LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 RECEIVED BY EXCHANGE 
 
 Class 
 
The Weight of a Falling Drop and the Laws of 
 Tate. The Determination of the Molec- 
 ular Weights and Critical Temper- 
 atures of Liquids by the Aid 
 of Drop Weights. 
 
 BY 
 
 RESTON STEVENSON, A.B., A.M. 
 
 DISSERTATION 
 
 SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR 
 THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF 
 PURE SCIENCE IN COLUMBIA UNIVERSITY, IN THE 
 CITY OF NEW YORK. 
 
 NEW YORK CITY. 
 1908 
 
 EASTON, PA. : 
 ESCHENBACH PRINTING Co. 
 
 1908. 
 
The Weight of a Falling Drop and the Laws of 
 Tate. The Determination of the Molec- 
 ular Weights and Critical Temper- 
 atures of Liquids by the Aid 
 of Drop Weights. 
 
 BY 
 
 RESTON STEVENSON, A.B., A.M. 
 
 DISSERTATION 
 
 SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR 
 THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF 
 PURE SCIENCE IN COLUMBIA UNIVERSITY, IN THE 
 CITY OF NEW YORK. 
 
 NEW YORK CITY. 
 1908 
 
 E ASTON, PA.: 
 
 ESCHENBACH PRINTING Co. 
 1908. 
 
at 
 
 >A -^ / 
 
CONTENTS. 
 
 I. Introduction. Object of investigation 5 
 
 II. Apparatus and method 9 
 
 III. Results H 
 
 IV. Discussion of results l8 
 
 V. Summary 22 
 
 183469. 
 
ACKNOWLEDGMENT. 
 
 This piece of work was suggested by Professor J. L. R. Morgan and 
 was carried out under his direction. Mr. Higgins has helped the author 
 in his preparation of this paper for publication. 
 
 R. S. 
 
OF THE 
 
 UNIVERSITY 
 
 OF 
 
 The Weight of a Falling Drop and the Laws of 
 
 Tate. The Determination of the Molecular 
 
 Weights and Critical Temperatures of 
 
 Liquids by the Aid of Drop Weights* 
 
 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 that tube 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 vary- 
 ing in diameter from o. i to 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 regarded as indefinitely thin." His weights were cal- 
 culated from the weight of from five to ten drops of liquid, which formed 
 at intervals of 40 seconds, and were collected in a weighed beaker. 
 
 Tate's law as we know it to-day, is supposed to be a summation of 
 the first two laws of Tate, but it must be said that it attributes to Tate 
 a meaning that he never indicated and probably never intended. The 
 analytical expression of this faulty law is the familiar 
 
 W = 2Trry, 
 
 where Wis the weight of the falling drop, r the radius of the tube on 
 which it forms, and y is the surface tension of the liquid. Of course, 
 
 1 Phil. Mag., 4th Ser., 27, 176 (1864). All other references to drop weight will 
 be found in the bibliography of that subject at the end of this paper. 
 
Tate's second law shows drop weight to be proportional to surface tension, 
 for the weight of a liquid rising in a tube by capillary action is propor- 
 tional to surface tension; and his first law shows drop weight to be pro- 
 portional to the diameter (or radius) of the tube; but he did not even 
 imply that drop weight is equal to the product of the circumference of 
 contact into the surface tension. The real anyltical expression of Tate's 
 first two laws as he actually announced them, in place of the obove, 
 shold be 
 
 W=KjD, 
 
 where K^ is a constant, and D is the diameter of the tube; or, when the 
 drops are all formed on the same tube (z. <?., where D is constant), 
 
 W=Ki, 
 K being a new constant. 
 
 Guye and Perrot, Ollivier, Lohnstein and others in their bibliograph- 
 ical summaries have similarly misunderstood Tate's laws. 
 
 Lebaigue showed experimentally that when 2 r applies to the cir- 
 cumference of the bore of the capillary tube that the equation which 
 has been assigned to Tate is not even remotely true, but that the weights 
 of the drops are nearly proportional to the circumference of the lower 
 surface of the tube. In Tate's work, as stated, the external and internal 
 diameters of the tube at the outlet were practically the same. Hagen 
 has shown that in the above equation r the radius of the tube does not 
 equal the radius of the drop at its point of separation because of the 
 meniscus which remains behind, kayleigh proposed the equation 
 W = 3,8r, but'this did not give accurate results except with a very few 
 liquids. Duclaux proposed the equation W = Kr, and by this formula 
 he determined surface tension with his "count pipette;" counting the 
 number of drops which a certain weight of liquid would give. He found 
 that K varied. Lohnstein used this same equation except that he de- 
 rived mathematically in a purely theoretical paper a table with which 
 he attempted to determine K for each value of r. He made K a geometri- 
 cal function of r. All of these corrections, however, were corrections 
 for the variations of drop weight with the size of the outlet of the tube. 
 The variations for different liquids still remained uncorrected and unac- 
 counted for. 
 
 Duclaux, Buhrer, Yvon, Ollivier, and others have shown how the 
 weight of the drop varied with the temperature, the nature of its atmos- 
 phere, electrical conditions, mechanical jarring, speed of outflow, etc., 
 
yet when the conditions were made constant and all disturbing factors 
 removed, the determination of surface tension by the method of drop 
 weights still remained inaccurate. 
 
 Drops of different sizes, from different kinds and forms of surfaces, 
 drops made with different speeds of outflow, (Gugliemo, Frankenheim, 
 Hagen, Guthrie, Ouincke, Lenard, Forch, Guye and Perrot, Rosset,) 
 have been studied and interesting data obtained. Drops have been photo- 
 graphed (Lenard) and projected (Worthington) , their forms calculated 
 mathematically (Mathieu, Dupre, Bertrand, Duclaux) and the vibra- 
 tion of drops when about to fall studied (Rayleigh). Other data have 
 been obtained (Quincke) but no method has been obtained by which 
 surface tension can be accurately determined from falling drops. 
 
