LIBRARY OF THE UNIVERSITY OF CALIFORNIA, RECEIVED BY EXCHANGE Class The Relationship Existing between the Weight of a Falling Drop and the Diameter of the Tip from which it Falls DISSERTATION SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRE- MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PURE SCIENCE IN COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK. BY JESSIE YEREANCE CANN, A.B., A.M. NEW YORK CITY 1911 EASTON, PA.: ESCHBNBACH PRINTING COMPANY. 1911. The Relationship Existing between the Weight of a Falling Drop and the Diameter of the Tip from which it Falls DISSERTATION SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRE- MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PURE SCIENCE IN COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK. BY JESSIE YEREANCE CANN, A.B., A.M. NEW YORK CITY 1911 EASTON, PA. : ESCHENBACH PRINTING COMPANY. 1911. ACKNOWLEDGMENT. The following investigation was suggested by and carried out under the direction of Professor J. Livingston R. Morgan. The author desires to extend her sincere thanks and ap- preciation to Professor Morgan for his helpful assistance, advice and encouragement during the course of the work. J. Y. C. 226928 The Relationship Existing between the Weight of a Falling Drop and the Diameter of the Tip from which it Falls INTRODUCTION. Object of the Investigation. In 1864, Thomas Tate, 1 as the result of his experiments with water, announced the following laws : I. Other things being the same, the weight of a drop of liquid (falling from a tube) is proportional to the diameter of the tube in which it is formed. II. The weight of the drop is in proportion to the weight which would be raised in a tube with a bore equal to the outer diameter by capillary action. III. The weight of a drop of liquid, other things being the same, is diminished by an augmentation of temperature. Tate's experiments were all made with thin- walled glass tubing, varying in diameter from 0.1-0.7 of an inch, the orifice in each case being ground to a ''sharp edge, so' that the tube at the part in contact with the liquid might be re- garded as indefinitely thin." His weights were calculated from the weight of from five to ten drops of liquid, which formed at intervals of forty seconds, and were collected in a weighed beaker. Tate's law is generally accepted as equivalent to the ex- pression w = 2 it r T, where w is the weight of the falling drop, r the radius of the tube on which it forms, and j- is the surface tension of the liquid. This expression is not exactly as Tate intended it to be formulated, for his law simply states a proportionality; so that the expression should be w = 2 n r f K, where K is some constant which will transform the pro- portionality into an equality. 1 Phil. Mag., 4th Ser., 27, 176 (1864). It has also been shown by Morgan and Stevenson, 1 Morgan and Higgins 2 and Morgan and Thomssen 3 contrary to the conclusions of all other workers since Tate that the weight of a single drop of a non-associated liquid falling from a definite tip is regulated by the following laws: I. The quantity w( J (w = weight of drop in milli- grams, M = molecular weight, d = density) is a linear func- tion of the temperature, becoming zero at a point 6 below the observed critical temperature or a fictitious critical temperature. Expressed mathematically we have then (in the form of Ramsay and Shields, for surface tension) w where t c is the critical temperature (observed or fictitious) and t is the temperature of observation and k a universal constant, defined by the equation MX /M although, as has been shown by Morgan, 3 it should not be calculated in this way, owing to the multiplication of error, but from w( j = 3(288.5 t 6) for benzene once for all. II. The temperature coefficient of the function w( J i. e. y the k B of the above equation is a universal constant for such liquids, leading, as has been shown by Morgan, 3 to the same value of t c for any one non-associated liquid at all temperatures of observation. It has further been shown by Morgan that the above laws hold also when applied to the results of Ramsay and Shields of surface tension, thus confirming Tate's second law. 1 /. A. C. S., 30, 360-376 (1908). 