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"i' ■ - . ■ -„ NEW METHODS MEASURING THE SUR'FACE -TENSION ^i OF LIQUIDS, 1 vf Proctor Hall. ^ Approved as a diasdrtation for the degree of Doctor of Philosc^hy in the Department of Pbystcs «t ClArk Uni^ersit^. ABTHOBXa. WBBfiTBX. -i ..,-.J From the Piiir.osopiiiaAL MAOAziHe fur November 1893. '■■.,ul^ i NEW METHODS OF MEASURING THB SURFACE-TENSION OF LIQUIDS. BY T. PROCTOR HALL. I. Historical. THE common way of measuring the surface-tension of liquids by finding the height to which they will rise in capillary tubes is simple and convenient, and is applicable to nearly all liquids. The degree of accuracy attainable is limited by (a) the narrowness of the tube, or else the short- ness of the elevated liquid column, which limits the accuracy of measurement ; by (l>) irregularities in the bore of the tube ; by (c) the difficulty in securing a clean surface, particularly in very small tubes ; and by (d) impurities, such as dissolved air, in the body of the liquid. It is to the last two causes tha't most of the differences seen in the following table are probably due. The table gives the values of the surface- tension of water as found by various observers by means of capillary tubes. All values are given in dynes per centimetre, and the numbers in the second column are, where necessary, deduced by Brunner's formula for the relation of surface- tension to temperature. a Air. T. Proctor Hull on New Methods of J^urface-Tension of Water, by {•n])illary tubes. T. 744 at 0° C. 7.5-2 -140.'))'. 740 lit 8°-fi. 7,50 at 0''. 75-4 -141 ^ 75 6 -HO I". 74!Jat8°-5. 73 7 lit U". 7»1 at 10°. 771 --179 ^ 710 at i9°-25. 71 It l()°-2. i72-lbetw.l5°&20°, 71-8 at i7°-.5. 797 -•204(1. 75-4 --144 if. 71'3 at l(i°-2. 75 8 -•14;.' ^ 7(i5 --144,'. 77^3 -•14nfi,'. 549. Tat 0°0. Mean 744 75^2 75-2 750 754 75-6 75-4 75-2 74-5 77-1 737 7;{3 y 743 79-7 75-4 73-6 75-8 7(V5 773 ? 75^4 Observer. Artup. Bruimer. Desiiin. Prankenlieim. Frankonheini. Frankeulieiiii & Sondliansa >• Qay-Liissac. Hagcn. Jiiger. Mogie. Quincke. Quincke. Kodonback. Simon. Sondhauss. Volkmann. Volfcinann. Wolf. Wolf. Wertheiui. Reforenee. Thiorie (Mmriitaircae la capillarite. Pogg. Ann. Ixx. p. 481 (1847). Ann. C'/iim. l>hi/i>. li. p. o83 0*^57). Pofig- '■'«". XXX vii. p. 409 (183()). " Pogg. Ann. Jxxii. p. 177 (1847). Juiirn. I'r. Chrm. xiiii. p. 401 (1841). f Poisson, Noui'clle Thiurie etc. nn. I 112,181(1831). '' Pogg. Ann. Ixvii. pp. 1, 152 (184(!). licM. xvi. p, 345 (1892) ; Wiener H1 (1882). Pogg. Ann. eii. p. .571 (1867). Ann. Ckim. Plii/.t.xUx. p. 2(1',) (1857) Pogg. Ann. eii. p. .598 (1857). Capillary plates have been used by u few iuvestimitor.s in punce of capi lary tubes, wich no apparent advantaoe? Volk- inann* found /or water .t i6° C, T = 71-8 dynes (74 at zero), while Werthennt and HagenJ obtained values approachim' 00 dynes. * * » Wertheini § and Hagen || obtained equally low values by measuring the capillary elevation of water at a single vertical plane wall. Quincke «[!, neglecting the curvature in glass bottles 50 inilhm. in diameter, deduced from the capiTlarv elevation of water in them T=86-2 dynes at zero. This method is obviously of no practical value. In all of these three methods il is assumed that when the solid wall is wet by the liquid the angle of contact is zero. Ihe validity ot this assumption has been questioned by 'Quincke, who maintains** the actual existence of a finite * Wied. A7in. xi. p. 177 (1880). t IW ^»n. on p 595 (1857). | Ibid. Ixxvii. p. 4.53 (1849) § Ibid. cii. p. 595 ( 1857). II Ibid. Ixvii. pf . 1, 153 (1846) J Ibid. cxxxv. p G41 (I868),and Phil. Mag. AugustYsGO, p 05 ^• ♦* Quinc) ., M led. Ann. xxvii. p. 210 (1886). ^ fcthnds of illiiry tubes. Heforoiico. '(mriitaireac la capillarite. n. Ixx. p. 481 (1847). '«. I'hi/K. li. p. o83 (1857). >i. xxxvii. p. 40»(18a(')). >i. Jxxii. p. 177 (1847). . Chem. xxiii. p, 4()1 (1841 ). Noufclh Theorie etc. nn. 81 (1831). ^^ I. Ixvii. pp. 1, 152 (184(5). . p. 34:) (1892) ; Hhncr . '.)!)& 100 (1801). II. XXV. p. 432(1885). '.oxxxir.p. 1 (1870); Pliil. [)ril 1871, p. 252. '. clx. p. 371 (1877). ). I(l.'