360 THORPE AXD RODGER: );SYVII.-Tlze Viscosity of iWixtwes of &Iiscible Liquids. By THOS. EDWr-aRD THORPE, LL.D., F.R.S., and JAS. \ J T ~ ~ ~ ~ ~ RODGER, xssoc. E.C.S. TT rarely happens that the properties of a mixture of liquids are identical with those which the mixture should possess on the assump- tion that each constituent exercises an influence proportional to its amount. The volumetric a i d thermal changes accompanying the admixture of certain liquids not known to exert chemical action on each other, can only be explained on the supposition that there are forces of attraction between the molecules in the mixture which disturb the equilibriuni previously existing. It may be that the effect of solution in such cases is to break down, to a greater or less extent, the complex molecular aggregates of which certain liquids appear, especially from surface-energy and viscosity observations, to be com- posed ; solution under these circumstances has much the same effect as heat, I n other cases, it may lead to the formation of aggregates of the same or of dissimilar molecules. Aggregates of the latter kind would not necessarily be chemical compounds in the ordinary sense, any more than those of the former kind.Still, it must be confessed, the differences between such physical aggregates and chemical compounds are rather of degree than of kind. Poiseuille (Menz. de Z’lnst. de Pc~s’is, 1546, 9, 433) was one of the earliest to attempt to use the property of viscosity as a measure of the play of internal forces between heterogeneous molecules in a liquid in the special case of mixtures of ethyl alcohol and water. He concluded that the maximum time of flow was shown by the mix- ture which manifested the maximum degree of contraction, and that both phenomena were connected with the formation of the hydrate C,HG0,3H,0.The same conclusion was arrived a t by Graham (Phil. Tyans., 1861, 373) who found that similar, although, as a rule, less pre- cise, relationships might be detected in mixtures of water with the ordinary mineral acids--nitric, sulphuric, and h ydrochloric-or with certain fatty acids-formic, acetic, butyric, and valeric. The work hitherto published is insufficient, both in extent and pre- cision, to admit of a final judgment. It must be admitted that Graham’s contention, that definite hydrates of these alcohols and acids may be recognised by viscosity observations, is not wholly established, The work of Noack on mixtures of ethyl alcohol and water, and that of Wijkander on mixtures of acetic acid and water, would seem to indicate that the phenomena of maximum contraction and maximum viscosity, if not independent, are a t least not directly related to theTHE VISCOSITY OF MIXTURES OF MISCIBLE LIQUIDS.361 existence of definite hydrates in the liquids. (c.$ Sprung, A m . Ph~s. CJmn., 1876,159, 1; Traube, Ber., 1886,19, 871 ; Arrhenius, P.X.? 1889, [v], 28, 3 9 ; D'Arcy, P.M., 1889, [Y], 28, 221.) A significant fact connected with the instances of the kind here referred to, is that they are all cases of the admixture of liquids containing molecular aggregates, but in what manner this circumstance is associated with the maxima of contraction and viscosity remains t o be shown.Wij kander (Lzcnds. Phys. Sccllsk. Jzcbel.skrift, 1878) has also measured the viscosity at various temperatures of mixtures of aniline and benzene, ether and chloroform, ether and carbon disulphide, ether and alcohol, and benzene and alcohol. Our knowledge of this paper is derived from the abstract in Beibl, 1879, 3, 8, from which it would appear that in no case was the viscosity identical with that calculated by the admixture rule; in general, the observed viscosity was less than the calculated value. I n the case of mixtures of ether with chloroform, and of ether with carbon disulphide, there were inflexion-points in the curves ; but no simple relation between the viscosity co-efficients of a mixture and those of its constituents could be deduced.C. E. Linebarger (Amer. J. Sci., 1896, [ivJ, 11, 331) has recently published a number of observations, made at the uniform tempera- ture of 25", on mixtures of pairs of chemically indifferent and miscible liquids, which in the main corroborate Wijkander's results. The observed viscosities in general are less than those calculated by the mixture-rule, except, possibly, in the case of mixtures of benzene ancl chloroform, and mixtures of carbon disulphide with benzene, toluene, ether, and acetic ether, where possibly the temperature of observation (25.) mas too near the boiling point of the carbon disulphide to make any specific influence which that liquid might exert a t lower temperatures perceptible.As a rule, the greater the difference between the viscosities of the pure liquids, the greater was the difference between the calcnlatecl and the observed values of the mixtures. I n previous communications (Phil. T~aizs., 1894, 185, 9. 