such as we have considered in these greatly simplified cases. There can be no doubt whatever of the existence of layers during the process of mixing. No one has watched the drifting of tobacco smoke in his study without noting how it is drawn out into gossamer-like layers. Since the fluidity is greatest when fluidities are additive, there would have to be a sudden drop in fluidity as the mixture became perfect, if the fluidities were no longer additive. This is not supported by any experimental evidence. We have already noted that when there is no chemical action between the components of a mixture, the viscosity-concentration curves are usually but not always sagged. Dunstan (1913) has put it: "It can therefore safely be predicted that wherever the two components show little tendency for chemical union a sagged curve, or one departing but slightly from linearity, will be found." If the fluidities of such mixtures are additive, these facts ought to be accounted for by the theory, peculiar as they may seem to be. We shall first prove that according to the theory that fluidities are additive, we should expect the viscosity- concentration curves to be sagged. Equations (25) and (24) represent the two assumptions that fluidities are additive and that viscosities are additive respectively but for convenience we shall assume that only two components are present in the mixture. From Eq. (24) we get that b2 When a = or 1, and 6 = 1 or respectively,

'. For all intermediate values of a and b we desire to learn VISCOSITY AND FLUIDITY 89 whether

l 2 22 2 - 0, which is a perfect square and therefore must be positive. Hence, when / . Our conclusions may be stated as follows : 1. The viscosity of a thorough mixture of chemically indifferent fluids must always be less than would be expected on the assump- tion that viscosities are additive, but this inequality will approach zero as the difference between the viscosities of the components approaches zero. 2. So, on the other hand, the viscosity of an emulsion must be greater than that of a perfect mixture of the same composition, because in emulsions the viscosities tend to become additive. Equation (25) may be expressed in the form 9 = i +(i)b, (29) where i + (i)b by (2 = 200) ob- served Differ- ence CH 2 Slope at ( = 200) Absolute tempera- ture ( = 200) calculated Per cent, differ- ence Hexane (255. 1) 1 \ (2 . 88) 254.6 0.2 Heptane 276.1 J (21.0) 277.3 0.4 Octane 299.1 23.0 2.44 300.0 0.3 Isohexane (249.0) (on 1\ (2.79) 247.0 0.8 Isoheptane 269.2 \\j . &) 2.68 269.7 0.2 Methyl iodide 290.2 19.0 1.92 287.4 1.0 Ethyl iodide 309.2 OO K 1.80 310.1 0.3 Propyl iodide 332.7 &6 . 1.82 332.8 0.0 Isopropyl iodide 324.5 01 f) 1.92 325.2 0.2 Isobutyl iodide 345 . 5 t\. . U 1.86 347.9 0.7 Allyl iodide 330.5 1.82 328.8 0.5 Ethyl bromide 268.7 27 9 2.22 273.5 1.8 Propyl bromide 296.6 2.08 296.2 0.1 Isopropyl bromide 289.4 oc a 2.22 273.5 1.8 Isobutyl bromide 315.0 ZO . O 2.08 311.3 1.1 Ethyl propyl ether (255.0) (94 01 (2.70) 256.1 0.5 Dipropyl ether 279 . f \6 = 200) Slope for (0 = 200) Association observed calculated Water 328.9 142.6 3.04 2.31 Formic acid (380.2) 185.5 (2.18) 2.05 Acetic acid 363.8 208.2 2.06 1.77 Propionic acid 362.0 230.9 1.92 1.57 Butyric acid 381.6 253.6 1.92 1.57 Isobutyric acid 371.6 246.0 2.00 1.51 Methyl alcohol 305.2 165.3 2.78 1.84 Ethyl alcohol 343.4 188.0 3.24 1.83 Propyl alcohol 365.6 210.7 3.76 1.74 Butyl alcohol 377.0 233.4 3.44 1.62 Ethyl formate 273.8 230.7 2.40 1.19 Ethyl acetate 284.0 253.4 2.50 1.12 Ethyl propionate 298.1 275.1 2.44 1.08 The test of our complete process of reasoning comes now when we compare the association obtained in this way with the values which have been obtained by other methods. The results of this comparison are shown by Table XXXI. So far as one is able to judge, the result seems to be all that could be desired. There are almost invariably values given by other methods which are both higher and lower than our values and such a degree of association is certainly not inconsistent with our knowledge of the chemical conduct of these substances. The fluidity method of obtaining the association factor seems to be freer from assumptions, to which questions maybe raised, than other methods which have been proposed, and it is to be hoped that it may prove useful in calculating this very important fac- tor. If eventually we are able to obtain thoroughly consistent FLUIDITY AND THE CHEMICAL COMPOSITION 121 TABLE XXXI. A COMPARISON OF THE VALUES OF ASSOCIATION AS DETER- MINED BY DIFFERENT INVESTIGATORS Substance R. & S.,i 16-46 R. & S., corrected by Traube Traube, 2 15 Longi- nescu* B. & H.,< tem- perature of ( = 200) Water /3.55 \1.64 1.79 3.06 4.67 2.31 Dimethyl ketone 1.26 1.18 1.53 1.60 1.23 Diethyl ketone 1.25 1.16 Methyl propyl ketone. . . 1.11 1.10 1.43 .25 1.14 Formic acid 3.61 2.41 1.80 .80 2.05 Acetic acid /3.62 \2.13 2.32 1.56 .75 1.77 Propionic acid 1.77 1.45 1.46 .55 1.57 Butyric acid 1 .58 1.35 1.39 .36 1.51 Isobutyric acid 1.45 1.28 1.31 1.51 Benzene 1.01 1.05 1.18 >1.17<1.31 Toluene 0.94 1.01 1.08 > 1. 08 < 1.517 Methyl alcohol !3. 43 2.53 1.79 3.17 1.84 2.32 Ethyl alcohol 2.74 1.80 1.67 2.11 1.83 1.65 Propyl alcohol 2.25 1.70 1.66 1.67 1.74 Isopropyl alcohol 2.86 2.00 1.53 1.75 Butyl alcohol .94 1.47 1.62 Isobutyl alcohol .95 1.53 1.54 1.66 Active amyl alcohol .97 1.54 1.53 1.54 Allyl alcohol .88 1.50 1.55 1.80 1.69 Methyl formate .06 1.07 (1.60) 1.12 1.25 Ethyl formate .07 1.08 1 . 39o 1.19 Methyl acetate .00 1.04 1.48o 1.09 1.17 Ethyl acetate 0.99 1.04 1.25 1.00 1.12 Propyl acetate 0.92 1.00 1.31 1.00 1 . 11 Ethyl propionate 0.92 1.00 1.27 0.94 1.08 Methyl butyrate 0.92 1.00 1.30o 1.00 1.10 1 RAMSAY and SHIELDS, Zeitschr. f. physik. Chem., 12, 464 (1893); 15, 115 (1894). ' TRAUBE, Ber. d. deutsch. chem. Gesell., 30, 273 (1897). /. Mm. Phys., 1, 289 (1903). 4 BINQHAM and HARBISON, loc. cit. results from the different methods, it is interesting to observe that it should be possible to calculate the volume, surface tension, et cetera, even of associated liquids from their atomic constants and their fluidities. Fluidity and Chemical Constitution. Dunstan and Thole (Viscosity of Liquids, page 31) have very properly called attention to the fact that the differences between the calculated and observed values of the fluidity in Table XXV "are due not only 122 FLUIDITY AND PLASTICITY to association but to want of sufficient data for calculating accu- rately the atomic 'constants' and also to constitutional effects, such as the mutual influence of groupings in the molecule, sym- metry and so forth." As was intimated earlier in this chapter, to chemical constitution has generally been attributed a very large effect on viscosity, but it often turns out on investigation that this supposed constitutive influence occurs in substances that are known to be associated and this association was not taken into account, and in other cases the supposed constitutive influ- ence is almost certainly purely a hypothesis framed to explain an unnoticed defect in the method of comparison. We shall now give some facts to support these bare statements and we shall then investigate the important question as to whether this dwind- ling constitutive effect, as distinct from the effect of association, can safely be disregarded altogether. In assigning values to the halogen atoms, Thorpe and Rodger (p. 669 et seq.) found it necessary to give a different value to chlorine in monochlorides, dichlorides, trichlorides and tetra- chlorides, but even then the results are not satisfactory since in ethylene and ethylidene chlorides the value which must be assigned the chlorine atom is certainly different. How the effect of the chlorine atom varies at the fluidity of 200 is shown in the fourth column of Table XXXII. TABLE XXXII. THE VALUE OF THE CHLORINE ATOM Substance Absolute tem- perature ( = 200), observed Hydro- carbon residue, calculated Chlorine Associa- tion Propyl chloride 261.5 127.3 134.2 1.105 Isopropyl chloride 255.2 119.7 135.5 .11 Isobutyl chloride 285.2 142.4 142.8 .13 Allyl chloride 256.0 123.3 132.7 .10 Ethylene chloride 336.5 45.4 145.5 .27 Ethylidene chloride.. . . 291.2 45.4 122.9 .10 Methylene chloride. . . . 279.1 22.7 128.7 .15 Chloroform 305.3 - 36.5 113.9 .04 Carbon tetrachloride . . 347.0 - 95.7 110.7 .01 Carbon dichloride 356.3 - 77.0 108.3 0.99 FLUIDITY AND THE CHEMICAL COMPOSITION 123 There is then a somewhat regular decrease in the apparent value of chlorine as the number of chlorine atoms in the molecule are increased. How much of this is due to constitutive influence directly and how much can be explained on the ground of asso- ciation? Ramsay and Shields and Traube agree that carbon tetrachloride is very little associated if at all, Ramsay and Shields giving the value 1.01 and Traube 1.00i 5 . If then we take the average of the closely agreeing values of the two compounds containing four chlorine atoms we obtain as the value of the chlorine constant 109.5 and with this we can calculate the asso- ciation of the other compounds.. The values thus obtained are given in the fifth column of Table XXXII. Ethylene chloride is seen according to this method of calculation to be highly associated, but Traube has given a still higher value for the asso- ciation at 15 of 1.46. Data for the other chlorides is lacking, but calculating the association of propyl chloride by the method of Traube, the author obtains the value of 1.11 which agrees excellently with our value of 1.105. The mono-halides seem to be usually associated according to Traube for he gives for methyl iodide 1.30, for ethyl iodide 1.19 and for ethyl bromide 1.28. It is greatly to be regretted that our available data is so meager, but for the present we can only conclude that the effect of con- stitution upon the value of the chlorine atom is too small to be detected. In reference to the lack of constancy in the value of a methyl- ene group in Table XXV, it seemed desirable to take the average of as large number of values as possible, but with the limited data on hand this made it necessary to include a number of compounds which are certainly associated. This does not mean that the value of the methylene group is therefore certainly in error because associated compounds can give this as well as others, provided the homologues are equally associated; and even if they are unequally associated, the average value for the methylene grouping may not be greatly in error although the individual differences may be large. Finally the fact that the calculated values in Table XXV differ from the observed values by less than 1 per cent seems to put a maximum limit upon certain kinds of constitutive influences. Hitherto it has been deemed necessary to give oxygen a differ- 124 FLUIDITY AND PLASTICITY ent value depending upon whether the oxygen was in a carbonyl group, hydroxyl, ether, et cetera. We will now attempt to show that this was necessary so long as viscosities formed the basis of comparison, but it was not an evidence of constitutive influence, and in comparing fluidities only one value for oxygen is obtained irrespective of the manner in which it is combined, and yet we have seen that satisfactory association factors are obtained. Let A B and A'B' in Fig. 47 represent two fluidity curves, parallel to each other and therefore presumably representing members of the same class of substances, and let a third fluidity curve CD be at an angle to the other two to represent a substance in another class. Since we have elected to compare absolute temperatures at a fluidity of 200, this amounts to comparing the intercepts of the curves on the line AD, whose equation is

Observed Specific volume observed

/dc 2 is negative. The increase in fluidity may be 160 THE FLUIDITY OF SOLUTIONS 161 attributed to breaking down of association or to dissociation which also give rise to the increase in volume. Benzene and ethyl acetate may be cited as an example of this type. III. When two liquids are mixed, perhaps more often than not, there is a decrease in the volume, particularly in aqueous solutions. With this decrease in volume there goes a positive heat effect and a decrease in the fluidity, so the fluidity-volume concentration curves are convex downward, i.e., d 2

2 = So a p 2 mvi + THE FLUIDITY OF SOLUTIONS 163 tion it follows that if we plot volumes against weight concentra- tion, we will obtain a linear curve such as curve I in Fig. 60; but if we plot specific volumes against volume concentrations, we will obtain not the linear curve III, Fig. 61, but curve IV. We have seen that the fluidity of a liquid is directly propor- tional to its free volume, but the fluidities are additive (Eq. (25)) 1.380 1.200 - Add itive Sp.Vol . Ca I c . by Vol ./o BT-Additive Sp.Vol.Calc. by Wt.%> V- Observed Benzene 25 50 15 100 Volume Concentration Ether Ether FIG. 61. Specific volume-volume concentration curve of mixtures of benzene and ether. (After D. F. Brown.) only when we use volume percentages; hence it follows that if a pair of liquids on mixing gave a linear specific volume-volume concentration curve (curve III) they would also give a linear fluidity-volume concentration curve, curve VI, Fig. 62. Since, however, the ideal mixture gives a volume-volume concentration curve which shows positive curvature, the fluidity-volume con- centration curve of the ideal mixture will also show positive curvature, curve VII, Fig. 62. 164 FLUIDITY AND PLASTICITY Since this sag in the fluidity curve is due to the mathematical necessities of the case and not to chemical combination or dissociation, it is evidently possible to calculate the fluidity of the mixture from the fluidities and volumes of the components. 400 // 350 / // -'/ vin / lffv x > // / A / $ '-5 3 250 / / /A / ft* / ix. d / / / / / M "c vn- Additive Fluic alculatedby\ Huidity Gala ?y Formula )bserved Poin- >ty roi/ jla+pd 150' // //' // y 1 ^& 25 50 75 IOC Benzene v | limp f nnr - M f r - + : rt ^ m r pu ,^ E + he FIG. 62. Fluidity-volume concentration curve of mixtures of benzene and ether. (After D. F. Brown.) We have seen that the observed specific volume of the mixture whereas the specific volume should be in order to give a linear fluidity-volume concentration curve (Eq. (25)), so the specific volume is too small by an amount represented by the specific volume difference, At>. THE FLUIDITY OF SOLUTIONS 165 Ay = avi + bv% mv\ nv z = (a m)v\ (n 6)y 2 = (a - m) (! - ,) (60) since a w = n b. If the fluidity is directly proportional to the free volume (Eq. 56), it seems reasonable to assume that if the volume is decreased for any reason by an amount A, the fluidity will be decreased by an amount which is some function of this fAv. Since in the ideal mixture the fluidity is only slightly less than that given by the linear formula (Eq. 25), we may assume as a first approxi- mation that the decrease in fluidity is directly proportional to the specific volume difference. We then obtain as our formula for the true fluidity $ 3> = k(v w) K&v = s? - KAv = dpi + b(f>2 K(a m) (v\ v%), (61) It may be possible later to evaluate the above function, but it is only necessary to know the fluidity of one or more mixtures in order to determine a value for the constant K, from which the fluidities of all other mixtures of the two components may be calculated. The physical significance of K will be explained later. We may take for an example carbon tetrachloride and benzene, the mixtures of which were studied carefully by Thorpe and Rodger, and at a single temperature by Linebarger. (C/. Table XLII.) In the first line at each temperature are given the fluidities observed. In the second line are given the fluidities (*) as calculated with the use of Eq. (61), using 40 as the value for K. The fluidities ( by the admixture rule to be 0.683, 0.784, and 0.896, using weight percentages. This accords 166 FLUIDITY AND PLASTICITY perfectly with the values 0.683, 0.785, and 0.897 obtained from the observed fluidity data for each mixture. The values of k in the Batschinski formula are 2,019, 1,937, 1,845 as calculated from the pure solvents, as compared with 2,034, 1,993, and 1,876 as obtained from the data for the mixtures. The values of the fluidities calculated by means of the former set of constants are not so close to the observed values as are the values calculated by the corrected fluidity formula. But they are at least as close to the observed values of the mixtures as the cal- culated fluidities of pure carbon tetrachloride are to the observed. It is impracticable here to consider in detail all of the examples TABLE XLI. SPECIFIC VOLUMES IN MILLILITERS PER GRAM OF MIXTURES OF CARBON TETRACHLORIDE AND BENZENE, FROM THORPE AND RODGER Per cen t benzene h y weight 22.37 43.79 67.71 100 Per cen t benzene b y volume 34.30 58.54 79.17 100 0.6127 0.7238 0.7242 0.8304 0.8309 0.9497 0.9501 1.1109 Observed Calculated 10 0.6202 0.7326 0.7329 0.8405 0.8412 0.9610 0.9614 1.1242 Observed Calculated 20 0.6278 0.7415 0.7418 0.8508 0.8511 0.9728 0.9730 1 . 1377 Observed Calculated 30 0.6355 0.7508 0.7509 0.8613 0.8615 0.9846 0.9849 1.1514 Observed Calculated 40 0.6435 0.7602 0.7604 0.8724 0.8723 0.9971 0.9973 1.1661 Observed Calculated 50 0.6518 0.7700 0.7702 0.8836 0.8836 .0099 .0103 1.1812 Observed Calculated 60 . 6604 0.7801 0.7803 0.8951 0.8952 .0231 .0234 1 . 1966 Observed Calculated 70 0.6(594 0.7907 0.7909 0.9071 0.9072 .0369 .0371 1.2124 Observed Calculated THE FLUIDITY OF SOLUTIONS 167 TABLE XLII. THE FLUIDITIES OF MIXTURES OF CARBON TETRACHLORIDE AND BENZENE FROM THORPE AND RODGER* AND FROM LiNEBARGER 2 Temperature Per cent benzene by weight (lOOn) 22.37 43.79 67.71 100 Per cent benzene by volume (1006) 34.30 58.54 79.17 100 74.1 '72! 6 83.6 84.3 86.7 82.2 91.9 92.7 95.6 90.4 100.6 100.9 103. 2 99. 1 110.8 108:9 Fluidity observed calculated, Eq. (61) tp calculated, Eq. (25) Fluidity calculated Eq. (54) 10 88.2 '88.4 100.0 100.6 103.0 99.9 110.1 110.6 113.5 110.0 120.2 120.2 122.5 119.9 131.5 isiis Observed calculated, Eq. (61)

calculated, Eq. (61)

calculated, Eq. (61)

calculated, Eq. (61)

calculated, Eq. (61)

\ \ ^f^ g N v x \ \ \ . ?- \ ^ V ^>. \ X x^ \ *^ *^ ^^ N ^^ \ X \ N \ "^ -<: : ^ 10 20 30 40 50 60 10 80 90 IOC Per Cent FIG. 70. Fluidities of potassium halide solutions in water at various tempera- tures. The curves show negative curvature which is most marked for the chloride, and at low temperatures and at low volume concentrations of the salt. At high concentrations or at high temperatures all of these solutions may show positive curvature, but the nitrate and iodide most readily. (After Gorke.) Miihlenbein (1903), however, showed that the dissociation hypothesis was by itself insufficient as an explanation since salts like NaNO 3 and K 2 SO 4 are highly ionized and yet do not show negative curvature as does KNO 3 . Now that it appears that urea and mercuric chloride solutions both show negative curva- ture, it would seem probable that electrolytic dissociation is not necessary for the phenomenon. Since these substances in solution are practically unionized. THE FLUIDITY OF SOLUTIONS 183 Jones and Veazey (1907) observed that potassium, rubidium and caesium are the elements with the largest atomic volume and they therefore reasoned that their salts would also be relatively fluid. From what has preceded we are prepared to find relations between fluidity and volume, but as a matter of fact the fluidity of the pure salts in the molten condition is very low. For example, Foussereau (1885) found the fluidity of ammonium nitrate to be 0.505 at 185C and 0.4037 at 162C, so that at ordi- nary temperatures the fluidity of the salt in the undercooled condition would certainly be very low, probably negligible as compared with water. Furthermore, there are salts which show negative curvature but in which the metal has a small atomic volume such as silver nitrate, mercuric chloride, and thallium nitrate. In view of the periodic relationship of the elements, the same coincidence noted by Jones and Veazey would occur with many other properties. Finally there are several salts of potassium and ammonium which have not been found to show negative curvature hence the explanation proposed by Jones and Veazey is not satisfactory. EXPLANATION OF THE INFLECTED CURVE As to the reason for positive curvature, it seems probable from what precedes that it is due to combination between the solvent and the solute. That many of the salts of potassium, rubidium, caesium and ammonium exhibit so slight positive curvature is due to their smaller tendency to form hydrates than is usually the case in aqueous solution. In contrast with the salts of potassium, no sodium salts show "negative viscosity." Perhaps the most striking difference between the salts of sodium and potassium, generally so similar, is the greater affinity for water on the part of sodium salts. None of the salts which show negative curvature crystallize from water with water of crys- tallization, and the few salts of potassium and ammonium which do not show negative curvature do exhibit a tendency to form hydrates. Examples are potassium carbonate, ferrocyanide and sulfate, and ammonium sulfate. It is true that hydrobromic acid solutions are probably hydrated, but according to the measurements of Steele, Mclntosh, and Archibald (1906) anhy- drous liquid hydrogen bromide has a high fluidity. The small- 184 FLUIDITY AND PLASTICITY ness of the positive curvature is then due to the small amount of hydration which is well-nigh universal in aqueous solution. The negative curvature, on the other hand, must be due to dissociation either (1) of the salt or (2) of the associated water. Since the negative curvature occurs in dilute solution, the electrolytic dissociation is immediately suggested. If the fluidity of the anhydrous salt in the form of an undercooled liquid is negligibly small, it is hard to conceive of how the dissociation of the salt into two, or at the most a few, ions would increase the fluidity so remarkably, for it must be remembered that there must be a substance present whose fluidity is higher than that of water. Then, as already pointed out, there are substances which give negative curvature which are very slightly dissociated into ions, such as urea. We are then compelled to seek further in our explanation and admit that water itself is dissociated by the presence of the salt or its ions. There is nothing inherently improbable in this since water is highly associated (2.3 at 56C). The association is less at high temperatures and in concentrated solutions so that under these conditions negative curvature would be less apparent as we have already seen to be the case. It is often assumed that electrolytic dissociation is brought about by union of simple water molecules with the ions of the salt, but if the ions have low fluidity, the fluidity of the sohition will evidently not be raised by uniting with even simple water molecules, hence hydration will not explain the phenomenon. In other words, the formation of larger molecules does not tend to raise the fluidity. Wagner (1890) has measured the volume of water required to make a liter of normal solution of the chlorides of various salts. In the cases of silver and thallium the nitrates were used instead. Salts like calcium chloride, which unite strongly with water to form hydrates, produce a contraction on going into solution, so that a comparatively large volume of water is required. But rubidium and caesium chlorides expand on going into solution so that the volume of water required is correspondingly small. The difference between the volume of water required and 1 1. is the volume of the salt together with the expansion. Calculating the volume of the salt from its specific gravity the expansion is obtained. The resulting numbers, plotted in curves IV and V in THE FLUIDITY OF SOLUTIONS 185 10 20 30 40 50 60 10 80 90 100 110 120 IJO 140 150 160 110 180 190 200 210 Atomic Weight FIG. 71. Some "periodic" relationships. 186 FLUIDITY AND PLASTICITY Fig. 71, show that in general the salts which occupy the largest volume in solution correspond to those having the highest fluidity curve II, but silver seems to be strongly exceptional. Here again we have evidence that fluidity is proportional to the free volume. The cause of the volume change is also the cause of the negative curvature. Ammonium iodide according to Getman (1908) and Ranken and Taylor (1906) shows negative curvature but it goes into solution with contraction, according to Schiff and Monsacchi. There is thus a lack of parallelism between the two properties of which one further example may be cited. In ammonium nitrate solutions, the expansion is least in a 7-weight per cent solution and yet the fluidity is a maximum in this solution at some temperature between 25 and 40C. Since we are dealing with inflected curves signifying simultaneous dissociation and chemical combination, these anomalies are to be expected. The limiting volume is continually changing and the specific volume is for that reason no measure of the free volume. There is need for further work in this very important field. Attempts have been made by Wagner and others to assign to each element a specific viscosity effect in solution. The fluidi- ties of nitrates, chlorides, and sulfates of certain metals in normal solution at 25C are given in Table XL VII as modified from Wagner. The table shows that the fluidity of the nitrates is TABLE XLVII. A COMPARISON OF THE FLUIDITIES OF VARIOUS METALS AND ACID RADICALS IN NORMAL SOLUTION AT 25C (AFTER WAGNER) NO 3 C1 3 S0 4 NO 3 Cl NO 3 sol K 114.7 113.3 101.2 1.012 1.133 K/H 1.053 1.081 0.974 H 108.9 104.8 102.5 1.039 1.062 K/Na 1.095 1.112 1.112 Na 104.7 101.9 91.0 1.027 1.151 K/Zn 1.195 1.199 1.239 Zn 96.0 94.5 81.7 1.015 1.175 K/Mg 1.201 1.218 1.239 Mg 95.5 93.0 81.7 1.26 1.169 THE FLUIDITY OF SOLUTIONS 187 always higher than that of the chlorides and that of the chlorides is always higher than the fluidity of the corresponding sulphate. The ratio of nitrate to chloride is 1.02 and of nitrate to sulphate 1.14. We may also compare the salts of different metals joined to the same acid radical and thus get a ratio in terms of one metal taken for reference, as potassium. Considering the com- plex effects due to dissociation, hydration and perhaps other causes, the presence of even imperfect relationships of this kind is remarkable. CHAPTER VI FLUIDITY AND DIFFUSION According to Stokes (1851) a sphere of radius r, impelled through a fluid under a force F, will attain the velocity v - (62 > This formula is of fundamental importance in the study of the settling of suspensions, diffusion, Brownian movement, the rate of crystallization of solutions, migration velocities and transfer- ence numbers of the ions and in the conductivities of solutions. Settling of Suspensions. In the case of a falling sphere, the force becomes 4 F = g 7T0r 3 (p 2 - pi) where pz and pi are the densities of the sphere and the medium respectively, so v = lg(pi - Pi>V (63) i7 This formula enables one to calculate the speed of settling of suspensions. It has been utilized in determining the viscosity of very viscous liquids, e.g., Tammann (1898) and Ladenburg (1907), for determining the radii of the particles in gold suspen- sions, Pauli (1913), for measuring the charge on the electron in air, Millikan (1910). The Diffusion Constant. Sutherland (1905), Einstein (1905) and Smoluchowski (1906) have derived the relation between the diffusion coefficient 5 and the fluidity, , _ RT 9 ~~ N "fcrr where T is the absolute temperature, R is the gas constant (83.2 X 10 6 c.g.s. units) and N is the number of molecules in a gram molecule (70 X 10 22 ). The diffusion coefficient is defined as the quantity of solute diffusing per second through a unit cube when the difference in concentration between the two ends of the cube is unity. But Stokes' Law was derived for particles 188 FLUIDITY AND DIFFUSION 180 which are spheres and having a radius large in comparison with the molecules of the solvent. If the particles are so small that the free path a of the molecules of the suspending medium is ap- preciable in comparison with the radius of the particles, Suther- land (1905), Cunningham (1910) and Millikan (1910) have shown that Stokes' formula becomes 1 + '-f-o-e^- (64) where A is a constant and equal to about 0.815. The following table from Thovert (1904) indicates that the product of the diffusion constant and the time of efflux is approxi- mately constant for a considerable number of substances. TABLE XLVTII. THE RELATION BETWEEN DIFFUSION AND VISCOSITY (THOVERT) Substance d x io 5 T, time of efflux 8XT X IO 4 Ether 3.10 315 98 Carbon disulfide 2.44 405 99 Chloroform 1.50 660 99 Mixture ethyl alcohol and ether . 1.51 660 100 Benzene 1.24 790 98 Methyl alcohol 1.16 820 95 Mixture ethyl alcohol and 1.03 950 98 benzene Water 0.72 1,330 96 Ethyl alcohol 0.59 1,620 96 Turpentine 0.48 2,020 97 Amyl alcohol 0.155 5,900 92 Glycerol solution 0.0104 94,000 98 On the other hand, Oeholm (1913) finds that 8rj is not exactly constant for a series of alcohols as compared with water when glycerol is the diffusing substance. Oeholm thinks that associa- tion and hydration will account for the variations, at least in part. Bell and Cameron have applied Poiseuille's formula to diffusion through capillary spaces and find that the distance y which a liquid moves in a given time t is given by the formula y n = kt, 190 FLUIDITY AND PLASTICITY where n and k are constants, and by derivation n = 2. The formula is important in dealing with diffusion through porous materials such as soils. But in this type of diffusion, it has often been noticed that there is a separation of the components of the diffusing substances. This subject will come up for con- sideration later. Brownian Movement. Einstein (1906) has shown that the mean square of the projections I of the displacement of the particle in time t on the axis of displacement is I 2 = 28t Substituting into this equation the value of the diffusion, given above v- RT .*L f65) " N 3rr This is the equation used by Perrin in his brilliant investigation of the Brownian movement. The Velocity of Crystallization. As a crystal forms in a solution, the molecules of the solute are drawn to the growing face of the crystal. The solution bathing the face of the crystal has therefore a lower concentration of solute than the main body of liquid and a process of diffusion must be set up to restore the equilibrium. The rate of crystallization must therefore depend upon the fluidity of the solution. Even in an under- cooled liquid, where there is no opportunity for a change in con- centration, the viscosity of the liquid retards the proper orienta- tion of the molecules, and crystallization does not take place instantaneously. H. A. Wilson (1900) has demonstrated that the velocity is directly proportional to the fluidity of the liquid at the face of the crystal, according to the formula, V = a(t - t }

v, calculated v, observed 35 2 8.77 1.15 1.25 33 4 8.19 2.14 2.5 31 6 7.31 2.90 3.2 29 8 6.49 3.40 3.7 27 10 5.84 3.82 3.9 25 12 5.16 4.05 4.0 21 16 3.90 4.08 4.1 19 18 3.51 4.13 4.1 15 22 2.77 4.00 4.1 Since for all of these liquids the fluidity is as a first approxi- mation a linear function of the temperature, for salol