2 Ibid., 30, 1055-68 (1908). 3 Ibid., May, 1911. The object of this investigation was to establish con- clusively the truth of the first of the above laws, i. e., to make an exhaustive study of the relationship existing between the weight of a falling drop and the diameter of the tip from which it falls. For this purpose sixteen different tips were employed, varying in size from about 3 mm. to approximately 8 mm. in diameter. Five representative liquids, including that with practically the largest, as well as that with the smallest possible drop volume, were chosen and the relation- ship between the drop weights, and the different sized tips studied exhaustively. Apparatus and Method, The apparatus used in this work is a new and simple form designed by Morgan 1 and especially adapted to the general needs of the investigator in other lines of chemistry. By it the weight of a falling drop of any liquid from any desired tip can be found at various temperatures, up to within a few degrees of the boiling point, with very great accuracy, every possible form of variable error having been foreseen and avoided. As the results of this work show, the method is indeed one of very great accuracy. In order to exclude any variation in the results due to changing temperature, all measurements were made in a constant temperature bath. This was of the Ostwald gas type with a transparent bath, stirred by a small electric motor. The temperature employed was 27.8 C., the greatest variation recorded being 0.03. The thermometer used here was a certified one reading in fiftieths of a degree. The five representative non-associated liquids were quinoline, pyridine, benzene, ether and carbon tetrachloride . These five liquids were considered the best because of their great differences in density, surface tension and general physical properties (i. e., viscosity, etc.). The weight of the drop was obtained by finding, first, that of thirty or more drops, in the following manner. The liquid is sucked over from the supply vessel into the capillary 1 /. A. C. S., March, 1911. 8 tubing, and allowed to form a drop on the tip. This drop is held at as nearly as possible its maximum size for 5 minutes, so that the vessel may become saturated with the vapor of the liquid used. Next, thirty consecutive drops are allowed to fall each drop falling of its own weight alone, and the time of the entire determination noted. Then the vessel with the vapor and thirty drops is weighed, being wiped with cheese- cloth to constant weight. After the apparatus has been set up again, and has assumed the temperature of the bath by remaining in it for a half hour or more, another determina- tion, a "blank" is taken. This time the liquid is sucked over in the same manner as before, the drop being allowed to hang five minutes, but only five consecutive drops are al- lowed to fall, the sixth drop being held on the tip without falling for the balance of the time consumed by the first determination. In this way the liquid in the weighing vessel in each determination is exposed for the same length of time to the same evaporating influence both for the hang- ing drop and the liquid which has fallen, so that the total loss is the same in both cases. By subtracting this 5 -drop blank from the 3O-drop determination, the weight of one drop is obtained, after dividing