-(!e80). (. J'/ii/8. xxxii. p. 5 (1851). '. Erg. viii. 1878, p. 2(i(i. *. xi.p. 177 (1880). (. xvii. p. 3<51 (1882). . fii. p. 571 (1857). .i%.».xlix. p. 2()'.)(1857). . pii. p. .W8 (1857). ew investigiitors in advantage. Volk- Jyiies (74 at zero), values approaching ally low values by at a single vertical curvature in glass from the capillary nes at zero. This ned that when the of contact is zero, en questioned by itence of a finite xvii. p. 4.53 (1849). vii. pp. 1, 153 (1846). just 1869, p. 06. Afeasuring the Surface-Tnislon of Lhiuids, 3 contact-angle in some cases in which the wall is wet by the liiiuid. In .^'iipport of this assertion ho gives the msnlt of a large ininiber of measurements of bubbles and drops, from wliicli tli(! surfac(vtension is found to be consitlerably greater than the values found from the measurement of elevations in capillary tubes. For water at 2.')° C the mean of a small number of niea.surements, which differ from each other by ten per cent, in some cases, gives* T = 8i dynes (84".5 at zero). Worthington f [joints out that Quincke's fornmla is only roughly ap[»roximate under the conditions of his measure- ments, and recalculates son»e of his results. The number 8 1 is thus reduced to 72'1 (7,5'G at zero). Magie| prefers the value 77"G (81 1 a, zero), calculating from the same data. J'rom his own measurements of drops ami air-oubbles Magie§ found for water T=7;-9 dynes .it ?2°-.5 C. (75-1 at zero). Timbergll from similar measurements fouml T = 80'5 — •182< for water. BravaisH and others have used the same method for otlier ]i([uids. The discussion regarding these results has j)ut a premium on methods which i^re independent of a contact- angle and whose mathematical relations are undisputed. Buys-Ballot**, who made a large number of determinations of the surface-tension of water between 10° and 97°'8 C. by a Ihesion-disks, calls attention to the rapid decrease in the adhesion ol the disk as the boiling-point is approached. This is no doubt due ;o disengagement of vapour near the surface of the disk, and may pemips be an indication .that the water was not compietel}' deprived of air. Buys-Ballot gives T = 7.5'l — 'SSfU dynes. Merianft objects both to the calcu- lation and to the formula used, and calculates from the same data T=: 7 8" 5 — * 253 ^ Hagen$+ finds by this method a result much too low for the tension of pure water. Weinberg §§ finds T=80-l — -177< dynes. Miss Poekels|||| obtained some interesting qualitative results with very simple apparatus. The surface-tension has been calculated from the weight of drops falling from a small disk or tube of known perimeter by HagenlTl, Timberg***, and others.' Quinckeftt founfl in a * Quinclie, Pogg. Ann. cxsxix. p. 1 (1870) ; Phil. Mag. April 1871, p. 253, t Phil. Mag. July 1885, p. 51. § Phil. Mag. Aug. 18^8, p. 171. H Ann. Chim. I'hys. v. p. ''92. +t Ibid. Ixxiii. p. 486 (1848). X Wied. Ann. xxv. p. 437 (188.5). li Wied. Ann. xxx. p. 545 (1887) ** Pogg. Ann. Ixxi. p, 191 (1847) X\ Ibid. Ixxvii. p. 4(54 (1849). §§ Bdbl. svi. p. 400 (1892) ; Jotirn. nc Physique, Sept. 1892, p. 378. III! 'Nature,' xliii. p. 4.37 (March 1891). ilH Porrg. Ann. Ixxvii. pp. 449, 458 (1849). *** Wied. Ann. xxx. p. 545 (1887). tt+ IVT' ''^nM. cxxxv'. p. 021 (18(>8). a 2 ii il 4 Mr. T. Proctor Hall on New Methodn of Hunilar way tho tension of metallic wires at or near their meltinjf-points. FroTunieasiireinontH of pendent drops of water Worthincton* found T=r75 dynes at 1(P C. (77 at zero). Henry f and Voillel measured the contrnctilo force of soap- bubbles formed on U-tubes. ^ Dupre§ sufrgcsted that the existence of a distinct tension ma soaj»-tilm mifj;ht be shown by its effect upon a straight wire laid across the legs of another U-shaped wire when a film is formed between. Van (ler Mensbrugghe II had already measured tho tension of such a film in a wire frame by finding the weight supported by tho free end of a string which was fastened to the frame and looped within it, so that tho film was bounded by the greater part of the wire frame together with the outer edge of the circular