/Aco Acetone 252.0 177.0 .41 316.0 225.0 1.41 Propionitrile 185.0 129.0 .43 242.0 165.0 1.47 Methyl alcohol 118.0 90.0 .31 172.0 124.0 1.39 Ethyl mustard oil 118.0 82.0 .44 162.0 106.0 1.53 Acetylacetone 87 57 52 128 82 1 56 Ethyl alcohol 55.9 37.0 1.51 92.6 60.0 1.54 Benzonitrile 51.6 35.5 1.45 80.0 56.5 1.42 Nitrobenzene 32.6 25.0 1.30 55.0 40.0 1.37 fluidity and conductivity very nearly identical. Walden (1906) has gone further and proved that tp/\ is a constant even when the solvent is varied widely. He used tetraethylammonium iodide in some forty different organic solvents and found

m (68) where m = 0.70 for lithium chloride and potassium chloride and 0.55 for hydrochloric acid. In the case of lithium chloride no single value for m can be found which will give entirely satis- factory results. As a matter of fact, Washburn (1911) has found that for the first six sucrose concentrations, a value of m of 0.94 gives better concordance than Green's 0.70. Johnston (1909) has determined the values of m for a number of other solvents using the data of Dutoit and Duperthius (1908) for sodium 196 FLUIDITY AND PLASTICITY iodide solutions, and he finds that in no case does the value of m depart from unity by more than 0.2. Johnston has calculated the value of m for many cations and anions using different temperatures from to 156, but found that no single value could be assigned for the hydrogen and hydroxyl ions. The following table will show the nature of his results. TABLE LIII. THE RELATION BETWEEN THE CONDUCTANCES AND THE FLUIDITIES OF THE INDIVIDUAL IONS AT DIFFERENT TEMPERATURES C (AFTER JOHNSTON) Ion A m ?/A P/A, 100 >/Ao> 156 K 40.4 0.887 1.39 1 71 1 81 NH 4 40.2 0.891 1.40 1 71 1 80 Cl 41 1 88 1 37 1 70 1 81 NO 3 40 4 807 1 39 1 98 2 19 Na 26.0 0.97 2.16 2.27 2.31 ^Ca 30.0 1.008 1.88 1.84 1.84 C 2 H 3 O 2 20.3 1.008 2.77 2.73 2.73 KSO 4 41.0 0.944 1.36 1 51 1 55 H 240.0 0.234 0.550 0.741 OH 105.0 0.535 0.806 0.971 The slightly hydrated ions K, NH 4 , Cl, and N0 3 have a high conductivity and a small value of m, corresponding to an increasing ratio of ^/A^; the presumably highly hydrated ions Na, J^Ca, C 2 H 3 O 2 , and 1/2SO 4 have a low conductivity, a high value of m and a nearly constant ratio of >/Aco' Hydrogen and hydroxyl are most like the unhydrated group of ions in that they have a very high conductance and a low but rapidly increasing value of ip/A^. The explanation of these curious facts is not at hand, but apparently we must assume that the conductivity does vary directly in proportion to the fluidity and seek to explain the inconstancy of the

is = cupi (69) where a is the volume percentage of the medium whose fluidity is o + 27T rvrdr. (83) t Jr, But from Eqs. (78) and (82) If* , D \ and from Eq. (81) 27r f rMr = 27T M f | ^ (fl 2 r - r 3 ) - f(Rr - r 2 ) 1 dr - - -- l6^ 6 41 \ 2 4/ 2 and introducing the value of r from Eq. (78), we have Introducing these values of the separate terms of Eq. (83) and simplifying, Eq. (83) becomes V /R*P R 3 f . _ 4 /2(f\ _ J^ /2g\-| t 81 L 3 \R/ 3P 3 \/ J and now introducing the value of p given by Eq. (77), THE PLASTICITY OF SOLIDS 225 For large values of the applied pressure, the last term of Eq. (86) becomes very small and the curve becomes very nearly linear and coincident with its asymptote -=>-!') m The curve rises above the asymptote as the applied pressure becomes very small, but it crosses the pressure (or shearing stress) axis when P = p (or F /) . On differentiating Eq. (86) in respect to the pressure one finds that the slope of the curve vanishes when P = p, hence the curve is tangent to the axis. The intercept of the asymptote is thus 4/3 of the true friction which would be obtained by other methods as, for example, plastic material confined between parallel planes which are being sheared over each other. If in practice conditions may be con- trolled so that all of the observed points lie on a straight line, it will mean that all of the observed points lie on a straight line, the capillary in telescoping layers, the term p 4 /3P 3 being negligible. Were we to assume that the material throughout the capillary flows in telescoping layers for all shearing stresses above /, we will obtain = -/) (89) which differs from Eq. (88) in having / in place of 4/3/. It is highly desirable that some one measure the friction both by the capillary tube method and other methods using a given material, to make sure that they give identical values for the friction. .Not being able to reproduce satisfactorily the data of Bingham and Green, Buckingham has attempted to allow for slippage. If there is a thin layer of viscous liquid of thickness e separating the plastic material from the wall, it will increase the velocity of the plastic material by the amount epF, hence the increase in the volume of flow per unit of time over that given by Eq. (88) is irR 2 e Traction 1.0X10- Torsion... 3.60 Pitch II 3. OX 10' ' Sagging 3.30 Pitch and tar I .8X10- Traction 2.4X10- 10 Torsion . . 3.07 Pitch and tar II .5X10- Traction.... 4.5X10- 10 Torsion... 3.04 Shoemaker's wax .9X10- Traction S.OXIO" 7 Torsion . . 2.95 Pitch and tar 3:1 III .3X10- Sagging 3.8X10-* Efflux 3.25 Pitch and tar 3:1 IV .1x10- Descending column 3.6X10-5 Efflux.... 2.91 THE THEORY OF PLASTIC FLOW A plastic solid is made up of particles which touch each other at certain points. The spaces between the particles may be empty or it may be filled with gas, liquid, or amorphous solid. Flow necessitates the sliding of these particles the one over the other according to the ordinary laws of friction, so long as the particles are large enough so that their Brownian movement is negligible. It is by no means necessary that the particles be touching at the maximum number of points, corresponding to "close-packing." As a matter of fact, close-packing of the particles prevents flow from taking place. It is merely necessary that the particles touching each other form arches capable of carrying the load, as already indicated on page 201 . It is evident THE PLASTICITY OF SOLIDS 229 that as aggregates of particles are formed in the process of collisions, and the size of these aggregates increases as the concentration of solid increases, there must come a time when such aggregates or clots will touch each other and form an arch or bridge across the space through which the flow is taking place. At that concentration the friction will have a finite value, and the material may be said to have a structure just as was the case of the jelly or foam already considered. The pore space may vary between very wide limits, but if the suspended particles are assumed to be uniform spheres, it can easily be calculated that cubical close-packing, would leave a pore space of 1 Tr/6 or 47.64 per cent by volume, irrespective of the size of the particles. It is possible to get the particles still closer together until with tetrahedral close-packing, which we have in a pile of cannon-balls, the pore space is 1 7r/3\/2 or 25.96 per cent by volume, but in this case the particles are interlocked and no true flow is possible but rupture, with dis- integration of the particles. When the pore space is roughly 50 per cent, the mobility is zero, and it is only as the pore space is in excess of this figure that the mobility has a finite value. This excess pore space thus plays a role which is analogous to the free volume of liquids. As there is a minimum in the allowable pore space in a plastic solid, so there is a maximum, for as the pore space increases the substance finally ceases to become a solid. This concentration of zero friction was found for a certain English china clay to be 19.5 per cent by volume when suspended in water containing one-tenth of 1 per cent of potassium carbonate. If the particles of clay were spheres of uniform size, suspensions of this material would show plasticity in concentrations of solid from 19.5 to 47.64, i.e., over a range of roughly 30 per cent. Colloidal graphite exhibits zero fluidity when there is only 5.4 per cent in suspension, hence it has a plasticity range of concentrations of over 40 per cent. On the other hand, suspensions of many coarse materials have a plasticity range which is much con- stricted, which for practical purposes, is sometimes a serious disadvantage. There is abundant evidence that as the diameter of the particles is decreased, the opportunity for the particles touching 230 FLUIDITY AND PLASTICITY is increased, which enhances the friction, but this effect reaches a limit eventually when the particles are so small that their Brownian movement becomes appreciable and strains in the material are not permanent. If, as we have intimated, the friction is subject to the laws of ordinary external friction, the friction should be closely dependent upon the adhesion of the particles to each other but independent upon the nature of the medium so long as it is inert. In confirmation of this we note that whereas the china clay referred to above showed zero friction when the volume concentration was 19.5 per cent, the same clay thoroughly shaken down in a measuring flask in the dry state showed a pore space of 18.4 per cent, the pore space in this case being filled with air. The two values are in very close agreement. Infusorial earth exhibited zero fluidity in water when present to the extent of 12.9 per cent by volume, whereas in ethyl alcohol the corre- sponding concentration was 12.1 per cent. Finally it has been observed that the temperature and therefore the fluidity of the medium is without effect upon the friction. Adhesion between the particles may be influenced in a marked degree by the addition of small amounts of substances of the most diverse character. Generally speaking, substances which yield hydrogen ions increase the adhesion, i.e., promote floccula- tion, while substances which yield hydroxyl ions decrease the adhesion and promote deflocculation. Colloids also have a noteworthy effect. In flocculation, structure is produced and therefore the friction is enhanced. In a given instance, using 50 per cent china clay in water, the friction was lowered from 78 to 59.5 by adding merely one-tenth of 1 per cent of potassium carbonate, which of course yields hydroxyl ions. The mobility is dependent upon the fluidity of the medium. This in turn is influenced by the temperature, hence we may expect that the mobility of a solid will be dependent upon the temperature. Thus in a 50 per cent clay suspension the mobility at 25 was found to be 5.11 and at 40, 7.88. The ratio between these mobilities is 1.54 which is very close to the ratio of the fluidities of water at these two temperatures ^ _ 166.9 _ 5 ~ 111.7 ~ THE PLASTICITY OF SOLIDS 231 The result of deflocculation is to greatly increase the mobility. Thus one-tenth of 1 per cent of potassium carbonate raised the mobility from 1.17 to 5.11 which is an increase of over 330 per cent, a truly remarkable effect. SEEPAGE AND SLIPPAGE When the shearing force is just a little less than the friction, there is generally a certain amount of flow which is due to two different causes. In the first place, under ordinary conditions of flow the pressure tends to cause the medium to seep through the material. With this filtration phenomenon there is a local change in concentration and therefore a change in the char- acter of the flow. Seepage is unimportant when the medium is viscous arid the suspended particles are small as in paint. The second difficulty is due to slippage, which comes from lack of sufficient adhesion between the material and the shearing surface. The shearing surface is wet with the liquid medium and the smooth surface affords little opportunity for the attachment or interlocking of the particles. The result is that there is a layer of liquid between the shearing surface and the main body of the suspension and flow takes place in this layer according to the laws of viscous rather than plastic flow. Green (1920) has observed this phenomenon in paint under the microscope, the material moving as a solid rod until the shear reaches a certain value when it begins to move in telescoping layers. This slippage causes the rate of flow-shear curve to be no longer linear when the rate of flow is small and the curve passes through the origin. Difficulties due to seepage and slippage can be overcome by using sufficiently high pressures, so that the viscous flow factor will become negligible. In this case there should be a linear relation between shear and rate of flow. HYDRAULIC FLOW AND THE PLASTIC STATE So far as known to the author, no one has yet used rates of flow high enough to bring about eddy currents, which are so troublesome in the case of liquids. But there is the same necessity for using long narrow tubes for measuring the flow, 232 FLUIDITY AND PLASTICITY rather than orifices or very short tubes, for the flow of a plastic material through an orifice gives no idea of the mobility of the material, just as the flow of a liquid through an orifice is largely independent of the viscosity of the liquid. Flow through an = 10 = 11 = 12 = 13 ' = 14 = 15 = 16 7 900 7 / 7 7 7 "0 10 20 JO 40 50 60 70 80 90.' 100 110 FIG. 81. Hydraulic flow of a plastic material after experiments of Simonis. orifice does, however, lead to a knowledge of the friction constant of the plastic substance, as proved by the experiments of Simonis (1905). Simonis used 40 g of Zettlitz earth with 100 g of water to which were added successive portions of a dilute solution of THE PLASTICITY OF SOLIDS 233 sodium hydroxide containing 1.795 g per liter. The pressure seems to have been measured as centimeters of water head, and the volume of flow in milliliters per 600 sec. He measured the flow of 16 mixtures and pure water, designated by the numbers on the curves in Fig. 81. The amounts of sodium hydroxide solu- tion added are noted in the second column of Table LXI. The curves are nearly linear except when the volume of flow is small. The curvature is probably due to seepage. ' The hori- zontal distance of the different curves from the curve No. 10 is evidently a relative measure of the friction constant. The values of the friction constant / as obtained graphically are given in the table. We have found that it is possible to calculate this relative friction constant /' by means of the formula /' - 154 - 14. Ic (94) where c represents the number of milliters of sodium hydroxide added. It appears, therefore, from a comparison of 'the values of / and /' that Simonis' experiments confirm our conclusion that the friction is a linear function of the concentration. We note that the friction constant continually decreases as water is added until 11 ml have been added after which further additions are without effect upon the rate of flow. On adding 11 ml, the material reaches the concentration of zero fluidity or zero friction, and the curve 10 should pass through the origin. That the curves 10 to 17 all coincide with curve 10 accords with what we should expect of liquids flowing through an orifice. The fact that all of the curves are sensibly parallel constitutes the remarkable difference between flow through a capillary and flow through an orifice. It does not signify that the plastic mixtures all have the same mobility any more than it signifies that all of the liquid mixtures have the same fluidity. It means simply that the rate of flow through an orifice is independent of the fluidity or mobility. If in the equations for the flow of a viscous or a plastic substance through a capillary we make the length of the capillary zero, we obtain the identical equation V )* aoo) where ot is the coefficient of expansion of a gas and C is a constant. This formula has had the most remarkable success of any that have been proposed, although it does not apply to vapors well. A single example of its performance is given in the following table, using Holman's (1886) data for carbon dioxide at atmos- pheric pressure. Examining Sutherland's formula, we observe that when the constant C is small in comparison with the absolute temperature the formula reduces to the simple theoretical formula 7, = KT" The discovery, (cf. Vogel (1914)), that Sutherland's formula fails at low temperatures indicates that it does not quite correctly take account of the deviation from the simple formula. Quite in harmony with the above, it is found that the values 248 FLUIDITY AND PLASTICITY TABLE LXVII. CONCORDANCE BETWEEN SUTHERLAND'S FORMULA AND HOLMAN'S DATA FOR CARBON DIOXIDE. C = 277, ij = 0.000,138,0 Temperature, degrees Centigrade n X 10 7 observed 77 X 10 7 calculated 18.0 ,474 ,471 41.0 ,581 ,584 59.0 ,674 ,671 79.5 ,773 ,766 100.2 ,864 ,864 119.4 ,953 ,951 142.0 2,048 2,056 158.0 2,121 2,127 181.0 2,234 2,227 224.0 2,411 2,409 of C for different substances increase with the critical tempera- ture or boiling-point of the substance. Rankine (1910) obtained an empirical relation between C and the absolute critical tempera- ture T cr T cr = 1.12C (101) TABLE LXVIII. THE RELATION OF THE CONSTANT C IN SUTHERLAND'S EQUATION TO THE BOILING-POINT AND CRITICAL TEMPERATURE Tcr, Critical T b , Boiling Substance tempera- ture, ab- C Tcr/C tempera- ture, ab- c/n solute solute Helium. 9 78 2 11 4 3 18 3 Hydrogen 37 83 0.45 20 4 4.1 Nitrogen 127.0 113.0 .12 77.5 .45 Carbon monoxide 133.0 100.0 .33 83.0 .20 Oxygen 154.0 138.0 .12 90.6 .52 Nitric oxide 179 5 167.0 .08 120 .39 Ethylene 383.6 249.0 .14 170.0 .46 Carbon dioxide 304.0 259.0 .17 194.0 .33 Ammonia 423.0 352.0 .20 240.0 .47 Ethyl ether 467.0 325.0 1.43 307.0 1.06 THE VISCOSITY OF GASES 249 which suggested to Vogel a similar relation to the absolute boiling temperature Tb C = \AlT b (102) This formula indicates that C increases considerably more rapidly than the temperature, and since Tb is comparatively large for vapors, the less perfect agreement of Sutherland's formula is partially explained. This, however, is not true of hydrogen and helium which present curious anomalies, as shown in Table LXVIII. VISCOSITY AND CHEMICAL COMPOSITION If the mass of a particle in a rarefied gas is increased n-fold by changing its chemical composition, the velocity will be n~^ times the original velocity, so that the momentum of each TABLE LXIX. THE VISCOSITIES OF PERMANENT GASES AND VAPORS AT 0C Substance Molecular weight rio X 10 7 T cr 7?cr X 10 7 Hydrogen 2.0 850 31.0 Helium 4.0 1,871 5. 21 Methane 16.0 1,033 183. Neon 20.2 2,981 Nitrogen 28.0 1,678 Carbon monoxide 28.0 1,672 133. Oxygen 32.0 1,'920 154. Argon 39.9 2,102 155.6 1,253 Nitrous oxide 44.0 1,362 Krypton 82.9 2,334 210.5 1,806 Xenon 130.2 2,107 288. 2,266 Ethyl alcohol 46.0 827 513. Acetone 58.0 725 510. Methyl formate 60.0 838 485. Ethyl ether 74.1 689 467. Benzene 78.0 689 561. Methyl isobutyrate 88.1 701 543. Ethyl acetate 88.1 690 523. Ethyl propionate 90.1 701 547'. 250 FLUIDITY AND PLASTICITY molecule will be w^-fold that of the smaller molecule. But the number of excursions of the molecules will be in proportion to n~^, so that the total loss of momentum will be the same as before, provided only that the number of particles per unit volume remains the same. In gases at ordinary pressure, there are considerable differences in viscosity ranging from 0.0000689 for benzene vapor to 0.0002981 for neon, but they are inconsiderable as compared with the vast differences we find in the liquid state and these viscosities are measured at and not under corresponding con- ditions. Table LXIX shows that the vapors have viscosities which are smaller than those of the permanent gases except FIG. 82. The relation between the viscosity of the elements at their critical temperature and their atomic weights. hydrogen. Their viscosities are so nearly identical that it is not certain whether the viscosity of a given class of chemical com- pounds such as the ethers differs from that of the esters or ketones. It . is quite impracticable with the data at hand to assign any effect to an increase in the molecular weight within a given class of compounds. Since the viscosities of the permanent gases at are not simply related to each other, it is natural to seek some other basis of comparison, and Rankine (1911) has achieved success along this line by comparing the viscosities of the rare gases rj c and their atomic .weights M at the critical temperatures. He finds them related together by the formula r,,* = 3.93 X 10- 10 M THE VISCOSITY OF GASES 251 as depicted in Fig. 82. The critical constants of neon and niton have not yet been determined. Rankine has further found that the same general formula applies to the halogens, but the constant is different being 10.23 X 10~ 10 . He gives for chlorine t\ c = 1,897 X 10- 7 and for bromine r, c = 2,874 X 1Q- 7 (cf. Fig. 82). Were we to use the molecular weights instead of the atomic weights, the constant would be 5.12 X 10~ 10 which is nearer that of the rare gases but still not identical with it. THE VISCOSITY OF GASEOUS MIXTURES Since in a rarefied gas the viscosity is proportional to the number of molecules in a unit volume, i.e., to the pressure, the viscosities will be additive when gases are mixed in varying percentages by volume; but since the viscosity of a rarefied gas is also independent of the weight of the molecules, the law loses its significance. In gaseous mixtures at ordinary pressures the simple deduced formula still applies, it being merely necessary to find the appropriate mean values of p, V, and L. This has been done by Maxwell (1868) and Puluj (1879), and one obtains the formula (cf. Meyer's Kinetic Theory of Gases, page 201 et seq.) .p p \r? 2 / w 2 J Graham (1846) observed that mixtures of oxygen and nitrogen or oxygen and carbon dioxide in all proportions have rates of transpiration which are the arithmetical mean of the two components. Thus for air, 0.0001678 X 0.7919 = 0.0001329 0.0001920 X 0.2081 = 0.0000399 Calculated viscosity of air . 0001728 Observed viscosity of air 0. 0001724 Vogel (1914). Graham and others have noticed that when hydrogen is mixed in 252 FLUIDITY AND PLASTICITY small amounts with other gases, as carbon dioxide or methane, the viscosity of the mixture is much greater than would be calculated by the simple formula of additive viscosities. In these cases Puluj (1879) and Breitenbach (1899) have found that the more complicated formula (103) gives good agreement. VISCOSITY OF GASES AND DIFFUSION AND HEAT CONDUCTIVITY We note that the diffusion coefficient D in a mixture of gases is D = 1 7i(N 2 L^, + NtLtQj/N (104) NI, LI, and Oi being the number of molecules of the first kind of gas per unit volume, the length of the mean free path, and the mean speed respectively, etc. Also N = NI + N%. Since the length of the mean free path can most easily be calculated from the viscosity, it becomes possible to calculate the diffusion coefficient from the viscosity. In the conduction of heat the two kinds of gas become identical, hence the above equation becomes D = 1 u-flL (105) O If we neglect the small difference between fii and ft due to temperature difference the conductivity of heat k becomes k = I vQLpC, (106) o Cv being the specific heat of the gas at constant volume, and combining this equation with the viscosity Eq. (97) we obtain k = Cr,C v (107) C being a constant (cf. Eucken (1913)). DETERMINATION OP THE ULTIMATE ELECTRICAL CHARGE It is well known that Sir J. J. Thomson (1898) devised a method for measuring the charge on the particle of a rarefied gas e by observing the rate of fall under gravity of the particles of an ionized fog which had been produced by sudden expansion and then observing the rate of fall of a similar cloud when it is sub- jected to the action of a vertical electrical field of known intensity superimposed upon gravity. THE VISCOSITY OF GASES 253 If v is the velocity of a droplet of mass m, density p under the action of gravity alone, and v\ its velocity when under the in- fluence of the electrical field whose strength is X in electrostatic units, then i = -jy dog) v\ mg + Xe Applying Stokes' Law, Eq. (62), to the sphere whose volume is 47rr 3 /3, we obtain (109) A beautiful application of this method has been made by Millikan (1909, etc.). He has found the most probable value for e to be 4.69 X 10~ 10 . This leads to the number of molecules in a gram molecule N = 6.18 X 10 23 and the mass of the hydro- gen atom as 1.62 X 10~ 24 g. Chapman (1916) and Rankine (1920-1) have calculated the diameters of the atoms of the monatomic gases from determina- tions of the viscosity. They regard the atoms as hard spheres having the well-defined absolute diameters given below. ATOMIC DIAMETERS OF SOME OP THE NOBLE GASES AFTER RANKINE Gas Viscosity Crystal measurement Neon... 2.35 X 10-' 61.30 X 10-' Argon Krypton Xenon 2.87 X 10-' 3.19 X 10- 1 3.51 X 10- 1 2.05 X 10- 1 2.35 X 10- 62.70 X 10- 1 These values agree very well with those obtained from van der Waal's equation but they are somewhat greater than the diameters of the outer electron shells of the atoms as obtained by Bragg from his crystal measurements. CHAPTER X SUPERFICIAL FLUIDITY The viscosity of a liquid may change, and it may change in a quite extraordinary manner, as the boundary of the liquid is approached. This must of necessity result wherever the surface tension is such as to bring about a change in concentra- tion at the boundary. We should therefore naturally expect soap and saponin solutions to show this phenomenon. Experi- mentally this field of study has not been much explored although, as we shall attempt to show, the promise of reward is very great and the need of such study in industry is pressing. However, Stables and Wilson (1883) have proved that a saponin solution has a viscosity at the surface which is 4,951 as compared with 3.927 for the surface of pure water. The viscosity was measured by the oscillations of a circular nickel-plated brass disk, of 7.625 cm diameter and 0.2 cm thickness, which was suspended in the liquid by means of a wire 119.8 cm long. As soon as the solution was allowed to rise 0.15 cm above the disk the viscosity fell to its normal value. The viscosity found by Stables and Wilson indicates that the surface layer of a supposedly dilute solution may nevertheless have a viscosity which is over a thousand-fold that of water at 20C (1,260 cp) or about the viscosity of castor oil. But for very small stresses, the viscosity may be still higher, for it is to be particularly noted that in a saponin solution a pendulum does not oscillate isochronously. Thus in one experiment with vibrations of large amplitude, Stables and Wilson found the time of vibration to be 10.52 seconds, whereas with small ampli- tudes the time of vibration was 9.73 sec. This would indicate that with very small stresses the viscosity might be found to be infinite, which would mean that we are here again dealing with plastic flow. The experiments of Stables and Wilson need confirmation and 254 SUPERFICIAL FLUIDITY 255 extension with our more recent knowledge of the nature of flow in mind, but whatever the surface of a given saponin solution may be, we may profitably distinguish three typical cases: (A) where the superficial layer is a true solution but of different concen- tration from the interior and is in contact with it own vapor or some gas; (B) where the surface is made up of a layer of immisci- ble liquid, which may be so thin as to be imperceptible by ordi- nary means; (C) where the surface is formed either by a continuous solid or by solid particles in more or less intimate contact with each other. It is evident that in the last two cases we are dealing not with the superficial fluidity of the liquid but of a heterogene- ous mixture of liquid-liquid or solid-liquid respectively. Soap solutions perhaps afford the best examples of the first case and if such solutions have extraordinarily high superficial viscosity, it serves to explain the stability of the soap bubble. The liquid between the two highly viscous surfaces can proceed downward very slowly in so narrow a space. Oil films on water give frequent examples of the second sort, and the use of oil "to calm troubled waters" is a practical appli- cation of superficial viscosity in the damping of vibrations. The simple harmonic motion of the wave causes the particles to move in vertical circles, so that an oil film is alternately stretched and compressed. The water underneath not being subjected to this same tendency is pulled along by the oil film and in this viscous flow energy is of course dissipated. A method for the measure- ment of viscosity by Watson (1902) depends upon the damping of small waves in a free surface, and apparently this method is capable of being used to measure superficial viscosity, but this appears not to have been attempted. The connection of superficial fluidity with emulsions must be mentioned at this point although we cannot stop to discuss it. We can merely refer the reader to the fascinating studies of Pla- teau, Quincke, and Lord Rayleigh upon the nature of contamina- ting films. The recent paper by Irving Langmuir (1919) on the theory of flotation is very suggestive. Many of the examples which we would naturally cite as exam- ples of the second case given above may really be examples of the third instead. It is certain that in most emulsions a third sub- stance is necessary to stabilize it and it may give rigidity. Scums 256 FLUIDITY AND PLASTICITY are apparently examples of this class. Gurney (1908) in investi- gating the contamination of pure water surfaces on standing, says "Water surfaces become noticeably rigid in a few hours or days: depending on the previous history of the fluid. Vigorous stirring destroyed the rigidity of the surface." To prevent possible misunderstanding, it must be stated again that rigidity in foams and emulsions arises largely from the fact that during shear the bubbles of a foam or the globules of an emulsion are distorted and may be disrupted, and thus work is done against the forces of cohesion opposing such disruption. Superficial viscosity has heretofore been considered at a free surface only. Such a view is too narrow as it would leave the most important examples out of consideration and from the theoretical aspect the extension of our conception of superficial fluidity involves no difficulty whatever. Having made this extension, the phenomenon of slipping falls into the third case, but the fluidity near the boundary is higher than that of the main body of material. Henry Green (1920) has studied this slippage under the microscope, using for observation paint colored with a little ultramarine, which may be subjected to shearing stresses in a capillary tube. With small stresses the shear takes place exclusively in the region near the boundary, but when the stress becomes greater than the yield value of the paint, the shearing takes place throughout the material. Green reasons that it is this mixture of the kinds of flow which causes- the shear to fail to be a linear function of the shearing stress, particularly when those stresses are near the yield shearing stress. In the above example, the layer next to the boundary was more fluid than the mam body of material, but more often the opposite is the case, the fluid near the boundary is less fluid, and we might therefore consider the general subject of adsorption under this head. And we would then show that it is possible to make a fractional separation of fluids by simply passing them through capillary tubes. Such a separation of a mixture into its components by means of capillary flow has actually been demonstrated, as in the case of petroleum forced through clay by Gilpin and his co-workers (1908). 1 Since the surface area of a capillary varies as the first power of the 1 Am. Chem. J. 40, 495 (1908); 44, 251 (1910); 50, 59 (1913). SUPERFICIAL FLUIDITY 257 radius whereas the volume of flow varies as the square of the radius, Eq. (6), we may expect to find the effects of superficial fluidity shown to the best advantage in very fine tubes. There are a variety of causes which may cause the fluid near the boundary to have a different fluidity. The most important cause results from the selective adhesion of the components of the fluid for the solid. If one of the components of the fluid is more strongly attracted than another, separation becomes possi- ble, and the magnitude of the fluidity of the mixture as measured will theoretically be affected The adhesion between solid and liquid or liquid and liquid is doubtless just as specific a property as is the better known cohesion or surface tension of liquids and we are coming to understand the nature of adhesion better through the efforts of Langmuir (1919) and Harkins (1920). We have seen that it is possible to greatly affect both the friction and the mobility of plastic substances by the addition of small amounts of acid or alkali. Just what happens in such cases might be subject to dispute, but it is certain that small amounts of substances adsorbed on to the surface of a solid may entirely change the character of the solid which is in contact with the liquid. Thus Henry Green (1920) has observed that the addition of small amounts of gum arabic to a suspension may greatly decrease the yield value and increase the mobility, in spite of the high viscosity of gum arabic solutions. This is interpreted as being due to the decrease in adhesion between the sus- pended particles. The well-known work of Schroeder (1903) upon the effects of electrolytes on the viscosity of gelatine and of Handowsky (1910) upon serum albumin should also be referred to. We have already proved on page 86 that if any cause results in the fluid near the boundary becoming different from the re- mainder of the liquid, the resulting fluidity will be changed. This theorem is therefore useful in explaining superficial fluidity. We will now prove that the components of a mixture under these conditions will undergo partial separation. The conditions will be made more general by using the non-homogeneous mixture considered on page 86. Considering the mixture as made up of the two components A and B, arranged in alternate plane layers, the total quantity of A flowing in a unit of time, regardless 258 FLUIDITY AND PLASTICITY of whether it is derived from the fluidity of A or B, is obtained from the terms of Eq. (26) containing r\, and is 2V 1 n I and similarly the rate of flow of component B is There will be separation of the two components only when the thickness of the different layers is considerable or when the passage through which the substances are forced is very small, for in either case n will be small. If n = , Ui a U 2 b and there will be no separation at all. The separation may be calculated from the expression Ui a na 2 , m U 2 b'-(n + l)a?i +nb