 The cause of the inaccuracy of the drop weight methods for surface 
 tension has been ascribed by Antonow and others to the unequal wetting 
 of the surfaces of the outlet by the different liquids. Also no known 
 property of liquids has been found according to which the errors in the 
 surface tension determinations varied (Hanney). Such a variation 
 did not occur regularly with the variation in the density, chemical com- 
 position, viscosity, refractive index, etc. Therefore, these variations 
 have been ascribed to a property of the liquids which is as yet unknown, 
 and therefore the errors were considered unavoidable and impossible 
 of correction (Guye). 
 
 Two methods have been tried to prevent this unequal wetting by 
 different liquids of the surface of the outlet: 
 
 (i) The sides of the tube or the surface of the exit nearly to the bore 
 were covered with a layer of some grease, of arsenic trioxide or of lycop- 
 odiurn powder, etc., (Ollivier). It was found that in this way accurate 
 results could sometimes be obtained. However, the layer was dissolved 
 by the liquids used, thus lowering greatly and to a varying extent the 
 surface tension of the liquids used, and the layer would sometimes be 
 unevenly wetted at the small points and would wash away unevenly. 
 Therefore, while a perfect layer of grease would give an outlet with which 
 accurate results could be obtained, in actual experiment the results were 
 found to be unreliable (Lebaigue, Traube). Ollivier has discussed the 
 defects of these layers and has recommended for the outlet of the tube 
 a metal disc with a small hole, the disc to be slightly greased with 
 paraffin up to the hole and then this layer to be thoroughly and thinly 
 
8 
 
 coated with soot. He gives only one experimental determination to 
 support his claim that accurate results are obtained by this method 
 and this one result, with water, is not accurate. 
 
 (2) The second method for the preventing of unequal wetting of the 
 surfaces by different liquids is that the one proposed by Antonow. The 
 outlet tube is immersed in a (comparatively) non-miscible liquid. The 
 liquid bath prevents the liquid in the tube from wetting at all the bot- 
 tom surface of the tube, so that all the drops fall from the bore of the 
 tube. However, apart from the experimental difficulties this method 
 does not measure the surface tension of the pure liquid A but of a satur- 
 ated solution of liquid B in liquid A. This, of course, varies with differ- 
 ent pairs of liquids used and with the temperature. 
 
 The general result of the work of all other investigators since the time 
 of Tate, on the subject of drop weight, may be summed up best, perhaps, 
 in the words of Guye and Perrot (1903), vis.: 
 
 "The law of the proportionality of the weight of a drop to the diameter 
 of the tube is no more generally justified than that of the proportionality 
 of the weight to the surface tension." 
 
 " The laws of Tate are not general laws, and, even in the case of static 
 (slow forming) drops, represent only a first approximation." 
 
 It will be seen from these conclusions that Guye and Perrot repudiate 
 not only the form of Tate's law as we know it to-day, but also his first 
 two laws in the form that he announced them. It must be said, however, 
 that no investigator has as yet fairly tested Tate's laws, for no one has as yet 
 exactly reproduced Tate's conditions. Practically all the results thus 
 far obtained have been for drops forming on capillary, instead of on thin- 
 walled tubes; and the effect produced by the "sharp edge" of the drop- 
 ping tube, as described by Tate, has never been even approximately ap- 
 proached, except under such conditions that the results were obscured 
 by other factors (Ollivier, Antonow). 
 
 The object of this investigation, is to test the truth of Tate's law (and 
 especially the second), as he originally stated them, more fairly and with 
 greater accuracy than has hitherto been done, reproducing his conditions in 
 a way that others have failed to do, paying particular attention to the effect 
 of the form of the tip, and excluding those errors which are so apparent in the 
 work of some of the previous investigators. And it was hoped that even if 
 
9 
 
 Tate's laws were found not to hold rigidly, it might still be possible to em- 
 ploy the temperature coefficient of drop weight of any one liqiud, in a 
 formula similar to that of Ramsay and Shields, 1 in place of their tempera- 
 ture coefficient of surface tension, as a means of ascertaining molecular 
 weight in the liquid state, and the critical temperature. 
 
 It may be said here, to anticipate, that the results of this work have 
 proven to be even better than was hoped, for they have shown that 
 not only molecular weights in the liquid state and critical tempera- 
 tures, can be calculated just as readily and accurately from the 
 temperature coefficient of drop weight, as from that of surface tension; 
 but also that the relative surface tensions of various liquids can be found 
 from drop weights, and that, thus found, they agree with those 
 determined by the capillary rise as well as do those by any of the 
 other methods, and almost as well as those for the same liquid by the 
 same method, carried out by different observers. This relation to sur- 
 face tension is true for the interpolated values of surface tension, and 
 further work, using the actual, experimental values, will probably only 
 show the relation to be even more rigid than this. 
 
 Apparatus and Method. 
 
 In order to avoid the complication which might be introduced by the 
 successive formation of several drops, I have measured, throughout 
 this work, the volume of a single drop, for that method, under these condi- 
 tions, is far more accurate and delicate than any weighing method. 
 
 Although, unlike Tate, I have used capillary tips upon which the 
 drop forms, they were so constructed them that one might expect to ob- 
 tain an effect similar to that obtained by Tate with the "sharp edge" 
 of his thin- walled tube. Apparently the effect of this "sharp edge" 
 is to delimit the area of the tube upon which the drop can hang, and to 
 prevent the liquid rising upon the outer walls of the tube. The form of 
 tip employed in the measurements is shown, in section, in Fig. i(O'), 
 both the bottom and bevel being highly polished. 
 
 Observation of a tip of this form shows that it behaves exactly as such 
 a one as described by Tate, and that the lower edge of the bevel, just as 
 Tate's "sharp edge," is the limit of the area upon which the drop hangs, 
 provided, of course, that its diameter is less than that of the maximum 
 drop of the liquid with the smallest maximum drop. The liquid forming 
 -a drop on this tip does not, under any condition, rise to wet the bevel or 
 1 Zeit, f. phys. Chem., 12, 431 (1893). 
 