379 ; Phil. TTC~?~ZS., 1897, 189, A. 71) we have given the results of the measurement of the viscosity of a considerable number of pure liquids a t various temperatures between 0' (except when the substances were solid a t that temperature) and their ordinary boiling points. I n the present paper, we communicate the results of some observations made with the view of throwing further light on the relation of the viscosity of a, mixture of two chemically indifferent and miscible liquids to the viscosity of its constituents.A sufficiently exact and sufficiently extensive study of this question would afford answers to many questions of interest. For example, it would enable us to say whether the viscosity was related to the number of molecules per unit-volume or per unit-surface, ancl hence it would throw light upon the question of how viscosity362 THORPE AND RODGER: observations, and indeed all observations which depend on surface effect, should be treated. It mould also enable us to determine whether, in the case of a mixture of a simple and a complex liquid, the values of the viscosity gave any indication of the decomposition of molecular aggregates, and how such decomposition was related t o dilution and temperature; whether, in fact, the effect of adding a chemically indifferent liquid to a complex one mas the same as raising the temperature. For such purposes, it would no doubt be generally convenient to select mutually soluble and chemically indifferent liquids of approximately the same boiling point, but of densities and viscosities its widely different as possible. Our previous work enables us to form a considerable number of pairs of such liquids, On the present occasion, we desire to communicate the results 01)- tained from observations of several series of mixtures of carbon tetra- chloride and benzene, methyl iodide and carbon disulphide, and ether and chloroform, the last pair of which we studied on account of the yelatively considerable evolution of heat which accompanies the admix- t,ure of these liquids.The method of observation mas the same as that previously employed, and the apparatus was identical with that described in our firstpaper (PluiZ. YTU~S., 1894, 185, p. 410, et Seq.). A .--Ccci.bon Tet ruth Zoride und Benzene. The carbon tetrachloride used in making the mixtures was obtained by repeated fractionation from a large quantity of the commercially pure liquid which had been well washed with potash solution, and dried over phosphoric oxide. It boiled constantly a t 76-62' (corr.) The benzene was free from thioplien. After digestion with sodium wire, it boiled constantly at 79-98" (corr.) and froze at 5.53". Three mixtures of these liquids were made, having respectively the following percentage composition : Carbon tetrachloridc.Benzene. RIixture I... ............ TT.63 22.37 ,, I1 ............... 56.31 43.79 ,) 111 ............... 32.30 67-71 The densities of the pure liquids and of the mixtures a t Oo/Oo were- Carbon t et rach lori d e ........................ 1 % 3 2 0 Mixture I .............................. 1,3816 ,, II .............................. 1-2042 ,, I11 .............................. 1.0530 Benzene ................................. 0.9001 Their densities a t higher temperatures are calculated from their thermal expansions, as determined by the dilatometric method describedTHE VISCOSITY OF MIXTURES OF MISCIBLE LIQUIDS. 363 by one of us in 1893 (Trans., 63, 262). The following table shows the relative volumes of the mixtures at intervals of 10".The values for carbon tetrachloride are those found by one of us in 1880 (Trans., 37, 200) ; those for benzene are the mean of the concordant observa- tions of Kopp, Luginin, and Adrienz. Temp. O0 10 20 30 40 50 60 70 Carbon tetra- chloride. 