pres- pres-

< ^ '0 10 20 30 40 50 60 70 Friction in dynes per crn 2 FIG. 91. Temperature-friction curve for a colloidal dispersion of 7. 70S weight percentage of nitrocellulose in acetone. Solubility and Plasticity. It is of course well-known that the so-called "solutions" of nitrocellulose, gelatine and other colloids are not true solutions, nevertheless the term solution as applied to colloidal dispersions often leads to confusion. Thus acetone is one of the best "solvents" for nitrocellulose, being superior to let us say, amyl acetate. But what does this statement mean? It cannot possibly mean that acetone will actually dissolve more nitrocellulose than will a similar amount of amyl acetate, for there is no point of saturation for either, i.e., both liquids will " dissolve" or better disperse an indefinite amount of colloid; hence the term solubility has here a very special, albeit a very definite, meaning, viz., that dispersive medium is the best solvent which with a given amount of colloid gives an emulsion having the maximum mobility. Here however there enters the 294 FLUIDITY AND PLASTICITY fact, which seems from the literature not to have been sufficiently considered, that acetone has a far greater fluidity than amyl acetate to start with, and this must of necessity affect the mobility of dispersions in these media. It is evident that this must be taken into account if we are to get a true measure of the dispersive power of different media. This work is being continued. APPENDIX A PRACTICAL VISCOMETRY The most essential part of the viscometer is shown in Fig. 29 , p . 76 . To use the apparatus an appropriate amount of the liquid whose viscosity is to be measured is pipetted into the right limb. The liquid at the desired temperature is forced over into the left limb until the right meniscus reaches the point N, it being noted that there is sufficient liquid so that the surplus runs over into the trap. The right limb is turned to air so as to prevent more liquid from flowing into the trap. Having adjusted the working volume, the left limb is connected with the pressure, and the time required for the left meniscus to fall from B to D is noted. The left limb is now turned to atmospheric pressure and the instru- ment is ready for an immediate duplicate determination in the opposite direction. In this second measurement the time is noted which is required for the left meniscus to rise from D to B. Knowing the pressure, p in grams per square centimeter, the time, t, in seconds, the two constants of the instrument, C and C", and the density of the liquid, p, the viscosity 77 at the given tem- perature is given by the formula, (cf. p. 74). 17 = Cpt - C'p/t (1) DETERMINATION OF THE CONSTANTS OF THE INSTRUMENT The second term of the right hand member of the above equa- tion is the kinetic energy correction which should never exceed 5 per cent of the value of the first term. For this reason the value of the constant C' and of the density p need be known with an accuracy of 2 per cent only in order to allow viscosity deter- minations to be made with an error of only one-tenth of 1 per cent. C' = 0.0446 V/l (2) where V is the volume in milliliters of the bulb C between the marks B and D, and Z is the length of the capillary EF, log. 0.0446 = 8.64895 - 10. 295 296 FLUIDITY AND PLASTICITY The value of the constant C is most conveniently obtained by filling the instrument with freshly distilled, dust-free water and determining the time of flow for each limb, at 20C. 0.01005* + C'p tt^2 W for water at 20. This constant may also be obtained by direct measurement C = 384.8r 4 /FZ (4) where r is the radius of the capillary in centimeters. If the acceleration of gravitation of the locality is not 980, the value of C must be increased 0.1 per cent for each unit in excess. Since the bulbs C and K may differ in level, it is evident that the pressure, p, used in calculating the viscosity is not necessarily equal to the pressure, p i} delivered by the compressed air at the top of the viscometer. If the bulb K is higher than the bulb C by a distance h, then it is evident that the pressure during the left limb determination is decreased by an amount h t p and the pres- sure during the right limb determination is increased by the same amount. Hence, Pi - /ZIP = ^ + c't P ^~ ^ left limb) ?> 2 + h lP = * + %' i ' /t * (right limb) and therefore hl = 2Cp \ti tj + 2C U a ~~ iff " ~2~ or if the two determinations are carried out with water at 20 using the same pressure 0.005034 where t, is the time of flow from right to left and fa is the time of flow from left to right. Log. 0.005034 = 7.70191 - 10. The value of C used in calculating the hydrostatic head is an approximate value obtained from Eq. (3) by employing the pres- sure, pi, uncorrected for hydrostatic head, which is legitimate since the hydrostatic head is at the most only a small correction term. J. W. Temple has worked out a simpler method for calculating APPENDIX A 297 the hydrostatic head when the flow in opposite directions is carried out at the same manometer pressure p. Let the time of flow in the one direction t L , under the true pressure corrected for hydrostatic head p L = p + hip, be supposed to be less than the time t R in the opposite direction under the pressure p R = p - h 1P . Then , PL ~ PR hi = s 2p and substituting into this equation the values of p L and p R given by Eq. (1), we have 1 h + C'p/t L r, + C'p/t R \ 2p\ Ct L Ct B I but in the kinetic energy correction, which is itself always small, the small hydrostatic head correction is of negligible influence, hence for our purpose we may write rj -f- C'p/t L = rj + C'p/t R so but from Eq. (1) we have that T? + C'p/t L = Cp L t L hence > THE TRUE AVERAGE PRESSURE It might inadvertently be assumed that if the two bulbs C and K are the same in shape and volume and also at the same level, the true pressure to be used in calculating the viscosity would necessarily be the pressure p\ delivered by the compressed air in the viscometer because the hydrostatic head as obtained above would then be zero. But since the hydrostatic head in the vis- cometer is really continually changing, the true average pressure may not be zero under the above conditions, and it must be obtained by integration. Bingham, Schlesinger, and Coleman (1916) 1 have shown that for cylindrical bulbs the true average pressure p would be 1 For other shapes of bulbs see original paper of Bingham, Schlesinger, and Coleman. For the possible importance of such corrections see Kendall and Munroe (1917). 298 FLUIDITY AND PLASTICITY where h is the height of the bulb and po is the pressure with all other corrections made. Fortunately if the height of the bulb BD, in Fig 29, is not more than one- thirtieth of the whole pressure, this correction is unnecessary to attain the desired accuracy of 0.1 per cent. In any case, however, the student should determine by experi- ment whether a change in manometer pressure is without effect upon the valve of C. THE PRESSURE CORRECTIONS OUTSIDE THE VISCOMETER Let the density of the liquid within the manometer be p at a temperature T in degrees Centigrade and the height read on the manometer scale corrected for scale error if necessary be h ; also let the viscometer bulbs be at a height h' above the middle point of the manometer. The pressure delivered to the air in the viscometer becomes Pi = h K L for a water manometer (8) Pi = M N for a mercury manometer (9) where the values of L are given in Table I and may be made entirely negligible in the setting up of the apparatus. TABLE I. VALUES OF L ho in centimeters 100 200 300 50 0.01 0.01 Q.02 100 0.01 0.03 0.04 200 0.03 0.05 0.08 300 0.04 0.08 0.11 APPENDIX A The values of K are given in Table II. TABLE II. VALUES OF K 299 Temperature, degrees centi- grade Manometer reading, ho 10 20 30 40 50 60 70 80 90 100 200 300 5 0.0130.025 0.039 0.053 0.066 0.079 0.094 0.108 0.122 0.136 0.285 0.482 10 0.016 0.030 0.046 0.064 0.078 0.095 0.112 0.129 0.145 0.162 0.337 0.533 11 0.017 0.032 0.050 0.068 0.083 0.101 0.119 0.137 0.154 0.172 0.357 0.563 12 0.018 0.035 0.053 0.072 0.089 0.108 0.126 0.145 0.163 0.183 0.379 0.596 13 0.019 0.037 0.057 0.077 0.095 0.115 0.135 0.155 0.175 0.195 0.403 0.632 14 0.020 0.040 0.061 0.082 0.102 0.123 0.144 0.165 0.187 0.208 0.429 0.671 15 0.022 0.043 0.065 0.088 0.110 0.131 0.154 0.177 0.199 0.222 0.457 0.713 16 0.023 0.046 0.070 0.094 0.118 0.140 0.165J0.189 0.212 0.238 0.489 0.761 17 0.025 0.049 0.075 0.101 0.126 0.150 0.17610.203 0.228 0.255 0.523 0.812 18 0.027 0.053 0.080 0.108 0.135 0.161 0.189J0.217 0.245 0.273 0.559 0.866 19 0.029 0.057 0.086 0.116 0.144 0.173 0.2030.233 0.262 0.292 0.597 0.923 20 0.031 0.060 0.092 0.124 0.154 0.185 0.2170.249 0.280 0.312 0.637 0.983 21 0.033 0.065 0.098 0.132 0.165 0.198 0.2320.265 0.299 0.333 0.679 1.046 22 0.035 0.069 0.105 0.141 0.176 0.211 0.2470.282 0.319 0.355 0.723 1.113 23 0.037 0.074 0.112 0.151 0.188 0.225 0.264 0.301 0.341 0.379 0.770 1.184 24 0.040 0.079 0.119 0.160 0.200 0.240 0.281 0.321 0.363 0.403 0.819 1.256 25 0.042 0.084 0.127 0.170 0.212 0.255 0.298 0.341 0.385 0.428 0.869 1.331 26 0.045 0.089 0.135 0.181 0.225 0.270 0.316 0.362 0.408 0.454 0.921 1.409 27 0.048 0.094 0.143 0.191 0.239 0.286 0.335 0.383 0.432 0.481 0.975 1.490 28 0.050 0.100 0.151 0.202 0.253 0.303 0.355 0.405 0.458 0.509 1.031 1.574 29 0.053 0.105 0.160 0.214 0.268 0.321 0.375 0.429 0.484 0.538 1.089 1.661 30 0.056 0.111 0.169 0.226 0.283 0.339 0.396 0.453 0.511 0.568 1.149 1.751 31 0.059 0.117 0.178 0.239 0.298 0.357 0.417 0.478 0.538 0.599 1.210 1.842 32 0.062 0.124 0.188 0.251 0.314 0.376 0.439 0.503 0.567 0.630 1.273 1.937 33 0.066 0.130 0.197 0.264 0.330 0.395 0.462 0.529 0.595 0.662 1.337 2.033 34 0.069 0.137 0.207 0.277 0.346 0.415 0.485 0.555 0.625 0.695 1.403 2.132 If the pressure is read on a mercury manometer at 20, the heights in mercurial centimeters may be converted into grams per square centimeter by means of Table III. 300 FLUIDITY AND PLASTICITY TABLE III. VALUES OF M. PRESSURES IN GRAMS PER SQUARE CENTI- METER, FOR HEIGHTS IN MERCURIAL CENTIMETERS Height, centi- meters of mercury .0 .1 .2 .3 : .5 .6 .7 .8 10 135.4 36.8 38.2 39.5 40.9 42. 2 43. 6 44.9 46.3 47.6 11 49.0 50.3 51.7 53.1 54.4 55.8 57.1 58. 5 59. 8 61.2 12 62.5 63.9 65.2 66.6 68.0 69.3 70.7 72.0 ! 73.4 74.7 13 76.1 77.4 78.8 80.1 81.5 82.9 84.2 85.6 : 86.9 88.3 14 89.6 91'. 92.3 93.7 95.0 96.4 97.8 99.1 "00.5 "01.8 15 203. 2 04.5 05.9 07.2 08.6 09.9 11.3 12.7 14.0 15.4 16 16.7 18.1 19.4 20.8 22.1 23.5 24.8 26.2 27.6 28.9 17 30.3 31.6 33.0 34.3 35.7 37.0 38.4 39.7 41. 1 42.5 18 43.8 45.2 46.5 47.9 49.2 50.6 51.9 53.3 54.6 56.0 19 57.4 58.7 60.1 61.4 62.8 64.1 65.5 66.8 68.2 69.5 20 70.9 72.2 73.6 75.0 76.3 77.7 79.0 80.4 81.7 83.1 21 84.4 85.8 87.2 88.5 89.9 91.2 92.6 93.9 95.3 96.6 22 98.0 99.3 *00.7 02.0 *03.4 04.8 *06.1 *07.5 08.8 *10.2 23 311.5 12.9 14.2 15.6 16.9 18.3 19.7 21.0 22.4 23.7 24 25.1 26.4 27.8 29.1 30.5 31.8 33.2 34.6 35.9 37.3 25 38.6 40.0 41.3 42.7 44.0 45.4 46.7 48. 1 49.5 50.8 26 52.2 53.5 54.9 56.2 57.6 58.9 60.3 61.6 63.0 64.4 27 65.7 67.1 68.4 69.8 71.1 72.5 73.8 75.2 76.5 77.9 28 79.2 80.6 82.0 83.3 84.7 86.0 87.4 88.7 90. 1 91.4 29 92.8 94.2 95.5 96.9 98.2 99.6 *00.9 *02.3 *03. 6 *05.0 30 406.3 07.7 09.1 10.4 11.8 13.1 14.5 15.8 17.2 18.5 31 19.9 21.2 22.6 24.0 25.3 26.7 28.0 29.4 30.7 32.1 32 33.4 34.8 36.1 37.5 38.9 40.2 41.6 42.9 44.3 45.6 33 47.0 48.3 49.7 51.0 52.4 53.7 55.1 56.5 57.8 59.2 34 60.5 61.9 63.2 64.6 , 65.9 67.3 68.6 70.0 71.4 72. 7 35 Oft 74.1 75.4 76.8 78.1 79.5 80.8 82.2 83.5 84.9 86.3 nn o 1.4 OO 37 87. 6 501.2 89. 02.5 90. 3 03.9 91 . 7 05.2 93. 06.6 94. 4 07.9 95. 7 09.3 97. 1 10.6 98. 4 12.0 99. 8 13.3 ( .i'o.i 38 14.7 16.1 17.4 18.8 20.1 21.5 22.8 24.2 25.5 26.9 ( .2 0.3 39 28.2 29.6 31.0 32.3 33.7 35.0 36.4 37.7 39.1 40.4 ( .3 0.5 ( .4 0.6 40 41.8 43.1 44.5 45.9 47.2 48.6 49.9 51.3 52.6 54.0 C .5 0.7 41 55.3 56.7 58.0 59.4 60.8 62.1 63.5 64.8 66.2 67.5 ( .6 0.8 42 68.9 70.2 71.6 72.9 74.3 75.6 77.0 78.4 79.7 81.1 ( .7 1.0 43 82.4 83.8 85. 1 86.5 87.8 89.2 90.5 91.9 93.3 94.6 ( .8 1.1 44 96.0 97.3 98.7 oo.o *01.4 *02.7 *04.1 *05.4 *06.8 *08.2 C .9 1.3 45 609.5 10.9 12.2 13.6 14.9 16.3 17.6 19.0 20.3 21.7 L 46 23.1 24.4 25.8 27.1 28.5 29.8 31.2 32.5 33.9 35.2 47 36.6 38.0 39.3 40.7 42.0 43.4 44.7 46.1 47.4 48.8 48 50.1 51.5 52.9 54.2 55.6 56.9 58.3 59.6 61.0 62.3 49 63.7 65.0 66.4 67.8 69.1 70.5 71.8 73.2 74.5 75.9 50 77.2 78.6 79.9 81.3 82.6 84.0 85.4 86.7 88.1 89.4 51 90.8 92.1 93.5 94.8 96.2 97.5 98.9 00.3 01.6 *03.0 52 704.3 05.7 07.0 08.4 09.7 11.1 12.4 13.8 15.2 10.5 53 17.9 19.2 20.6 21.9 23.3 24.6 26.0 27.3 28.7 30.1 54 31.4 32.8 34. 1 35.5 36.8 38.2 40.9 42.2 43.6 55 45.0 46.3 47.7 49.0 50.4 51.7 53! 1 54.4 55.8 57.1 56 58.5 59.9 61.2 62.6 63.9 65.3 66.6 68.0 69.3 70.7 57 72.0 73.4 74.7 76. 1 77.5 78.8 80.2 81.5 82.9 84.2 58 85.6 86.9 88.3 89.6 91.0 92.4 93.7 95.1 96.4 97.8 59 99.1 00.5 01.8 *03.2 *04.5 *05.9 07.3 08.6 *10.0 11.3 60 812.7 14.0 15.4 16.7 18.1 19.4 20.8 22.2 23.5 24.9 61 26.2 27.6 28.9 30.3 31.6 33.0 34.3 35.7 37.1 38.4 62 39.8 41. 1 42.5 43.8 45.2 46.5 47.9 49.2 50.6 52.0 63 53.3 54.7 56.0 57.4 58.7 60.1 61.4 62.8 64. 1 65.5 64 66.8 68.2 70.9 72.3 73.6 75.0 76.3 77.7 79.0 65 80.4 81.7 83! 1 84.5 85.8 87.2 88.5 89.9 91.2 92.6 66 93.9 95.3 96.6 98.0 99.4 *00.7 *02.1 03.4 04.8 06.1 67 907.5 08.8 10.2 11.5 12.9 14.3 15.6 17.0 18.3 19.7 68 21.0 22.4 23.7 25.1 26.4 27.8 29.2 30.5 31.9 33.2 69 34.6 35.9 37.3 38.6 40.0 41.3 42.7 44. 1 45.4 46.8 APPENDIX A 301 TABLE III. Continued Height, centi- meters of mercury .0 . 1 1 .2 .3 .4 .5 | .6 1 1 1 .7 .8 .9 70 48.1 49.5 50.8 52.2 53.5 54.9 56.2 57.6 58.9 60.3 71 61.7 63.0 I 64.4 65.7 67.1 68.4 69.8 71.1 72.5 73.8 72 75.2 76.6 77.9 79.3 80.6 82.0 83.3 84.7 86.0 87.4 73 88.7 90.1 91.5 92.8 94.2 95.5 96.9 98.2 99.6 00.9 74 1002.3 03.6 05.0 06.4 07.7 09.1 10.4 11.8 13.1 14.5 75 15.8 17.2 18.5 19.9 21.2 22.6 24.0 25.3 26.7 28.0 76 29.4 30.7 32.1 33.4 34.8 36.1 37.5 38.9 40.2 41.6 77 42.9 44.3 45.6 47.0 48.3 49.7 51.0 52.4 53.8 55.1 78 56.5 57.8 59.2 60.5 61.9 63.2 64.6 65.9 67.3 68.7 79 70.0 71.4 72.7 74.1 75.4 76.8 78.1 79.5 80.8 82.2 80 83.6 84.9 86.3 87.6 89.0 90.3 91.7 93.0 94.4 95.7 81 97. li 98.4 99.8 01.2 02.5 03.9 '05.2 *06.6 07.9 *09.3 82 83 1110. 6| 12.0 24.21 25.5 13. 3 26.9 14. 7 28.2 16. 1 29.6 17. 4 31.0 18. 8 32.3 20. 1 33.7 21. 5 35.0 22. 8 36.4 1.4 84 37.7! 39.1 40.4 41.8 43.1 44.5 45.9 47.2 48.6 49.9 85 51.3 52.6 54.0 55.3 56.7 58.0 59.4 60.7 62.1 63.5 0. 1 0. 1 86 64. 8i 66.2 67.5 68.9 70.2 71.6 72.9 74.3 75.6 77.0 D.2 0.3 87 78. 4i 79.7 81.1 82.4 83.8 85.1 86.5 87.8 89.2 90.5 5.8 0^5 88 91.9 93.3 94.6 96.0 97.3 98.7 oo.o *01.4 02.7 *04.1 04 06 89 1205.4 06.8 08.2 09.5 10.9 12.2 13.6 14.9 16.3 17.6 0.5 0.7 90 19.0 20.3 21.7 23.1 24.4 25.8 27.1 28.5 29.8 31.2 0.6 0.7 0.8 1.0 91 32.5 33.9 35.2 36.6 37.9 39.3 40.7 42.0 43.4 44.7 8 1 1 92 46.1 47.4 48.8 50.1 51.5 52.8 54.2 55.6 56.9 58.3 09 13 93 59.6 61.0 62.3 63.7 65.0 66.4 67.7 69.1 70.5 71.8 94 73.2 74.5 75.9 77.2 78.6 79.9 81.3 82.6 84.0 85.4 95 86.7 88.1 89.4 90.8 92.1 93.5 94.8 96.2 97.5 98.9 96 1300.2 01.6 03.0 04.3 05.7 07.0 08.4 09.7 11.1 12.4 97 13.8 15.1 16.5 17.9 19.2 20.6 21.9 23.3 24.6 26.0 98 27.3 28.7 30.0 31.4 32.8 34.1 35.5 36.8 38.2 39.5 99 40.9 42.2 43.6 44.9 46.3 47.7 49.0 50.4 51.7 53.1 100 54.4 55.8 57.1 58.5 59.8 61.2 62.5 63.9 65.3 66.6 200 2708. 7 10.0 11.4 12.7 14.1 15.5 16.8 18.2 19.5 20.9 300 4062.8 64.2 65.5 66.9 68.2 69.6 71.0 72.3 73.7 75.0 302 FLUIDITY AND PLASTICITY If the temperature of the mercury is other than 20 a correc- tion is applied using Table IV. TABLE IV. VALUES OF N. CORRECTION IN PRESSURES (GRAMS PEI SQUARE CENTIMETER) FOR VARIOUS TEMPERATURES AND MERCURIAL HEIGHTS Temperature, degrees Centigrade Height of mercury, centimeters 10 20 30 40 50 60 70 80 90 100 5 0.4 0.7 1.1 .5 .8 2.2 2.6 2.9 3.3 3.7 6 0.3 0.7 1.0 .4 .7 2.1 2.4 2.7 3.1 3.4 7 0.3 0.6 1.0 .3 .6 .9 2.2 2.6 2.9 3.2 8 0.3 0.6 0.9 .2 .5 .8 2.1 2.4 2.6 2.9 9 0.3 0.5 0.8 .1 .4 .6 1.9 2.2 2.4 2.7 10 0.2 0.5 0.7 1.0 .2 .5 1.7 2.0 2.2 2.4 11 0.2 0.4 0.7 0.9 .1 .3 1.5 1.8 2.0 2.2 12 0.2 0.4 0.6 0.8 .0 .2 1.4 1.6 1.8 2.0 13 0.2 0.3 0.5 0.7 0.9 1.0 1.2 1.4 1.5 1.7 14 0.2 0.3 0.4 0.6 0.7 0.9 1.0 1.2 1.3 1.5 15 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.2 16 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 17 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.7 . 18 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.5 19 0.0 0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 20 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 0.0 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.2 22 -0.1 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -0.5 23 -0.1 -0.1 -0.2 -0.3 -0.4 -0.4 -0.5 -0.6 -0.7 -0.7 24 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0 25 -0.1 -0.2 -0.4 -0.5 -0.6 -0.7 -0.9 - .0 -1.1 -1.2 26 -0.2 -0.3 -0.4 -0.6 -0.7 -0.9 - .0 - .2 -1.3 -1.5 27 -0.2 -0.3 -0.5 -0.7 -0.9 - .0 - .2 - .4 -1.5 -1.7 28 -0.2 -0.4 -0.6 -0.8 - .0 - .2 - .4 - .6 -1.8 -2.0 29 -0.2 -0.4 -0.7 -0.9 - .1 - .3 - .5 - .8 -2.0 -2.2 30 -0.2 -0.5 -0.7 - .0 - .2 - .5 - .7 -2.0 -2.2 -2.4 31 -0.3 -0.5 -0.8 - .1 - .4 - .6 - .9 -2.2 -2.4 -2.7 32 -0.3 -0.6 -0.9 - .2 - .5 - .8 -2.1 -2.4 -2.6 -2.9 33 -0.3 -0.6 -1.0 - .3 - .6 -1.9 -2.2 -2.6 -2.9 -3.2 34 -0.3 -0.7 -1.0 - .4 - .7 -2.1 -2.4 -2.7 -3.1 -3.4 35 -0.4 -0.7 -1.1 - .5 - .8 -2.2 -2.6 -2.9 -3.3 -3.7 APPENDIX A 303 The correction for the difference in level between the middle of the manometer and the viscometer is made negligible in setting up the apparatus. MEASUREMENT OF TIME We have seen that the pressure in grams per square centimeter must always be 30 times as great as the distance between the bulbs. On the other hand the pressure must always be kept small enough so that the time of flow can be measured to the desired accuracy. Thus the time should not fall below 200 sec. since one cannot measure the time more accurately than to 0.2 sec. with a stop-watch. The stop-watch should be tested repeatedly against the second hand of a good time piece. It should not gain or lose as much as 0.2 sec. in 5 min. It is well to keep the watch in the same posi- tion during successive measurements, as well as not to allow it to be nearly run down during a measurement. In selecting a stop- watch it should be noted that watches show better performance whose mechanism continues to run whether the split-second hand is in use or not. The performance of the watch may be tested at the U. S. Bureau of Standards. TEMPERATURE The viscometer is kept at a constant temperature by means of a large, well-stirred bath which is regulated by hand, if a series of temperatures are to be measured, or by a thermostat, if the bath is to be used for a long time at a single temperature. Since at the fluidity of water increases 0.1 per cent for every 0.03 rise in temperature it is clear that the temperature regulation must be to at least 0.03. For more viscous substances a still more precise regulation is necessary if the same degree of accu- racy is to be obtained. A thermometer should be used which is graduaded to tenths and calibrated through its entire length. The ice point should be determined from time to time. If it is impracticable to have the entire thread of mercury immersed at all times a correction should be made for the emergent stem. The following table may be used: 304 .FLUIDITY AND PLASTICITY TABLE V. CORRECTION OF A NORMAL THERMOMETER FROM TO 100C FOR EMERGENT STEAM GRADUATED IN TENTHS OF A DEGREE Difference in temperature between mean temperature Number of de- of emergent steam and bath. Corrections in degrees to be grees of mercury added to the observed temperature 30 40 50 60 70 80 10 0.05 0.05 0.05 0.05 0.10 0.10 20 0.10 0.15 0.15 0.15 0.20 0.20 30 0.20 0.25 0.25 0.25 0.30 0.35 40 0.30 0.30 0.35 0.40 0.45 0.50 50 0.35 0.40 0.45 0.50 0.55 0.60 Since measurements are always preferred for even degrees it is a great advantage for the worker to have on the bath before him a table showing what temperatures on the thermometer must be employed in order to obtain a desired even temperature. The temperatures of 0, 10, 20, 40, 60, 80, 100 are sufficient to give a good curve over this range. THE PRESSURE REGULATOR Viscosity measurements have usually been carried out without the use of a pressure regulator, but due to the withdrawal of the air in use and to possible small leaks in the connections and to changes in temperature, the pressure rises and falls and is hardly ever constant during the time of a single measurement. With a pressure regulator the pressure will often stay constant to the limit of the experimental error for a day or more at a time, with- out temperature regulation of the room, heat insulation of the apparatus or any particular care in using the air. Not only is this a saving of time and annoyance to the experimenter but by using only a few pressures at the most there is a considerable saving of time in calculation. Hence the pressure regulator is a necessity for extended work. The diagrammatic view of the apparatus with pressure regula- tor is given in Fig. 92. Air is forced in through a needle valve A to a storage reservoir B whose pressure in pounds per square inch is shown on the gauge C. In adjusting the pressure regulator the air is very slowly admitted to the stabilizing reservoir F by APPENDIX A 305 means of the needle valve D. The valve E is convenient in locat- ing leaks in the apparatus, etc., but is not often used. The valve G is a direct connection to air which is also seldom used. The pressure regulator consists of five brass tubes 6 cm. in diameter which are filled with water let in at K, the valves O f , 0" etc. being open and the valve N closed. When the water begins to overflow at M into the drain pipe, the water is shut off FIG. 92. Diagram of viscometer set-up with multiple tube water stabilizer. at K, and as soon as equilibrium is reached, the drain pipe is also closed off at Z and the valves 0', 0", etc. are closed. By allowing air to pass very slowly through the valve D the air will be gradually forced down the tube H' until it bubbles out through the water, and, if the pet-cock /' is open, into the air. If the stream of air is very slow, say a bubble or two per second, it is evident that the pressure will be constant. If a higher pres- sure is desired the pet-cock /' is closed when the pressure becomes the sum of the pressures obtained by the two tubes separately and so on for the five different pressures up to the maximum capacity of the regulator. In lowering the pressure one must be careful to turn the pet-cocks to air in the reverse order 7 V 7 IV J 111 and J u J l in order that the air under pressure may not cause the water to be drawn back into the system. The advan- 20 306 FLUIDITY AND PLASTICITY tage of the drain pipe U is that of securing day by day practically identical pressures, without the loss of time in adjustment. If other pressures than these are desired, they may be obtained by drawing off some of the water from one or more of the stand pipes. The glass gage at /', etc., aid the manipulator in adjusting the cur- rent of air. They may be cleaned by unscrewing the pet-cocks above and using a small brush. The beginner must be cautioned particularly against turning the system to air at the viscometer since it may result in filling the manometer, etc. with water. To prevent such an accident and to dry the air, the reservoir P containing granular calcium chloride is introduced. Any liquid should be drained at intervals. THE MANOMETER The manometer consists of a plate glass mirror which must be mounted vertically, on which is stretched a 2-m steel tape graduated in millimeters. Over the tape is fixed the glass tube of the manometer bent so that both the right and left limbs may be read on the same tape. The manometer may be filled with either mercury or water. If water is used for low pressures another manometer will be desired for mercury. Since it is possible to read the manometer to 0.01 cm one can use the mer- cury manometer down to 10 cm (135 g per square centimeter) with the desired accuracy. With water one can go down to about 50 g per square centimeter, but not much further unless a correction is made for the true average pressure. A thermometer near the middle of the manometer is needed to give the tem- perature of the manometer fluid. THE BATH The viscometer V is mounted on a massive brass frame Fig. 93 by means of brass clips designed especially for this purpose. The frame slides in grooves on the side of the bath so that the viscometer may be easily kept in a vertical position. The viscom- eter is connected by heavy-walled rubber tubing to the pressure by way of the three-way glass stop cocks L and R, the third connection being to air. The temperature of the bath is raised by means of a burner W which is connected without the use of rubber to the gas supply. The second burner Y with stop cock and pilot flame is used as needed to obtain the fine regulation. APPENDIX A 307 _, Pycnometer No. 2 Log C' = 8 37698-10 Log ~ = 6 22122 Time Manometer, upper read- Temperature bath Limb Min- Sec- Time, sec- onds ing, lower reading Temper- ature differ- ence = Weight pyc. utes onds ho Start Finish 20 L 5 7.0 307.0 259.46 259.46 21.2 287 . 