the difference by 25. Exactly the same method is to be employed with each liquid used. The densities used were those determined by Morgan and Higgins. Liquids. The benzene used in this work was Kahlbaum's special K. The quinoline was distilled frequently, for when it contains water the results are too low, while when allowed to stand it decomposes, becoming thicker and yellow, and giving high results. Because of the "sticky" nature of quinoline great care had to be taken each time between determinations to clean the capillary tube very thoroughly, and then to prevent liquid rising until the first drop was run over, so that no threads of liquid would be spurted over before the drop, and thus cause the weight to be too large. The pyridine used was Kahlbaum's special K, and remained unchanged pure and colorless throughout the entire period of work. It was found in working with pyridine, particularly with the larger tips, that each drop had to be drawn back into the capillary tube, before being allowed to fall, so that each drop would be exactly like the first drop. It was apparent to the eye in these cases that the regular procedure caused the successive drops to grow smaller, and that the liquid did not extend out to the edge of the tip, and hence would give too low a result. The carbon tetrachloride used was from Baker and was redistilled often. Great care had to be taken in making determinations with this liquid, for the drop volume and surface tension are so small that unless the drop is perfectly controlled at the moment of fall the result will be too large. With tips larger than 4.5 mm. this control is extremely difficult, if possible at all on this form of apparatus, and the results obtained are always too high. This perfect control, however, is one of the essential principles of the drop weight method. The ether was from Kahlbaum, and was al- ways redistilled several times before a determination. With- out redistillation the results are always found to be too high. Results. In Tables I-V are the experimental results obtained with the sixteen tips used for the liquids studied, together with the /M\ values of the function w ( I , where w is the drop weight and d the density, both at the same temperature, while M is the molecular weight. TABLE I. BENZENE. wt. Diameter 30 drops of tip. and vessel. Mm. Grams. AT. wt. Wt. Av. wt. of 30 drops 5 drops of 5 drops and vessel, and vessel, and vessel. Grams. Grams. Grams. Av. wt. of i drop. a/f^S Mgs. v rf/ ' 10.3560 9.9222 3.048 I0.356I 10.35606 9.9222 9.9222 17-355 347-51 I0.356I 3-929 11.1960 10.6569 11.1960 11.1960 10.6569 10.6569 21.564431.77 II . 1960 10 TABLE I. (Continued}. [10.4067 9-8585 4. ooo I0 ' 4 67 jio.4071 10.40695 9/8587 9.8586 21.934439.18 [10.4073 4-5I4 i 10.0359 9.4292 I0 -0359 10.03586 9-4 2 9! 9 42915 24.269 485.72 10.0358 9.9938 9.3626 9.9938 9.3626 9-9936 9-99373 9-3626 9.3626 25.245 505.47 9-9937 4.978 10.8887 10.2198 10.8887 10.88863 10.2198 10.2198 26.753 535-67 10.8885 5-306 (25 drops) 11.2625 ii .2622 10.6918 11.2619 11-26233 10.6918 10.6918 28.526 571.17 ii .2627 11.2137 10.4754 soil J o-4756 ,11.2137 11-2137 10.4755 10.4755 29.528 591-23 [11-2137 10.4755 5-500 9-7253 8-9873 9.7255 9.7256 8.9873 8.9873 29.532 591-31 9.7260 5.689 9-7554 8.9922 9-7555 9-7554 8.9920 8.9921 30.532 611.33 9-7553 5-845 6.200 11.3907 10.6067 11.3905 11.39056 10.6068 10.60683 31.349 627.70 11.3905 10.6070 11.3815 10.7159 11.3816 11.38163 10.7159 10.7159 33.287 666.48 11.3818 II 6-550 6.844 7-387 TABLE I. (Continued). 25 drops) 11-5351 10.8287 n-5357 n-5357 10.8282 n-5357 11.5352 11.53548 10.8285 10.82846 35-351 707-82 H-5357 n-5357 H-535I (25 drops) 10.4305 9.6872 10.4302 10.4299 10.43023 9.6870 9.6871 37-156 743-97 10.4303 (25 drops) 11.4210 10.6057 11.4207 11.42073 10.6058 10.60575 10.749 815.91 ii .4205 (25 drops) . (11.4978 10.6215 7.859)11.4980 11.4981 10.6215 10.6215 43.83 [11.4985 TABLE II. QUINOLINE. 