10 
 
 walls of the tithe as it might on an ordinary one. This effect has also been 
 obtained, during the course of our work, by two other investigators 
 (Antonow and Ollivier), 
 but only by the use of 
 foreign substances, which 
 contaminate the liquid. 
 
 The complete appara- 
 tus used in the prelimi- 
 nary experiments is 
 shown in section, in Fig. 
 i . P is a translucent por- 
 celain scale, 55 centime- 
 ters long, divided into 
 millimeters. AB is a 
 capillary burette of such 
 a bore that i millimeter 
 contains about 0.0003 cc. 
 This tube was carefully 
 calibrated with mercury, 
 and a curve prepared, 
 from which the volume 
 between any two scale 
 readings could be found. 
 One end of this burette, 
 A, was connected by rub- 
 ber tubing to the rubber 
 compression bulb K. This 
 bulb was so arranged in 
 a screw clamp that the 
 pressure upon it could be gradually increased or decreased, thus giving abso- 
 lute and delicate control over the movement of the liquid in the burette. The 
 larger tubing BC, which is the continuation of the tip, passes through the 
 rubber stopper R, and thus supports the dropping cup D. F is a dipper 
 which can be raised, lowered, or swung around to any position by means of 
 the rod G. From this the burette can be filled with liquid, and into it the 
 drop from the tip O ultimately falls. The bottom of the cup D is covered 
 with a thin layer of the liquid, and the tube H, through which G passes, is 
 stuffed with filter paper, saturated with the liquid. 
 
 Fig. I. 
 
II 
 
 The object of this form of apparatus was to prevent evaporation of the 
 liquid of the drop, and to enable one to measure drop volumes at any de- 
 sired temperature, by immersing the entire apparatus to the point m in 
 a waterbath. 
 
 Before making a measurement with this apparatus, the cup, dipper, 
 tube and tip are thoroughly cleansed with chromic-sulphuric acid, water, 
 alcohol, and ether, and dried by a current of air. The liquid is then placed 
 in the cup and in the dipper, from which, after the stopper R is fastened 
 tightly, the tube is filled to such an extent that the lower meniscus is just 
 about to enter the tip O when the other end of the column (in the burette 
 tube A B) is at zero, or some point just below it. This point (the zero point) 
 is then recorded, and the bulb very gradually compressed until the drop 
 formed at the tip O falls off. The reading of the other end of the column, 
 at the instant of fall, then enables one, knowing the zero-point, to find the 
 volume of the maximum drop that can form on the tip ; I shall designate 
 this as the pendant drop (P. D.). By drawing the liquid, that is left on the 
 tip, back into the tube again, until the lower meniscus is once more just 
 about to enter the tip 0, it is possible to find the volume of the drop that 
 has remained clinging to O\ this I shall call the clinging drop (C. D.). 
 Subtracting the volume of this from that of the pendant drop, one finally 
 finds the volume of the falling drop (F. D.). 
 
 Experiments with this preliminary apparatus showed the method to be 
 excellent, but made apparent the fact that greater delicacy was desirable. 
 The second, and final form of apparatus, as shown, in section, in Fig. 2, 
 is simply a modification of the first. Here the dropping tube is sealed 
 into a glass stopper, and the cup is provided with a wide rim to allow the 
 use of mercury as a seal. An elastic band, passed from the hooks Q over 
 the stopper, and between the two tubes, holds stopper and cup together, 
 rnd prevents the passage of either mercury or the water of the bath into 
 the cup. To obtain a more delicate setting, in determining the zero-point, 
 than is possible by observing the passage of the meniscus into the tip, 
 the dropping tube, here, is constricted at 5, and the lower meniscus, in all 
 readings, is held to a mark at that point. 
 
 Two pieces of apparatus in this form were used, the burette in one case 
 (tube 2) holding approximately 0.000,08 cc., and the other (tube) 30.000,056 
 cc. per millimeter. 1 In order that a scale of the same length as before 
 might be used, these measuring tubes were bent in the form shown in Fig. 
 
 1 These tubes were calibrated with mercury at room temperature, and no cor- 
 rection in volume was made when they were used at higher temperatures, for the varia- 
 tions were found to be well within the experimental error. 
 
12 
 
 2. In tube 2 there were three small 
 bulbs blown in the first length of 
 the burette, while tube 3 had a single 
 bulb V, with an approximate capac- 
 ity of 0.027 cc. The use of a bulb 
 or bulbs enabled one to get the total 
 volume of liquid necessary for a 
 drop, without an excessive length of 
 the tubing. For liquids forming 
 drops of large volume, the zero- 
 point must be above the bulb or 
 bulbs; for those giving smaller vol- 
 umes it must be below the single 
 bulb, or, in case there are three 
 bulbs, below one or more of them. l || 
 
 With these pieces of apparatus, 
 only the volumes of the falling drops 
 were measured, for the results with the 
 first apparatus showed that, of the 
 three kinds of drops, they only were 
 related to surface tension. The rea- 
 son for originally determining the 
 volumes of all three kinds of drops, 
 when Tate considered only the fall- 
 ing drop, was the suggestion of 
 Ostwald 1 that the pendant drop from 
 a capillary tube would probably cor- 
 respond to falling drop from a thin- 
 walled tube, such as Tate used. Ex- 
 periment shows, however, that here, 
 also, the falling drop is the impor- 
 tant factor. 
 
 To measure the volume of the fall- 
 ing drop with this piece of appara- 
 tus, the zero-point is found, just as 
 before, by drawing the liquid back 
 into the burette, until, when the 
 
 V 
 
 Fig. 2. 
 