58 28.12 231.34 20 R 5 8.2 308.2 259.48 259.48 21.1 287.60 28.12 231.36 ' hip K hi P KL Po cv Ct P 1 in cp "o c ll Open end Bulb end O i w 5 *> H .S g .0 I ! & g |l ll 1 -2 Tempera perimen Volume < at 10C 1 1 2 3*5 111 ^ IQ I o 10 385.870 3,505.75 i jjj CO J5 jjj o 739. 114 1,830.75 d d d d TO 773.443 1,750.00 Do. Do. Do. Do. Do. Do. 0.6 co 774.291 2,327.75 5.0 773. 400 2,025.25 10.0 773.443 1,750.00 15.0 773. 597 1,528.00 20.0 775. 093 1,344.50 25.0 774. 886 1,195.00 30.1 775. 058 1,067.50 35.1 774.451 962.25 40.1 774. 354 871.50 45.0 774. 827 793. 25 51.068 20,085.0 97.764 10,361.0 S 8 147. 834 6,851.0 Ai w 2 Do. Do. Do. 193. 632 5,233.0 o d 3 d 387. 675 2,612.5 738. 715 1,372.5 774.676 1,308.0 98.404 6,921.0 S 148. 320 4,594.0 A 11 ~ o o Do Do. Do. Do. 193.421 3,515.0 in d d 387. 445 1,757.0 j 774.810 878.0 .0 i i 1 1 Do. Do. Do. Do. 387. 520 774.895 880.0 448.0 (N j d 24. 661 8,646.0 49. 591 4,355.0 K5 98.233 2,194.0 A Era Do. Do. Do. Do. Do. Do. 148.233 1,455.0 -< 194.257 1,116.0 388.000 571.0 775. 160 298.0 23.638 5,570.0 49. 185 2,699.0 99. 221 1,360.0 A v S Do Do. Do. Do. Do. Do. 148. 623 918. 5 d 193.315 718.0 387.737 381.0 774.620 207.0 332 FLUIDITY AND PLASTICITY TABLE 1. (Continued) g Diameter of capillary in g ii - "S centimeters S c 'S M **- ^ s "3 J "8 '5 o *TJ 'a o a 1 Open end Bulb end J= e i 3 5 *> s i Length it 1* S * li 11 ll H Volume ( at 10C Ih 5-0 III 24. 753 3,828.75 50.001 1,923.75 K5 99.343 994.00 A V I Is Do. Do. Do. Do Do. Do. 148.618 682.00 d 193.010 537. 75 387. 887 291.50 773. 790 165.75 4.783 3,926.75 6.204 3,072.00 12. 129 1 , 685. 50 24.003 974.25 j 1 49.040 571.75 A v " o Do. Do. Do Do. Do Do. 98. 832 348. 75 148.475 267.00 193.501 224.00 387.972 144.00 773. 717 95.00 : < ifl 388.256 4,103.5 B 22 S 3 o S 4 a 1 <3i 739.333 2,156.0 o o * 777. 863 2,060.0 2 6 e 55. 286 21,430.0 97. 922 12,079.0 S g 148. 275 7,981.5 Bi i o o Do. Do. Do. Do. 193.947 6,100.0 ^ e 387. 695 3,052.0 739.467 I 1,600.0 774.891 I 1,526.5 99.163 ' 7,804.0 i(5 ^ B 149.679 ' 5,165.0 B" Jo 2 O) O o Do. Do. Do. Do. 193.441 I 3,997.0 * b 6 387.130 1,995.0 774.796 ! 999.0 49.091 7,471.0 CO 98.315 3,729.0 B"i 12 2 2 Do. Do. Do. Do. 148.571 2,473.0 S 193. 877 1,892.0 *i 388.100 946.0 774.880 473.0 APPENDIX D TABLE I. (Continued) 333 _ | Diameter of capillary in , S ^ -3 i 1 centimeters IM _n .i * "S a "o 1 1 Open end Bulb end o ! s S s !l l! I ! 3 1 * J-a ** CS .1.2 !'! aj C 1 i 1] Volume ( at 10C iii ill 24.756 5,543.0 49. 857 2,762.0 3 2 99. 214 1,400.0 B IV 5 O Do. Do. Do. Do. 149.082 935.0 d d d 193. 194 728.9 387. 024 375.0 774. 540 199.0 | 24. 290 2,386.0 49. 578 1,193.0 5 S 99. 139 621.0 B v n 3 Do. Do. Do. Do. 149.098 428.0 6 d , d 193. 130 34.00 387.024 189.0 I 773. 282 110.0 ! J 0.5 774.048 j 2,816.75 5.0 774.047 2,422.75 6.0 773. 848 2,350.50 1 10.0 774.030 2,093.50 M Mean diam. 15.2 1^ 774.070 1,826.00 ' C at 1 0C 20.0 2 774. 110 1,612.75 d 0. 085 25. N 774.841 1,427.50 30. 774. 503 1,280.50 35. 774.574 1,149.50 40. 774. 676 1,042.50 45. 774. 678 949.00 S i 10 t~ 385.158 4,210.00 C g 1 - 738.969 2,192.00 2 1 d d d o ; -. 774.030 2,093.50 52.257 23,135.00 98.411 12,280.00 s 149.241 8,098.00 Ci 8 Do. Do. Do. Do. Do 193.314 6,250.00 i^ d 387. 562 3,118.00 738. 767 1,636.00 774.757 1,560.50 99.868 7, 997! 00 1C rf 149.034 5,362.00 c o 8 Do. Do. Do. i Do. 193. 867 4,117.00 d d 386. 915 2,065.00 i 774. 563 1,029.00 334 FLUIDITY AND PLASTICITY TABLE I. (Continued) Diameter of capillary iu g ^ 3 i 1 I centimeters <*- J 3 & 3 a 8 B 8 Open end Bulb end o 1 a 'S g .s I a | ! Length ii jfl 1* |1 O QQ | 1 Tempera perimen Volume ( at 10'C jii So 111 49. 702 7,765.00 .0 98.921 3,899.00 Cm 5 3 8 Do. Do. Do. Do. 148. 303 2,598.50 d d 193. 544 1,994.00 387. 157 995.00 774. 677 498.00 24. 791 6,186.75 1 49.931 3,073.00 ! 10 98. 322 1,559.75 Civ i S Do Do. Do. Do. Do. Do. 148. 795 1,029.50 ' 194. 102 788.00 387. 191 399.00 774. 607 203.00 24. 192 3,587.00 50.506 1,768.00 10 99. 102 904.00 i 149. 119 606.50 C v d Do. Do. Do. Do. Do. Do 194.217 470.00 387. 237 245.00 773. 327 131.50 o ; o 386. 247 9,708.00 D 1 i 1 1 o ! o 738.137 ~ i | 773.970 5,080.00 4,846.00 2 d d d d d 54.785 35,460.00 S S 55. 796 34,798.00 >o s co 99. 508 19,517.00 Z)i 1 i I 8 1 Do. 149.219 13,021.00 d d d d 192. 907 10,071.00 386. 555 5,025.00 774.617 2,506.00 Do. Do. Do. Do. Do. Do. 5.00 Do. 774.887 2,898.50 10.00 774.617 2,506.00 15.00 773.271 2,199.00 Mean diam. 20.00 774. 119 1,928.00 0.004 40406 25.05 775.045 1,713.75 30.07. 774.356 1,532.50 35.00 675.429 1,375.50 40.00 774.475 ,246.75 45.10 774.077 ,138.00 APPENDIX D TABLE I. (Continued) 335 1 i Diameter of capillary in ^ s i 0) centimeters L .S tf M S * .Q A >. c 3 s +3 d i Open end Bulb end "o 3 *> 1 s 1 1 S a i! I 1 I -a Ji -|.2 1 i ll H Volume ( at 10C III "o "o |I1 98.917 10,149.00 10 s 147.857 6.789.00 D 11 - s 1 Do. Do. 2 Do. 193.485 5,178.00 ' o 664.36 84.50 Fii Do Do Do. Do. Do. Do. 1,323.58 45.00 OJ 1,984.95 31.00 2,585.33 25.00 5,207.73 15.00 10,454.54 9.00 82.08 345.00 163. 78 175.00 329. 77 91.00 2 S 660.97 50.00 Fm 1 I i Do. Do. Do. Do. 1,323.56 28.00 d d 1,983.20 21.75 2,590.76 17.50 5,160.07 11.00 10,456.45 7.00 82.36 191.00 163. 39 104.00 328.04 59.75 S g 661.59 35.00 ftr 1 1 I Do. Do. Do. Do. 1,321.19 21.75 . ~ "". n I e o 1,985.00 16. 75 2,614.60 13.50 5,205.08 9.00 10,458.02 6.00 APPENDIX D TABLE I. (Continued) 337 3 2 1 Diameter of capillary in centimeters i g S *-> "I " "8 _g "o 3 1 Open end Bulb end -3 1 "8 s 1 3 ~ i 9 i 4* | is j. II fig 8-8 111 Q j s - S S s S H ft > * s " P 3 74.29 114.00 83.89 130.00 162.89 63.00 329. 39 39.00 pv s Do. Do. Do Do. Do. Do. 653. 49 25.00 ^ 1,306.69 16.00 1,985.29 13.00 2,606.37 10.75 5,146.62 7.50 10,456.65 5.00 j 1.087.200 407.00 G i ^ M 8.60 SO 1,586.340 281.00 o ; o 8.70 S 2,084.060 213.00 666 6 8.80 J5 2,602.300 170.00 18.70 145.300 2,290.00 18.90 269.220 1,232.00 18.90 520. 240 634.00 *" 18.90 1,019.870 323.00 G 1 Do. Do. Do. Do. 18.80 Do. 2,014.160 162.00 s 18.70 3,437.360 97.00 18.80 6,841.370 48.75 , 18.80 10,191.540 33.00 ON 1 g 18.95 145. 300 1,115.00 S 2 S 19.25 269.220 597.00 _ i 19.30 Do. 518. 940 305.50 6 6 6 6 19.50 1,019.670 155.00 19.50 2,014.360 79.75 g c? 11.00 2,316.870 9,048.00 // i g g 11.00 0.5 3,837.000 5,438.00 SO 6 6 11.10 6,117.600 3,460.00 10.80 3,850.160 388.00 t * 10.90 4,610.230 319.00 / 8 11.00 1.0 5,370.130 267.00 N 6 6 11.00 6,127.360 235.00 7.50 6,130.080 261.00 so o 11.00 54.987 8,590.00 K 1 S 11.00 11.00 1.0 210.129 419.645 2,250.00 1,125.75 o 6 6 11.00 835. 565 565.00 12.00 1,576.000 286.00 338 FLUIDITY AND PLASTICITY TABLE I. (Continued) 1 1 Diameter of capillary in centimeters 8 c OS a ^ It "3 a 3 1 Open end Bulb end s 1 11 ! .5 1 If |i ii .2 Tempera perimen Volume at 10C j|l 3 o ^ 11.00 1.0 2,338.376 197.50 2 11.00 3,095.540 154.00 K I 11.00 11.00 3,856.939 4,616.534 123.00 106.25 s d 11.00 5,376.534 88.25 11.00 6,136.534 77.50 7.00 6,136.534 86.75 o g | M 8 8 8 8 8 10.00 8 775.000 1,240.00 * c o o Mi Do. Do. Do. Do. Do. Do. 775.000 84.50 6 1 APPENDIX D 339 TT . i O *O LC O Tf 00 ddddddddd _ O t~*- 1C ^O i-H O3 00 OOOOb-COOO>O- < *'*T<'<*c-U3CO'-HOOOOOt^-CO r-I^H^IrH^-ldddd t^OO-^COTfCDTtlCO %% CJ O ^H 1C OO OO I> CO d d d d 340 FLUIDITY AND PLASTICITY TABLE III. FLUIDITY AND VISCOSITY OF WATEH CALCULATED BY FORMULA' FOR EVERY DEGREE BETWEEN AND 100C Tem- pera- ture, C Flu- idity Vis- cosity in cp Tem- pera- ture, C Flu- idity Vis- cosity in cp Tem- pera- ture, C Flu- idity Vis- cosity in cp 55.80 .7921 33 132 . 93 0.7523 67 236 . 25 0.4233 1 57.76 .7313 34 135.66 0.7371 68 239.57 0.4174 2 59.78 .6728 35 138.40 0.7225 69 242.91 0.4117 3 61.76 .6191 36 141.15 0.7085 70 246.26 0.4061 4 63.80 .5674 37 143.95 0.6947 71 249 . 63 0.4006 5 65.84 .5188 38 146.76 0.6814 72 253 . 02 0.3952 6 67.90 .4728 39 149.60 0.6685 73 256.42 0.3900 7 70.01 .4284 40 152.45 0.6560 74 259.82 0.3849 8 72.15 .3860 41 155.30 0.6439 75 263.25 0.3799 9 74.28 .3462 42 158.20 0.6321 76 266.67 0.3750 10 76.47 .3077 43 161.11 0.6207 77 270.12 0.3702 11 78.66 .2713; 44 164.02 0.6097 78 273 . 57 0.3655 12 80.89 . 2363 45 167.00 0.5988 79 277.04 0.3610 13 83.14 . 2028 46 169.97 0.5883 80 280.53 0.3565 14 85.40 . 1709; 47 172.95 0.5782 81 284.03 0.3521 15 87.69 .1404 48 175.95 0.5683 82 287.53 0.3478 16 90.00 .1111 49 178.95 0.5588 83 291.03 0.3436 17 92.35 . 0828 50 182.00 0.5494 84 294.54 0.3395 18 94.71 .0559 51 185.05 0.5404 85 298.06 0.3355 19 97.10 .0299 52 188.14 0.5315 86 301 . 63 0.3315 20 99.50 .0050 53 191.23 0.5229 87 305.21 0.3276 20.20 100.00 i.ooool 54 194.34 0.5146 88 308.78 0.3239 21 101.94 0.98101 55 197.45 0.5064 89 312.35 0.3202 22 104.40 0.9579 56 200.62 0.4985 90 315.92 0.3165 23 106.86 0.9358 57 203.78 0.4907 91 319.53 0.3130 24 109.38 0.9142 58 206.95 0.4832 92 323.13 0.3095 25 111.91 0.8937 59 210.13 0.4759 93 326 . 74 0.3060 26 114.45 0.8737 60 213.33 0.4688 94 330.38 0.3027 27 117.03 0.8545 61 216.54 0.4618 95 334.01 0.2994 28 119.62 0.8360 62 219.80 0.4550 96 337.65 0.2962 29 122.25 0.8180 63 223.07 0.4483 97 341 . 30 0.2930 30 124.89 0.8007 64 226.34 0.4418 98 344.96 0.2899 31 127.54 0.7840 65 229 . 64 0.4355 99 348.63 0.2868 32 130.22 0.7679 66 232.94 0.4293 100 352.30 0.2838 4> = 2. 1482 { (t - 8.435) + V8078.4 + (t - 8.435) 2 } - 120. Cf. p. 137. APPENDIX D 341 TABLE IV. FLUIDITY OF ALCOHOL-WATER MIXTURES 1 Weight percentage of ethyl alcohol Tem- 10 20 30 39 40 45 50 60 70 80 90 100 ture Volume percentage of ethyl alcohol at 25C 1 12.36 24.09 35.23 44.92 45.83 50.94 55.93 65.56 74.80 83.59 92.01 100 55.8 30.2 18.8 14.4 13.8 14.0 14.4 15.2 17.4 21.0 27.1 36.6 56.4 5 65.8 38.8 24.6 18.9 17.8 17.9 18.2 19.0 21.6 25.6 32.0 43.3 61.6 in 76.5 45.9 31.6 24.7 22.8 22.8 23.0 23.9 26.5 30.6 36.9 47.6 68.2 15 87.7 55.8 38.2 30.7 28.4 28.3 28.5 29.1 31.8 36.1 43.3 55.5 75.1 20 99.5 65.0 45.8 36.9 34.7 34.4 34.7 34.8 37.4 42.2 49.8 62.1 83.3 25 111.9 75.6 55.1 45.9 42.5 42.5 41.9 41.7 44.6 49.1 57.2 70.2 91.2 30 124.9 86.2 64.4 53.4 50.0 49.4 49.5 49.6 51.9 56.6 65.3 78.2 99.7 35 138.4 99.4 75.1 63.3 58.6 58.3 57.7 58.0 60.1 65.4 73.8 87.2 109.4 40 152.4 110.2 86.2 73.1 67.9 67.5 66.9 66.7 69.1 74.4 83.1 96.6 119.9 45 167.0 123.2 98.5 84.1 77.9 77.6 76.5 77.3 78.7 84.1 92.5 106.5 130.8 50 182.0 136.3 110.2 95.2 89.0 88.3 87.1 86.6 88.7 94.2 103.3 117.9 142 . 5 55 197.4 150.9 122.9 107.6 100.7 100.2 98.4 98.0 100.3 106.0 115.3 130.8 155.2 60 213.3 164.3 135.8 119.9 113.0 112.0 110.3 109.5 110.8 116.8 126.7 142.1 168.9 65 229.6 180.5 150. l!l33.0 125.3 124.7 122.6 122.3 124.1 130.6 140.7 156.0 181.5 70 246.3 194.5 164.5 146.4 138.0 137.5 135.2 135.1 137.2 143.9 153.9 169.9 198.6 75 263.2 210.21178.8 160.3 151.5 150.8 148.9 148.7 150.8 157.1 166.6 183.0 212.5 80 280.5 232.7 198.lll76.4 167.1 166.5 164.1 163.5 165.7 TABLE V. SUCROSE SOLUTIONS, BINGHAM AND JACKSON Tem- Percentage sucrose by weight Tem- Percentage sucrose by weight pera- pera- ture 1 ture 20 40 60 20 40 60 55.91 26.29 6.77 0.42 55 197.16 113.12 45.06 8.57 5 65.99 31.71 8.65 0.64 60 212.72 123.79 50.47 10 17 10 76.56 37.71 10.21 0.91 65 229.41 134.81 56.24 11.99 15 87.67 44.11 13.39 1.34 70 246.18 145.97 62.17 13.98 20 99.54 51.02 16.13 1.77 75 263.57 157.56 68.41 16.12 25 111.84 58.69 19.28 2.28 80 281.21 169.53 74.96 18.51 30 124.70 66.51 22.82 2.96 85 299.31 181.80 81.92 21.14 35 138.79 75.12 26.58 3.77 90 317.87 89.06 24.07 40 153.07 83.82 30.78 4.70 95 335.46 96.41 26.85 45 167.84 93.42 35.13 5.82 100 354.49 104.11 29.96 50 181.92 103 . 07 40.05 7.14 1 Values given are the weighted average of those of Stephan (1862), Pagliani and Batelli (1885), Traube (1886), Noack (1886) and Bingham and Thomas (1913). 342 FLUIDITY AND PLASTICITY TABLE VI. RECIPROCALS No.' i Dif. 1.0 1.0000 9901 9804 9709 9615 9524 9434 9346 9259 9174 1.1 0.9091 9009 8929 8850 8772 8696 8621 8547 8475 8403 1.2 8333 8264 8197 8130 8065 8000 7937 7874 7813 7752 1.3 7692 7634 7576 7519 7463 7407 7353 7299 7246 7194 1.4 7143 7092 7042 6993 6944 6897 6849 6803 6757 6711 1.5 0. 6667 6623 6579 6536 6494 6452 6410 6369 6329 6289 1.6 6250 6211 6173 6135 6098 6061 6024 5988 5952 5917 1.7 5882 5848 5814 5780 5747 5714 5682 5650 5618 5587 1.8 5556 5525 5495 5464 5435 5405 5376 5348 5319 5291 1.9 5263 5236 5208 5181 5155 5128 5102 5076 5051 5025 2.0 0.5000 4975 4950 4926 4902 4878 4854 4831 4808 4785 2.1 4762 4739 4717 4695 4673 4651 4630 4608 4587 4566 2.2 4545 4525 4505 4484 4464 4444 4425 4405 4386 4367 2.3 4348 4329 4310 4292 4274 4255 4237 4219 4202 4184 2.4 4167 4149 4132 4115 4098 4082 4065 4049 4032 4016 2.5 0.4000 3984 3968 3953 3937 3922 3906 3891 3876 3861 2.6 3846 3831 3817 3802 3788 3774 3759 3745 3731 3717 2.7 3704 3690 3676 3663 3650 3636 3623 3610 3597 3584 2.8 3571 3559 3546 3534 3521 3509 3496 3484 3472 3460 2.9 3448 3436 3425 3413 3401 3390 3378 3367 3356 3344 3.0 3333 3322 3311 3300 3289 3279 3268 3257 3247 3236 3.1 '3226 3215 3205 3195 3185 3175 3165 3155 3145 3135 3.2 3125 3115 3106 3096 3086 3077 3067 3058 3049 3040 3.3 3030 3021 3012 3003 2994 2985 2976 2967 2959 2950 3.4 2941 2933 2924 2915 2907 2899 2890 2882 2874 . 2865 3.5 0. 2857 2849 2841 2833 2825 2817 2809 2801 2793 2786 3.6 2778 2770 2762 2755 2747 2740 2732 2725 2717 2710 3.7 2703 2695 2688 2681 2674 2667 2660 2653 2646 2639 7 3.8 2632 2625 2618 2611 2604 2597 2591 2584 2577 2571 3.9 2564 2558 2551 2545 2538 2532 2525 2519 2513 2506 4.0 0.2500 2494 2488 2481 2475 2469 2463 2457 2451 2445 4.1 2439 2433 2427 2421 2415 2410 2404 2398 2392 2387 4.2 2381 2375 2370 2364 2358 2353 2347 2342 2336 2331 4.3 2326 2320 2315 2309 2304 2299 2294 2288 2283 2278 4.4 2273 2268 2262 2257 2252 2247 2242 2237 2232 2227 4.5 0. 2222 2217 2212 2208 2203 2198 2193 2188 2183 2179 4.6 2174 2169 2165 2160 2155 2151 2146 2141 2137 2132 4.7 2128 2123 2119 2114 2110 2105 2101 2096 2092 2088 4.8 2083 2079 2075 2070 2066 2062 2058 2053 2049 2045 4.9 2041 2037 2033 2028 2024 2020 2016 2012 2008 2004 5.0 0.2000 1996 1992 1988 1984 1980 1976 1972 1969 1965 4 5.1 1961 1957 1953 1949 1946 1942 1938 1934 1931 1927 5.2 1923 1919 1916 1912 1908 1905 1901 1898 1894 1890 5.3 1887 1883 1880 1876 1873 1869 1866 1862 1859 1855 5.4 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 5.5 0.1818 1815 1812 1808 1805 1802 1799 1795 1792 1789 5.6 1786 1783 1779 1776 1773 1770 1767 1764 1761 1757 5.7 1754 1751 1748 1745 1742 1739 1736 1733 1730 1727 5.8 1724 1721 1718 1715 1712 1709 1706 1704 1701 1698 5.9 1695 1692 1689 1686 1684 1681 1678 1675 1672 1669 APPENDIX D 343 TABLE VI. RECIPROCALS (Continued) No. 1 2 3 4 5 6 7 8 9 Dif. 6.0 0. 16667 16639 16611 16584 16556 16529 16502 16474 16447 16420 27 6.1 16393 16367 16340 16313 16287 16260 16234 16207 16181 16155 28 6.2 16129 16103 16077 16051 16026 16000 15974 15949 15924 15898 26 6.3 15873 15848 15823 15798 15773 15748 15723 15699 15674 15649 25 6.4 15625 15601 15576 15552 15528 15504 15480 15456 15432 15408 24 6.5 0. 15385 15361 15337 15314 15291 15267 15244 15221 15198 15175 23 6.6 15152 15129 15106 15083 15060 15038 15015 14992 14970 14948 23 6.7 14925 14903 14881 14859 14837 14815 14793 14771 14749 14728 22 6.8: 14706 14684 14663 14641 14620 14599 14577 14556 14535 14514 21 6.9 14493 14472 14451 14430 14409 14388 14368 14347 14327 14306 21 7.00.14286 14265 14245 14225 14205 14184 14164 14144 14124 14104 20 7.1 14085 14065 14045 14025 14006 13986 13966 13947 13928 13908 7.2 13889 13870 13850 13831 13812 13793 13774 13755 13736 13717 19 7. 3 13699 13680 13661 13643 13624 13605 13587 13569 13550 13532 7.4 13514 13495 13477 13459 13441 13423 13405 13387 13369 13351 18 7. 5 0. 13333 13316 13298 13280 13263 13245 13228 13210 13193 13175 7.6 13158 13141 13123 13106 13089 13072 13055 13038 13021 13004 17 7.7 12987 12970 12953 12937 12920 12903 12887 12870 12853 12837 7.81 12821 12804 12788 12771 12755 12739 12723 12706 12690 12674 18 7.9 12658 12642 12626 12610 12594 12579 12563 12547 12531 12516 8.0 0. 12500 12484 12469 12453 12438 12422 12407 12392 12376 12361 8. 1 12346 12330 12315 12300 12285 12270 12255 12240 12225 12210 15 8.2 12195 12180 12165 12151 12136 12121 12107 12092 12077 12063 8.3 12048 12034 12019 12005 11990 11976 11962 11947 11933 11919 8.4 11905 11891 11876 11862 11848 11834 11820 11806 11792 11779 14 8 50. 11765 11751 11737 11723 11710 11696 11682 11669 11655 11641 8.6 11628 11614 11601 11587 11574 11561 11547 11534 11521 11507 8.7! 11494 11481 11468 11455 11442 11429 11416 11403 11390 11377 18 8 8 11364 11351 11338 11325 11312 11299 11287 11274 11261 11249 8.9 11236 11223 11211 11198 11186 11173 11161 11148 11136 11123 9.00. 11111 11099 11086 11074 11062 11050 11038 11025 11013 11001 9 1 10989 10977 10965 10953 10941 10929 10917 10905 10893 10881 12 9. 2 10870 10858 10846 10834 10823 10811 10799 10787 10776 10764 9. 3 10753 10741 10730 10718 10707 10695 10684 10672 10661 10650 9.4j 10638 10627 10616 10604 10593 10582 10571 10560 10549 10537 9. 5 0. 10526 10515 10504 10493 10482 10471 10460 10449 10438 10428 11 9.6' 10417 10406 10395 10384 10373 10363 10352 10341 10331 10320 9. 71 10309 10299 10288 10277 10267 10256 10246 10235 10225 10215 9.8 10204 10194 10183 10173 10163 10152 10142 10132 10121 10111 9.9 10101 10091 10081 10070 10060 10050 10040 10030 10020 10010 10.00.10000 9990 9980 9970 9960 9950 9940 9930 9921 9911 10 10. 11 09901 9891 9881 9872 9862 9852 9843 9833 9823 9814 10. 2 9804 9794 9785 9775 9766 9756 9747 9737 9728 9718 10. 3 9709 9699 9690 9681 9671 9662 9653 9643 9634 9625 10.4 9615 9606 9597 9588 9579 9569 9560 9551 9542 9533 10. 5 0. 09524 9515 9506 9497 9488 9479 9470 9461 9452 9443 9 10.6 9434 9425 9416 9407 9398 9390 9381 9372 9363 9355 10.7 9346 9337 9328 9320 9311 9302 9294 9285 9276 9268 10.8 9259 9251 9242 9234 9225 9217 9208 9200 9191 9183 10.9 9174 9166 9158 9149 9141 9132 9124 9116 9107 9099 11.00.09091 9083 9074 9066 9058 9050 9042 9033 9025 9017 11.1 9009 9001 8993 8985 8977 8969 8961 8953 8944 8937 11.2 8929 8921 8913 8905 8897 8889 8881 8873 8865 8857 11.3 8850 8842 8834 8826 8818 8811 8803 8795 8787 8780 11.4 8772 8764 8757 8749 8741 8734 8726 8718 8711 8703 11.50.08696 8689 8681 8673 8666 8658 8650 8643 8636 8628 11.6 8621 8613 8606 8598 8591 8584 8576 8569 8562 8554 11.7 8547 8540 8532 8525 8518 8511 8503 8496 8489 8482 11.8 8475 84 eV 8460 8453 8446 8439 8432 8425 8418 8410 11.9 8403 8396 8389 8382 8375 8368 8361 8354 8347 8340 344 FLUIDITY AND PLASTICITY TABLE VI. RECIPROCALS (Continued) No. 1 2 3 4 5 6 7 8 9 Dif. 12.00.08333 8326 8320 8312 8306 8299 8292 8285 8288 8271 12.1 8264 8258 8251 8244 8237 8230 8224 8217 8210 8203 12.21 8197 8190 8183 8177 8170 8163 8157 8150 8143 8137 7 12.3! 8130 8124 8117 8110 8104 8097 8091 8084 8078 8071 12.4 8064 8058 8052 8045 8039 8032 8026 8019 8013 8006 12.50.08000 12. 6 7936 7994 7930 7987 7924 7981 7918 7974 7912 7968 7905 7962 7899 7955 7893 7949 7886 7942 7880 12. 7 7874 7868 7862 7856 7849 7843 7837 7831 7825 7819 12.8 7812 7806 7800 7794 7788 7782 7776 7770 7764 7758 12.9 7752 7746 7740 7734 7728 7722 7716 7710 7704 7698 13.00.07692 7686 7681 7675 7669 7663 7657 7651 7646 7640 13. 1 7634 7628 7622 7616 7610 7605 7599 7593 7587 7581 13.2 7576 7570 7564 7559 7553 7547 7542 7536 7530 7524 13.3 7519 7513 7508 7502 7496 7491 7485 7480 7474 7468 13.4 7463 7457 7452 7446 7441 7435 7430 7424 7418 7413 13.5 0.07407 7402 7396 7391 7386 7380 7375 7369 7364 7358 13.6 7353 7348 7342 7337 7332 7326 7321 7315 7310 7305 6 13.7 7299 7294 7289 7283 7278 7273 7268 7262 7257 7252 13.8 7246 7241 7236 7231 7226 7220 7215 7210 7205 7200 13.9 7194 7189 7184 7179 7174 7169 7164 7158 7153 7148 14.0 0.07143 7138 7133 7128 7123 7118 7113 7108 7102 7097 14.1 7092 7087 7082 7077 7072 7067 7062 7057 7052 7047 | 14.2 7042 7037 7032 7027 7022 7018 7013 7008 7003 0998 i 14.3 6993 6988 6983 6978 6974 6969 6964 6959 6954 6949 14.4 6944 6940 6935 6930 6925 6920 6916 6911 6906 6901 14.5 0. 06897 6892 6887 6882 687& 6873 6868 6863 6859 6854 14.6 6849 6845 6840 6835 6931 6826 6821 6817 6812 6807 S 14.7 6803 6798 6793 6789 6784 6780 6775 6770 6766 6761 14.8 6757 6752 6748 6743 6739 i 6734 6729 6725 6720 6716 14.9 6711 6707 6702 6698 6693 6689 6684 6680 6676 6671 15.0 0.06667 6662 6658 6653 6649 6645 6640 6636 6631 6627 15.1 6623 6618 6614 6609 6605 6601 6596 6592 6588 6583 15.2 6579 6575 6570 6566 6562 6557 6553 6549 6545 6540 15.3 6536 6532 6527 6523 6519 6515 6510 6506 6502 6498 15.4 6494 6489 6485 6481 6477 6472 6468 6464 6460 6456 15.5 0.06452 6447 6443 6439 6435 6431 6427 6423 6419 6414 15.6 6410 6406 6402 6398 6394 6390 6386 6382 6378 6373 15.7 6369 6365 6361 6357 6353 6349 6345 6341 6337 6333 15.8 6329 6325 6321 6317 6313 6309 6305 6301 6297 6293 4 15.9 6289 6285 6281 6277 6274 6270 6266 6262 6258 6254 16.0 0.06250 6246 6242 6238 6234 6231 6227 6223 6219 6215 16.7 6211 6207 6203 6200 6196 6192 6188 6184 6180 6177 16.2 6173 6169 6165 6161 6158 6154 6150 6146 6143 6139 16.3 6135 6131 6127 6124 6120 6116 6112 6109 6105 6101 16.4 6097 6094 6090 6086 6083 6079 6075 6072 6068 6064 16.5 0.06061 6057 6053 6050 6046 6042 6038 6035 6031 6028 16.6 6024 6020 6017 6013 6010 6006 6002 5999 5995 5992 ! 18.7 5988 5984 5981 5977 5973 5970 5966 5963 5959 5956 i 16.8 5952 5949 5945 5942 5938 5935 5931 5928 5924 5921 16.9 5917 5914 5910 5907 5903 I 5900 5896 5893 5889 5886 17.0 0.05882 5879 5875 5872 5868 5865 5851 5858 5854 5851 17.1 5847 5844 5841 5838 5834 5861 5828 5824 5821 5817 17.2 5814 5811 5807 5804 5800 5797 5794 5790 5787 5784 a 17.3 5780 5777 5774 5770 5767 5764 5760 5757 5754 5750 17.4 5747 5744 5741 5737 5734 5731 5727 5724 5721 5718 | 17.50.05714 5711 5708 5704 5701 5698 5695 5692 5688 5685 ! 