10000 121 245 372 502 637 778 924 Mixt. I. 10000 121 245 373 503 638 778 924 Mixt. 11. 10000 121 2 45 372 505 640 779 923 Mixt. 111. 10000 119 243 368 500 635 774 919 Benzene. 10000 118 240 364 495 6 30 770 916 It is evident that inno case does the volume of a mixture differ very much from the value calculated by the admixture rule from the volumes of the constituents a t the same temperature. The following table shows the densities at Oo, 20°, 40", and 60" of the mixtures, calculated from the densities a t 0", and the volumes a t the respective temperatures, as given above.These are compared with the values of the densities of the mixtures, calculated from the known densities and thermal ex- pansions of carbon tetrachloride and benzene, on the assumption that no change in volume occurs on admixture. Temp. Mixt. I. Mixt. 11. Mixt. 111. oo Obs. 1-3816 1.2042 1.0530 Calc. 1.3809 1,2035 1.0525 2oo Obs. 1.3486 1.1754 1.0280 Calc. 1.3481 1.1750 1.0278 4oo Obs. 1,3154 1,1463 1.0029 Calc. 1.3151 1.1464 1.0027 6oo Obs. 1.2819 1.1172 0.9774 Calc. 1.2815 1.1171 0.9771 The observations would appear to show that a very slight contraction occurs on mixing carbon tetrachloride and benzene, as already found by F. D. Brown (Trans., 1881, 39, 207), who concluded that the maximum contraction occurred in the case of a mixture containing about 40 per cent.of the tetrachloride. The following table shows the values of the viscosities of the various mixtures a t different temperatures :364 THORPE AND RODGER: Mixture 1. Temp. 7. 0.66" 0.01 184 10.59 0.00990 21-26 0.00833 31.41 0.00719 41-32 0*00630 51.62 0.00555 62-38 0.00491 Mixture 11. Temp. 7. 0*41° 0.01080 10.24 0-00905 20.58 0.00770 30.79 0.00663 40.85 0.00577 52.30 0.00499 64-05 0.00437 73.33 0.00398 Mixture 111. Temp. 1. 0.55" 0.00984 10.06 0.00831 21-10 0.00696 31.70 0.00598 39-93 0.00536 52.0'7 0.00468 63.15 0.00407 73.6 1 0.00365 The following table shows the visccsity of the several mixtures at intervals of 10" between 0" and 70", taken from the curves representing the foregoing observations : Temp.O0 10 20 30 40 50 60 70 Mixt. I. 0*01196 0~01000 0.00850 0,00734 0.00641 0,00566 0*00503 Mixt. 11. 0.01088 0 -0 0 9 08 0.00776 0.00671 0.00583 O-OO513 0-00456 0.0041 1 Mixt. 111. 0;00994 0-00832 0.00707 0.00612 0.00536 0.00473 0.00422 0-00379 The following table gives, for 0" and for 60°, the observed value of the viscosity in the case of the three mixtures, and the values calculated on the assumption that, if the mixture contains na grams of liquid n and n grams of liquid b, the viscosity of the mixture is (@% + n%)/(m + n). Temp. Mixt. I. Mixt. 11. Mixt. 111. Obs. 0.01196 0.01088 0 -009 9 4 O0 Calc. 0.01247 0.01 152 0.01046 Obs. 0.00503 0.00456 0,00422 ' O 0 Calc. 0-00540 0.00499 0.00453 It will be seen that at both temperatures the observed values are less than the calculated values by about 6 per cent.The admixture rule, therefore, does not apply. Linebarger (Zoc. cit.) has measured the viscosity of three mixtures of carbon tetrachloride and benzene a t the temperature of 25", and, although our results confirm his conclusion that the actual viscosities of such mixtures are lower than those calculated from the admixture rule, the values obtained by us differ to some extent from those given in his memoir. On plotting our numbers showing the relation betweenTHE VISCOSITY OF MIXTURES OF MISCIBLE LIQUIDS. 365 viscosity and composition a t the different temperatures, we find, for mixtures of the composition of those made use of by Linebarger, the following viscosity values, which, it will be seen, are uniformly higher than those obtained by him.C,H@ CCI,. Linebarger. T. and R. 13-73 86.27 0.00808 0.00821 40.78 59-28 0.00706 0.00739 58.60 41.40 0*00660 0*00680 The difference is mainly due to the circumstance that the viscosity coefficient for carbon tetrachloride at 25" found by Linebarger is notably less than that indicated by our observations. Thus, for carbon tetrachloride at 25", we found 0.00901 ; Linebarger, 0.00883. For benzene at 25', we found 0.005998 ; Linebarger, 0.00599. The foregoing results, expressed in terms of the composition of the mixtures as abscissse and viscositycoefficients as ordinates, are graphi- cally represented in Fig. 1 (p. 366). The straight