877.58 Wt. Av. wt. Diameter 30 drops of 30 drops of tip. and vessel, and vessel. Mm. Grams. Grains. 3.048 4-000 4-5I4 10.6755 10.6759 10.67566 10.6756 10.8235 10.8238 10.82376 10.8240 10. 802 I IO.8O2O IO.8O2 I 10.8022 (20 drops) 10.0749 10.0749 10.0755 10.0752 10.0755 Wt. Av. wt. 5 drops of 5 drops Av. wt. of and vessel, and vessel. i drop Grams. Grams. Mg. 9 9739 9-9743 9-9741 9-9594 9-9595 '(f) 1 - 9.9741 28.063 677.48 9-95945 34-573 834.62 848.93 9.9229 9.9230 9.92296 35-165 9.9230 9-4979 9.4979 9-4979 38-487 929-11 12 4-978 5-5oi TABLE (20 drops) ii .4198 11.4196 11.4197 11.4197 11.7336 11.7330 11-7333 n-7333 {10.2444 5 . 500 10 . 2443 10 . 2444 [10.2445 5.689 10.2932 10.2939 10.2938 10.2935 10.2931 [11.6891 5.845) 11.6892 11.68923 [ i i . 6894 (20 drops) 1 i . 6005 i i. 6010 11.6007 1 i . 6006 (20 drops) 11.7617 ii .7611 11.7617 11.76158 11.7618 II. (Continued'). 10.7825 10.7825 10.7825 10.5604 10.5604 10.5604 9.0713 9.0715 9-0714 9.0714 9 . 0802 9 . 0798 9 . 0800 10.6955 10.6953 10.6954 6.200 6-550 (25 drops) [ 10.6615 6.844! 10.6605 10.66106 10.6612 (20 drops) 11 .6620 11.6615 11.66186 11 .6621 (20 drops) 11.7521 11.7517 11.75176 7-859 10.8104 10.8106 10.8105 10.9261 10.9261 10.9261 9.7894 9.7894 9-7894 10.7150 10.7150 10.7150 10.7372 10.7372 10.7372 42.48 1025.52 46.916 1132.61 46.92 1132.71 48.54 1171.00 49.692 1199.61 52.68 1271.73 55.698 1344-62 58.111 1402.87 63.124 1523-90 67.638 1632.10 13 TABLE III. PYRIDINE. Wt. Av. wt. Wt. Av. Wt. Diameter 30 drops of 30 drops 5 drops of 5 drops Av. wt. of of tip. and vessel, and vessel. and vessel, and vessel. i drop Mm. Grams. Grams. Grams. Grams. Mg. 3.048 io. 5 H4 9-9470 lo. 5 H3 10.51446 9 9470 9-947O 22.699 4 2 5-4 2 10.5147 [10.6369 9.9288 3 . 929 10 . 6368 10 . 6369 9-9287 9 . 9288 28 . 324 530 . 85 [10.6370 9.9289 [ 10. 7625 10.0422 4.ooolio.7628 10.76246 10.0422 10.0422 28.81 539-96 [10.7621 10.2604 9.4654 4-5I4 4.978 5-5QI 10.2610 10.2606 9.4651 9 46533 31.811 596.20 10.2604 9-4 6 55 ii . 1390 10.2609 11.1392 11.13913 10.2605 10.2607 35-137 658.54 11.1392 11.1435 10.1744 11.1436 11.1435 10.1745 10.17445 38.762 726.48 11.1434 [10.0003 9-0311 5.500110.000410.00033 9.0312 9.0311638.767 726.57 10 . 0003 9 03 i 2 5.689 5.845 10.0387 9-0363 10.0385 10.0384 9.0368 9-03655 40.074 751-07 10.0380 11.6846 10.6545 11.6840 11.68446 10.6546 10.65455 41.197 772.11 I I . 6848 (25 drops) [11.8020 10.8792 I 11.8029 ' 55 ] i i. 8022 11.80227 10.8795 10.87935 46.146 864.88 ii .8020 9-7405 9 7405 9.7405 48.20, 903-37 TABLE III. (Continued). (25 drops) 10.7045 6.844 10.7044 10.7045 10. 7046 (25 drops) , f i i . 7069 7.387111.7069 11.7069 [ 1 1 . 7069 (25 drops) f i i. 8022 10.6807 7.859] ii .8023 11.80223 10.6806 10.68066 56.078 1051.02 10.6599 10.6599 10.6599 52.35 981.15 ii .8022 10.6807 TABLE IV. CARBON TETRACHLORIDE. Wt. Av. wt. Diameter 30 drops of 30 drops of tip. and vessel, and vessel. Mm. Grams. Grams. Wt. Av. wt. 5 drops of 5 drops Av. wt. of and vessel, and vessel. i drop. Grams. Grams. Mg. (50 drops) 10.5284 10.5280 10.5283 10.5279 [10.3811 3.929! 10.3812 10.3811 [ 10.3810 (10 drops) 9.9077 9.9077 9.8895 9.8896 9 . 8894 4.000 4-514 (50 drops) [ 8.5932 1 8.5937 8.5930 8-5931 (50 drops) 8.1205 8.1208 8.1203 8 1 . i 204 (10 drops) 7 7934 59323 7-7932 1205 7 9593 7 9593 7-9594 7 9593 7 95933 7. 1108 7. 1108 7-37I3 7-37io 7.3710 7-3708 7-37i8 9-9077 I5-5I5 328.97 9.8895 19.664 416.94 7-7933 I9-998 424-03 7.1108 22.438 475-76 7.37118 23.526 498.83 4.978 TABLE IV. (Continued). r 9-5975 8.9709 9-5977 8.9710 9-598o 9-59775 8.9714 8.9711 25.066 531.46 9-5978 r ii. 3661 10.6910 '3 '[11.3661 11.3661 10.6910 10.6910 5-5oi 10.8320 10. 