17. 6| 5682 5679 5675 5672 5669 5666 5663 5659 5656 5653 i 17.7| 5650 5647 5613 5640 5637 5634 5631 5627 5624 5621 17.81 5618 5615 5612 5609 5605 5602 5599 5596 5593 5590 17.9 5587 5583 5580 5577 5574 5571 5568 5565 5562 5559 i APPENDIX D TABLE VII. LOGARITHMS 345 No. 1 2 3 4 5 6 7 8 9 Dif. 10 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 42 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 as 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 35 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 32 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 ao 15 17(11 1790 1818 1847 1875 1903 1931 1959 1987 2014 28 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 2ft 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 25 18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 28 19 ! 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 22 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 21 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 20 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 1 23 ' 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 18 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 18 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 17 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 1ft 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 16 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 IS 29 ' 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 16 30 | 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 14 31 i 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 32 1 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 IS 34 i 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 36 : 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 12 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 38 ! 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 i 39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 11 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 10 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 48 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 r,o 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 52 7160 7168 7177 7185" 7193 7202 7210 7218 7226 7235 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 54 7324 7332 7340 7348 7356 ' 7364 7372 7380 7388 7396 8 346 FLUIDITY AND PLASTICITY TABLE VII. LOGARITHMS (Contimied) No. 1 2 3 4 5 6 7 8 9 Dif. 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 06 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 57 7559 7566 7574 7582 7589 | 7597 7604 7612 7619 7627 68 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 50 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 M 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 82 7924 7931 7938 7945 7952 ! 7959 7966 7973 7980 7987 7 68 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 60 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 ' 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 73 8633 8639 8645 8651 8657, 8663 8669 8675 8681 8686 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 71 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 70 8976 8982 8987 8993 8998 i 9004 9009 9015 9020 9025 so 9031 9036 9042 9047 9053 : 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 ! 9112 9117 9122 9128 9133 82 9138 9143 9149 9154 9159 ! 9165 9170 9175 9180 9186 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 | 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 i u 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 ! 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 \ 87 9395 9400 9405 9410 9415 j 9420 9425 9430 9435 9440 8 88 9445 9450 9455 9460 9465 i 9469 9474 9479 9484 9489 1 80 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 00 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 : 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 02 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 I 04 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 ! 06 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 i 06 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 07 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 : 08 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 | 00 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 BIBLIOGRAPHY AND AUTHOR INDEX Black-faced type refers to pages in this treatise. 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Handlingar och Tidskrift 413 (1913); 32pp. ,350 INDEX VAN AUBEL, EDM. Compt. rend. 173, 384 (1921); 4 pp. Influence de la temperature sur la viscosite des liquides normaux. AUERBACH, F. (1) Magnetische Untersuchung. Wied. Ann. 14, 30 (1881); (2) Plasticitat und Sprodigkeit. Wied. Ann. 46, 277 (1892); 15 pp. AUGENHEISTER. Bcitrage zur Kenntniss der Elasticitat der Metalle. Diss. Berlin (1902). AUSTIN, L. Experimentaluntersuchungen iiber die elastiche Langs-und Torsionsnachwirkung in Metallen. Wied. Ann. 60, 659 (1893); 19 pp.; Cp. Nature 49, 239 (1894). AXELROD, S. Gummizeitung 19, 1053 (1905); Gummizeitung 20, 105 (1905); Gummizeitung 23, 810 (1910). The Viscosity of Caoutchouc Solutions. Cp. Gummizeitung 19, 1053 & 20, 105. AXER, J. A Viscometer Consisting of a Vertical Cylinder Filled with the Material into Which Another Perforated Cylinder Dips. Ger. pat. 267, 917 (1913). AYRTON, W. & PERRY J. On the Viscosity of Dielectrics. Proc. Roy. Soc. 27,238 (1878); 7 pp. BACHMANN. 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Ann. chim. anal. chim. appl. 1, 379 (1915); 5 pp. BAYLISS, W. M. 286, (1) The kinetics of tryptic action. Arch. d. Sciences Biologiques 11, 261 (1904); 35 pp.; (2) Causes of the Rise in Electrical Conductivity under the Action of Trypsin. J. of Physiol. 36, 221 (1907); 31 pp.; (3) The Nature of Enzyme Action. Longmans Green &Co. (1914); 179pp. BAZIN. Experiences nouvelles sur la distribution des vitesses dans les tuyaux. Compt. rend. 122, 1250 (1896); 3 pp. BEADLE, C. & STEVENS, H. P. The Viscosity of Rubber Solutions. India Rubber J. 46, 1081 (1913); 1 p. BECK, C. & HIRSCH, C. (1) Die Viskositat des Blutes. Arch. f. exp. Path, u. Pharm. 64, 54 (1905). BECK, K. (1) Beitrage zur Bestimmung der Relativen inneren Reibung von Flussigkeiten. Habilitationschrift, Leipzig (1904); (2) Beitrage zur Bestimmung der Relativen inneren Reibung von Flussigkeiten, im besondefn des menschlichen Blutes. Z. physik. Chem. 48, 641 (1904); 40 pp.; (3) The Influence of the Red Corpuscles on the Internal Friction of the Blood. Kolloid-Z. 26, 109 (1919); 1 p. BECK, K. & EBBINGHOUSE, K. Beitrage zur Bestimmung der inneren Reibung. Z. physik. Chem. 68, 409 (1899); 16 pp. BECKER, A. t)ber die innere Reibung und Dichte der Bunsenflamme. Ann. Physik. (4) 24, 823 (1907); 39 pp. BECKER, G. F. Strain & Rupture in Rocks. Geol. Surv. 1897-1902. BELL, J. & CAMERON, F. 189, The Flow of Liquids through Capillary Spaces. J. Phys. Chem. 10, 658 (1906); 17 pp. VAN BEMMELEN. Z. anorg. Chem. 6, 466; 13, 233; 18, 14, 98; 20, 185; 22, 313. INDEX 353 32. BENCE, J. (1) Klinische Untersuchungen iiber die Viscositat des Blutes bei Storungen der CO Ausscheidungen. Deutsch. med. Wochschr. #15 (1905); (2) Klinische Untersuchungen iiber die Viscositat des Blutes. Z. klin. Med. 27, (1907); (Abt. fur innere Med.). Do. 58, (1909). BENTON, A. F. The End Correction in the Determination of Gas Viscosity by the Capillary-Tube Method. 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Munchen (1903); 59 pp.; (2) Bemerkung zu der Abhandlung des Herrn Markowski liber die inneren Reibung von Sauer- stoff, Wasserstoff, chemischen und atmospharischen Stickstoff und ihre A'nderung mit der Temperatur. Ann. Physik. (4) 15, 423 (1904); 2pp. BIEL, R. Uber den Druckhohenverlust bei der Fortleitung tropbarer und gasformiger Fliissigkeiten. Mitt. Forschungsarbeiten Verein deutscher Ingenieure, Heft 44. Springer Berlin (1907), abst. Zeitschr. d. Ver. deutsch. Ing. 1035, 1065 (1908); 59pp. BILTZ, W. & VON VEGESACK, A. & Steiner, H. 205, Uber den osmotischen Druck der Kolloide. II.. Der osmotische Druck einiger Farbstoff- losungen. Section 5. Uber die Zahigkeit von Nachtblaulosungen. Z. physik. Chem. 73, 500 (1910). BINGHAM, E. C. 126, 142, 271, 289, (1) The Conductivity and Viscosity of Solutions of Certain Salts in Mixtures of Acetone with Methyl Alcohol, Ethyl Alcohol and Water. Diss. Johns Hopkins (1905); 78 pp. Cp. Jones & Bingham; (2) Viscosity and Fluidity. Am. Chem. J. 35, 195 (1906); 23 pp.; (3) Viscosity and Fluidity. Am. Chem. J. 40, (1908); 4 pp.; (4) Viskositat und Fluiditat. Z. physik. Chem. 66, 238 (1909); 17 pp.; (5) Viscosity & Fluidity. Am. Chem. J. 43, 287 (1910); 23 pp.; (6) Viscosity and Fluidity of Matter in the Three States of Aggregation, and the Molecular Weight of Solids. Am. Chem. J. 45, 264 (1911); 18 pp.; (7) Fluidity and Vapor Pressure. Am. Chem. J. 47, 185 (1912); 12 pp.; (8) Viscosity & Fluidity. A Summary of Results. I. Phys. Rev. 35, (1912) ; 26 pp. ; (9) Viscosity & Fluidity. A Summary of 23 354 INDEX Results. II. Phys. Rev. (2) 1, 96 (1913); 27 pp.; (10) A Criticism of Some Recent Viscosity Investigations. J. Chem. Soc. 103, 959 (1913); 6 pp.; Proc. Chem. Soc. 29, 113 (1913); (11) The Viscosity of Binary Mixtures. J. Phys. Chem. 18, 157 (1914); 8 pp.; (12) A New Vis- cometer for General Scientific & Technical Purposes. J. Ind. Eng. Chem. 6, 233 (1914); 8 pp.; (13) Fluidity as a Function of Volume, Temperature and Pressure. The Equation of State and the Two Kinds of Viscous Resistance. The So-called "Slipping" in Gases. J. Am. Chem. Soc. 36, 1393 (1914); 16 pp.; (14) A review of Dunstan and Thole's "Viscosity of Liquids." J. Am. Soc. 36, 1320 (1914); 2 pp.; (15) Plastic Flow. J. Wash. Acad. Sci. 6, 177 (1916); 3 pp.; (16) An Investigation of the Laws of Plastic Flow. Bull. U. S. Bur. of Standards 13, 309 (1916); 43 pp.; (17) The Variable Pressure Method for the Measurement of Viscosity. Proc. Am. Soc. Testing Materials 18, Pt. II, 373 (1918); 11 pp.; (18) Cutting Fluids. Tech. Paper 204, U. S. Bur. of Standards 16, 35 (1922) 41 pp. BINGHAM, E. C. and DURHAM, T. C. 64, 201, 208, 215, The Viscosity and Fluidity of Suspensions of Finely-Divided Solids in Liquids. Am. Chem. J. 46, 278 (1911); 20 pp. BINGHAM, E. C. and GREEN, H. 220, et seq., Paint, a Plastic Material. and not a Viscous Liquid; The Measurement of Its Mobility and Yield Value. Proc. Am. Soc. Testing Materials. II, 19, 640 (1919); 36 pp. Cp. Green. BINGHAM, E. C. & Miss HARRISON, J. 121, Viskositat und Fluiditat. Z. physik. Chem. 66, 1 (1909); 32 pp. BINGHAM, E. C. and JACKSON, R. F. Standard Substances for the Cali- bration of Viscometers. Bull. U. S. Bur. of Standards 14, No. 298, 59 (1917); 28 pp. J. Wash. Acad. Sci. 7, 53 (1917); 2 pp. BINGHAM, E. C. and SARVER, L. Fluidities and Specific Volumes of Benzyl Benzoate and Benzene. J. Am. Chem. Soc. 42, 2011 (1920); 11 pp. BINGHAM, E. C., SCHLESINGER, H. I. and COLEMAN, A. B. 298, Some Sources of Error in Viscosity Measurement. J. Am. Chem. Soc. 38, 27 (1916); 15 pp. BINGHAM, E. C., VAN KLOOSTER, H. S. and KLEINSPEHN, W. G. The Fluidities and -Volumes of Some Nitrogenous Organic Compounds. J. Phys. Chem. 24, 1 (1920); 21 pp. BINGHAM, E. C. & WHITE, G. F. 6, 21, 28, 97, (1) Viscosity and Fluidity of Emulsions, Crystallin Liquids and Colloidal Solutions. J. Am. Soc. 33, 1257 (1911); 11 pp.; (2) Fluiditat und die Hydrattheorie. I. Die Viskositat von Wasser. Z. physik. Chem. 80, 670 (1912); 17 pp. BINGHAM, E. C., WHITE, G. F., THOMAS, A. & CADWELL, J.-L. 142, 169, 178, Fluidity and the Hydrate Theory. II. Z. physik. Chem. 83, 641 (1913); 32 pp. BLANCHARD, A. The Viscosity of Solutions in Relation to the Constitution of Dissolved Substances. J. Am. Chem. Soc. 26, 1315 (1904); 24 pp. (Ionic migration velocity.) BLANCHARD, A. & PUSHES, H. B. The Viscosity of Solutions of the Metal INDEX 355 Ammonia Salts. J. Am. Chem. Soc. 34, 28 (1912); 4 pp. Cp. J. Am. Chem. Soc. 26, 1315. BLANCHARD, A. & STEWART, M. The Viscosity of Solutions of Metallic Salts; Its Bearing upon the Nature of the Compound between Solvent and Solute. Science (N. S.) 18, 98 (1903); 1 p. BLASIUS, H. Das Ahnlichkeitsgesetz bei Reibungsvorgangen in Flussig- keiten. Mitt. Forschungsarbeiten, Verein deutscher Ingenieure. Julius Springer. Heft. 131 (1913); 40 pp. BLEININGER, A. V. (1) The Effect of Preliminary Heating Treatment Upon the Drying of Clays. Technologic Paper, Bur. of Standards #1 (1911); (2) The Viscosity of Clay Slips. Trans. Am. Ceram. Soc. 10, 389; (3) The Effect of Electrolytes upon Clay in the Plastic State. Orig. Comm. 8th Intern. C. Appl. Chem. Cp. Univ. 111. Bull. 6, #25 (1909). BLEININGER, A. V. & BROWN, G. H. (1) Testing of Clay Refractories with Special Reference to their Load Carrying Capacity at Furnace Temperatures. Tech. Paper of the U. S. Bur. of Standards #7; (2) Note on the V. of Clay Slips. Trans. Am. Ceram. Soc. 11, 596 (1909); 9 pp.; (3) The Effect of Prelim. Heat Treatment upon Clays. U. S. Bur. Stand. Bui. 1. Trans. Am. Ceram. Soc. 11, 392 (1909); 15 pp. BLEININGER, A. V., CLARK, H. H. Note on the Viscosity of Clay Slips as Determined by the Clark Apparatus. Trans. Am. Ceram. Soc. 12, 383 (1910); 9pp. BLEININGER, A. V. & FULTON, C. E. The effect of Acids and Alkalies upon Clay in the Plastic State. Am. Ceram. Soc. 14, 827 (1912). BLEININGER, A. V. & Ross, D. W. (1) The Flow of Clay under Pressure. . Trans. Am. Ceram. Soc. 16, 392 (1914); 9 pp. BLEININGER, A. V. and TECTOR, P. The Viscosity of Porcelain Bodies. Trans. Am. Ceram. Soc. 16, 328 (1913); 9 pp. Also Tech. Paper, U. S. Bur. Standards #30. BLUNSCHY, F. Beitrage zur Lehre der Viscositat des Blutes. Diss. Zurich (1908); 43 pp. BOGUE, R. H. Properties and Constitution of Glues and Gelatins. II. Chem. Met. Eng. 23, 61 (1920); 6 pp.; J. Am. Chem. Soc. 43, 1764 (1921); 10 pp. The Viscosity of Gelatin Sols. BOLLE, B. Beitrag zur Kenntniss der Viscositat des Blates, des Serums u. des Plasmas. Diss. Berlin (1909); 29 pp. BOLTZMANN, L. 237, (1) Zur Theorie der elastische Nachwirkung (2A) Wien. Sitzungsber. 70, 275 (1875); 31 pp.; (2) Zur Theorie der elastis- chen Nachwirkung. Pogg. Ann. Erganzungsband 7, 624 (1876); 31 pp.; (3) Uber einige Probleme der Theorie der elastischen Nach- wirkung und liber eine neue Methode, Schwingungen mittels Spiegel- ablesung zu beobachten, ohne den Schwingenden Korper mit einen Spiegel von erheblicher Masse zu belasten. Wien. Situngsber. (2A) 76, 815 (1878); 28 pp.; (4) Zur Theorie der elastische Nachwirkung. Wied. Ann. 5, 430 (1878); 3 pp.; (5) Zur Theorie der Gasreibung. Wien. Sitzungsber. (2A) 81, 117 (1880); 42 pp.; (6) Do., Part II, 356 INDEX Wien. Sitzungsber. (2A) 84, (1881); 95 pp.; (7) Do., Part III. Wicn. Sitzungsber. (2A) 84, 1230 (1881); 34 pp.; (8) Vorlesungen iiber Gastheorie. Earth, Leipzig 2 vols. (1896); (9) Geschichte unserer Kenntniss der inneren Reibung und Warmeleitung in verdunnten Gasen. Physik. Z. 1, 213 (1900); 1 p. BOND, W. N. The Properties of Plastic Crystals of Ammonium Nitrate. Phil. Mag. 41, 1 (1921); 21 pp. BORELLI L. & DATTA. (1) Viscometry of the Urine. Riv. crit. clin. Med. 11, 289 (1910); 7 pp.; (2) Saggi di viscosimetria clinica. La clinica medica italiana 45, 149 (1905); (3) Saggi di viscosimetria clinica. Nota II. Viscometria degli essudati e trasudati. Riv. crit. clin. Med. 7, 181 (1906). BORN, M. The Mobility of the Electrolytic Ions. Z. Elektrochem. 26, 401 (1920); 3 pp. BOSCOVICH, R. J. 1, Opera pertinentia ad opticam et Astronomician. 5 vols. (1785) Bassani vol. 5 opusculum III. BOSE, E. 96, 100, 102, 209, 210, (1) Uber die Viskositatsanomalien von Emulsionen und von anistropen Fliissigkeiten. Physik. Z. 9, 707 (1908); 1 p.; (2) Viskositatsanomalien anistroper Flussigkeiten in hydraulischen Stromungzustanden. Physik. 7. 10, 32 (1909); 5 pp. Cp. Willers. BOSE, E. & BOSE, M. The Viscosity of Liquids in the Condition of Turbu- lent Flow. Physik. Z. 12, 126 (1910); 10 pp. BOSE, E. & CONRAT, F. The Viscosity at the Clarifying Point of So-called Crystalline Liquids. Physik. Z. 9, 169 (1908); 5 pp. BOSE, E. & RAUERT, D. 97, Experimental Study of the Viscosity of Liquids in the Condition of Turbulent Flow. Physik. Z. 10, 406 (1909); 3 pp. BOSSUT. 1, 18, (1) Traite" 61ementaire d'hydrodynamique. Paris (1775); (2) Nouvelles exp6riences sur la resistance des fluides, Paris (1777). BOTAZZI, F. (1) L'Orsi, giornale di chimica, formacia, ecc. Firenze 20, 253, 289 (1897). Chem. Zentr. 1, 83 (1898); (2) Recherches sur la viscosit6 de quelques liquides organiques et de quelques solutions aqueuses de substances prot&ques. Arch. ital. de Biologie 29, 401 (1898); Naturw. Rundsch 14, 47 (1899); (3) Ricerche sull' attrito interno (viscosita) di alcune liquidi organic! e di alcune soluzioni acquose di sostanze proteiche. Principi di Fisiologia I Chimica-Fisica Societa editrice libraria 316 (1906); (4) Some colloidal properties of hemo- globin. Atti. Acad. Lincei 22, II, 263 (1913). BOTAZZI, F. & D' Agostino, E. Viscosity and Surface Tension of Suspensions and Solutions of Muscular Proteins Under the Influence of Acids and Alkalies. Atti. Accad. Lincei 22, II, 183 (1913); 9 pp. BOTAZZI, F. & D'ERRICO, G. 207, 208, Pfliigers Arch. f. Physiol. 115, 359 Biochem. Z. 7, (1908). BOTAZZI, F. & JAPPELI. Viscosity of blood serum of cattle. Rend. Line. (5) 17, [2] 49 (1908), Cp. Japelli. BOTAZZI, F. and VICTOROW, C. Surface Tension, Viscosity, and Appear- INDEX 357 ance of Dialysed Marseilles Soap of Unknown Composition, With or Without Addition of Alkali. Rend. R. Ac. Line. (5) 19, I, 659 (1910). BOTTOMLEY, L. On the Secular Experiments in Glasgow on the Elasticity of Wires. Rep. Brit. Assoc. 537 (1886); 1 p. BOUSFIELD, W. R. 196, Z. physik. Chem. 53, 303 (1905). Ionic Size in Relation to the Physical Properties of Silver Solutions. Phil. Trans. A. 206, 129 (1906); 13 pp.; (2) Ionic Size in Relation to Viscosity. Phil. Trans. (A) 206, 101 (1906); 59 pp. BOUSFIELD, W. & LOWRY, T. 192, (1) The Influence of Temperature on the Conductivity of Electrolytic Solutions. Proc. Roy. Soc. London 71, 42 (1902); 13 pp.; (2) The Electrical Conductivity and other Properties of Sodium Hydroxide in Aqueous Solutions as Elucidating the Mech- anism of Conduction. Proc. Roy. Soc. London 74, 280 (1904); 4 pp. Phil. Trans. (A) 204, 253 (1905); 69 pp. BOUSSINESQ, J. 6, 18, 50, (1) Essai sur la th6orie des eaux courantes. M6m. presentes par divers savants a 1'Acad. des Scien. 23, (1877); 680 pp.; (2) Additions et e"claircissements au memoire institute": Essai sur la theorie des eaux courantes. Do. 24, (1877); 64 pp.; (3), Lec.ons synthetiques de Mecanique ge'ne'rale, servant d'introduction au Cours de Mecanique physique de la Faculte des Sciences do Paris. Gauthier- Villars (1889); (4) Theorie du regime permanent graduellement varie qui se produit pres de 1'entree evasee d'un tube fin, ou les filets d'un liquide qui s'y ecoule n'ont pas encore acquis leurs inegalites normales de vitesse. Compt. rend. 110, 1160 (1890); 6 pp.; (5; The"orie de mouvement permanent qui se produit pres de 1'entree evasee d'un tube fin: application a la deuxieme s6rie d' experiences de Poiseuille. - Compt. rend. 110, 1238 (1890); 5 pp.; (6) Sur 1'explication physique dela fluidite. Compt. rend. 112, 1099 (1891); 3 pp.; (7) Sur la Maniere dont les vitesses, dans un tube cylindrique de section circulaire, evase & son entree, se distribuent depuis cette entree jus q'aux endroits on se trouve etabli un regime uniforme. Compt. rend. 113, 9 (1891); 6 pp. ; (8) Calcul de la moindre longueur que doit avoir un tube circu- laire, evase a son entree pour qu 'un regime sensiblement uniforme s'y e'tablisse et de la depense de charge qu'y entratne 1'etablissement. Compt. rend. 113, 49 (1891); 2 pp.; (9) Theorie analytique de la chaleur Vol. II. Note I, 196-265. Sur la resistanse opposee aax petits mouve- ments d'un fluide indefini par un solide immerge' dans ce fluide. Gauthier-Villars, Paris, 1903; (10) Existence of Surface Viscosity in the Thin Transition Layer Separating a Liquid from a Contiguous Fluid. Ann. chim. phys. 29, 349 (1913); 8 pp.; (11) Application of Surface Viscosity Formulas to the Surface of a Spheroidal drop Falling with Uniform Velocity into a Fluid of less Specific Gravity. Ann. chim. phys. 29, 357 (1913); 7 pp.; (12) Velocity of the Fall of a Spherical Drop into a Viscous Fluid of Less Specific Gravity. Ann. chim. phys. 29, 364 (1913) ; 7 pp. ; (13) Internal Friction and Turbulent Flow. Compt. rend. 1517 (1896). 358 INDEX BOUTARIC, A. Sur quelques consequences physico-chimiques des mesures de viscosite. Rev. gen. Sci. 25, 425 (1914); 8 pp. BOUTY and BENDER. 192. BOVEY, H. Some Experiments on the Resistance to Flow of Water in Pipes. Trans. Roy. Soc. of Canada Sect. 3 (1898); 14 pp. BOYNTON, W. P. Application of the Kinetic Theory to Gases, Vapors, Pure Liquids and the Theory of Solutions. Macmillan Co. (1904); 288 pp. BRAUN, W. Uber die Natur der elastischen Nachwirkung. Pogg. Am. 159, 337 (1876); 62 pp. BRAUN, W. & KURZ, A. (1) Uber die Dampfung der Torsionsschwingungen von Drahten. Carl's Repert. Exp.-physik. 15, 561 (1879); 16 pp.; (2) Do., II, Carl's Repert. Exp.-physik. 17, 233 (1881); 21 pp.; (3) Uber die elastische Nachwirkung in Drahten. III. Carl's Repert. Exp.-physik. 18, 665 (1882); 8 pp. BREDIG, G. 192, Beitrage zur Stochiometrie der lonenbeweglichkeit. Z. physik. Chem. 13, 190 (1894); 98 pp. BREITENBACH, P. 79, 252, (1) tlber die innere Reibung der Gase und deren Anderung mit der Temperatur. Diss. Erlangen (1898); Wied. Ann. 67, 803 (1899); 25 pp; (2) Do., Ann. Physik. 