dotted lines shorn the calculated viscosity values, as given by the mixture-rule. It will be seen that the actual viscosities of the mixtures are uni- formly lower than those calculated on the supposition that each con- stituent exerts an influence proportional to its amount.The greatest difference from the calculated value occurs in a solution containing from 35 to 40 per cent. of benzene, or, in other words, in a mixture of about equal molecules of the two constituents. At Oo, the maximum difference between the observed and calculated values is equivalent to a rise of temperature of about 3.7'; a t 60", the maximum difference is equivalent to a rise of 6.6". I n other respects, there is not'hing ab- normal in the course of the curves. We may assume that, if a mixture has been formed from y C.C. of liquid r6 and q C.C. of liquid b, the time of flow of the volume of the mixture produced will be the sum of the times of flow of p C.C.of liquid CL and p C.C. of liquid b. On this assumption, if m grams of liquid a, having a density pa be mixed with 'rz grams of liquid 6, having a density pb to form m + n grams of a mixture having a density pm, then As this rule would, in all probability, be most, closely obeyed by a mixture produced without contraction or expansion, the case before us affords a good means of testing its validity, since, as already shown, carbon tetrachloride and benzene mix with very little alteration in volume. The results obtained a t O', loo, 20°, 40" and 60' are given in the following table :THORPE AND RODGER: FIG. 1. -COEFFICIENTS OF VISCOSITY. d k t i c r c s of Benzene and Curbon Tetrachloride.Dynes per Xq. Centim. 0 10 20 30 40 50 60 70 80 90 100 Percentage of C,H,.THE VJSCOSITY OF MIXTURES OF MISCIBLE LIQUIDS. 367 Mixture 0" 10" 20" 40" 60" I Obs. 0.01196 0.01000 0.00850 0-00641 0.00503 Calc. 0.01195 0*01005 0.00860 0.00654 0.00517 Obs. 0*01058 0*00908 0*00776 0.00683 0.00456 'I Calc. 0*0108'i 0.00914 o.00782 0-00594 0.00470 Obs. 0 *00994 0.00832 0*00707 0.00536 0.00422 'I1 Calc. 0.00995 0.00837 0°00716 0.00543 0.00431 It will be seen that there is a close agreement between the observed and calculated values a t the lower temperatures, but that, as the tem- perature increases, the difference becomes slightly larger ; that is, the mixtures are less viscous than they should be if calculated from the re- lative amount of their constituents.This may be connected with differences of molecular complexity due to the solution of the benzene. We hare already stated (Zoc. cit., p. 561) that the curve showing the re- lation of the viscosity of benzene to temperature is, as compared with those of its homologues, toluene, ethylbenzene and para- and meta-xylenes, altogether abnormal. At 0", benzene has actually a greater viscosity than any of these hydrocarbons, and it is only at the respective boiling points that the viscosity-constants follow the order of the gaseous molecular weights. B.--iWethyZ Iodide ccncl Cadon DisuZp?Lide. The methyl iodide used was made from pure methyl alcohol. About a litre of t,he product was shaken with mercury, allowed to stand for a couple of days over phosphoric oxide, and distilled.It boiled constantly a t 42.44' (corr.). The carbon disulphide was rectified, placed over anhydrous copper sulphate for a week, decanted, shaken with pow- dered potassium permanganate, filtered, and thereafter shaken with mercury. It was then mixed with an equal volume of olive oil, and after standing for a day, was distilled from a water bath and placed over phosphoric oxide for a meek. It boiled constantly at 46.27" Five mixtures of the two liquids were made of the following per- centage composition : Mixt. I. Mixt. 11. Mixt. 111. Mixt. IV. Mixt. V. Methyl iodide ......... 78.40 61.19 51.89 31-19 17.61 Carbon disulphide ...... 21.60 38.81 48.11 68.81 82.39 (corr.). The densities of the pure liquids and of the mixtures at Oo/Oo were found to be- CH,I. Mixt.I. Mixt. 11. Mixt. 111. Rlixt. IT. Mixt. V. CS,. 2.3335 1.9848 1.7720 1,6782 1.4982 1.3994 1.292368 THORPE AND RODGER: The thermal expansions of three of the mixtures were found to be as follows : Temp. CHJ. Nixt. I. Mixt. 111. Mixt. V. CS,. 