1265 10.8322 10.8321 10.1265 10.1265 10.8321 _ nn , 9-6945 8.9873 5 ' 5 I 9-6944 9-69445 8.9871 8.9872 5.689 9-7327 9-7327 8.9938 8.9938 27.004 28.224 28 .29 29-556 572.58 598.45 599.82 626.69 5.845 11.3760 10.6089 11.3762 11.3761 10.6084 10.60865 30.698 650.90 11.3761 6.200 11.5330 11.5330 10.7172 10.7172 6.550 11.6985 11.6985 10.8317 10.8317 6.844 10. 6061 10. 6061 9.6906 9.6906 TABLE V. ETHER. Wt. Av. wt. Diameter 30 drops of 30 drops of tip. and vessel, and vessel. Mm. Grams. Grams. Wt. Av. wt. 5 drops of 5 drops. and vessel, and vessel. Grams. Grams. (50 drops) (10 drops) 7.2107 7.6045 7-6045 7.2109 7.2108 8.7205 8.4134 3.929] 8.7206 8.7205 8.4133 8.4134 [ 8.7204 8.4135 32-632 34.672 36.62 Av. wt. of i drop. Mg. 9.843 12.284 691 .91 735-17 776.47 219.23 273.61 4.000 (50 drops) (i i drops) 8.2272 7-7400 8.2272 8.2279 8.22743 7-7401 7-74003 12.497 278.36 8.2274 7.7400 i6 V. ( Continued} . (50 drops) (10 drops) 9.1339 8.5816 A SlJ 9-1344 8.5818 9.1347 9.13448 8.5820 8.58194 13.813 307.67 9-1349 8.5823 8.5820 [ 7-7829 7-4019 4-695 7-7831 7-7830 7-4019 7-40193 15-243 339-51 I 7-7830 7.4020 5-501 5-500 5.689 5-845 7.6328 7.2122 7.6327 7.6328 7.2121 7.21216 16.825 374-76 7.6329 7.2122 7-7575 7-3367 7-7574 7-75746 7-3369 7-3368 16.827 374-79 7-7575 7-3368 7-7775 7-3400 7.7776 7-77753 7-3400 7-3400 17-501 389-82 7-7775 7-7895 7-3394 7.7894 7-7895 7-3393 7-3394 18.004 401.02 7-7896 7-3395 8.9719 8.4555 6-550) 8.9720 8.97196 8.4556 8.4555 20.659 460.14 8.9720 8.4554 6.844 7.387 7-859 8.6478 8.1043 8.6480 8.6479 8.1045 8.1044 21.74 484.23 8.6479 8.1044 8.6256 8.0254 8.6257 8.6256 8.0255 8.0254 24.008 534-75 8.6255 8.0253 8.4755 7-8232 8.4759 8.47546 7-8230 7-8231 26.095 581-23 8.4750 17 On all three tips below 4.514 mm. benzene, quinoline, pyridine and ether showed drop profiles which were very much larger at the bottom of the drop than at the top or than the diameter of the tip itself, so that on all these tips we should expect the results to be non-concordant when various liquids are compared, for the amount of the bulging, and consequently of the weight of the liquid falling is here inde- pendent of the diameter of the tip from which it falls. On the tips from 4.514 up to and including 5.507 the control of the drop was perfect with all the liquids except carbon tetrachloride, and at most the profile of the drop showed that the edges of the lower part are simply a continuation of the edges of the tip and none extends beyond. Carbon tetrachloride can only be perfectly controlled on tip of 4.514 and on the two sizes below, the drop on all the larger tips spurting at the last moment and carrying down with it an excess of liquid. This is due to the small drop volume, together with the small surface tension of this liquid, which makes the drop at its lower extremity very small, and very liable to break down. It is to be remembered here that the perfect control is lost only on the form of apparatus in question, for the long capillary burette used by Morgan and Higgins would un- doubtedly show perfect control on considerably larger tips, for the* long tail of liquid in the narrow capillary only allows a very slow formation of the drop at best. Bther is found to be difficultly controlled on the 5.689; while only on the larger ones is trouble experienced with benzene, pyridine and quinoline. We should expect then on the tips from 3.929 up to and including 4.514 that carbon tetrachloride would be the criterion for other like liquids, for its drop volume is so small that the edges of the drop never extend beyond lines parallel to the edges of the tip itself. As soon as perfect control is lost, the drop which falls is too large for it does not fall of its own weight alone, but has projected with it some of the liquid which under perfect con- trol would remain on the tip. This increase