5, 166 (1901); 4 pp. BRIDGMAN, P. W. (1) Mercury, Liquid and Solid, Under Pressure. Proc. Amer. Acad. 47, 345 (1912); 94pp.; (2) On the Effect of General Mech- anical Stress on the Temperature of Transition of Two Phases, with a Discussion of Plasticity. Phys. Rev. (2) 7, 215 (1916); 9 pp. BRIGGS, BENNETT and PIERSON. J. Phys. Chem. 22, 256 (1918). BRILLOUIN, M. 32, 38, 42, 142, (1) Theorie elastique de la plasticite et la fragilite des corps solides. Compt. rend. 112, 1054 (1891); 2 pp.; (2) Viscosity of Liquids as a Function of the Temperature. Ann. chim. phys. (7) 18, 197 (1899) ; 16 pp. ; (3) Sur la viscosite des fluides. Compt. rend. 144, 1151 (1907); 2 pp.; (4) Lecons sur la viscosite des liquides des gaz.; Part I. Gcneralite" des viscosite's des liquides. VII + 228 pp. Part II. Viscosite des gaz. Caracteres generaux des th6ories molimentales relatives au mouvement dc 1'eau dans les tuyaux. Paris (1857); M6m. par divers, savants a 1'Acad. des Scienc. de 1'Inst. 15, 141 (1858); 263 pp. Cp. Memoiren der kaiser. Akademie der Wissenschaften 16. INDEX 363 D'ARCY, R. Viscosity of Solutions, Phil. Mag. (5) 28, 221 (1889); 11 pp. DAVIDSON, G. F. Flow of Viscous Fluids through Orifices. Proc. Roy. Soc. London (A) 89, 91 (1913); 8 pp. DAVIS, N. B. The Plasticity of Clay. Trans. Am. Ceram. Soc. 16, 65 (1914); 15pp. DAVIS, P. B., ET AL. (1) Studies on Solution in its Relation to Light Absorption, Conductivity, Viscosity and Hydrolysis. Carnegie Inst. of Washington, D. C., 144 pp.; (2) A Note on the Viscosity of Caesium Salts in Glycerol-Water Mixtures. Carnegie Inst. Pub. 260, 97 (1918); 1 p.; (3) The Conductivity and Viscosity of Organic and Inorganic Salts in Formamide and in Mixtures of Formamide with Ethyl Alcohol. Carnegie Pub. 260, 71 (1918); 26 pp. DAVIS, P. B., HUGHES, H. & JONES, H. C. Conductivity & Viscosity of Rubidium Salts in Mixtures of Acetone & Water. Z. physik. Chem. 85,513 (1913); 39 pp. DAVIS, P. B. and JONES, H. C. Conductivity and Negative Viscosity Coefficients of Certain Rubidium & Ammonium Salts in Glycerol and in Mixtures of Glycerol and Water at 25 to 75. Z. physik. Chem. 81, 68 (1913); 45 pp. DAWSON, H. M. The Estimation of Mixtures of Isomers and Other Closely Related Substances. J. Soc. Dyers Colourists 35, 123 (1919); 6pp. DAY, H. The Effect of Viscosity on Thermal Expansion. Am. J. Sci. (4) 2, 342 (1896); 5 pp.; Nature 55, 92 (1896-7). DEAN, E. W. and JACKSON, L. E. Effect of crystalline paraffine wax upon the viscosity of lubricating oil. U. S. Bur. Mines Reports of Investi- gations, #2249 (1921); 3 pp. DEELEY, R. M. Oiliness and Lubrication. Engineering 108, 788 (1919); Proc. Phys. Soc. London, II 28, 11 (1919); Do., II 32, 1 (1920); 11 pp. (Discussion by Deeley, Martin, Allen, Skinner, Southcombe, and Hardy.) DEELEY, R. M. & PARR, P. H. 239, (1) The Viscosity of Glacier Ice. Phil. Mag. (6) 26, 85 (1913); 26 pp.; (2) The Hintereis Glacier. Phil. Mag. (6) 27, 153 (1914); 24 pp. DEERING, W. H. & REDWOOD, B. Report on Castor Oils from Indian Section of the Imperial Inst. J. Soc. Chem. Ind. 13, 959 (1894); 2 pp. DE GUZMAN, J. Anales Soc. Expan. fis. quim 11, 353 (1913); 9 pp. DENISON, R. B. 172, Liquid Mixtures, II. Chemical Combination in Liquid Binary Mixtures as Determined in a Study of Property Com- position Curves. Trans. Faraday Soc. 8, 35 (1913). DENNHARDT, R. Ann. Phys. 67, 325 (1899). DEWAR, J. The Viscosity of Solids. Nature 50, 238 (1894); Chem. News 69, 307 (1894); 1 p. DETERMANN, H. (1) Ein einfaches, stets gebrauchfertiges Instrument zur Messung der Inneren Reibung von Fliissigkeiten. Physik. Z. 9, 375 (1908); 1 p.; Munich, Med. Wochenschr. #42 (1907); (2) Viscosity and Protein Content of the Blood with Different Diets Especially with 364 INDEX Vegetarians. Med. Klin. No. 24 (1909); Berlin, klin. Wochenschr. 664 (1909). Cp. Munich Med. Wochenschr. #23 (1907). DETERMANN, H. & BOOKING. Does the Administration of Iodine Influence the Viscosity of the Blood? Deut. Med. Wochschr. 38, 994 (1912); lp. DETERMANN, H. and WEIL, F. Viscosity and Gas Content of Human Blood. Z. Klin. Med. 70, 468 (1911); 6 pp. DICKENSCHEID, F. 209, Untersuchungen iiber Dichte, Reibung, und Kapillaritat kristallinischer Flussigkeiten. Diss. Halle (1908); 44 pp. DIENES, L. Viscosity of Colloidal & Non-Colloidal Liquids. Biochem. Z. 33, 222 (1910); 3pp. DOELTER, C. 287, (1) Silikatglaser und Silikatschmelzen. Chem. Tech. Ztg. (2) 9, 76 (1906); Sitzber. Wien. Akad. 114, I, 529 (1905); (2) tJber den Einfluss der Viskositat bei Silikatschmelzen. Centr. Min. 193 (1906); (3) The Viscosity of Silicate Melts. Chem. Ztg. 36, 569 (1913). DOELTER, C. & SIRK, H. The Determination of the Absolute Value of the Viscosity of Silicate Melts. Monatsber. 32, 643 (1912); Sitzber. Wien. Akad. 20, I, 659 (1911). DOLAZALEK, F. und SCHULZE, A. Zur Theorie der binaren Gemische und konzentrierten Losungen IV Das Gemisch: Athylather-Chlo reform. Z. physik. Chem. 83, 45 (1913); 34 pp. DOLFUS, C. Bull. Soc. Ind. Mulhouse 5, 14-23. DONLINSON, H. The Influence of Stress and Strain on the Physical Prop- erties of Matter. Phil. Trans. London 177, Pt. II, 801 (1886); 37 pp. DONNAN, F. The Relative Rates of Effusion of Argon, Helium and Some other Gases. Phil. Mag. (5) 49, 423 (1900); 23 pp. DOOLITTLE, O. 328, The Torsion Viscometer. J. Am. Chem. Soc. 16, 173 (1893); 5 pp.; J. Soc. Chem. Ind. 12, 709 (1893); 1 p. DORN, E. & VOLLMER. Uber die Einwirkung von Salzsaure auf metallisches Natrium bei niederen Temperaturen. Ann. Physik. 60, 468 (1897); 10 pp. DOROSHEVSCHII, A. G. and ROZHDESTORNSKII. 195, Electrical Conductivity of Mixtures of Alcohol and Water. J. Russ. Phys. Chem. Soc. 40, 887 (1908); 21 pp. DOWLING, J. J. Steady and Turbulent Motion in Gases. Proc. Roy. Soc. Dublin 13, 375-98 (1913); 23 pp. DRAPIER, P. 98, 99, 100, 102, 103, Viscosity of Binary Liquid Mixtures in the Neighborhood of the Critical Solution Temperature. Bull. acad. roy. belg. 1, 621 (1911); 19 pp. DREW, E. A Determination of the Viscosity of Water. Physik. Rev. 12, 114 (1901); 7 pp. DRXJCKER, K. Fluidity. I. Z. physik. Chem. 92, 287 (1917); 32 pp.; J. Chem. Soc., II 112, 409. DRUCKER, K. & KASSEL. 104, The Fluidity of Binary Mixtures. Z. physik. Chem. 76, 367 (1911); 18 pp. DUBRISAY, R. A Method of Testing the Viscosity of Lubricating Oils. Ann. fals, 10, 301 (1917); 4 pp.; J. Soc. Chem. Ind. 36, 1123 (1917). INDEX 365 DuBuAT, C. 1, Principes d'hydraulique verifies par un grand nombre d'experiences. nouv. ieure sur les systemes affecte's d'hysteresis et de viscosit^. Compt. rend. 138, 1075 (1904); 1 p.; (II) Effet des petites oscillations de la temperature sur un systeme affecte d'hyste"resis et de viscositS. Compt. rend. 138, 1196 (1904); 3 pp.; (12) Sur la viscosite et le frottement au contact de deux fluides. Proces-verb. de Bordeaux (1902-03), 27 (1903); 3 pp.; (13) Les conditions aux limites. Le theoreme de Lagrange et la viscosit^. Les coefficients de viscosit6 et la viscosit^ au voisinage de I'Stat critique. Recherches sur 1'hydrodynamique, 2 series. Paris, Gauthier-Villers (1904). DUMANSKII, A., ZABOTINSKII, E. & EVSEYER, M. A Method for Deter- mining the Size of Colloidal Particles. Z. Chem. Ind. Kolloide 12, 6 (1913); 5pp. DUMARESQ, F. The Viscosity of Cream. Proc. Roy. Soc. Victoria (2) 25, 307 (1913); 15 pp.; Expt. Sta. Record 30, 170. DUNCAN, J. & GAMGEE, A. Notes of some Experiments on the Rate of 366 INDEX Flow of Blood and some other Liquids through Tubes of Narrow Diameter. J. Anat. and Physiol. 5, 155 (1871); 8 pp. DUNSTAN, A. 81, 88, 92, 178, (1) Viscosity of Liquid Mixtures. J. Chem. Soc. 86, 817 (1904); 10 pp.; Z. physik. Chem. 49, 590 (1904); 7 pp.; (2) Do., Part II. J. Chem. Soc. 87, 11 (1905); 6 pp.; Z. physik. Chem. 61, 732 (1905); 7 pp.; (3) Do. Part III. Proc. Chem. Soc. 22, 89 (1906); 1 p.; (4) Innere Reibung von Fliissigkeitgemischen. Z. physik. Chem. 66, 370 (1906); 10 pp.; (5) The Viscosity of Sulphuric Acid. Proc. Chem. Soc. 30, 104 (1914); 2 pp. Cp. Thole, Hilditch and Mussel; (6) Viscosity of Solutions and its Bearing on the Nature of Solution. J. Soc. Chem. Ind. 28, 751 (1910). Cp. Hilditch, and Thole. DUNSTAN, A. & JEMMETT, W. Preliminary Note on the Viscosity of Liquid Mixtures Ethyl Acetate & Benzene, Benzene & Alcohol, Alcohol & Water. Proc. Chem. Soc. 19, 215 (1903); 1 p. DUNSTAN, A. E. & HILDITCH, T. P. Relations between Viscosity and other Physical Properties. II. Influence of Contiguous Unsaturated Groups. J. Chem. Soc. 102, II, 435. Z. Elektrochemie 18, 185 (1913); 4 pp. DUNSTAN, A. E. & LANGTON, H. 112, Viscometric Determination of Transition Points. J. Chem. Soc. 101, 418 (1912); 7 pp.; Proc. Chem. Soc. 28, 14 (1912). DUNSTAN, A. E. & MUSSEL, A. G. (1) The Application of Viscometry to the Measurement of the Rate of Reaction. J. Chem. Soc. 99, 565 (1911); 7 pp.; Proc. Chem. Soc. 27, 59 (1911); (2) Viscosity of Certain Amines. J. Chem. Soc. 97, 1935 (1910); 10 pp.; Proc. Chem. Soc. 26, 201 (1910). DUNSTAN, A. E. & STEVENS, J. E. The Viscosity of Lubricating Oils. J. Soc. Chem. Ind. 31, 1063 (1913); 1 p. DUNSTAN, A. & STUBBS, J. The Relation between Viscosity and Chem. Constitution. Pt. III. J. Trans. Chem. Soc. 93, 1919 (1909); 8 pp. DUNSTAN, A. & THOLE, F. B. Ill, 121, 142, 279, (1) The Relation Between Viscosity and Chemical Constitution. Part IV. Viscosity and Hydra- tion in Solution. J. chim. phys. 7, 204 (1909); J. Chem. Soc. 96, 1556 (1909); 6 pp.; Proc. Chem. Soc. 25, 219 (1909); (2) Relation between Viscosity and Chemical Constitution. V. Viscosity of Homologous Series. Proc. Chem. Soc. 28, 269 (1913); VI. Viscosity an Additive Function. J. Chem. Soc. 103, 129 (1913); 4 pp.; Proc. Chem. Soc. 28, 269 (1913); VII. Effect of Relative Position of Two Unsaturated Groups on Viscosity. With P. Hilditch. J. Chem. Soc. 103, 133 (1913); 11 pp.; Proc. Soc. 28, 269 (1913); (3) The Existence of Racemic Compounds in Solution. Trans. Chem. Soc. 97, 1249 (1910); 8 pp.; (4) The Viscosity of Liquids (1914); VIII + 92 pp., Longmans Green & Co. Monographs of Inorganic & Physical Chem. edited by Alexander Findlay; (5) The Relation between Viscosity and the Chemical Con- stitution of Lubricating Oils. J. Inst. Petroleum Tech. 4, 191 (1918); 38 pp.; Petroleum Review 38, 245, 267 (1918); 3 pp. INDEX 367 DUNSTAN, A., & THOLE, F. B. & HUNT. Relations between Viscosity and Chemical Constitution. Proc. Chem. Soc. 23, 207 (1907); J. Chem. Soc. 91, 1728 (1907); 8 pp. DUNSTAN, A., THOLE, P. and BENSON, P. The Relation between Viscosity and Chemical Constitution. Part VIII. Some Homologous Series. Trans. Chem. Soc. 105, 782 (1914); 12 pp.; Proc. Chem. Soc. 29, 378. DUNSTAN, A. & WILSON, R. (1) The Viscosity of Liquid Mixtures. Proc. Chem. Soc. 22, 308 (1907); J. Chem. Soc. 91, 83 (1907); 9 pp.; (2) The Viscosity of Fuming Sulphuric Acid. J. Chem. Soc. 93, 2179 (1908) ; 2 pp. DUPERTHIUS, H. Contribution a 1'etude des dissociants autres que 1'eau. Conductibilites limites. Viscosite". Chaleurs de dissociant. Diss. Laus- anne (1908); 47 pp. Du PRE DENNING. Cp. Pre Denning. DURHAM, T. C. 54, 201 et seq. 208. Cp. Bingham and Durham. DUSHMAN, S. Methods for the Production and Measurement of High Vacua. Part XL Temperature Drop, Slip, and Concentration Drop in Gases at Low Pressures. Gen. Electric Rev. 24, 890 (1921); 11 pp. DUTOIT, P. & DUPERTHIUS. 195, Relations qui existent entre les conduc- tibilite's limites et la viscosite. Arch. sci. phys. nat. 25, 508 (1908); 1 p.; J. chim. phys. 6, 726 (1909); 5 pp. DUTOIT, P. & FREDERICK, L. Sur la conductibilit6 des electrolytes dans les dissolvants organiques. Bull. soc. chim. (3) 19, 321 (1898); 17 pp. DYSART, A. S. A Viscometer. 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Wochschr. 25, 735 (1912); 5 pp. ELIE, B. 83, Variation du coefficient de viscosite avec la vitesse. J. physique (2) 1, 224 (1882); 2 pp. ELLIS, R. Properties of Oil Emulsions. II. Stability and Size of Globules. Z. physik. Chem. 80, 597 (1913); 20 pp. ELLIS, R. L. Relation between Temperature and Viscosity of Lubricants. Met. Chem. Eng. 10, 546 (1912); 2 pp. 368 INDEX ELSEY, H. M. Conductivity and Viscosity of Solutions in Dimethyl- amine, Trimethylamine, Ethylamine, Diethylamine, Triethylamine, and Propylamine. J. Am. Chem. Soc. 42, 2454 (1920); 23 pp. EMDEN, R. (1) ITber die Ausstromungserscheinungen permanenter Gase. Habilitationsschrift, Tech. Hochschule Miinchen, Earth. Leipzig (1899); 96 pp.; Ann. Phys. Chem. 69, 426 (1899); 28 pp. EMLEY, W. E. 281, 282, (1) Measurement of Plasticity of Mortars and Plasters. Tech. Paper U. S. Bur. Stands. No. 169 (1920); 27 pp.; Trans. Am. Ceram. Soc. 19, 523 (1917); 11 pp.; (2) The Compressive Method of Measuring Plasticity. Proc. Nat. 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Do. 23, 177 (1920); 8pp. HOLLAND, R. Uber die Anderung der electrischen Leitfahigkeit einer Losung durch Zusatz von kleinen Mengen eines Nichtleiters. Wied. Ann. 60, 261 (1893); 32 pp. INDEX 383 HOLMAN, S. 246, 247, (1) On the Effect of Temperature on the Viscosity of the Air. Prdc. Am. Acad. 12, 41 (1876); 10 pp.; (2) A New Method of Studying the Relation between the Viscosity and Temperature of Gases. Phil. Mag. (5) 3, 81 (1877) ; 6 pp. ; (3) On the Effect of Tempera- ture on the Viscosity of the Air. Proc. Am. Acad. 21, 1 (1885); (4) On the Effect of Temperature on the Viscosity of Air and Carbon Dioxide. Phil. Mag. (5) 21, 199 (1886); 24 pp. HOLMGREN, I. The Influence of White Blood Corpuscles upon the Viscosity of the Blood. Deut. Med. Wochschr. 39, 217 (1913); 2 pp. HONDA, K. and KONNO, S. On the Determination of the Coefficient of Normal Viscosity of Metals. Phil. Mag. 42 (6) 115 (1921); 8pp. HORIBA. J. Tok. Chem. Soc. 31, 922 (191 ). HORTON, F. 237, The Effects of Changes of Temperature on the Modulus of Torsional Rigidity of Metal Wires. Phil. Trans. London (A) 204, 1 (1904); 55pp. HOSKING, R. 6, (1) Viscosity of Solutions. Phil. Mag. (5) 49, 274 (1900); 13 pp. Cp. Lyle & Hosking; (2) The Electrical Conductivity and Fluidity of Solutions of Lithium Chloride. Phil. Mag. (6) 7, 469 (1904) ; 29 pp. ; (3) The Viscosity of Water. J. Proc. Roy. Soc. N. S. W. 42, 34 (1909); 23 pp. Do., do. 43, 34 (1910); 5 pp. HOUBA. Over de strooming van vloeistoffen door buizen. Nijmegen (1883). Cp. Wied. Ann. 21, 493 (1884). HOUDAILLE, F. Mesure du coefficient de diffusion de la vapeur d'eau dans 1'atmosphere et du coefficient de frottement de la vapor d'eau. These Paris (1896); Fortsch. Physik. (I) 52, 442 (1896); 1 p. HOWARD, W. B. Penetration Needle Apparatus for Testing the Viscosity of Asphalt. U. S. Pat. 1,225,438, May 8 (1917). HOWEL and COOKE. Action of the Inorganic Salts, of Serum, Milk, Gastric Juice, etc., upon the Isolated Heart, etc. J. of Physiol. 14, 198 (1893). HUBBARD, P. & REEVE, C. Methods for the Examination of Bituminous Road Materials. U. S. Dept, Agric. Bull. No. 314. Cp. also Eng. Contr. 54, 16 (1920); 4 p. HUBENER, T. 17.8, 179, Untersuchungen iiber die Transpiration von Salz- losungen. Pogg. Ann. 150, 248 (1873); 12 pp. HUBNER, W. 286, Die Viscositat des Blutes. Bemerkungen zu der gleich- namigen Arbeit von C. Beck. u. C. Hirsch. Arch. f. exp. Path. u. Pharm. 54, 149 (1905). HURTHLE, K. (1) Uber den Widerstand der Blutbahn. Deutsch. med. Wochschr. 23, #51, 809 (1897); 3 pp.; (2) Do. Arch. ges. Physiol. (Pfluger's) 82, 415 (1908); 3 pp. HUMPHREY, E. and HATSCHEK, E. The Viscosity of Suspensions of Rigid Particles at Different Rates of Shear. Proc. Phys. Soc. London 28, 274 (1916). HURST. Lubricating Oils, Fats, and Waxes. 3d Ed. (1911). HUTCHINSON, J. Viscometer for Use with Coal-Tar, etc. Brit. 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Anat. und Phys. 304 (1861); 25 pp. Cp. Ber. d. Naturf. Vers. in Konigsberg (1862) (1867). JAGER, G. 131, (1) tlber die kinetische Theorie der inneren Reibung der Flussigkeiten. Wien. Sitzungsber. (2A) 102, 253 (1893); 12 pp.; (2) t)ber die innere Reibung der Losungen. Wien. Sitzungsber. 251 (1894); 15 pp.; (3) Uber den Einfluss des Molecularvolumens auf die innere Reibung der Case. Wien. Sitzungsber. (2A) 108, 447 (1899); 9 pp.; (4) Do. Wien. Sitzungsber. (2A) 109, 74 (1900); 7 pp. Cp. Wien. Anzeiger Kaiserl. Akad. Wissens. math.-naturw. Kl. 11 (1900); 1 p.; (5) Der innere Druck, die innere Reibung die Grosse der Molekeln und deren mittlere Weglange bei Flussigkeiten. Wien. Sitzungsber. (2A) 111, 697 (1902); 10 pp.; (6) Kinetische Theorie der Gasen. Hand- INDEX 385 buch der Physik. Winklemann. 2 ed. 3, 734 (1906); 13 pp.; (7) The Kinetic Theory of the Internal Friction of Gases. Sitz. Akad. Wiss. Wien. (IIA) 127, 849 (1918); 22 pp. JAPPELI, G. Contribute allo studio dell'influenza della aumentata viscosita del sangue sulla meccanica cardio-vascolare. Arch, di Fisiologia 4, 101 (1907). Cp. Botazzi. JEANS. The Dynamical Theory of Gases. Camb. Univ. Press (1904); 347 pp. JEAUCARD & SATIE. Tension superficielle et viscosite de quelques huiles essentielles. Bull. Soc. chim. (3) 25, 519 (1901); 5 pp. JEVONS, W. S. On the Movement of Microscopic Particles Suspended in Liquids. Quarterly J. of Science, London (1878); 22 pp. JOB. Nouvelle methode experimentale pour 1'etude de la transpira- tion des gaz. Soc. franc, d. phys. 157, 2 (1901). Cp. Fortsch. Physik. 67, 280 (1901). JOHNSON & BLAKE. On Kaolinite and Pholerite. Amer. J. Sci. (2) 93, 351 (1867); llpp. JOHNSTON, J. 195, 196, (1) The Change of the Equivalent Conductance of Ions with the Temperature. J. Am. Chem. Soc. 31, 1010 (1909); 11 pp.; (2) A Correlation of the Elastic Behavior of Metals with Certain of their Physical Constants. J. Am. Chem. Soc. 34, 788 (1912); 15 pp. JOHNSTON, J. & ADAMS, L. H. On the Effect of High Pressures on the Physical and Chemical Behavior of Solids. (Effect of Pressure on Viscosity, p. 229.) Am. J. of Sci. 35 (4) 205 (1913); 48 pp. JONES, G. C. Ann. Reports on the Progress of Chem. 9, 195 (1913); 1 p. JONES, H. C. & COLLABORATORS. The Freezing-Point Lowering, Conduc- tivity and Viscosity of Solutions of certain Electrolytes in Water. Methyl Alcohol, Ethyl Alcohol, Acetone and Glycerol, Carnegie Publ. 180. Cp. Davis. JONES, H. C. & BINGHAM, E. C. The Conductivity and Viscosity of Solutions of Certain Salts in Mixtures of Acetone with Methyl Alcohol, with Ethyl Alcohol, and Water. Am. Chem. J. 34, 481 (1905); Cp. Bingham. JONES, H. & BINGHAM, E. & McMASTER, L. Cp. Jones and Bingham; and Jones and McMaster. Z. physik. Chem. 67, 193 (1906); 115 pp. JONES, H. & CARROLL, C. A Study of the Conductivities of Certain Elec- trolytes in Water, Methyl and Ethyl Alcohola, and Mixtures of these Solvents Relations between Conductivity and Viscosity. Am. Chem. J. 32, 521 (1904); 63 pp.; Z. physik. Chem. 57, 257 (1906); 63 pp. JONES, H., LINDSAY, C., CARROLL, C., BASSETT, H., BINGHAM, E., ROUILLER, C., MCMASTER, L. & VEAZEY, W. Conductivity and Viscosity of Mixed Solvents. Carnegie Institution of Washington, Publ. 80 (1907), 227 pp. JONES, H. & MAHIN, E. Conductivity and Viscosity of Dilute Solutions of Certain Salts in Water, Methyl Alcohol, Ethyl Alcohol, Acetone, and Binary Mixtures of these Solvents. Am. Chem. J. 36, 325 (1906); 85 pp.; Conductivity and Viscosity of Dilute Solutions of Lithium 386 INDEX Nitrate and Cadmium Iodide in Binary and Ternary Mixtures of Acetone with Methyl Alcohol, Ethyl Alcohol, and Water. Z. Physik. Chem. 69, 389 (1909); 30 pp. Cp. Guy. JONES, H. & VEAZEY, W. 183, Possible Explanation of the Increase in Viscosity when Alcohols are Mixed with Water and of the Negative Viscosity Coefficients of Certain Salts when Dissolved in Water. Am. Chem. J. 37, 405 (1907); 5 pp. JONES, O. G. 6, The Viscosity of Liquids. Phil. Mag. (5) 37, 451 (1894); 12pp. JOHNS. Studien zur Viscositat des menschlichen Blutes beim Gesunden und Kranken. Med. Klinik #28 (1909). KANITZ, L. F. Einige Bermerkungen iiber Coulomb's Verfahren die Coha- sion der Flussigkeiten zu bestimmen. Pogg. Ann. 70, 74 (1847); 4 pp. Cp. Moritz. KAESS. Untersuchungen tiber die Viscositat des Blutes bei Morbus Bosedowi (1913); 17pp. KAGAN, G. Zur Technik der Viskositatsbestimmung. Inaug. Diss. Bern (1911); 24pp. KAHLBAUM, W. Uber die Durchgangsgeschwindigkeit verdiinnter Luft durch Glasrohren verschiedenen Durchmessers. Verhandl. d. Ges. deutscher Naturforscher, Ntirnberg 1893, 56 (1894). KAHLBAUM, G. & RABER, S. Die Konstante der inneren . Reibung des Ricinusols und das Gesetz ihrer Abhang von der Temperatur. Nova Acta, Abhand. Kaiserl. Leop. Carol, deutsch. Akad. Naturf. 84, 203 (1905). Cp. Raber. KAHRS, F. Viscometer. U. S. Pat. 1,062,159, May 20 (1913). KALMUS, H. Electrical Conductivity and Viscosity of Electrolytes. (1906); 54 pp.; Electrical Conductivity and Viscosity of Some Fused Electrolytes. Diss. Zurich (1906); 54 pp. Cp. Lorenz and Kalmus, and Goodwin and Kalmus. KAMMERER. Mitteilung iiber Forschungsarbeiten auf dem Gebiete des Ingenieurwesens. Ver. d. Ingenieure. Heft 132, Berlin Julius Springer (1913). KANITZ, A. 179, tlber die innere Reibung von Salzlosungen und ihren Gemischen. Z. physik. Chem. 22, 336 (1897); 21 pp. KANN, L. tJber die innere Reibung des Broms und dessen Abhangigkeit von der Temperatur. Wien. Sitzungsber. (2A) 106, 431 (1897); 5 pp. KAPFF. Die Reibung von Schmierolen bei hoheren Warmegraden. Kraft, und Licht, Dusseldorf 7, 126 (1901); 2 pp. KAPLAN, V. The Laws of Flow with regard to Fluidity and Friction. Z. Ver. deut. Ing., Sept. 28 (1912). KARIYA, S. Influence of Adrenaline on Viscosity of the Blood in Acute Beriberi. Mitt. Med. Ges. Tokio, 26, #15 Zentr. Biochem. Biophys. 12, 372. VON KARMIAN, T. The Viscosity of Liquids in the State of Turbulent Flow. Physik. Z. 12, 283 (1911); 2 pp. INDEX 387 KARSS, W. Untersuchungen liber die Viscositat des Blutes bei Morbus Basedowi. Diss. Heidelberg (1912); 17 pp. KASSEL, R. Viskositat binarer Fliissigkeitgemischen. Cp. Drucker & Kassel. Diss. Leipzig (1910) ; 50 pp. KATZENELSOHN, N. Diss. Berlin (1867); Wied. Beibl. 12, 307 (1888). KAWALKI, W. (1) Untersuchungen iiber die Diffusionsfahigkeit einiger Electrolyte in Alcohol. Ein Beitrag zur Lehre von der Constitution der Losungen. Wied. Ann. 52, 166 and 300 (1894); 25 pp., 28 pp.; (2) Die Abhangigkeit der Diffusionsfahigkeit von der Anfangsconcen- tration bei verdunnten Losungen. Wied. Am. 69, 637 (1896); 15 pp. KAWAMURA, S. Measurements of Viscosity Particularly Fitted for the Study of the Coagulation Phenomena of Al(OH)s. J. Coll. Science Imp. Univ. of Tokyo, Japan 26, #8 (1908); 29 pp. LORD KELVIN (THOMSON, SIR. W.). 218, 238, (1) On the Elasticity and Viscosity of Metals. Phil. Mag. (4) 30, 63 (1865); 9 pp.; Do., Proc. Roy. Soc. London 14, 289 (1865); 9 pp.; (2) Stability of Fluid Motion. Rectilinear Motion of a Viscous Fluid between two Parallel Planes. Phil. Mag. (5) 24, 188 (1887); 9 pp.; (3) Stability of Motion. Broad River flowing down on Inclined Plane Bed. Do. (5) 24, 272 (1887); 6 pp.; (4) On the Propagation of Laminar Motion through a Turbulently Moving Inviscid Liquid. Phil. Mag. (5) 24, 342 (1887); 12 pp.; (5) On the Stability of Steady and of Periodic Fluid Motion. Phil. Mag. (5) 23, 459 (1887); 6 pp.; (6) On the Stability of Steady and of Periodic Fluid Motion. Phil. Mag. (5) 23, 529 (1887); 11 pp. KENDALL, J. 92, 104, 105, (1) The Viscosity of Binary Mixtures. Medd. K. Vetenskapsakad. Nobelinst. 2, #25, 1 (1913); 16pp.; (2) The Exten- sion of the Dilution Law to Concentrated Solutions. J. Am. Chem. Soc. 36, 1069 (1914); 20pp. KENDALL, J. and BRAKELEY. Compound Formation and Viscosity in Solutions of the Types Acid: Ester, Acid: Ketone and Acid: Acid. J. Am. Chem. Soc. 43, 1826 (1921); 9 pp. KENDALL, J. and MONROE, K. P. (1) Viscosity of Liquids. Viscosity- Composition Curves for Ideal Liquid Mixtures. J. Am. Chem. Soc. 39, 1787 (1917); 15 pp.; (2) Ideal Solutions of Solids in Liquids. Do. 39, 1802 (1917); 4 pp.; (3) Ideality of the System: Benzene-Benzyl Benzoate and the Validity of the Bingham Fluidity Formula. Do. 43, 115 (1921); 11 pp. KENDALL, J. and WRIGHT, A. H. 168, Ideal Mixtures of the Types Ether- Ether and Ester-Ether. J. Am. Chem. Soc. 42, 1776 (1920); 9 pp. KEPPELER, G. & SPANGENBERG, A. Increasing the Plasticity and Binding Power of Clay, Kaolin, etc. U. S. Pat. 1,013,603. KERNOT, G. and POMILIO, U. Cryoscopic and Viscometric Behavior of Some Quinoline Solutions. Rend. Acad. Sci. fis. mat. Napoli 17, 358 (191-); 15pp. KHARICHKOV, K. V. Uber den Einfluss des Wassers auf den Entflammungs- punkt und Viskositat von Mineralschmierol und Naphtaruckstanden. Chem. Ztg. Rep. 376 (1907). 388 INDEX KILLING, C. (1) Eine einfache Methode zur Untersuchung von Butter auf fremde Fette. Z. angew. Chem. 642 (1894); 3 pp.; (2) Do. Chem. Ztg. 22, 78, 100 (1898); (3) Do. Chem. Rev. Fettind. 