 1 Hand- und Hilfsbuch zur ausftihrung Physiko-chemischer Messungen. 
 1893, PP- 300-301. 
 
upper meniscus is at zero or just below it, the lower meniscus is 
 exactly at the mark in the constricted portion of the tube 5; then, 
 as before, the liqiuid is very gradually forced over until the drop on 
 the tip O falls off. No reading for the pendant drop is attempted, 
 but the liquid is at once drawn back to the mark, and, after allowing suffi- 
 cient time for drainage, the position of the upper meniscus is observed. 
 The difference in volume of the burette tube, between the zero-point and 
 the latter point, is then the volume of the drop that has fallen. The pres- 
 sure on the rubber bulb in all cases must be increased very gradually at 
 the instant when the drop is about to fall, for a sudden increase in pressure 
 at that time tends to increase the volume of the falling drop. 
 
 It was necessary before using these delicate forms of apparatus to prove 
 conclusively that no evaporation takes place from the drop as it is forming. 
 To ascertain this the tube was filled with liquid, and the zero-point noted. 
 Then gradually the pressure on the bulb was increased until a large drop, 
 though not sufficiently large to fall, was formed at O. After standing in 
 this condition for several minutes, care being taken, as it must always be r 
 that the apparatus was not jarred or disturbed, the liquid is drawn back 
 until the lower meniscus is again at the mark at 5. Any decrease in vol- 
 ume of the liquid, from that originally observed, is then to be attributed, 
 with such tips as were used, to evaporation from the drop. Even the 
 first observations for this purpose, however, showed that there was no 
 evaporation, for one invariably found an increase in the volume of the liquid, 
 instead of a decrease; in other words, liquid was always deposited upon the 
 hanging drop, no matter how often it was formed and drawn back. After 
 a number of attempts to avoid this deposition upon the forming drop, 
 by partially filling the cup with glass beads, sand, or filter paper, moistened 
 with the liquid , and also by the use of a vertically placed bundle of short 
 closed tubes, each filled with the liquid and presenting a meniscus of ap- 
 proximately the diameter of the drop itself, it was found that it could be 
 avoided entirely by depositing the liquid (before the experiment) as a fog, upon 
 the walls of the cup D. This fog can be produced very readily by heating 
 the cup in a waterbath (after the apparatus has been set up and filled) 
 10 to 20. In this way minute drops of the liquid are deposited upon 
 the walls of the cup, and change the condition within, so that there is then 
 neither evaporation from the hanging drop, nor deposition upon it, and the 
 upper meniscus always returns to the same point, no matter how often 
 the drop may be formed and drawn back. Before each measurement 
 it was made certain, in this way, that such a condition was attained. 
 
 It will be seen that the delicacy of this method depends simply upon the 
 size of the capillary tubing used as the burette. Tube 3(1 mm. = 0.000,056 
 cc.) was the smallest tubing available at the time, except, of course, the 
 
very narrow thermometer tubing, which offered too great a resistance to 
 the flow of liquids, for this purpose. 1 
 
 In all cases the apparatus was immersed in a waterbath with transparent 
 sides, the temperature of which was kept constant to the point within o . i . 
 
 Results. 
 
 In Tables I, II, and III are given the results for drop volumes and drop 
 weights, and the relation observed between drop weight and surface ten- 
 
 TABLE I. 
 
 Diameter of tip = 0.622 cm. approximately, i mm. on burtte = 0.0003 cc. 
 
 Weight of drop _ w 
 Surface tension *" 7 
 
 Substance. 
 
 Ether 
 
 dyi 
 Temp. 
 2O O 
 
 Surface 
 tension, 
 ics per cm, 
 
 16.80 
 29.38 
 30.00 
 32. io 
 
 37.35 
 39.19 
 44.10 
 
 45.13 
 
 70.60 
 
 Weights of drop in mgs. 
 
 WP.D. 
 34-6 
 56.0 
 53-2 
 66.0 
 78.5 
 77-3 
 81.8 
 86.6 
 
 127. I 
 
 WF.D. 
 21.4 
 35-2 
 36.1 
 41.4 
 5O.O 
 49.8 
 52.9 
 57.o 
 80. i 
 
 Wc.D. 
 
 13.2 
 
 20. 6 
 
 17.2 
 24.6 
 28.4 
 27.6 
 28.7 
 29.6 
 37 . .S 
 
 Benzene 
 
 . 22. 5 
 
 Ethyl iodide 
 
 10 I 
 
 Chlorbenzene. . . . 
 Guaiacole 2 
 
 . 2O. O 
 
 io 6 
 
 Benzaldehyde. . . 
 Aniline 
 
 .. 15.4 
 
 . 17 5 
 
 Quinoline 
 
 je A 
 
 Water. . 
 
 . 20.0 
 
 KP.D. KF.D. 
 
 KC.D. 
 
 2.06 
 
 .27 
 
 0.79 
 
 1.91 
 
 .21 
 
 0.71 
 
 1.77 
 
 .20 
 
 0.57 
 
 2.05 
 
 30 
 
 0.77 
 
 2.10 [ 
 
 34] 
 
 0.76 
 
 1.97 
 
 .27 
 
 0.71 
 
 1.86 
 
 . 21 
 
 0.65 
 
 1.92 
 
 .26 
 
 0.65 
 
 i. 80 
 
 .26 
 
 0.53 
 
 Diameter of tip 
 
 Substance. 
 Benzene. . 
 
 Temp. 
 30-5 
 
 " 60.7 
 
 Chlorbenzene ... 28.5 
 ... 65.0 
 
 Aniline 27.8 
 
 " 58.2 
 
 Quinoline 28.0 
 
 " 65.0 
 
 Water 25.5 
 
 " 56-9 
 
 " 79-2 
 
 Kp.D.= 
 
 Average KF.D. = i.248o.oi2 
 Mean error of a single result = 0.035 
 TABLE II. 
 0.62 cm. approximately, i mm. on burette = 0.00,008 cc. 
 
 Weight of 
 
 falling drop 
 
 in mgs. 
 
 WF.D. 
 
 33.64 
 28.50 
 39.10 
 34-07 
 50.99 
 45.91 
 53.58 
 48.47 
 87-85 
 80.55 
 75.20 
 
 Volume of 
 
 falling drop, 
 
 cc. 
 