0' 10000 10000 10'300 10000 10000 10 11s 120 122 116 116 20 243 244 244 236 236 30 372 373 370 358 360 40 505 506 500 485 489 Dobriner's value for methyl iodide (AizntcZen, 1888, 243, 30) and the values for carbon disulphide published by one of us in 1880 (Eoc. cit.) are introduced for the sake of comparison. The numbers show that the volumes of the mixtures differ but little from those of the pure liquids at the corresponding temperatures, and that in the case of the Mixtures I1 and IV the volume may be taken without sensible error in the reduction of the viscosity observations as intermediate between those c;f I and 111, and 111 and V respectively.The following table gives the comparison, a t O', 20°, and 40°, of t h e densities, deduced by means of the preceding data, with those calculated on the assumption that no change in volume occurs on admixture : Temp. Mixt. I. 3lixt. 11. Nist. 111. Mixt. 1V. Xlixt. V. oo Obs, 1.9842 1.7720 1.6782 1.4982 1.3994 Calc. 1.9878 1.7780 1.6821 1.5017 1.4030 Obs. 1.9369 1.7298 1.6382 1.4631 1.3671 Ualc. 1.9411 1.7365 1-6428 1,4669 1:3705 20O Obs. 1.8886 1.6871 1.5983 1.4279 1.3347 400 Cals. 1.8938 1.693'3 1.6021 1.4318 1.3378 It will be seen in this case that the calculated values are uniformly greater than those actually observed, or, in other words, expansion occurs on mixing methyl iodide and carbon disulphide. The following table contains the mean values of the viscosity co- efficients of the mixtures : Mixt.I. X x t . Temp. rl Temp. 10.02 0.004727 8.87 20.85 0.004303 17.74 30.01 0.003994 25.70 39.01 0.003723 33.48 39.30 0.38O 0*005164 0 ~ 4 1 ~ 11. Jtixt. 111. 7 Teiii y. ?1 0*004807 0.34' 0.004680 0.004475 9.66 0.004357 0.004171 21.57 0.003984 0.003926 30.56 0.003739 0.00371 4 39.38 0.0035 12 0.00355 9THE VISCOSITY OF MIXTURES OF MISCIBLE LIQUIDS. 360 Mist. IV. DIixt. T:. Temp. 17 Temp. 17 0.42O 0.004478 0.50' 0.004358 10.02 0.004131 9.90 0*004037 19.911 0.003825 19.47 0.003752 30.00 0.003566 29-09 0.003494 39.97 0.003341 38.47 0.003268 The values at intervals of loo, as read from the curves obtained by plotting these numbers, are given below : Temp.Mixt. I. Mist. 11. DIixt. 111. Mist. IV. Mixt. V. 0" 0.00518 0.00482 0,00469 0'00449 0.00438 10 0.00473 0 '00443 0 *00435 0-00413 0'00403 20 0'00433 0'00410 0 -00403 0.00382 0'00373 30 0 '00399 0.00350 0 -00374 0 '0 0 35 7 0.00347 40 0.00369 0'00354 0-00350 0 '0 033 4 0 *00323 The values a t Oo and 40°, calculated by the ordinary admixture rule, are given in the following table. Temp. Mist. I. bIixt. 11. Mixt. 111. Mixt. IV. Mixt. V. Obs. 0*00518 0.00482 0.00469 0.00449 0.00438 '" Calc. 0.00558 0.00530 0.00515 0.00480 0.00458 Obs. 0.00369 0.00354 0.00350 0.00334 0.00323 Calc. 0.00389 0.00374 0.00365 0.00347 0.00334 40° It will be observed in this case, as in that of the mixture of carbon tetrachloride and benzene, that the admixture rule does not apply; the viscosity-coefficient s are uniformly lower than the calculated values, the differences between the observed and calculated values becoming less as the t'emperature increases.These results are graphically repre- sented in Fig. 2 (p. 370). The maximum difference between the observed and calculated values occurs in a mixture containing about 40 per cent. of carbon disulphide, that is, in a mixture of about equal molecular proportions of the two liquids. The maximum variation between the observed and calculated values at Do is equivalent to a rise of about 10' in temperature ; a t 40°, the difference is equivalent to a rise of about 7'. I n the following table is given, for temperatures of Oo, ZOO, and 40°, the comparison of the observed viscosities with the values caicu- lated on the assumption that the time of flow of a given volume of a pure liquid is retained when that volume of it is present in a mixture.Temp. Mixt. I. Mixt. 11. Mixt. 111. Mixt. IV. Mixt. V. Obs. 0.005 18 0.00482 0.00469 0.00449 0-00438 O0 Calc. 0.00538 0*00504 0.00489 0.00461 0.00445370 THORPE AND RODGER: Temp. Mixt. I. Xixt. 11. Mixt. 111. Mixt. 1V. Xixt. V. 203 Obs. 0,00433 0.00410 0*00403 0.00382 0.00373 Calc. 0.00446 0.00421 O.OC411 0.00389 0.00379 Obs. 0.00369 0.00354 0.00350 0,00334 0.00323 400 Calc. 0*00378 0.00359 0.00351 0.00336 0.00327 The observed viscosity-coefficients are uuiforrnly lower than the calculated values, although the differences become less and less as the FIG.2. -COEFFICIENTS O F VISCOSITY. Mixtzcres of Methyl Iodide and Car6on Disztlphicle. Dynes per Sq. Ceibtim. 