loop. Van der Menshrugghet also added weights to the lower of two equal horizontal circular wire lings until the barrel- shaped bubble formed between them became cylindrical. Sondhauss**, who employed the same method, dispensed with the lower ring and suspended the upper from the arm of a balance above the liquid. In this way he obtained as an approximation T=:7(j--18«< dynes for water between l°-6 and lti°-(; C. Timbergtt found T = 80-8- -221 < dynes, using for calculation the maximum increase of weight as tho ring ia raised from the water-surface. CantorJI calculated tho mtio of the maximum weight to the surface-tension, and found for water T=72-3 dynes at a temperature not stated. Terquem§§ connected the ends of a horizontal wire by two equal strings to the ends of another wire of the same length above it. He then hung a small weight to the lower wire and measured the curvature of the strings when a film was formed between them. Magie || || measured the curvature of the lower part of the meniscus in a capillary tube, and concluded that if any contact- angle exists at all when the liquid wets the tube it is very smalL He found for water at iy°-250., T = 70-8 dvnes (73-6 at ! «f°f- ^"^^ ?"''• ''^^"- P- ''^"2 (1881) ; Phil. Mag Jan. 1885, p. 46. t Phil. Mag. June 1845, p. 3G;1. X Journ.de P!iysique, iv. p. 313. § Theorie micanique de la'Chaleur, 1869. II Phil. Map. April 18»7, p. 270. % Ibid. ** Popg. Ann. Erg. viii. (1878) p. 266. tt Wied. Ann. xxx. p. 545 (1887). tt Ibid, xlvii. p. 390 (1892). §§ JoHin. de Physique, vii. p. 406 (1878). nil Wied. Ann. xxv. p. 482 (1885). »p Methiuh of iros at or near their if water Wortliington* itractilo force of soap- ) of a cliHtinct tension ;!ff(!ct upon a straight -sliajied wire when a measured the tension the weight supported istened to the frame was hounded hy the ith the outer edge of 'ights to the loAver of gs until the barrel- l)ecanie cylindrical. )tliod, dispensed with 'r from the arm of a ' he obtained as an wat(>r between 1°'6 — '221 1 dynes, using weight as the ring is \ calculated the mtio nsion, and found for it stated. rizontal wire by two e of the same length t to the lower wire ngs when a film was lie lower part of the d that if any contact- i the tube it is very = 70-8 dynes (73-6 at Jag Jan. 1885, p. 40. A. . xlvii. p 3y0 (1892). Meaanring the Sur/aee- '/'fusion of fji/uids. 5 zero) as compared witli 7I'() by the common method at the same temperature. Willu'lmy* weighed a rectangular plate of known dimen- sioMs and specific gravity wht>n (lippetl u determinate distance into tli(^ Ii<|uid. Ho made a large number of determinations which agreed closely for any one plate, but varied greatly for [dates of different materials in the same liquid. Using a glass plate in water at {f C be found T = 77-il dynes, assuming that the angle of contact is zero. Waterstont and WorthiugtonJ modified Wilhelmy's method, touching only the lower edge of the plate to the limiid surface. Sentis§ measured with a spheromoter the hiMglit of a weighed ami measured rectangular iron plate floating on mercury, eliminated the irregularity due to the corners by nujans of a second i)late of the samo thickness and density, and deduced the value of the surface-tension of the nu'rcury. Lenard || arranged a regular succession of falling drojts so as to be seen by intermittent light ; measured the extent and time of their oscillations ; and from these dai calculated the surface-tension. For water he found T = 70-3 dvnos at 1(5° C. (72'G at zero), the mean of a considerable number of deter- minations. With reasonable care in this method u clean surface is ensured, and no question of contact-angle interferes with confidence in the results. RayleighH measured the wave-length of the transverse vibrations of water-jets issuing under constant pressure from elliptical orifices. The results, which are not closely con- cordant, are in harmony with the supposition that the surface- tension is about 7G dynes. Rayleigh** also measured the wave-length of ripples and calculated the surface-tension by Thomson's formula. Par- ticular attention was given to the