 0.03880 
 0.03420 
 0.03561 
 O.O3220 
 0.05033 
 0.04675 
 0.04912 
 0.04572 
 0.08812 
 0.08180 
 0.07742 
 
 Specific 
 gravity. 
 
 0.867 
 
 0.833 
 
 1.098 
 
 1.058 
 
 I.OI3 
 
 0.982 
 
 1.091 
 
 1. 060 
 
 0.9969 
 
 0.9848 
 
 0.9722 
 
 Surface ten- 
 sion, dynes 
 per cm. 
 
 7 
 
 26.58 
 22.77 
 31.02 
 26.91 
 40.69 
 37.32 
 42.30 
 38.22 
 69.70 
 64.79 
 60.97 
 
 Average K F . D . = i . 253 o 004 
 
 Mean error of a single result = 0.013 
 1 It has since been possible to obtain still smaller tubing, and the work is now 
 
 being continued in this laboratory with a burette on which i millimeter corresponds 
 
 to about 0.000,046 cc. 
 
 * Commercial and impure; omitted in computing the average. 
 
15 
 
 t 
 
 ft 
 
 ff 
 
 Substance. 
 
 NO-*". Oi w 01 Oi Oi Oi M Temp. 
 
 *4 ON> O^JOiOi^l 10 00 
 
 g 
 
 a-S 
 
 oooooooooo 
 
 O O O 
 4*. 4* 4* 4* 
 K> 00 4 
 
 Oi Oi Oi Oi Volumeoffallingdrop.ee. 
 
 vO ^4 vO 4- Oi Oi M On 4* 
 *jOwtotOf*tovoONOi 
 
 MOMOOMMOO 
 
 bbobioOMOooo Specific gravity. 
 
 4*vo-4Mtost->O>o^i 
 vO 4* O 00 vO 
 
 ON vO 4>. O Oi 
 
 OO 00 00 Cn 
 n Oi 00 Ol 
 
 Weight of falling drop, tugs. WP.D. 
 
 ON Oi Surface tension, dynes. % 
 
 00 Ol *J 
 
 If 
 
 O M 
 
 8 S 
 
 ON 
 
 IMMMWMMNMM 
 
 M KJ ON Oi ^4 
 
 WF.D. 
 
 7. 
 
 Itl 
 
 t 
 
 '-'" 
 
 H- H- 
 
 O K) 
 
 M M M M M .' 
 
 
 b b M 
 
 ^i Oi O 
 
 jo 23 5 S * 
 
 ^ 
 
 II 
 
 0? ^ 
 
 
 
 vO ON 
 
 
 
 1! II 
 
 rr* n 
 O/*^ k\ 
 
 
 1 
 ^ 
 
 \J Is} 
 
 M -S -b 
 
 X S Oi 
 
 * o * M o S ep 
 
 Oi Oi to *^j O *^ 
 
 Oi Oi ON -^4 4> a) 
 
 
i6 
 
 sion, together with the data necessary for the calculations. The surface 
 tensions given, except those for water, are interpolated from the results 
 determined under the same conditions as our drop weights, i. e., against 
 saturated air of Renard and Guye, 1 those for water being interpolated 
 from the results of Ramsay and Shields, 2 against the vapor pressure of the 
 liquid. K p D , K F D , and K c D , in Table I, and K F D in Tables II and III, 
 are the factors by which the surface tension in dynes must be multiplied 
 to give the drop weight, in milligrams, from these tips. K F D is the con- 
 stant already mentioned in the real analytical expression of Tate's laws,, 
 when the same tip is employed. The tips used in Tables I, II, and III, 
 although made from the same tubing, have slightly different diameters 
 exposed, owing to the bevels being cut at slightly different angles. The 
 diameter of the tubing itself was about 6.5 millimeters. 
 
 Table I shows the reason for determining the weight of only the falling 
 drop with the more delicate form of apparatus. 
 
 In order that errors in the interpolations of the values of surface ten- 
 sion, as well as possible errors in the surface tensions themselves, might 
 not influence the conclusions as to the accuracy of Tate's laws, in Table 
 III, where the determinations are the most accurate, a check, has been 
 secured without any direct comparison with surface tension, by substi- 
 tuting the drop weights, of the same liquid at two different temperatures, 
 for the surface tensions in the well-known law of Ramsay and Shields, 
 and then comparing the constancy, for the various liquids, of the constant,, 
 ^temp. w ith that of those of Ramsay and Shields, (& R & s ) and Renard and 
 Guye (k R & G ). In other words, for 7- in dynes, in the relation 
 
 = = 2.12 ergs,* 
 
 has been substituted W FT> in milligrams, so that if surface tension (as 
 altered by temperature) and falling drop weight are proportional, for 
 any one liquid from the same tip, one should find the expression 
 
 ft y &temp. 
 
 just as constant as the other for all so-called "non-associated" liquids. 
 
 1 J. chim. phys., 5, 81 (1907). 
 
 2 Z. physik. Chem., 12, 431 (1893). 
 
 8 M is here the molecular weight as a liquid, d the density, and t the temperature. 
 
All the densities are interpolated from results found in the literature * 
 as were also those of both Ramsay and Shields, and Renard and Guye, 
 so that uniformity in the compared results is thus secured. 
 
 All chemicals, with the exception of guaiacol (Table I), which was im- 
 pure, were specially purified for the purpose. 
 
 The drop volumes throughout are each the average of several deter- 
 minations, the extreme variation in tube 3 (Table III) being 0.2-0.4 per 
 cent. 
 
 TABLE IV. 
 Drop weights for various tip diameters, t = 27. 
 
 WF.D. 
 WF.D. 
 
 6. 190 
 
 8.764 
 
 D. 
 Substance. DI = 4.68 mm. D 2 = 6.22 D 3 =7.i2. D a . D 2 . 
 
 Benzene 26.10 34-6o 39. 15 5-577 5-563 
 
 Chlorbenzene 29 . 70 40 . 40 45 . 10 6 . 348 6 . 495 
 
 Quinoline 41. 15 55.00 62.40 8.792 8.843 
 
 In Table IV are given the drop weights issuing from beveled tips of 
 various diameters. These results are not as accurate as some of the others, 
 for tube 2 was used as the burette, and the error in measuring the lower 
 end of the bevel is necessarily large. Under K' are the values of tfre con- 
 stant of Tate's first law, i. e., weight of falling drop divided by the diame- 
 ter of the tip. 
 