in weight con- tinues to increase with the diameter of the tip until the i8 maximum drop volume has been attained, after which the edges of the drop pull away from the tip; when, provided the control were still perfect, too small a drop for that tip would result. As the control, however, is not perfect, we should expect the value to become too high as control is lost, then to become correct when lack of control is just balanced by the decreasing effect of the drop pulling away from the tip; and finally the drop would probably remain of the same weight on all larger tips. Although the diameters of the above tips were measured on a dividing engine, the mean of a number of determinations on each of three diameters being taken, the accuracy is certainly not much greater than o.oi mm. owing to the fact that the tips were never perfectly circular in section, and in some cases flaws had developed in the edge which made the measurement difficult, although probably it affected the drop weight but slightly. 1 In TABLE VI. Values for-. Diameter of tip. Benzene. Quinoline. Pyridine. d ecu. Ether. Mm. Mg. Mg. Mg. Mg. Mg. 3 .048 .5 .6970 9 .2069 7 -4470 5 .O9O2 3 .2291 3 .929 5 .4884 8 .7992 7 .2089 5 0008 3 .1265 4 .000 5 .4835 8 7913 7 .2025 4 9995 3 1243 4 514 5 .3762 8 5260 7 .0471 4 9706 3 .0601 4 695 5 3769 o 0108 4 .978 5 3743 8 5335 7 0585 [5 0353] 3 .0620 5 .306 5 3752 5. 0883 5 .501 5 3677 8 .5286 7 0463 5 1307 3 0585 5 .500 5 3694 8 5309 7 .0484 5- H36 3 0593 5 .689 5 3668 8 5126 tj 0441 5- 1952 [3 0763] 5 .845 5 3630 8 5009 7 0477 $: 2516 O .0880 6 .200 5 3688 8 4967 5' 2621 6 550 [5 3971] 8. 5035 7 0452 5- 2934 3 1532 6 .844 5 .4290 8 4908 7 O426 5- 3506 3' 1779 7 .387 5 5157 [8- 5447] [7 086 3 ] 3 2498 7 .859 5 .5766 8.6058 7- 1340 3' 3201 Table VI are given the values of w/d for each liquid on each tip. From this all those things mentioned above as to the 1 In this connection it may be said that the 5.501 tip is the one used by Morgan and Thomssen, the results here being slightly lower, due to slight flaws, presumably, which have since developed. 19 bulging or the loss of control are made clearer than they would be in a small curve, for the difference there would hardly be noticeable. It will be noted here that from 3.929 to 4.514 the value of w/d for carbon tetrachloride is constant and then increases continually with the size of the tip, showing the effect of lack of control, and later the combination of that with the pulling away of the drop from the edge ; while for all the other liquids, on the contrary, up to 4.514 the value decreases then remains constant for a greater or less variation in diameter. The loss of control of ether is first observed on the 5.689 tip, while benzene is lost on the 6.55, and pyridine and qivinoline on the 7.387. TABLE VII. NORMAL BENZENE CONSTANTS. Diameter /M\ of tip. Mm. \d/ 288.5 27.8 6 3.048 347-51 I-3644 3.929 431-77 1.6952 4.000 439 .18 I-7243 4.514 485-72 1.9078 4.695 505-47 1.9846 4.978 535-67 2.1032 5.306 571-17 2.2425 5-501 591-23 2.3213 5.500 59 I -3 I 2.3216 5.689 611.33 2.4002 5.845 627.70 2.4645 6.200 666.48 2.6168 6.550 707.82 2.7791 6.844 743-97 2.9210 7-387 815.91 3-2034 7-859 877.58 3-4456 The 4.514 tip is the only one which gives correct results for carbon tetrachloride, for above this tip the results are too high, due to lack of control; while below it, it is impossible to use benzene as the standard because of the bulging of the drop. The carbon tetrachloride k is then the only true one for small tips, and hence in the future will be the liquid used for the standardization of small tips when they are used for 20 determining the drop weights of liquids similar to that of carbon tetra chloride, i. e., liquids with a very high density and small surface tension. The value of t c is then to be taken as 283.15 as found on the 4.514 tip, and the normal value of the constant k of the tip calculated from it. In Table VII are the k B values found from benzene by use of the formula = B (288. 