0 10 20 30 40 50 60 70 80 30 100 Percentage of CS,. temperature is raised-exactly the opposite to that which obtains in the case of a mixture of carbon tetrachloride and benzene. This cir- cumstance is probably connected with the slight expansion which O C C I ~ ~ S on mixing methyl iodide and carbon disulphide. C. -Et It el* and C?b I wt-o f orm. About a lifre of ' pure ' ether was shaken with a strong solution of acid sodium sulphite, decanted, mixed with 10 per cent. potash solution, separated, washed with water, and treated three times in succession with dehydrated calcium chloride. After repeated treatment with phosphoric oxide, i t boiled betweenTHE VISCOSITY OF MIXTURES OF MISCIBLE LIQUIDS.3'71 34-83" and 34.89". Corr. and reduced b. p., 34-57', The number given in our previous paper is 34.48'. After standing over phosphoric oxide for a fortnight, it was found t o distil completely between 61.46" and 61.63'. Bar., 770.5 mm. The corr. and reduced b. p. = 61.34". Four mixtures of these liquids were employed. They had the following percentage composition : Bar,, 767.9 mm. For the chloroform, we are indebted to Mr. David Howard. Nixt. I. Mixt. 11. Mixt, 111. Mixt. IV. Chloroform.. . . . . 84.06 59.86 40.20 30.70 Ether ............ 15.94 40.14 59.80 79.30 The densities of the pure liquids and of the mixtures a t O", and the values calculated by the admixture rule, are given in the following table : CHC1,.Rlixt. I. Mixt. II. Mixt. 111. Mist. IV. C',H,,,O. Obs. 1,5255 1.3136 1*0801 0.9389 0.8292 0,7362 Calc. 1.3029 1.0666 0.9295 0.82415 The comparison shows that a notable contraction occurs when ether and chloroform are mixed. The observed densities are found t o lie on n smooth curve showing no inflexion-points. There is, as already pointed out by Bussy and Buignet, a considerable rise of temperature on mixing ether and chloroform. Since the experiments with the other liquids showed that where the difference between the coefficients of thermal expansion of the con- stituents is small, the coefficients of the mixtures may be calculated with sufficient accuracy by the admixture rule, it was deemed unneces- sary for so small a range of temperature to make observations on the thermal expansion of the mixtures. The mean values of the viscosity-coefficients of the several mistnree, ~ L S observed, are given in the following table : Mixtnre I.Mixture IT. 0.43' 0.006744 0.36" 0.005590 9-38 0.005995 9.33 0.004934 20.60 0.005243 19.66 0*004318 29.93 0.004724 39.35 0*003848 Temp. rl Temp. 9 Mixtura 111. Temp. ?1 0.45" 0.004371 9-83 0.003894 19-86 0.003463 29-77 0*003106 3 1-47 0*003060 Mixture I V. 0.45' 0.003483 11.71 0 -00 3 0 6 9 20.64 0.002 79 6 28.92 0.0025 72 Temp. 9372 THORPE AND RODGER: The last observation in the case of Mixture I11 was made 70 minutes after the one previously taken. obtained a t 31-47" lies on the curve obtained by plotting the other- observations proves that the composition of the mixture suffers no sensible alteration on standing even for more than an hour a t the highest temperature a t which measurements were made.The values of r) a t Oo, loo, 20°, and 30°, read from the curves obtained on plotting t.he above numbers, are given below. The fact that the value of Temp. Mixt. I. Mixt. 11. Mixt. 111. Mixt. IV. 0" 0.00678 0.005 62 0*00440 0.00350 10 0.00595 0.00489 0.00388 0.00312 20 0.00528 0 *O 0 4 30 0.00346 0.00281 30 0.00472 0.00382 0.00310 0-00254 The values a t 0' and a t 30°, compared with those calculated by the admixture rule, are given in the following table. Temp. Mixt. I. Mixt. 11. Mixt. 111. Mixt. IV. oo Obs. 0.00678 0.00562 0*00440 0.00350 Calc. 0.00634 0.00535 0.00454 0.00373 3oo Obs. 0.00472 0*00382 0*@0310 0.00254 Calc. 0.00463 0.00391 0.00332 0.00274 These results are graphically represented in Fig.3, where the abscissz of the curves are the percentage amounts of ether in the mix- tures, and the ordinates the viscosity-coefficients at the corresponding temperatures. The dotted lines show the calculated viscosity-values, as given by the admixture rule. It will be seen that there are points of inflexion in €he curves of the observed values, as already found by Wij kander. Wijkander's actual values, however, are not strictly comparable with ours on account of the character of the ether he employed. His viscosity-coefficients