 TABLE V. 
 
 Substance. 
 
 Alcohol. . . 
 
 >-v- 7 
 
 Rounded tip. 
 Temp. A in Fig. 3. 
 
 58.4 0.907 
 21.5 0.934 
 
 / lor ups 01 various lorms. 
 Approx- 
 Bevel at 30. Sharpened edge, s^face 
 
 Temp. B i 
 60. 1 
 22.5 
 65.0 
 22.1 
 
 n Fig. 3. 
 .070 
 .090 
 .119 
 .127 
 
 Temp. C in Fig. 3. 
 21. 1 1.123 
 
 tensions. 
 
 19 
 22 
 21 
 29 
 
 Benzene. . . . 
 
 
 .... 
 
 . . 
 
 Chlorbenzene 
 
 64.0 
 
 0.932 
 
 67-9 
 
 .109 
 
 
 27 
 
 
 22.5 
 
 0.965 
 
 24.0 
 
 .129 
 
 22.0 I.I45 
 
 32 
 
 Quinoline. . . 
 
 64.0 
 
 1.024 
 
 72.0 
 
 .164 
 
 .... ... 
 
 38 
 
 Water 
 
 21.0 
 23.1 
 
 I.04I 
 I.OSO 
 
 22.6 
 25-5 
 
 .189 
 .220 
 
 22.6 I.I57 
 21.0 I.I55 
 
 43 
 72 
 
 
 Average 0.983+0.025 
 
 1 Approximately of same diameter. 
 
 i.i35o.oi7 
 
 . I45o.oo8 
 
18 
 
 Table V gives the results obtained by use of tips of various forms, but 
 of approximately the same diameter (see Fig. 3). Tip A, here, is rounded 
 at the end, B has a bevel at an angle of about 30, not sufficient to have 
 
 ABC 
 
 Fig. 3- 
 
 the effect of a sharp edge, and C, without bevel, has a very sharp edge. 
 All these were measured in tube 2, and consequently the determinations 
 are not as accurate as those in Table III. 
 
 TABLE VI. CRITICAL TEMPERATURES. 1 
 
 Prom 
 Fr m 7 (^) 2/3 = k(r-d). 
 
 Substance. M -\d/ R. & G. R. & S. Observed. 
 
 Benzene 286.6 285.8-289.6 288 280.6-296.4 
 
 Chlorbenzene 354-1 357.2-358.4 359-7 360.0-362.2 
 
 Pyridine 352.0 344.7-346.9 342 
 
 Aniline 439.4 448.1-449.1 404.9 425.7 
 
 Quinoline 492 . 3 495 . 6-496 . 9 466 . i <52O 
 
 And, finally, in Table VI, are the critical temperatures of the liquids 
 in Table III, as calculated by the substitution of the drop weight, W p D , 
 and k icmp for the surface tension 7-, and k in the Ramsay and Shields rela- 
 tion, 
 
 y(^)" /3 =(r-6), 
 
 where r is the difference between the critical temperature and that of ob- 
 servation, and M, d and k have the same meaning as before. 
 
 Discussion of Results. 
 
 It will be seen, even from Table I, where the experimental error in drop 
 weight is comparatively large, that Contrary to the conclusion of Guye 
 
 1 Here, in all cases, the temperature coefficient (k or ktemp.) used is the one found 
 for the specific liquid, and not the average values. 
 
 2 Calculated extremes from surface tensions. 
 8 Given by Ramsay and Shields, Loc. cit. 
 
19 
 
 and Perrot, the relationship between drop weight, from a properly con- 1 
 structed tip, and surface tension in saturated air, 4 is very much more than a 
 first approximation, even when the liquids examined include that giving 
 the highest, and that giving almost the lowest, surface tension known, 
 i. e., water at 70.6 and ether at 16.8 dynes per centimeter. 
 
 The results in Table II make this conclusion even more striking, for 
 they show that much of the variation in I is due to experimental error. 
 And, finally, Table III, where the accuracy in the determination of drop 
 volume and drop weight was the greatest possible at the time, shows the 
 variation in the constant relationship, for some of the same liquids ex- 
 amined in I and II, to be very small indeed. Here, with five liquids, 5 
 varying in surface tension from 25.88 to 52.62 dynes, each being studied 
 at two temperatures, the mean value of K F D for all cases, from a certain 
 tip, is 1.226 ;+ 0.0026; the mean error of a single result being +0.0083. 
 
 Although in these results the error is small, the discrepancy is still too 
 great granting the accuracy of the drop weights and surface tensions to 
 conclude that the proportionality is rigidly exact; even though the agree- 
 ment is about as good as that observed in results for surface tensions by 
 different methods, and little worse than that shown in the results by any 
 one method, by different observers. The error in drop weight cannot 
 in any case exceed 0.4 per cent., taking all things into consideration, and 
 is generally much less, consequently the discrepancy is only to be explained 
 either by errors in the interpolated surface tensions, or by actual failure 
 of the law of proportionality to hold closer than this (due possibly to a very 
 slight and variable, but unnoticeable, rise of the liquids on the walls of 
 the tip). When it is remembered, however, that the interpolations of the 
 values for surface tension were made from smoothed curves, which could 
 not always be made to pass through all the few points available, it becomes 
 very apparent that in some cases errors in the interpolated surface tensions 
 even as high as one per cent., are quite possible. If this be true, the law 
 of the proportionality between falling drop weight (from a proper tip) 
 and surface tension becomes rigid. To prove this directly and conclusively 
 has been impossible, for it could be done only by aid of a more delicate 
 
 4 According to Renard and Guye, surface tensions in saturated air and those un- 
 der the vapor pressure of the liquid do not differ by more than 0.5 per cent. 
 