5 27.8 6) Wherever both benzene and the other liquid give constant weisfht results of - we would expect to find a constant value diameter of k necessary to give the values of t c as found from the work of Morgan and Higgins by Morgan, 1 on substituting the values of M and d for that liquid in These t c values are 346.6 for pyridine, 521.3 for quinoline, 195 for ether and 283.2 for carbon tetrachloride. TABLE VIII. M w t c 27.8 6 Diameter of tip. mm. Benzene. Quinoline. Pyridine. Ether. CCL*. 4.514 1.9078 I.9Ol6o I.9O46I I.9O9I 1.9081 4.695 1.9846 [2.0004] 4.978 2.IO32 2.IOT36 2.10^54 2.1066 [2.I3II] 5.307 2.2425 [2.2777] 5.500 2.3216 2.32^35 2.3^230 2.3256 [2.3856] 5.501 2.3213 2.3233 2.32^30 2.3254 [2.3801] 5.689 2.4002 2.4037 2.4012 [2.4188] In Table VIII are given those k values for the tips from 4.514-5.501 inclusive, between which we should expect the liquids to be concordant in result, with the exception of weicrht carbon tetrachloride, since the values of . - are constant diameter 1 J. A. C. S., May, 1911. 21 on them. The value of this latter on the 4.695 tip shows the effect of the lack of perfect control which was noted when the determination was made. Since, as has been shown by Morgan, surface tension in dynes can be found from drop weight in milligrams by aid of the proportion f\-w\ :K B : & B , where K B is the value found from Ramsay and Shields very accurate benzene values, calling t c = 288.5, * e -> 2.1012; while k B is the similarly determined value for drop weight on the tip in question (see Table VIII). Table IX contains the values of surface tension in dynes, calculated from drop weight in milligrams by aid of the above relation for the tips considered in Table VIII. TABLE IX. SURFACE TENSIONS. Diameter of tip. * Quinoline. Pyridine. Ether. CCU. 4-5*4 4-695 4 978 I . 9078 I . 9846 2.1032 42-39 42.44 35-04 35-io 15.22 I5-23 24.71 5 307 2.2425 5-501 5-500 5.689 2.3213 2.3216 2 . 4OO2 42.47 42.47 42.49 35-09 35-09 35-o8 I5-23 I5-23 [I5-32] Average, 42.45 35.08 15.23 TABLE X. k VALUES. Diameter of tip. Mm. Benzene. Quinoline. Pyridine. Ether. ecu. 3-048 1.3644 I-3897 I .3601 1.3603 1-3194 3-929 1.6952 I .7121 I.697I 1.6977 1.6722 4.000 I-7243 I.74H 1.7264 1.7272 I . 7007 -5-689 2 . 4002 2.4037 2.4012 2.4188 2.4930 5-845 2.4645 2 . 4608 2.4685 2.4883 2.5893 6.200 2. 6l68 2.6088 2.7524 6.550 2.7791 2.7582 2.7651 2.8552 2.9245 6.844 2.9210 2.8777 2.8881 3 . 0046 3.0888 7.387 3-3034 3.1260 3.1368 3-3181 7.859 3-4456 3-3495 3.3601 3.6065 22 Table X contains the k values and Table XI the 7- values calculated similarly for the other tips, which from their weight j: relations should not be perfectly satisfactory. It will be noted here that the results are exactly what has already been shown by the simpler w/d ratios, so that we need not discuss them further. TABLE XI. SURFACE TENSIONS. Diameter, of tip. Mm. Benzene. Quinoline. Pyridine. Ether. CC1 4 . 3 .048 26 73 43 .21 34 .96 15 .16 23 .89 3 929 26 73 42 85 35 . 10 15 . 22 24 37 4 .000 26 73 42 85 35 .11 15 23 24 37 5 .689 26 73 42 49 35 .08 15 32 25 .87 5 .845 26 73 42 37 35 . 12 15 35 26 17 6 .200 26. 73 42 30 26. 20 6 550 26 73 42 . ii 34 8 9 15 .62 26. 21 6 .844 26. 73 4* 80 34 67 15 .64 26. 34 7 .387 26 73 4i .40 34 34 15 75 7 .859 26 73 4 1 25 34 20 15 .91 For benzene, using the value of w/d (see Table VI) we find the following relationships (holding for tips from 4.514 to 5.501 inclusive), and w = 1.710 X 7T X 2 r where w is given in milligrams and r in millimeters. The relationship existing between diameter, drop weight and surface tension in dynes per cm. (found from the above, knowing further that w constant X 7*) for any liquid is then w = 0.063972 X (2 r) x r- Although this relationship was found for benzene it must hold for all the other liquids since the assumption in obtain- ing it was only that w is proportional to 7-. In Table XII are given the values of 7- as calculated from the above equation. 