for that liquid are about 10 per cent. higher than ours, which were deduced from two independent and closely concordant series of observations made on two different preparations of ether (Phil.Tmns., 1894, p. 518). That the differ- ences are not due to the method of observation is shown by the fact that Wijkander's and our values for chloroform, benzene, and carbon disulphide are in very good accord. Ether is one of the most mobile of liquids, and the correction for kinetic energy may in its case become of considerable importance. Wij kander's higher values may be partly caused by imperfect correction for kinetic energy, or by the presence of small quantities of ethyl alcohol in the sample employed. A s alcohol a t 0' is more than 6 times as viscous as ether, a relatively small amount of alcohol has a marked effect upon the viscosity of the ether.THE VTSCOSlTY O F MIXTURES O F MISCIBLE LIQUIDS. 3’73 The course of the curves is altogether different from that shown by the other mixtures studied by us. Instead of being uniformly lower than the calculated value, the observed value starts by being higher, but, as the amount of ether increases, the variation from the calculated FIG.3. -COEFFICIENTS OF VISCOSITY. Mixtures of Chloroform aitd Ether. Dyiics per Sq. Centinz. Percentage of Ethcr. amount becomes less and less until a t a certain point, depending on the temperature, the two values become identical, after which the actual viscosity becomes less than the calculated value, the general course of the curve resembling that of the other mixtures studied. It is VOL. LXXI, D D374 THORPE AND RODGER : THE VISCOSITY OF MIXTURES, ETC. evident from the curves that as 35O, the boiling-point of ether under ordinary conditions, is approached, the mixture mould resemble other mixtures in having a viscosity uniformly lower than the calculated value, or, in other words, the condition which determines the peculiar behaviour of the mixture is destroyed a t about that temperature.I n t,he following table are given for the temperatures O", lo", 20", and 30" the observed values of q, and those calculated on the assump- tion that a given volume of a liquid when mixed with another liquid maintains the same time of flow as when unmixed. Te m 1'. Mixt. I. hIixt. 11. oo Obs. 0.00678 0.00562 Calc. 0.00589 0.00466 Obs. 0.00595 0.00489 loo Calc. 0.00527 0.00417 Obs. 0.00528 0.00430 20" Calc. 0.00474 0.003'76 Obs. 0.00472 0.00382 300 Calc. 0.00430 0.00341 The actual viscosity is uniformly greater Mixt.111. Mixt. IV. 0.00440 0*00350 0.00393 0.00336 0.00388 0.00312 0.00352 0*00301 0.00346 0.00281 0.0031 S 0.00273 0*00310 0.00254 0*00288 0.00247 than the value calculated on the above assumption, although the differences tend to become less as the temperature rises, or as the quantity of ether increases, The observations described in this paper afford additional evidence of the fact indicated by Wijkander, and supported by Linebarger, that the viscosity 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 a liquid in a mixture pre- serves the particular viscosity it possesses in the unmixed condition. To judge from the instances hitherto studied, the viscosity of the mix- ture is, as a rule, uniformly lower than the mixture rule would indicate, but no simple relation can yet be traced between the viscosity of a mixture and that of its constituents. I n the case of a mixture of ether and chloroform, where there is considerable contraction, and therefore considerable development of heat, on mixing, the viscosity a t low temperatures is greater than the admix- ture rule would indicate, but as the temperature is raised, or asthemixture giving the maximum contraction is diluted, the viscosity eventually ')ecornes less than the calculated value, when the general course of the curve resembles that of such mixtures as carbon tetrachloride and ben- zene, or of methyl iodide and carbon disulphide. The behaviour of a mixture of ether and chloroform would seem, to begin ivith, to beFENTON: A NEW SYNTHESIS IN THE SUGAR GROUP. 375 analogous to that of a mixtureof ethyl alcohol and water, but the con- dition which determines the contraction and the maximum viscosity, whether it be a feeble chemical combination or a molecular aggregation of a purely physical character, is destroyed by heat or dilution.