 6 Unfortunately, ether could not be used in either tube 2 or tube 3, owing to in- 
 terference of a bulb; and the volume of tube 3 was too small to permit water to be 
 used with the beveled tip. 
 
2O 
 
 apparatus, with measurements of drop weights at the exact temperatures 
 at which the surface tensions themselves have been determined. 1 Below, 
 however, it is shown that the interpolated values of surface tension for 
 any one liquid are burdened with error, so that analogy would force the 
 conclusion that they, also, are at the root of the error when different liquids 
 are considered. 
 
 The conclusion follows then, from Tables I, II, and III, and from the be- 
 havior of tip C in Table V, that Tate's second law the weight of a falling 
 drop (from a proper tip) is proportional to the surface tension (against 
 saturated air) of the liquid is true. Because surface tensions calculated 
 from drop weights agree, even with those possibly faultily interpolated 
 from results by capillary rise, as well as those determined by other meth- 
 ods agree with these, when directly determined. 
 
 Consideration of the columns & temp , R & G ., and k K & s , in Table III, shows 
 that the constants, though calculated from results at only two tempera- 
 tures, are as constant as those of Renard and Guye, which are in each 
 case the mean of determinations made at several pairs of temperatures, 
 and are very much more constant than those of Ramsay and Shields, 2 from 
 results at two temperatures. It will also be observed that the variation 
 of & temp . from its mean value is always (when worth considering) in the same 
 direction as that of Renard and Guye's, for the same liquid. 
 
 This certainly proves conclusively that, with any one liquid, from any one 
 tip, drop weight is proportional to the surface tension, as it is altered by changes 
 in temperature, for, by substitution of drop weight for surface tension in the 
 Ramsay and Shields expression, leaving out any direct comparison with 
 the interpolated values of surface tensions, a result is obtained which is as 
 constant as that found by the use of directly determined not interpolated 
 surface tensions. And this is true when the interpolated values of surface 
 tension at the two temperatures lead to a discrepancy in the two values of 
 K F D , as calculated for that liquid. Although this proof is not direct, as far 
 as concerns different liquids, it leaves very little possibility of the slight dis- 
 crepancy in K F D being due to anything but the errors in the interpolated sur- 
 face tensions as concluded above. 
 
 We would conclude from the constancy of & temp ., in Table III, then: 
 
 1 This is now being done in this laboratory. 
 
 2 Although Ramsay and Shields' s values were calculated from surface tensions ob- 
 served under different conditions, their constants are still to be compared with the 
 others as to constancy. 
 
21 
 
 That Tale's third law the weight of a falling drop decreases with in- 
 creased temperature is true. And, further, that the change in drop 
 weight for a change in temperature can be calculated accurately for non- 
 associated liquids, by the substitution of the drop weight at one tempera- 
 ture for the surface tension, and & temp for k in the Ramsay and Shields 
 relation 
 
 -*, 
 
 and solving for the other drop weight. 
 
 Or, knowing the drop weights, & temp ., and the densities, it is possible to 
 find the molecular weight of the liquid, with an accuracy equal to that 
 attained when surface tensions are employed directly in the above rela- 
 tion. 
 
 Since the molecular temperature coefficient, & temp> , is found to be constant, 
 it is possible, by extrapolation, to find the temperature at which the drop 
 weight would become zero; i. e., the critical temperature of the liquid, for at 
 that point the drop would disappear, there being then no distinction be- 
 tween the gas and the liquid. It is only necessary, for this calcula- 
 tion, to substitute W T D for 7- and & temp . for k, in the other form of the Ram- 
 say and Shields relation, i. e., 
 
 and solve for the critical temperature (r plus the temperature at which 7- 
 (or W F D ) is determined). (See Table VI.) 
 
 It must be remembered here, however, that in all cases in which this 
 method has been applied, it has been done so at a disadvantage, for only two 
 points were had through which to draw the curve. Further than that I have 
 worked at low temperatures (never above 80), and consequently must 
 extrapolate from these two points through a much greater distance than 
 either Renard and Guye, or Ramsay and Shields, from their larger number. 
 The first objection holds for all the liquids, though least for benzene, but 
 the second hardly affects benzene, for 73.2 is not far from its boiling-point. 
 With all high-boiling liquids, both objections hold, and both increase with 
 the boiling point (and critical temperature). 
 
 From the equal constancy of k temp and k, however, it is evident that just as 
 accurate critical temperatures can be calculated from drop weights as from 
 surface tensions, against saturated air, provided in both cases the determinations, 
 
22 
 
 from which the molecular temperature coefficients are found, are made at 
 as many temperatures, and carried to as high a temperature. 
 
 Table IV, it is thought, shows that from such tips, between these diam- 
 eters, there is a direct proportionality between drop weight and diameter 
 of the tip (Tale's first law). At least there is no decided trend in the pro- 
 portional factor, for it varies just as one might expect it to from the known, 
 and fairly large, experimental error. It must be remembered that tips 
 larger than the diameter of the maximum drop would always deliver one 
 constant maximum drop weight; while, when the tip becomes small, there 
 is probably a point beyond which the drop will not decrease appreciably 
 in weight for a considerable change in diameter, for it would then be 
 difficult to prevent in any way the rise of liquid upon walls of the tip. 
 
 Table V shows that when rounded, a tip behaves differently from the one 
 in Table III ; the liquid rises to various heights on the outer walls, and the 
 diameter of the basis for the drop varies with the nature of the liquid. 
 This is also true, though to a lesser degree, with the tube that is insuffi- 
 ciently beveled. In neither case is K FI) even approximately constant. 
 Tip C, on the other hand, compares very favorably with the other beveled 
 one, used with Tube 2 (Table II). Whatever theory may be advanced, 
 then, as to the tip, it will be seen that the point to be considered is the 
 effect of the tip (Tate's "sharp edge") in delimiting the portion upon 
 which the drop can hang, especially by preventing the rise of liquid upon 
 the walls, for that would be variable with different liquids, and lead to 
 variable weights. Undoubtedly it is only the failure to follow Tate's 
 directions in this respect that has caused the determinations of drop 
 weights, since his time, to negative his conclusions. 
 