9, 202 (1902). KING, L. V. Turbulent Flow in Pipes and Channels. Phil. Mag. 31, 322 (1916). KINGSBURY, A. (1) Trans. Am. Soc. M. E. 17, 116 (1895); (2) Experiments with an Air Lubricated Journal. J. Am. Soc. Nav. Eng. 9, #2 (1897); 29pp. KINNISON, C. S. A Study of the Atterberg Plasticity Method. Trans. Am. Ceram. Soc. 16, 472 (1914); 13 pp.; Tech. Paper, TJ. S. Bur. of Standards #46 (1915). KIRCHOF, F. Math. Physik. 26 Vorelesung. Mechanik 2 Aufl. 370 (1877). KIRCHOF, F. The Influence of the Solvent on the Viscosity of India-Rubber Solutions. Kolloid-Z. 15, 30 (1914). KIRKPATRICK, F. A. and ORANGE, W. B. Tests of Clays and Limes by the Bureau of Standards Plasticimeter. J. Am. Ceram. Soc. 1, 170 (1918); 15pp. KOCH, K. R. 35, External Friction in Liquids. Ann. Phys. 35, 613 (1911) ; 4pp. KOCH, S. (1) t)ber die Abhangigkeit der Reibungskonstanten des Queck- silbers von der Temperatur. Wied. Ann. 14, 1 (1881); (2) tJber die Reibungskonstante des Quecksilberdampfes und deren Abhangigkeit von der Temperatur. Wied. Ann. 19, 857 (1883); 15 pp. KLAUDY, J. Werth eines Schmiermittels. Jahresber. der chem. Tech- nologic. 45, 1088 (1899); 2 pp. KLEINHANS, K. The Dependence of the Plasticity of Rock Salt on the Surrounding Medium. Physik. Z. 15, 362 (1914); 1 p. KLEINT, F. Innere Reibung binarer Mischungen zwischen Wasserstoff, Sauerstoff, und Stickstoff. Verh. D. physik. Gesell. 7, 146 (1905). Diss. Halle (1904). KLEMENCIC, I. .(1) Beobachtungen iiber die elastische Nachwirkung am Glase. Carl's Repert. Exp.-physik. 15, 409 (1879); 18 pp.; (2) Beitrag zur Kenntniss der inneren Reibung im Eisen. Carl's Repert. Exp.- physik. 15, 593 (1879); 7 pp.; (3) tlber die Dampfung der Schwingungen fester Korper in Fliissigkeiten. Wien. Sitzungsber. (2A), 84, 146 (1881); 22 pp. KLING. La viscosite" dans ses rapports avec la constitution chimique. Rev. gen. sci. Paris 17, 271 (1906); 6 pp. VAN KLOOSTER, H. S. Normal and Abnormal Cases of Specific Volume of Binary Liquid Mixtures. J. Am. Chem. Soc. 35, 145 (1913); 5 pp. KNIBBS, G. 18, 19, 20, 25, 26, 34, 58, 127, (1) The History, Theory, and Determination of the Viscosity of Water by the Efflux Method. J. Proc. Roy. Soc. N. S. W. 29, 77 (1895); 70 pp.; (2) Note on Recent Determinations of the Viscosity of Water by the Efflux Method. J. Proc. Roy. Soc. N. S. W. 30, 186 (1896); 8 pp. KNIETSCH, R. t)ber die Schwefelsaure und ihre Fabrication nach der Contactverfahren, Ber. 34, 4113 (1901); 2 pp. INDEX 389 KNUDSEN, M. The Law of Molecular Flow and Viscosity of Gases Moving through Tubes. Ann. Physik. (4) 28, 75 (1909); 55 pp.; Polemical. Physic. Rev. 31, 586 (1910;; 2 pp. Cp. Fisher. KNUDSEN, M. & WEBER, S. Luftwiderstand gegen die langsame Bewegung kleinen Kugeln. Ann. Phys. 36, 981 (1911); 14 pp. KOBLER, B. Untersuchungen iiber Viskositat und Oberflaschenspannung der Milch. Diss. Zurich (1908); 72 pp. KOCH, K. R. Uber die aiissere Reibung tropfbarer Fliissigkeiten. Ann. Phys. 36, 613 (1911); 4 pp. KOCH, S. 128, (1) Uber die Abhangigkeit der Reibungskonstanten des Quecksilbers von der Temperatur. Wied. Ann. 14, 1 (1881); (2) Uber die Reibungskonstante des Quecksilberdampfes und deren Abhangigkeit von der Temperatur. Do., 19, 857 (1883). KONIG, W. 6, 34, (1) Bestimmung einiger Reibungscoefficienten und Versuche iiber den Einfluss der Magnetisirung und Elektrisirung auf die Reibung der Flussigkeit. Wied. Ann. 26, 618 (1885); 8 pp.; (2) Uber die Bestimmung von Reibungscoefficienten tropbarer Fliissig- keiten mittelst drehender Schwingungen. Wied. Ann. 32, 193 (1887). KOLLER, H. Uber den elektrischen Widerstand von Isolatoren. Wien. Sitzungsber. (2A) 98, 894 (1889;; 15 pp. KOHL. Viscometer nach Engler mit konstanter Niveau. Z. f. Chem. App.-kunde 3, 342 (1908). KOHLRAUSCH, F. 237, (1) Uber die elastische Nachwirkung bei der Torsion. Pogg. Ann. 119, 337 (1863); 32 pp.; (2) Beitrage zur Kenntniss der elastischen Nachwirkung. Pogg. Ann. 128, 1 (1866); 20 pp.; (3) Do. Pogg. Ann. 128, 207 (1866); 21 pp.; (4) Do., Pogg. Ann. 128, 339 (1866); 21 pp.; (5) Bemerkungen zu Hrn. Neesen's Beobachtungen iiber die elastische Nachwirkung. Pogg. 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Johns Hopkins (1906). MEGGITT. A New Viscometer. J. Soc. Chem. Ind. 21, 106 (1902). MEISSNER, W. 328, (1) The Influence of Errors in the Dimensions of Engler's Viscometer. Chem. Rev. Fett-Harz-Ind. 17, 202 (1909) ; 8 pp. ; (2) Chem. Revue iiber die Fett-Harz-Industrie 17, 202 (1910); 7 pp.; (3) Vergleichende Untersuchungen iiber den Englischen, Redwood' schen, u. Sayboltschen Zahigkeitsmesser. Chem. Rev. Fett-Harz- Ind. 19, 9 (1912); 9 pp.; Book, Vienna (1912); (4) Comparison of the Engler, Redwood, and Saybolt Viscometers. Chem. Rev. Fett-Harz- Ind. 19, 30, 44 (1912); 10 pp.; Petroleum 7, 405; (5) Comparative Examination of Viscometers. Chem. Rev. Fett-Harz-Ind. 21, 28 (1913); 4 pp.; (6) Viscosity of Nitrocellulose. Moniteur Scientifique 79 (1915). MELIS-SCHIRRU, B. Changes in the Viscometric Coefficient of Human Blood Serum after Blood-Letting. Biochem. terap. sper. 4, 49 (1914); 8pp.; Zentr. Biochem. Biophys. 15, 596 (1914). MELLOR, J. W. Clay & Pottery Industries. Griffin & Co., London (1914). MENNERET, M. Oscillatory and Uniform Motion of Liquids in Cylindrical Tubes. J. physique (5) 1, 753 (1912); 13 pp.; Do. 1, 797 (1912); 7pp. MERCANTON, P. L. Simple Lecture Exps. Physik. Z. 13, 85 (1912); 1 p. MERCZYNG, H. H. (1) J. Russ. Phys. Chem. Soc. 21, 29 (1889); (2) Uber die Bewegung von Fliissigkeiten, Wasser und Petroleum in weiten Rohren. Wied. Ann. 39, 312 (1890); 7 pp.; (3) Sur le mouvement des liquides a grande vitesse par conduits tres larges. Compt. rend. 144, 70 (1907); 2 pp. MERRILL, G. P. Non-metallic Minerals. Wiley & Sons, p. 221 (1904). MERRY, E. & TURNER, W. The Viscosities of Some Binary Liquid Mix- tures containing Formamide. J. Chem. Soc. 106, 748 (1914); 1 p. Cp. English. 398 INDEX MERTON, T. R. The Viscosity and Density of Caesium Nitrate Solutions. J. Chem. Soc. London 97, 2460 (1910); 10 pp. MERVEAU, M. J. Recherches sur le Viscosite 1 , Lons le Saunier. 64 (1910); 8pp. DE METZ, G. Rigidite des liquides. Compt. rend. 136, 604 (1903); 3 pp. MEYER, J. & MYI,IUS, B. Viscosity of Binary Liquid Mixtures. Z. Physik. Chem. 95, 349 (1920); 29 pp. MEYER, L. 245, (1) tlber Transpiration von Dampfen. Part I. Wied. Ann. 7, 497 (1879); 39 pp.; for Part II Cp. Meyer and Schumann; for Part III Cp. Steudel; (2) Do. Part IV. Wied. Ann. 16, 394 (1882); 5pp. MEYER, L. & SCHUMANN, O. tlber Transpiration von Dampfen. Part II. Wied. Ann. 13, 1 (1881); 19 pp. MEYER, O. E. 2, 6, 29, 50, 79, 127, 242, 243, 251, (1) tlber die Reibung der Fliissigkeiten. Crelle's J. rein. Angew. Math. 59, 229 (1861); 75 pp.; (2) Do., Pogg. Ann. 113, 55 (1861); 32 pp.; (3) Do., Pogg. Ann. 113, 193 (1861); 46 pp.; (4) Do., Pogg. Ann. 113, 383 (1861); 42 pp.; (5) tlber die innere Reibung der Gase. Part I. Pogg. Ann. 125, 177 (1865); 33 pp.; (6) Do., Pogg. Ann. 125, 401 (1865); 20 pp.; (7) Do., Pogg. Ann. 125, 564 (1865); 36 pp.; (8) tlber die Reibung der Gase. Pogg. Ann. 127, 253 (1866); 29 pp.; (9) Do., Pogg. Ann. 127, 353 (1868); 30 pp.; (10) tlber die innere Reibung der Gase. Part III. Pogg. Ann. 143, 14 (1871); 12 pp.; (11) Do., Part IV. Pogg. Ann. 148, 1 (1873); 44 pp.; (12) Do., Part V. Pogg. Ann. 148, 203 (1873); 33 pp.; (13) Pendelbeobachtungen. Pogg. Ann. 142, 481 (1871); 43 pp.; (14) Theorie der elastische Nachwirkung. Pogg. Ann. 151, 108 (1874); 11 pp.; (15) Hydraulische Untersuchungen. Pogg. Ann. Jubelb. 1 (1874); (6) Bemerkung zu der Abhandlung von Dr. Streintz iiber die Dampfung der Torsionsschwingungen von Drahten. Pogg. Ann. 154, 354 (1875); 7 pp.; (17) Beobachtungen von A. Rosen- cranz iiber den Einfluss der Temperatur auf der innere Reibung von Fliissigkeiten. Wied. Ann. 2, 387 (1877); 20 pp.; (18) tlber die elastis- che Wirkung. Wied. Ann. 4, 249 (1878); 19 pp.; (19) tlber die Bestim- mung der inneren Reibung nach Coulomb's Verfahren. Wied. Ann. 32, 642 (1887); 7 pp.; Sigzungsber. Bayr. Acad. 17, 343 (1887); 21 pp.; (20) Ein Verfahren zur Bestimmung der inneren Reibung von Fliissigkeiten. Wied. Ann. 43, 1 (1891;; 14 pp.; (21) De Gasorum Theoria. Diss. Uratislaviae (1866); 15 pp.; (22) tlber die Bestimmung der Luftreibung aus Schwingungsbeobachtungen. Carl's Repert f. Exper. Physik. 18, 1 (1882); 8 pp.; (23) The Kinetic Theory of Gases. Longman & Co. (1899); 466 pp.; (24) tlber die pendelnde Bewegung einer Kugel unter dem Einflusse der inneren Reibung des ungebenden Mediums. J. f. du reine und ungewandte Math. 73, 1 (1870); 40 pp.; (25) tlber die Bewegung einer Pendelkugel in der Luft. Do., 336 (1872); 12 pp. MEYER, O. & ROSENCRANZ, A. 6, 93, 127, 134. Cp. Meyer, Wied. Ann. 2, 387 (1877). INDEX 399 MEYER, O. & SPRINGMUHL, F. tJber die innere Reibung der Gase. VI. Pogg. Ann. 148, 526 (1873); 30 pp. MEYER, P. Apparatus for determining the viscosity of liquids. Ger. Pat. 244,098, June 16 (1911). MICHAELIS, G. Uber die Theorie der elastischen Nachwirkung. Wied. 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Pt. 44, 505 (1913); 8 pp. MINNEMANN, J. Note on Restoration of Plasticity to Pottery Scrap Clay. Trans. Am. Ceram. Soc. 16, 96 (1914). v. MISES, R. Elemente der Technical Hydrodynamik. Phys. Z. 12, 812 (1911). MOLES, E., MARQUINA, M. & SANTOS, G. Viscosidad y conductibilidad electrica en soluciones concentradas de FeCU. Anales soc. espan. fis. y. quim. 11, Pt. I, 192 (1913). MOLIN, E. (1) Calculation of Degree of Viscosity of Mineral Oil Mixtures. Chem. Ztg. 38, 857 (1914); 2 pp.; (2) Examination of Searle's Method for Determining the Viscosity of very Viscous Liquids. Proc. Cambridge Soc. 1,20,23 (1920); 12pp. MONROE. 105, Cp. Kendall and Monroe. MONSTROV, S. (1) Study of Substances Having Large Coefficients of Viscosity. VI. Determination of some Mechanical Properties of Asphalt. J. Russ. Phys. Chem. Soc. Phys. Pt. 44, 492 (1913); 10 pp.; (2) VII. Supplement to the Article by S. I. Monstrov. Do., 44, 503, B. P. Veinberg (1913); 1 p.; (3) VIII. Viscosity of Asphalt. 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The Displacements of Particles and Their Paths in some Cases of Two Dimensional Motion of a Frictional Liquid. Proc. Roy. Soc. London (A) 89, 106 (1913); 19 pp. MORUZZI, G. The Effect of Area on the Viscosity and Conductivity of Protein Solutions. Biochem. Z. 28, 97 (1911); 9 pp.; Do., 22, 232 (1909). MOSELEY, H. (1) On the Uniform Flow of a Liquid. Phil. Mag. (4) 41, 394 (1871); 3 pp.; (2) On the Steady Flow of a Liquid. Phil. Mag. (4) 42, 184 (1871); 14 pp.; (3) Do., Phil. Mag. (4) 42, 349 (1871); 13 pp.; (4) Do., Phil. Mag. (4) 44, 30 (1872); 27 pp. MUCHIN, G. Fluidity Measurements of Solutions. Z. Elektrochem. 19 819 (1914); 2pp. MUELLER. Romberg Deutsch Med. Woch. 48 (1904). MUNZER, E. & BLOCH, F. (1) Die Bestimmung der Viskositat des Blutes mittels der Apparate von Determann und Hess nebst Beschreibung eines eigenen Viskosimeters. Z. exp. Path. Ther. 11, 294 (1913); Med. Klinik, #9, #10, #11 (1909); (2) Experimentelle Beitrage zur Kritik der Viskositatsbestimmungsmethoden. 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(G) 2, 342 (1901); (2) tlber die temporare Doppelbrechung des Lichtes in bewegten reibenden Fliissigkeiten. Z. physik. Chem. 39, 355 (1902); 9 pp.; (3) Uber die Fortpflanzung einer kleinen Bewegung in einer Flussigkeit mit innerer Reibung. Z. physik. Chem. 40, 581 (1902); 16 pp.; (4) tJber die Dissi- pationsfunction einer zahen Flussigkeit. Z. physik. Chem. 43, 179 (1903); 6 pp.; (5) tlber die Deformation einer plastisch-viskosen Scheibe. Z. physik. Chem. 43, 185 (1903); 18 pp.; (6) t)ber einige von Herrn B. Weinstein zu meiner Theorie der inneren Reibung gemachte Bemerkungen. Physik. Z. 4, 541 (1903); 2 pp.; Cp. Bull. Int. Acad. Scienc. de Cracovie 95, 161 (1901); Do. 19, 488, 494 (1902); Do., 268, 283 (1903); Also Krakauer Anz., 95 (1901); Do., 488 (1902); Do., 268, 283 (1903). NAVIER. 1, 29, (1) Mmoire sur les lois du mouvement des fluides. Mem. de 1'Acad. roy. des Sciences de Finst. de France 6, 389 (1823); 52 pp.; (2) McSmoire sur l'6coulement des fluides elastiques dans les vases et les tuyaux de conduit. M6m. de 1'Acad. roy. des Sciences de 1'Inst. de France 9, 311 (1830); 68 pp. NAYLOR, R. B. Testing Device for Determining the Viscosity of Rubber. U. S. Pat. 1,327,838, Jan. 13 (1920). NEESEN, F. (1) Beitrag zur Kenntniss der elastischen Nachwirkung bei Torsion. Pogg. Ann. 163, 498 (1874); 27 pp.; (2) tlber elastische Nachwirkung. Pogg. Ann. 167, 579 (1876); 17 pp.; (3) Monatsber. d. Kgl. Preuss. Acad d. Wissens. (1874); Feb. NENSBRUGGHE, G. VAN DER. Superficial Viscosity of Films of Solutions of Saponine. Bull. sci. acad. roy. belg. 29, 368 (1870). NETTEL, R. Eine neue Viscositatsbestimmung fur helle Mineralole. Chem. Ztg. 29, 385 (1905); 2 pp. NEUFELD, M. W. Influence of a Magnetic Field on the Velocity of Flow of Anistropic Liquids from Capillaries. Diss. Danzig. (1913); Physik. Z. 14, 646 (1912); 4 pp. Cp. Kruger. NEUMANN, F. 2, 14, 17, (1) Vorlesungen iiber die Theorie der Elasticitat der Festen Korper und des Lichtathers. Leipzig. Teubner (1885); 374 pp. ; (2) Einleitung in die theoretische Physik. Herausgegeben von C. Pape. Leipsig. Teubner (1883); 291 pp. NEVITT, H. G. Chart of Viscosities in Different Systems. Chem. Met. Eng. 22, 1171 (1920). NEWTON, I. 1, The Mathematical Principals of Natural Philosophy (1729). Of the Motion of Bodies. Vol. 2. Of the Motions of Fluids and the Resistance Made to Projected Bodies. Section VII. NEWTON, J. F. and WILLIAMS, F. N. Testing Illuminating Oils. Petro- leum Age 6, 81 (1919); 3 pp. NICOLARDOT, P. & BAUME, G. A Contribution to the Study of the Viscosity of Lubricating Oils. Chimie & Industrie 1, 265 (1918;; 6 pp. NICOLARDOT, P. and MASSON, P. J. Dubrisay's Method of Examining lubricating Oils. Ann. fals. II, 77 (1918); 2 pp.; Analyst 43, 276 (1918); NICOLLS, W. Hsemodynamics. J. of Physiology 20, 407 (1896). 26 402 INDEX NISHIDA, H. 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Soc. 34, 454 (1912); 31 pp. NOYES, A. & GOODWIN, H. The Viscosity of Mercury Vapor. Physic. Rev. 4, 207 (1896); 10 pp.; Z. physik. Chem. 21, 671 (1896); 9 pp. NUTTING, P. G. A New General Law of Deformation. J. Franklin Inst. 191, 679 (1921); 8 pp.; Proc. Am. Soc. Testing Materials (1921). OBERBECK, A. 6, Uber die Reibung in freien Flitssighkeitsoberflachen. Wied. Ann. 11, 634 (1880); 19 pp. v. OBERMAYER, A. 246, (1) tJber die Abhangigkeit des Reibungscoefficienten der atmospharischen Luft von der Temperatur. Wien. Sitzungsber. (2A) 71, 281 (1875); 28 pp.; Carl's Repert. Exp.-physik. 12, 13 (1876); 26 pp.; (2) tlber die Abhangigkeit des Coefficienten der inneren Reibung der Gase von der Temperatur. Wien. Sitzungsber. (2 A) 73, 433 (1876); 42 pp.; Carl's Repert. Exp.-physik. 12, 465 (1876); 1 p.; (3) Ein Beitrag zur Kenntniss der zahfliissigen Korper. Wien. Sitz- ungsber. (2A) 75, 665 (1977); 14 pp.; (4) Das absolute Maas fur die Zahigkeit der Fliissigkeiten. Carl's Repert. Exp.-physik. 15, 682 (1879); 5 pp.; (5) Uber die innere Reibung der Gase. Carl's Repert. Exp.-physik. 13, 130 (1877); 29 pp. Cp. Wien. Anz. 90 (1877). ODEN, S. 203, Physikalisch-chemische Eigenschaften der Schwefel- hydrosole. Z. physik. Chem. 80, 709 (1912); 38 pp. OEHM. Einige Versuche liber Gummilosung als Nahrfltissigkeit fur Frosch- herz. Arch. exp. Path. Pharm. 34, 29 (1904). OEHOLM, L. W. 189, (1) Free Diffusion of Non-Electrolytes the Hydro- Diffusion of some Organic Substances. Medd. K. Vetenskapakad. Nobel. Inst. 2, No. 23, 52 pp.; (2) Investigation of the Diffusion of some Organic Substances in Ethyl Alcohol. Do. No. 24, 34 pp.; (3) The Dependence of the Diffusion on the Viscosity of the Solvent. Do. No. 26, 21 pp. OELSCHLAGER, E. The Viscosity of Lubricating Oils. Z. Ver. deut. Ing. 62, 422 (1918); 6pp. INDEX 403 OERTEL, E. tjbcr die Viscositiit der Milch. Diss. Leipzig. (1908); 47 pp. OERTEL, F. Eine Abanderung der Poiseuilleschen Methode zur Unter- suchung der inneren Reibung in stark verdtinnten wasserigen Salz- losungen. Diss. Breslau (1903); 48 pp. OHOLM, L. W. (1) Innere Reibung von wasserigen Losungen einiger Nichtelektrolyten iiber die Reinigung des hierbei angewandte Wassers. Oversight. Finska Vetenskaps soc., Forhandlingar 47, 1 (1904;; 18 pp.; (2) The Influence of Non-Electrolytes on the Diffusion of Electrolytes and on the Electric Conductivity, also a Study of the Viscosities of Solu- tions of those Substances. Oversigt. Finska Vetenskaps. soc., For- handlingar 65, afd. A., #5 (1913); 99 pp. Cp. Akad. afh. Helsing- fors (1902). OFFERMANN. Viscosity Determinations of Small Quantities of Oil in Engler's Viscometer. Chem. Rev. Fett.-Hartz-Ind. 18, 272 (1911); 3pp. ONFRAY & BALADOINE. Viscosity of the Blood and Hemorrhage of the Eye. Soc. ophth. Paris, Dec. 5 (1911); Klin. Monatsbl. Augenheilk. 13, 242. ONNES, KAMERLINGH. 131, (1) The Coefficients of Viscosity for Fluids in Corresponding States. Communications from the Laboratory of Physics at the Univ. of Leyden #2; (2) Arch. Ne<5rl. 30, 134 (1897); also Enzykl. d. mathem. Wisenschaften V. 10, 699. ONNES, K., DORSMAN & WEBER, S. The Internal friction of gases at low temps. I. Hydrogen, II. Helium. Verslag. K. Akad. Wetenschappen 1375 (1913); 10 pp. ORR. Proc. Roy. Irish Acad. 27A, #2 & 3 (1907). ORTH, P. Viscosity of Saccharin Solutions. Bull, assoc. chim. sue. dist. 29, 137 (1911); 11 pp. ORTLOFF, W. Uber die Reibungskoefficienten der drei Gasen Aethan (C 2 H 6 ), Aethylen (C 2 H 4 ), Acetylen (C 2 H 2 ). Diss. Jena (1895). ORTON, E. (1) Keram. Rundschaw (1901); (2) The plasticity of clay. Brick 14, 216 (1901); 4 pp. OSEEN, C. (1) Zur Theorie der Bewegung einer reibenden Fliissigkeit. Arkiv. for Mat. Astron. och Fys. 3, 84 (1907); (2) Do., Arkiv. Mat. Astron. Fysik. 4, 1 (1908); #9, 23 pp. OSMOND, F. Sprodigkeit & Plastizitat. 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Ann. 4, 232 (1878); 17 pp.; (5) Uber die Torsion. Wied. Ann. 10, 13 (1880); 22 pp.; (6) Magnetische Untersuchungen. I. tlber einige Wirkungen der Coercitivkraft. Wied. Ann. 13, 141 (1881); 24 pp. WARBURG, E. and BABO, L. VON. 138, 244, (1) tJber eine Methode zur Untersuchung der gleitenden Reibung fester Korper. Wied. Ann. 2, 406 (1877); 12 pp.; (2) tlber den Zusammenhang zwischen Viscositat und Dichtigkeit bei fliissigen inbesonders bei gasformig fltissigen Kor- pern. Wied. Ann. 17, 390 (1882); 37 pp.; Cp. Ber. liber Verhand- lungen der naturforschenden Gesellschaft zu Freiburg 8, 1 (1862); 44pp. WARBURG, E. and SACHS, J. 138, 140, t)ber den Einfluss der Dichtigkeit auf die Viscositat tropf barer Fliissigkeiten. Diss. Freiburg; Wied. Ann. 22, 518 (1884); 5 pp. WASHBURN, E. W. 196, 197, (1) The Laws of "Concentrated" Solutions: II. The Estimation of the Degree of lonization of Electrolytes in Moderately Concentrated Solutions. J. Am. Chem. Soc. 33, 1461 (1911); 18 pp.; Cp. Tech. Quarterly 21, 2023 (1908); (2) A Factory Method for Measuring the Viscosity of Pot-Made Glass during the 426 INDEX Process of Manufacture, together with Some Discuss on of the Value of Viscosity Data to the Manufacturer. J. Am. Ceram. Soc. 3, 735 (1920); 15 pp.; (3) Physical Chemistry, 2d. ed., McGraw-Hill Book Co. WASHBURN, E. W. & MAC!MES, D. A. The Laws of "Concentrated" Solutions. III. The lonization and Hydration Relations of Elec- trolytes in Aqueous Solution at 0C. J. Am. Chem. Soc. 33, 1687 (1911); 28 pp. WASHBURN, E. W. & WILLIAMS, G. Y. (1) Precision Viscometer for Measurement of Relative Viscosity and the Relative Viscosities of Water at 0, 18, 25, and 50. J. Am. Chem. Soc. 35, 737 (1913); 33 pp.; (2) The Viscosities and Conductivities of Aqueous Solutions of Raffinose. J. Am. Chem. Soc. 36, 750 (1913); 4 pp. WATSON, F. 7, 256, Viscosity of Liquids as determined by measurement of Capillary Waves. Physic. Rev. 16, 20 (1902); 19 pp. WAY, J. T. On the Power of Soils to absorb Manure. Roy. Agric. Soc. J. 11 (1850); 66 pp. WEBB, J. The Viscous Dynamometer. Science (N. S.) 16, 338 (1902); 2 pp. WEBER, F. (1) Plasma Viscosity of Plant Cells. Z. allegemein Physiol. 97, 1 (1918); 20 pp.; (2) Viscometry of Living Protoplasm. Kolloid- Z. 20, 169 (1917); 4pp. WEBER, W. 237, (1) Vorlesung de fili bombycini vi elastica. Gotting. Gelehrt. Anz., St. 8, 65 (1835); 12 pp.; (2) Uber die Elasticity der Seidenfaden. Pogg. Ann. 34, 247 (1835); 11 pp.; (3) Pogg. Ann. 34, 1 (1841); Cp. Comm. Soc. Gottingen 3, 45 (1841). WEINBERG. Cp. Veinberg. WEINSTEIN, M. B. The Internal Friction of Gases. I. The First Coeffi- cient of Friction. Ann. Physik. 50, 601 (1916); 53 pp.; Do., II. The Second Coefficient of Friction, the Thermodynamic-Hydrodynamic Equations of G. Kirchhoff, and Maxwell's Gas Theory. Do., 60. 796 (1916); 18pp. WEISBACH. 18, Lehrbuch der Ingenieur und Machinenmechanik. Experi- mental hydraulik, 3d. Ed. 1, 736. WELLS, H. M. and SOUTH COMBE, J. E. Theory and Practice of Lubrication: "Germ" Process. J. Soc. Chem. Ind. 39, 51 (1920); 9 pp.; Cp. South- combe Petroleum Times 3, 173, 201 (1920); 4 pp. WELSH, W. N. Viscosity of the Blood. Heart 3, 112 (1912); 19 pp. WENDRINER, M. Ein einf aches Viscosimeter. Z. f. angew Ch. 545 (1894); 2pp. WENDT, P. Reply to Ubbelohdes's Article "The Theory of the Friction of Lubricated Machine Parts." Petroleum 8, 678 (1913); 8 pp. WERIGIN, N., Lewkojeff, J., and TAMMANN, G. 236, tJber die Ausfluss- geschwindigkeit einiger Metalle. Ann. Physik. (4) 10, 647 (1903); 8 pp. Cp. Tammann. WEST, G. D. The Resistance to the Motion of a Thread of Mercury in a Glass Tube. Proc. Roy. Soc. London (A) 86, 25 (1910); 11 pp. INDEX 427 WETZSTEIN, G. 68, tTber Abweichungen von Poiseuilleschen Gesetz. Diss. Munchen (1899); Wied. Ann. 68, 441 (1899); 30 pp. DE WHALLET, H. C. and SIEGFRIED. A Gravimetric Method of Comparing Viscosities of Varnish, etc. Analyst 44, 288 (1919) ; 1 p. WHEELER. Clay Deposits. Chap. V. Plasticity of Clay. Mo. Geol. Survey 11, 97 (1896); 17 pp. WHETHAM, W. 31, 32, 213, (1) On the Alleged Slipping at the Boundary of a Liquid in Motion. Proc. Roy. Soc. London 48, 225 (1890); (2) On the Velocity of Ions. Phil. Trans. (A) 186, 507 (1896); 16 pp. WHITE, G. F. 97, 104, (1) Study of the Viscosity of Fish Oils. J. Ind. Eng. Chem. 4, 106 (1912); 4 pp.; (2) Fluidity of Fish Oils as an Additive Property. Do. 4, 267 (1912); 3 pp.; (3) Ein Neues Viscosimeter und seine Anwendung auf Dlut und Blutserum. Biochem. Z. 37, 482 (1911); 7 pp.; Cp. Bingham. WHITE, G. F. & THOMAS, A. Studies on Fish Oils. III. Properties of Fish and Vegetable Oil Mixtures. J. Ind. and Eng. Chem. 4, 878 (1912); 5 pp. WHITE, G. F. & Twixnra, R. H. (1) The Fluidity of Butter Fat and its Substitutes. J. Ind. Eng. Chem. 6, .568 (1913) ; 5 pp. ; (2) The Viscosity of Undercooled Water as Measured in a New Viscosimeter. Am. Chem. J. 60, 380 (1913); 9 pp. WEECHERT, E. 237, tTber elastische Nachwirkung. Diss. Konigsberg (1889); 64 pp. WIEDEMANX, E. 79, 246, (1) Arch. sci. phys. nat. 66, 273 (1876) ; (2) tlber die Beziehung zwischen dem Reibungs und Leitungs-widerstand der Losungen von Salzen in verschiedenen Losungsmitteln. Wied. Ann. 20,537 (1883); 2 pp. WIEDEMAXN, G. & VERDET. 2, 6, 192, Mmoire sur le mouvement des liquides qui s'observe dans le circuit de la pile voltaique et au les rela- tions de ce mouvement avec 1'electrolyse. Ann. de chim. et. de phys. (3) 62, 224 (1858); 30 pp.; Extraits par Verdet Pogg. Ann. 99, 77 (1856). WLTKANDEB. 