23 XII. SURFACE TENSIONS. Diameter of tip. Mm. Benzene. Quinoline. Pyridine. CC1 4 . Ether. 4-5I4 26.75 42.42 35.06 24.73 I5-23 4-695 26.75 4.978 26.74 42.46 35-12 I5-24 5-306 26.75 5-500 26.72 4 2 -45 35-07 15.22 5-501 26.71 42.44 35-06 15.22 5.689 26.70 42.45 35-05 [I5-3I] Av., 26.73 42-44 35-07 24.73 15.23 Conclusions. I. The drop weights of benzene, quinoline, pyridine, ether and carbon tetrachloride have been determined at a constant temperature from sixteen different .tips varying in size from 3.048 to 7.859 mm. in diameter. II. All liquids from water, forming practically the largest drop volume to carbon tetrachloride, practically the smallest, follow Tate's law as to proportionality with surface tension on a tip of 4.514 mm. diameter; while, excluding carbon tetrachloride and a few similar liquids with small surface tensions and large densities, the law is found to hold rigidly on tips between 4.514 and 5.501 mm. III. Smaller tips than 4.514 are adapted only to related liquids when the lower end of the drop bulges in the same way, or those which like carbon tetrachloride form on them normal looking drops similar to those of other liquids on the larger tips. IV. Tips larger than 5.501 will also hold for similar liquids only, for here it is simply a question of the perfection in the control of the drop. V. All these things can be observed by closely watching the drop; and a liquid can be said to be satisfactory or not as soon as its drop profile on the tip in question is observed. This is also shown for a series of tips by the values of the weight ratios . - . diameter VI. Surface tensions in dynes per cm. calculated from drop weight in milligrams by multiplication with the ratio of k r /k w show the same values for the liquids considered when calculated for all tips, the variation being considerably smaller than that from capillary rise by the same observers with different tubes. VII. It is found that drop weight in milligrams, diameter of the tip in millimeters and surface tension in dynes are related, for tips from 4.514 to 5.501 by the following equation w = 0.063972 (2 r) n f VIII. It is shown clearly why such a law cannot hold for all liquids on smaller or larger tips than these, but it must be recognized that even on tips beyond these, in either direction, that the results, in terms of surface tension, agree with the others fully as well as do those values determined by aid of capillary rise by various observers. BIOGRAPHY. Jessie Yereance Cann was born May 17, 1883, in Newark, New Jersey. In June 1901 she graduated from the Newark High School, and was awarded a four-year scholarship in the Woman's College of Baltimore (Goucher College). She completed her college course in three years, receiving the degree of A.B. in June, 1904. During the years 1904-1909 she taught Science in the Belleville (N. J.) High School. She was a graduate student in Physical Chemistry at Colum- bia University during the years 1909-1911,^3 well as during the Summer Sessions of 1907, 1908, 1909 and 1910; and the holder of a Curtis Scholarship 1909-1910, receiving the degree of A.M. in June, 1910. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW Books not returned on time are subject to a fine of 50c per volume after the third day overdue, increasing to $1.00 per volume after the sixth day. Books not in demand may be renewed if application is made before expiration of loan period. SEP 80 1919 MAR 50m-7,'16