 Summary. 
 
 The results of this investigation may be summarized as follows: 
 
 1. An apparatus is described by which it is possible to make a very accu- 
 rate estimation of the volume of a single drop of liquid falling from a tube, 
 and consequently of its weight. 
 
 2. With this apparatus was used a capillary tip, beveled at an angle 
 of 45, which, contrary to those used by other investigators, had the same 
 effect as the one originally used by Tate, i. e., it delimits the area of the tip 
 wetted, by preventing the rise of liquid upon the walls, and thus forces 
 all liquids to drop from one and the same area. 
 
23 
 
 3- It is shown that whenever this effect is obtained, either by use of a 
 properly beveled tube, or one ground to a sharp edge, the drop weight 
 has a different meaning than it has when the drop is formed on either a 
 rounded tip, or on one insufficiently beveled. 
 
 4. The falling drop from a capillary tip, and not the pendant drop, is 
 proportional in weight to that of the falling drop from a thin-walled 
 tube with a sharp edge. 
 
 5. From such tips as were used, it is concluded that Tate's second 
 law the weight of a drop, other things being the same, is proportional 
 to the surface tension (against saturated air) of the liquid is true. 
 
 6. It is shown that from such a tip, Tate's third law the weight of a 
 drop is decreased by an increase in temperature is true. 
 
 7. Falling drop weights for the same liquid at two temperatures, from 
 such a tip, can be substituted for the surface tensions in the relation of 
 Ramsay and Shields, and molecular weights in the liquid state calculated 
 with an accuracy equal to that possible by aid of surface tensions, under 
 the same, saturated air, conditions. And, by aid of this formula, know- 
 ing the molecular weight of a non-associated liquid, the falling drop weight 
 at one temperature, and the densities, it is possible to calculate the weight 
 of the drop falling from the same tip at another temperature. 
 
 8. Critical temperatures can be calculated by aid of Ramsay and Shields' s 
 
 (M\ 2 f 
 ) 3 = k(r 6), by substituting a drop weight for surface 
 
 tension, and the molecular temperature coefficient of drop weight for k, with 
 the same accuracy attained by the use of surface tensions (against saturated 
 air), provided the drop weights (from which the coefficient is found) are 
 determined at as many temperatures, and at as high a temperature as 
 the surface tensions. 
 
 9. For beveled tips, when the diameters lie between 4.68 and 7.12 mm., 
 Tate's first law the drop weight of any one liquid is proportional, under 
 like conditions, to the diameter of the dropping tube is true. 
 
BIBLIOGRAPHY OF DROP WEIGHT ALPHABETICALLY ARRANGED. 
 
 Autonow, G. N. 
 Bolle, J. 
 Duclaux. 
 Dupre". 
 
 Eschbaum, F. 
 Guglielmo, G. 
 Guthrie. 
 Guye and Perrot. 
 
 Hagen. 
 
 Hannay, J. B. 
 
 Kohlrausch, F. 
 
 Lebaigue. 
 
 Leduc and Larcdote. 
 
 Lohnstein, F. 
 
 Mathieu. 
 
 Ollivier. 
 
 Rayleigh. 
 
 Rosset. 
 
 Tate, T. 
 
 Traube. 
 
 Volkmann, P. 
 Worthington. 
 
 J. chim. phys., 5, 372 (1907). 
 
 Geneva Dissertation, 1902. 
 
 Ann. chim. phys., 4th ser., 21, 386 (1870). 
 
 Ibid., 9, 345 (1866). 
 
 Ber. pharm. Ges., Heft 4, 1900. 
 
 Accad. Lincei Atti., 12, 462 (1904); 15, 287 (1906). 
 
 Proc. Roy. Soc., 13, 444 (1864). 
 
 Arch, scien. phys. et naturelle, 4th ser., n, 225 (1901); 4t 
 
 ser., 15, 312 (1903). 
 Berl. Akad., 78, 1845. 
 Proc. Roy. Soc. Edin., 437, 1905. 
 Ann. phys., 20, 798 (1906); 22, 191 (1907). 
 J. pharm. chim., 7, 87 (1868). 
 J. phys., i, 364 and 716 (1902). 
 C. r., 134, 589; 135, 95 and 732 (1902). 
 
 Ann. phys., 20, 237 and 606; 21, 1030 (1906); 22, 737 (1907). 
 J. phys. [2], 3, 203 (1884). 
 Ann. chim. phys., 8th ser., 10, 229 (1907). 
 Phil.Mag., 5th ser., 20, 321 (1899). 
 Bull. soc. chim., 23, 245 (1900). 
 Phil. Mag., 27, 176 (1864). 
 J. pr. Chem. [2], 34, 292 and 515 (1886). 
 Ber., 19, 874 (1886). 
 Ann. physik. (2), n, 206. 
 Proc. Roy. Soc., 32, 362 (1881). 
 Phil. Mag., 5th ser., 18, 461 (1884); 19, 46 (1885); 20, $ 
 
 (1885). 
 
BIOGRAPHY. 
 
 Reston Stevenson was born May 5, 1882, in Wilmington, N. C. He 
 received the degree of A.B. at the University of North Carolina, June, 
 1902 ; A.M. at the same institution, June, 1903. During the years 1 903-^4 
 and 1 904-' 05 he was assistant instructor in chemistry at The Cornell 
 University where he pursued, simultaneously, graduate work in chemistry 
 and physics. In May, 1905, he accepted a position as research chemist 
 with the Eastern Dynamite Company. He left this company to become 
 chemist at the Hudson River Works of the General Chemical Company. 
 In September, 1906, he left the General Chemical Company to become 
 Tutor in Chemistry at the College of the City of New York, and still 
 occupies this position. He has at the same time completed his graduate 
 work for the degree of Ph.D. at Columbia University. 
 
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