81, 92, Lunds Physiogr. Sallsk. Jubelskr. Lund (1878); Wied. Beibl. 3, 8 (1879). WILBERFORCE, L. 17, On the Calculation of the Coefficient of Viscosity of a Liquid from its Rate of Flow through a Capillary Tube. PhiL Mag. (5, 31, 407 (1891); 8 pp. WILKIXS. Elektrotechn. Zeitschr. 26, 135 (1904). WILLERS, F. Viscosity Anomalies of Emulsions in the Conditions of Turbulent Flow. Physik. Z. 10, 244 (1908); 4 pp. WILSOX, H. A. 7, 190, 191, On the Velocity of Solidification of Super- cooled Liquids. Proc. Camb. PhiL Soc. 10, I, 25; Phil. Mag. 60, 238 (1900); 13pp. WI.NKELMA.VN. Handbuch der Physik. 578-582 (1891). Cp. Graetz & Jager. WINKLER, L. Gesetzmassigkeit bei der Absorption der Gase in Flussig- keiten. Z. physik. Chem. 66, 171 (1992); 13 pp.; Cp. 2. physik. Chem. 10, 144 (1892); (2) Do., Z. physik. Chem. 66, 344 (1906); 11 pp. 428 INDEX WOLFF, H. (1) The Determination of the Viscosity of Varnishes. Farben. Ztg. 17,2108; (2) Beitrag zurKenntniss der Leitf ahigkeiten gemischter Losungen von Elektrolyten. Z. physik. Chem. 40, 222 (1902); 34pp. WOUDSTRA, H. 205, Uber die innere Reibung kolloidaler Silberlosungen Z. physik. Chem. 63, 619 (1908); 4 pp.; Cp. Chem. Weekblad 6. 303, 602; (2) The Degree of Dispersion and Viscosity. Z. Chem. Ind. Kolloide 8, 73 (1911); 8 pp.; (3) The Viscosity and Coagulation of Caoutchouc Solutions. Z. Chem. Ind. Kolloide 6, 31 (1909); 2 pp.; (4) Kolloid.-Z. 8, 73 (1911). WRIGHT. 105. C. Kendall and Wright. WROBLEWSKI, S. VON. (1) tlber die Abhangigkeit der Constante der Verbreitung der Gase in einer Fltissigkeit von der Zahigkeit der letztern. Wied. Ann. 7, 11 (1879); 13 pp.; (2) tJber die Natur der Absorption der Gase. Wied. Ann. 8, 29 (1879); 24 pp. WULLNER. Lehrbuch der Experimental physik. 4th Ed., 259 (1882). YEN, KIA-LOK. An Absolute Determination of the Coefficients of Viscosity of Hydrogen, Nitrogen, and Oxygen. Phil. Mag. 38, 582 (1919); 16 pp. ZAHM, A. Atmospheric Friction on Even Surfaces. Phil. Mag. (6) 8, 58 (1904); 9 pp. ZAKRZEWSKTEGO, K. O oscylacyi krazka w plynie lepkin. Rozprawy Akademii (A) 42, 392 (1902); 7 pp. ZANDA, G. B. 286, (1) Viscosity of the Blood During the Absorption of Glucose. Arch. Ital. Biol. 62, 79 (1910); 4 pp.; Zentr. Biochem. Bio- phys. 10, 1006; (2) Azione dei farmaci sulla digestione pepsinica dal punto di vista fisico-chimico. Giornale della R. Ace. di. Torino 10, #7 and 8 (68). ZAREMBA, S. Krakauer Anz. 380, 403 (1903); Rozpr. Akad. (A) 43, 14 (1904); 7 pp.; Krakauer Anz. 86 (1903); 8 pp. ZEMPLEN, G. (1) Bestimmung des Koefficienten der inneren Reibung der Gase nach einer neuen experimentalen Methode. Ann. Physik. (4) 19, 783 (1906); 23 pp.; (2) Do., Ann. Physik. (4) 29, 869 (1909); 39 pp.; Cp. Math, natro. Ber. Ungarn 19, 74 (1904;; 7 pp. and Math. Termt. Ert. Budapest 23, 561 (1905); (3) Investigations on the Vis- cosity of Gases. Ann. physik. 38, 71 (1912;; 54 pp. ZERI, A. (1) La viscosita della bile umana. Arch, di farmac. speriment. e scienze affini 4, 279 (1905); (2) Un Nuovo carattere differenziale tra essudati e trasudati. II Politecnico. Sezione pratica 12, 1373 (1905). ZEUNER. 18, Civilingenieur 1, 84. ZIMMER, O. (1) The Viscosity of Ethylene and Carbon Monoxide and its Changes at Low Temperatures. Ber. deut. physik. Ges. 471 (1912). ZOJA, L. Physikalisch-chemische Untersuchung der Reaktionen zwischen Eiereiweiss und Essigsaure. Roll. Z. 3, 249, 269 (1908) ; 20 pp. INDEX 429 ZOLLEK, H. F. (1) The Viscosity of Casein Solution. I. The Effect of P//. Science 60, 49 (1919); (2) Casein Viscosity studies. J. Gen. Physiol. 3,635 (1921); 16pp. ZSCHOKKE, B. (1) Untersuchungen tiber die Plastizitat der Thone. Bull. Soc. d'Encouragement d'Industrie Nationale 103, 619 (1902); 40 pp.; (2) Untersuchungen tiber die Bildsamkeit der Thone. Baummaterial- ienkunde 7, 377, 393 (1902); 7 pp.; (3) Untersuchungen iiber die Plas- ticitat der Thone. Do., #1, 2, 3, 4, 5, 6 (1903); 18 pp. ZUR NEDDEN, F. Induced Currents of Fluids. Proc. Am. Soc. Civ. Engi- neers 41, 1351 (1915); 54 pp. SUBJECT INDEX Decimals indicate the location of reference on the page. Two or more references on the same page are indicated by a + sign. Absorption 235, 259, 427.9, 428.3 Acetic anhydride, 410.7 acid, 402.2 Acetylene, 403.6 Acids, aliphatic, 115 Additivity of fluidities, 82, 83, 104, 412.8 Adhesion, 31, 221, 230, 257, 261, 268, 274 Adsorption, 378.9, 394.2 Adulteration, 370.4 Air, 361.5, 369.2, 373.5+, 374.2, 376.1, 382.5+, 383.1, 386.4, 396.1, 399.4, 402.6, 407.9, 409.1, 410.1, 414.3, 415.2, 421.6 Albumen, 404.6, 416.4, 419.1, 428.9 Alcohols, 116, 177, 349.7 Alloys, 349.4, 361.6, 424.9 Aluminium hydroxide, 372.1, 387.2 oleate in oil, 406.8 Amalgams, 415.4 Amides, 370.1 Amines, 366.5, 368.1, 371.3, 420.7 Ammonia, 371.3 Ammonium iodide, 186 nitrate, 180, 356.2, 374.6 thiocyanate, 374.6 Aniline, 416.2 + Anisotropic liquids, 96, 209, 356.4, 359.6, 367.7, 390.4, 392.7, 401.6, 405.8, 407.7, 413.5 Annealing, 212 Antifriction metals, 278 Antimony chloride, 391.2 Antipyrine solutions, 414.9 Argon, 364.5, 389.8, 408.7, 409.3 +, 413.7, 414.8, 420.2 Asphalt, 365.3, 399.5+, 410.5, 423.9 -base oils vs. paraffin-base oils, 274 Association, 92, 112, 119, 161, 184, 378.1, 415.7, 420.6 Atomic constants, 108, 111, 126, 144, 186, 196 diameters, 253 weights and v. of gases, 250 Avogadro's constant, 253 B Barium sulphate, 349.8 Bath, 307 Beater-stock, 360.1 Belting, 283 Bent capillaries, 376.6 Benzene, 354.6, 366.3, 381.8 Benzyl benzoate, 354.6 Bile, 359.8, 428.8 Binders, sticking strength of, 347.2 Biology, 284 Blood, 284, 348.1, 349.3, 350.5, 352.6+, 353.1, 355.6+, 356.9, 359.3+, 360.2 + , 361.8, 362.3+, 363.9, 364.1, 365. 1+, 367.8, 368.4+, 369.4+, 370.6 +, 372. 1+, 374.3, 375.2, 376.9, 379.1, 380.8, 381.6, 382.4, 383.2+, 385.1, 386.2+, 387.1, 389.9. 390.5, 392.2, 393.1 +. 394.6+, 397.1, 400.5, 403.4, 404.7, 405.7, 406.3+, 409.9, 411.6, 412.6, 413.4, 414.8, 421.5, 422.6 + , 423.4, 426.3+, 427.3, 428.6 431 432 INDEX "Body," 269 Body fluids, 417.3 Boiling-point, 155 Brittleness, 403.7 Bromides, 114 Bromine, 386.8, 408.8 Brownian movement, 188, 190, 358.7, 415.5 Bunsen flame, 352.8 Butter, 281, 388.1, 427.4 Cadmium and zinc alloys, 424.9 iodide, 386.1 Caesium nitrate, 398.1 Calcium chloride, 416.4 Calculation of fluidity, 314 of plasticity, 323 Caoutchouc, cp. rubber. Capillarity, 56, 70, 361.5, 370.8, 406.1, 414.1, cp. surface tension. Capillary tube method for plas- ticity, 222 Carbon black, 405.2 dioxide, 146, 383.2, 405.6, 408.1 monoxide, 428.9 tetrachloride and benzene, 167 Carbonyl sulphide, 359.4 Casein, 361.4, 419.1, 429.1 Castor oil, 363.7, 386.5, 408.4 Celluloid, 348.3, 415.2 Cellulose acetate, 351.1, 402.3 esters, 351.2, 360.3, 365.2, 373.7, 403.7, 417.9, cp. nitro- cellulose. Cements, 424.6 Centipoise, 61 Ceramics, 286 Chart for conversion, 401.7 Chemical composition, 106, 112, 172, 249, 375.1, 387.6, 390.3, 407.4, 409.9, 422.7 Chloral solutions, 391.1 Chlorides, 381.3 Chlorine, 122, 144, 408.8 Chloroform and ether, 175, 364.4 Chromium salt solutions, 370.7, 374.9, 416.8 Clay, 221, 229, 281, 349.9, 355.3, 376.5, 388.4, 391.7, 397.7, 399.5, 403.6, 408.1, 410.6, 411.9, 415.4+, 416.5, 418.9, 429.1 Close-packing, 228, 229 Cloud method, 399.4 Coagulation, 284, 371.9, 387.2, 396.8, 411.6, 428.2 Cohesion, 148, 212, 386.3, 400.1, 415.3 Cold working, 211 Collisions, 149, 200 Collisional viscosity, 147, 151 Colloidal solutions, 3, 198, 348.5, 351.8, 353.7, 360.6, 364.2, 369.1, 371.8, 372.7, 374. 1+, 377.2, 378.8, 379.5, 380.7, 381.4, 392.9+, 393.2+, 403.9, 411.6+, 412.8, 413.8, 414.6, 417.2, 421.6, 428.1 Colloidoscope, 198 Colophonium, 52 Color of solutions, 416.3, cp, chromium. Comparable ^temperatures, 115, 410.4 * Compressible fluids, 49 Conductivity, electrical, 191, 192, 193, 194, 349.1, 349.4 + * 353.7, 357.2, 360.6, 364.7, 367.2+, 368.1, 371.2 + , 374.6, 375.6, 376.3+, 377.4, 379.7, 382.9, 383.4, 386.6, 389.7, 390.1, 392.7+, 394.3+, 396.3+, 399.6, 402.3, 403.2, 405.9, 406.1, 412.1, 414.1, 415.4, 416.3, 417.1, 418.5, 423.8, 424.7, 425.1 +,427.5 thermal, 252, 358.7, 360.8, 368.7, 380.3, 390.8, 406.7 Conjugate double bonds, 111 INDEX 433 Consistency, 235, 361.8 Constants of viscometer, 296, 313 Constitution, chemical, 121, 352.1, 354.9, 358.8, 359.1, 367.1, 366.4+, 372.8, 382.1, 388.8, 390.7, 405.1, 407.5, 413.4 Construction of viscometer, 315 Corresponding states, 403.4 Cream, 365.9 Criterion of Reynolds, 40 Critical-solution temperature, 94, 102, 364.8, 372.1 Critical state, 365.4, 419.1, 422.7 velocity of flow, 361.9 Crystalline liquids, 96 ; 208, cp. anis- otropic liquids. Crystallization, 190, 371.8, 372.2, 375.9, 379.3, 420.2 Cutting fluids, 269, 272, 348.5, 354.3, 420.3, 425.1 Curcas oil, 348.9 Curved pipes, 368.9 Deflocculation, 208, 229, 231 Demonstration of Maxwell's Law, 406.2, cp. lecture demon- strations. Density determination, 309 tables, water, 309; mercury, 311 and v., 412.5, 425.5 + Dextrine, 280, 381.1 Diastase, 347.3 Dielectrics, 350.4, 381.5 Diet, effect on v. of blood, 285 Diffusion, 188, 189, 214, 252, 360.8, 380.8, 387.2, 390.6, 402.8, 405.9, 419.9, 421.4 Diffusional v., 147, 150, 242 Disk method of v. measurement, 86 Displacement of particles, 400.3 Dissipation function, 401.1 Dissociation, 9, 161, 169, 184, 187, 195, 413.9 Double-bond, 118 Dough, 380.5 Drainage, 66 Dynamical theory, 396.6, 410.3 E Eddies, 14, 39, 42 Effusion, 241 Elastic after-effect, 237, 355.9, 358.2 388.7, 389.5+, 390.9, 392.5, 398.5, 399.2, 401.5, 406.2, 408.5, 414.6, 425.6, 427.5 deformation, 4, 212, 217, 218, 350.2, 353.4, 357.1, 361.7, 365.5, 369.8, 375.4, 387.3, 400.9, 401.7, 412.9, 421.5, 424.9 limit, 211, 237 Electric field, v. in an, 34, 368.6, 404.4, 408.3, 413.3, 415.6 Electronic charge and Stoke's Law, 411.8, 421.1 Electroosmosis, 371.9 Emulsions, 83, 89, 94, 100, 102, 210, 350.8, 354.8, 356.4, 367.9, 396.1,405.8,410.8 End correction, 21, et seq., 315, 353.2 Engine grease, 211 Enzyme reactions, 347.4 Ethane, 403.6 Ethers, 113, 364.4, 374.1, 381.8, 407.1 Ether-alcohol mixtures, 350.7 Ethyl acetate, 366.3 alcohol, 361.2, 366.3, 425.1 water mixtures, 341 Ethylene, 403.6, 428.9 Expansion, thermal, 65, 363.5 External friction, 372.4, 376.2, 388.4, 389.2 Eye fluids, 360.5, 393.7, 396.5 Falling sphere, cp. sphere. Ferric hydroxide, 407.3 434 INDEX Filling viscometer, 310, 312 Films as plastic substances, 255 Fineness of grain, 235 First regime, 39 Flashing, 39 Flotation, 361.7 Flour, 394.4 + Flow through orifices, 233, 234, cp. hydraulics, in thin films, 380.2 of metals, 235, 236 theory, 365.2, 403.7, 411.3, 418.6, 419.3, 423.7, 427.7 Fluid defined, 215 Fluidity definition, 5, 364.9 table for reference, 318 in a magnetic field, cp. magnetism, in an electrostatic field, cp. electric field. Foam, 211, 229, 409.4 Formamide, 368.5, 397.9 Free volume, 142 Friction, cp. yield value, 238, 262, 280, 392.3, 415.9, 428.5 Fused salts, 193, 371.7, 374.5, 386.6, 394.1, 406.4 Gases, 241, 242, 351.4, 355.9, 358.4, 360.9, 361. 1+, 362.6, 367.3 + , 368. 1 + , 371.1, 374.9, 377.4, 384.9, 385.3, 388.6, 389.1, 392.2, 398.3, 403.5, 404.2, 410.8, 414.3, 419.8, 420.6+, 422.1, 424.5 + , 426.6, 428.7 Gasoline, 380.9 Gelatine, 198, 212, 280, 289, 349.1, 352.4, 355.7, 375.8, 380.8, 384.6, 392.9, 393.6, 394.3, 400.2, 412.8, 414.5, 415.9, 419.1 Geophysics, 287 Glass, 286, 377.9, 384.7, 392.6, 418.1, 424.6, 425.9 Glue, 280, 355.7, 370.4 Gluten, 280, 419.1 Glycerol, 358.9, 413.3, 414.1 + Gold value, 393.2 Graphite, 229 Greases, 281, 361.8, 395.3 Gums, 419.' Haemodynamics, 401.9 Halogens, 250 Hardness, 3, 235, 391.4 Heat of vaporization and v., 372.9 of fusion, 378.2 Hemoglobin, 356.8 Helium, 364.5, 403.5, 409.3, 413.7, 414.8, 420.2 Heptane as a standard for vapor pressure comparisons, 157, Hexamethylene, 277 High temperature v., 349.1, 370.1 Homogenizing, 211, 281. Hydrate theory, 354.8 Hydraulic flow and plastic state, 231 Hydraulics, cp. also turbulence, 365.1, 369.9, 371.6, 372.3, 380.6, 394.2, 395.3+, 398.5, 400.1, 407.7 + , 408.9, 412.2, 417.4, 421.4 Hydrocarbons, 113, 351.3, 372.8 Hydrocellulose, 353.2 Hydrodynamics, 1, 212, 351.9, 353.6, 356.6, 358.1, 362.9, 368.8, 369.1, 373.9, 391.9+, 394.1, 395.9, 399.5, 401.3, 401.8, 406.7, 410.3, 415.9, 418.3+, 424.3, 426.6 Hydrogen, 353.5, 376.8, 389.8, 395.9, 403.5, 408.1, 409.3, 424.5, 428.4 bromide, 397.3 chloride, 397.3 iodide, 397.3 sulphide, 397.3 INDEX 435 Hydrogenation, 281 Hydrolysis, 359.4, 362.2 Hysteresis, elastic, 360.3, 368.9, 391.5 Ice, 239, 363.7, 371.6, 381.5, 395.4, 397.2, 400.7, 405.6, 422.9, 424.2 Ideal mixtures, 162 Immiscible liquids, 87, 211 Inflection curves, 178 Infusorial earth, 230 Interrupted flow, 28, 60 Iodides, 114 Ionic size, 357.1, 391.6 Ionic mobility, 358.3, 395.1, 381.7, 427.2 lonization, 195, 350.9, 394.9 Iron and steel, 348.2, 375.4, 388.7, 407.6, 410.5 Iso-grouping, 108, 117, 125, 144 Isothermals of fluidity, 146 K Kaolinite, 385.4 Kinetic energy, 2, 17, et seq., 59, 373.5,384.9, 385.2, 420.1 Law of Batschinski, 142, 247 Poiseuille, 8, et seq., 365.4, 367.9, 374.2, 375.8, 377.2, 386.8, 400.9, 403.1, 406.5, 409.7, 427.1 Stokes, 188, 402.2, 411.8 Lard oil as a cutting oil, 270 Lava, 287 Lecture demonstrations, 397.8, 410.9 Lime, 281, 388.4 Limiting volume, 142 Linear flow, 410.2 Liquid mixtures, 363.4+, 364.4 + , 366.1, 367.2+, 368.6, 369.7, 370.8, 373.6, 387.1, 387.5, 391.3, 392.7, 393.5, 397.9, 398.2, 402.2, 412.3, 413.6, 415.7, 421.3, 422.7 Liquids, 359.4, 361.5, 374.8, 379.9, 386.2, 398.3, 400.4+, 405.2, 406.9, 421.1, 426.3 Lithium chloride, 195, 374.6, 383.4 nitrate, 386.1 Logarithmic decrement, 236 homologues, 45 viscosities, 104 Lubricant, air as a, 388.2 Lubricants, 367.9, 384.1, 400.1, 412.8 Lubricating oils, 370.9, 386.8, 387.9, 388.5, 390.5, 391.8, 394.4, 395.6, 401.6, 401.9, 42.9, 406.8 value, 269 Lubrication, 261, 264, et seq., 347.8, 347.9, 348.2, 4, 5, 6, 9, 353.2, 363.6, 369.2, 377.1, 378.9, 379.1, 394.8, 396.2, 399.2, 405.3, 409.2, 410.2, 416.6, 417.4, 417.6, 419.6, 421.5, 421.9, 423.1, 426.7, 426.8 and adhesion, 268 M Magnetism, 34, 350.1, 351.4, 360.4, 375.4, 389.3, 394.7, 401.6, 421.8 Manometer, 307 Marble, flow of, 347.5 Marine glue, 235 Mass of hydrogen atom, 253 Mayonnaise, 211 Mean free path, 243 Measurement of high v., 378.3 Medicine, 284 Melting point of tars, 415.8 Menthol, 235 Mercury, 352.1, 358.4, 361.9, 368.3, 436 INDEX 388.4, 389.2, 415.4, 416.7, 423.5, 424.6 425.5, 426.9 stabilizer, 294 vapor, 388.4, 402.4 Metal ammonia salts, 355.1 Metals, 348.1, 377.5, 383.2, 384.4, 385.4, 387.4, 394.3, 398.6, 404.9, 410.8, 416.9, 417.9, 419.6, 421.7, 424.9, 426.8 Metallurgy, 284 Methyl chloride, 130, 171, 371.3 Methylene group, 117, 123 Migration velocity, 185, 191 Milk, 284, 286, 351.8, 359.6, 359.7, 360.5, 372.4, 377.4, 389.2, 389.8, 390.2, 394.6, 395.2, 403.1,404.2,423.3 Mixtures, 84, 90, et seq., 251, 349.7, 354.1, cp. liquid mixtures. Mobility, 217, 218, 219, 220, 221, 226, 257, 280 of ions, 356.3 Mobil oil BB, 141 Molecular attraction and viscosity of gases, 246 limiting volume, 142, 144 viscosity work, 107, 109, 110, 111 volume, 392.5 inner and outer, 145 Mortars, 368.2 Motor fuels, 400.1 Multiviscometer, 341.5 N 397.6, 402.1, 405.9, 415.1, cp. cellulose esters. Nitrogen, 353.5, 354.7, 395.9, 400.6, 428.4 Nomenclature, 7 Non-electrolytes, 400.7 Normal mixtures, 81 Ohm's Law, 83 Oil, films on water, 255 Oiliness, 269 Oils, 360.1, 360.4, 361.2, 362.1, 364.9, 366.6, 366.9, 368.4, 370.2, 372.9, 373.8, 380.5, 381.9, 382.7 + , 383.9, 399.6, 401.8, 405.6, 408.5, 412.4, 412.6, 417.7, 418.8, 419.6, 423.5, 424.8 blown, 395.6 essential, 385.2 fish, 427.2, etc. fixed, 406.3 flow in pipes, 407.3 from Oklahoma t>s. Pa., 404.7 mixtures, 415.2 on metals, 409.6 Olive oil, 130, 359.3, 410.2 Opalescence, 94, 411.8 Orifices, 363.1 Ortho phosphoric acid, 417.1 Oscillatory motion, 397.7 Oxycellulose nitrate, 353.2 Oxygen, 124, 144, 353.5, 395.9, 428.4 Naphthenic acids, 408.2 Negative v. and negative curvature, 160, 169, 178, etc., 183, etc., 3734, 386.1, 420.4, etc. Nickel, 372.7, 375.4 Nitric acid, 361.2 Nitrobenzene, 420.7 Nitrocellulose, 280, 291, 350.7, 373.7, 382.1, 393.2, 396.3, Paint, 222, 282, 354.4, 400.2, 411.1 Pastes, 360.3, 381.1, 396.6 Pendulum method, 2, 6, 350.6, 374.2,376.1,398.5 Penetrance, 259, 351.9, 414.1 Pepsin action, 417.8 Periodic relationships, 185, 250 Pharmacy, 284 Phenol, 412.7, 420.6 INDEX 437 Phosphine, 397.3 Pigments, 282 Pitch, 216, 235, 406.4, 422.6, 423.9, 424.2 Plasma, 347.4, 426.4 Plastic flow, 4, 52, 228, 254 measurement, 321 Plasticity, 215, etc.; 349.3, 349.8, 350.1, 354.3, 355.3, etc.; 356.2, 390.3, 358.5, 358.6, 359.5, 362.7, 363.1, 367.7, 368.2, 376.5, 388.2, 388.6, 390.5, 391.3, 392.8, 399.3, 401.2, 403.7, 405.2, 406.4, 409.7, 411.2, 417.3, 418.9, 423.7, 427.1, 429.1 and bacteria, 419.5 calculation, 323 of clay, 387.8 definition, 216 and fusibility, 411.9 of ice, 239, cp. ice. of salt rocks, 391.6 series of metals, 236 and solubility, 293 of steel and glass, 392.6 Plastics, 368.2, 374.2 Plastometer, 375.5, 406.8 Plate glass flow, 39 Pleural exudate, 390.3 Poise, 61 Polar colloids, 208, 212 Polarization and fluidity, 35 Polydispersed systems, 394.4 Positive curvature and chemical combination, 172, 183 Potassium bromide solutions, 182 halide solutions, 381.2 iodide, 373.5, 374.6 nitrate, 374.6 thiocynate, 374.6 Precipitation of colloids, 380.7, 384.5, 384.6 Pressure, 138, et seq., 243, 351.6, 354.2, 361.8, 369.7, 372.5, 379.7, 384.1, 385.5, 391.7, 410.9, 418.3 Pressure, corrections, 299 regulation, 294, 305 true average, 298 Proteins, 356.7, 361.3, 373.1, 393.6, 399.2, 400.3, 404.9, 410.7, 423.6, 426.4 Pseudoglobulin, 361.3 Pyridine, 379.3 Quartz, viscosity of, 377.6 R Racemic compounds, 112, 366.8 Radius of capillary, 315 Raffinose solutions, 426.2 Rare gases, 250, 378.8 Rate of crystallization, 190, cp. solidification, of hydration, 410.7 of reaction, 366.4, 376.3 Reciprocal properties, 83 Refractive index, 393.8 Regimes, 4, 142 Relaxation number, 128 Residual affinity, 112 Resistance, cp. conductivity. Reynolds critical velocity, 40 Rigidity, 128, 218, 256, 384.4, 398.1 Ring grouping, 124 Road building, 282 Rocks, 352.8, 353.3 Roentgen rays as affecting viscosity, 410.1 Roughness of surfaces, 149 Rubber, 212, 280, 350.3, 352.6, 353.3, 371.5, 372.9, 388.3, 394.5, 410.4, 406.7, 411.5, etc., 413.6, 418.7, 423.4, 428.2 Rupture, 229 S Sagging beam method, plasticity, 227 Salt solutions, 347.2, 348.7, 349.4+, 438 INDEX 355.1, 359.1, 363.2, 368.7, 374.6, 376.4, 376.6, 378.4, 379.7, 381.2, 383.4, 383.7, 384.8, 385.6, 386.7, 396.3, 399.9, 402.3, 408.6, 412.2, 418.1, 420.5, 425.2 +, 427.5, 403.6 Saponine, 254, 401.5, 418.1 Saybolt Universal Viscometer, 324, etc. Scums, 256 Sealing wax as a viscous liquid, 216, 235 Seawater, 390.4 Second regime, see turbulent flow. Seeding, 272 Seepage, 213, 223, 231 Separation of components of mixture by flow, 257, 258, 259 Serum, 393.4, 396.9, 397.7, 411.6 Settling of suspensions, 188 Shales, viscosity of, 359.1 Shear, viscosity at low, 365.3 Sheet glass flow, 39 Shifting of minimum in fluidity, cone, curves, 174 Silicate melts, 287, 364.3, 370.3, 375.7, 393.8 Silver nitrate, 181, 374.6 Size of molecules, 367.8, 384.9 of particles in colloid, 365.9, 380.6, 419.9, 428.1 Slags, 287, 370.3 Slipping, 14, 29, et seq., 148, 223, 225, 231, 244, 378.4, 380.4, 395.7, 425.5, 427.2 and superficial fluidity, 256 Slip, 367.3 Soap solutions, 254, 291, 357.1, 369.6,374.4,396.9,397.1 Sodium chloride, 394.7 hydroxide, 357.3 nitrate, 374.6 salt solutions, of organic acids, 392.4 Softening temperature, 133 Soil moisture, 359.5 Solid, definition of, 215 friction, 262, 373.2 Solidification velocity, 190, 420.1, 427.8 Solids, 238, 239, 351.5, 353.9, 358.3, 363.8, 375.3, 375.4, 377.5, 378.6, 381.8, 407.2, 409.7, 414.2, 415.6, 416.8, 420.9, 422.3, 422.5, 424.1, 425.5 Solubility of glass, effect of on viscosity, 377.3 and plasticity, 293 Solutions, 160, 280, 363.1, 400.5, 410.1 Sound and viscosity, 380.4 Specific volume differences, 164, 165 heat and viscosity, 368.7, 371.1 volumes of binary liquid mix- tures, 382.8, 388.8 Sphere, falling, 2, 6, 357.9, 362.6, 373.7, 397.4, 414.4 Stabilizer, 294 Standard substances, 354.6 Stannic chloride, 391.2 Starches, 373.4, 395.1, 406.8, 419.1 Steel, 351.8, 361.3, 392.6 Stereoisomerism, 420.6 Stokes' method, 253, 329, 349.2 Strain, 235 Stress, influence of on properties, 364.5 Structure, 198 Sugar solutions, 407. 1 Sulphur, 359.2, 369.6, 395.6, 411.8, 417.1, 422.2 dioxide, 371.3 Sulphuric acid, 361.2, 366.2, 388.9 Superficial fluidity, 254, 357.8, 401.5, 402.5, 409.4, 414.7 Surface films as plastic solids, 255 tension, 35, 56, 96, 101, 211, 271, 356.8, 356.9, 359.3, 371.6, 376.7 Surtension and viscosity, 395.8 Suspensions, 102, 104, 203, 205, INDEX 439 350.8, 367.6, 383.9, 385.2, 399.3, 400.8 of sulphur, 402.7 Sutherland's equation, 247 Swelling of colloids, 404.2 Syrups, 371.7, 407.1, 407.6 Tables, fluidities and viscosities of water, 339, 340 of ethyl alcohol water mix- tures, 341 of sucrose solutions, 341 logarithms, 345 radii limits for capillaries, 318 radius corresponding to weight of mercury, 316 reciprocals, 342 values of K, 300 of M, 301 of N, 303 "Tackiness," 411.5 Tallow as a plastic solid, 216 Tars, 415.8 Tautomerism, 111 Technical viscometry, 324 Temperature, 13, 92, 127, et seq., 238, 245, 304, 350.1, 365.3, 376.9, 379.9, 409.8 Tensile strength and plasticity, 235 Tetraethylammoniumiodide, 194 Textiles, 282 Third or mixed regime, 35, 42 Thymol, 413.1 Time of relaxation, 128 measurement, 304 Tortion method, 226, 364.6 Traction method, 226 Tragacanth, 394.5 Transition points, 112, 293, 366.4 Transpiration, 2, 6, 241 Trypsin, 352.5, 424.4 Turbulence, 4, 35, 51, 97, 356.5, 357.9, 364.7, 371, 386.9, 388.1, 392.6, 399.2, 411.9, 412.9, 415.7, 417.5, 427.8 Turpentine, 53, 273 U Ultimate electric charge, 252 Undercooled liquids, 420.1 Unsaturation, 366.8 Urea, 181 Urethane, 410.4 Urine, 356.2, 359.9 Vapor pressure, 155, 156, 276, 353.9, 406.9 Vapors, 246, 398.2, 407.2 + , 409.1, 414.9, 418.7 Varnish, 358.8, 372.6, 400.2, 415.5, 423.6, 428.1 Velocity of crystallization, cp. solidification. Viscometer, 7 air bubble, 350.7 Barbey, 350.6, 405.1, 412.5 Clark, 368.2 constant pressure, 62, et seq., 404.8, 416.2 Engler, 350.6, 367.5, 375.5, 380.9, 389.4, 397.5, 403.3, 405.1,408.4,423.1 Fischer, 370.9 Flowers, 371.4, 381.2 Gurnbel, 413.8 Gurney, 377.2 Lunge, 394.5, 413.6 MacMichael, 328, 416.1 Maxwell, 414.2 Ostwald, 403.8 Redwood, 397.5 Saybolt, 324, 380.9, 397.5, 375.5 Schulz, 414.7 Searle, 415.5 Stormer, 410.6, 411.1, 419.5 Washburn, 426.2 Viscose, 280 Viscosity definition, 5, 378.6 measurement, 6 Viscous liquids, 374.7, 391.7, 399.7, 402.6, 415.8, 418.2, 423.9 Volume, 141, 142, 184, 373.5 + 440 INDEX W Y Yield value, 217, et seq., 237, 257 Water, 347.6, 351.1, 364.8, 373.3, 375.8, 383.4, 383.5, 388.9, Z 391.4, 395.5, 399.8, 404.3, Zero fluidity concentration, 54, 201, 408.3, 416.8, 427.4 203, 205, 220 Whipped cream, 211 Zinc-cadmium alloys, 424.9 Wide tubes, 397.8 Zinc sulphate, 394.3 QC 171 B UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles This book is DUE on the last date stamped below. Ubr f pp i AA 000508110 4 UCLA-Physics Library QC 171 B51f L 006 579 223 6