purity of tlie water-surface, and the results appear to be free from constant errors. Individual determinations differ by 2 dynes in a few cases. The mean of all, for both distilled water and tap water, is T= 73"9 dynes at 18° C, corresponding to 75-4 at zero, which happens to be exactly the mean of all the results quoted for capillary tubes. The correctness of the assumption formerly made, that when a liquid wets a solid the angle between the two surfaces may be considered zero, is now pretty well established. * Togg. Ann. cxix. p. 186 (1863). + Phil. Mag. Jan. 1858, p. 4. t Ibid. Jan. 1885, p. 43. § Jouni. de Phys. ix. p. 384 (1890) ; or Phil. Mag. Dec. 1891, p. 564. II Wied. Ann. xxx. p. 209 (1887). ^ Proc. Roy. Soc. xxix. p. 71 (1879). •* Phil. Mag. Oct, ISiX), p. 386. - ^w - tfiw w' ii wj!i A .¥J i fj it v m m ^ nn 9 u m m f ^ J* fl I\lr. T. Proctor Hull on New Methods of 'bioiw of tlic iiictliod-* in use seem to exceed In f,'en(r cdnvenience tlio ordinary plan witii caiiiilary tuhoH, tlie liniitah'onH of wliidi liavo heon aireiuly rofcrred to. Tlio direct dependence (yf siirt'ace-tonsion upon niolectdar cohesion, and itsconse(|iient importance as areiialtle indication of clian;i('s of condition in iicpiids, niakes it very dcHiralde that some more accurate plan of measurement shoiihl he devised. • II. Nk\v ]\Ii.:tiioi)s. Two yours ajjo, iif tlie sne;/uids. if the greatest attainable accuracy is desired, I p' lid advise a different arrangement. A deep, thin-walled gl.. s dish with a close-fitting cover in which are three holes — one in the centre for the arm of the frame, one for the thermometer, and one for the stirrer — should fit loosely into a double-wallod box, also partly covered over the top, within which are air- or water-pipes, resistance-c jils, or other arrangement for con- trolling the temperature. The large wooden closet of figure 2 may then be replaced ly a simple subsbelf for the box. For volatile liquids it is necessary to keep a slow current of air passing down the tube from the balance, to prevent condensa- tion of the liquid on I'he rod that carries the frame. A small correction is required for the capillarity of the sides n w of each frame. When the film is broken after the first weighing, a capillary elevation remains completely surround- ing each side, n (fig. 1). But our calculation of the tension is based on the assumption that during the second weighing no tension is exerted at all between the sides 7in. In effect, the difference between the two weighings gives the tension of a film a little narrower than the frame. The amount of this correction was found by laiving the tension of the same liquid with two or more frames of the same thickness but of different widths. An example will explain the method. The surface-tension of distilled water at 19°* 5 C. was mea- sured with three frames, whose widths a, b, c, and whose ten- gion-weights m, n, r, were respectively a = 5*2321 centim. 6 = 2-0325 „ c=0-2037 „ 7u = "774:2 gram. n=-3001 „ r = -0291 „ Disregarding the capillary correction, the resulting values for the surface-tension in grams per centim. are : — 2a"" •073985, n •073825, r 2c ~ •0714. The true value of the tension, however, is T = m 2(a-.i-) 2{6-.<;) 2(c-.i') ';1WBS*— ■' 10 Mr. T. Prootor Hall on New Methods of Eliminating ,v by the principle of proportion T = m—n m — r n—r also 2{n-lj) 2{a-c) 2(/>-o)' "^"""^T" 2T ■ c— 2T' from which the following; values aro obtained : — T (grnni) X (ceutini.). •074089 •074088 •074092 •0074 ■0073 •0073 Mean ... -074090 •0073 The value of .v, for rigid frame.s, depend.s almost wholly upon the thickness of the vertical sides n n. If the frame be so slender as to allow these sides to approaci each oth(>r sensibly under the tension of the film, the value of .x will be increased. The following results were obtained in the course of my work : — Widths of frames, in centim. 5-23 203 0-20 1V76 092 11^22 1-06 11-88 O-Ofi Thickness of sides (centim.). 025 to 029 ■038 to 040 •076 to 080 •028 to •033 Liquid. Water. .50 per cent, alcohol. Water, T (dynes). .1- (contiin.). •0073 JCotOR. Frames nearly rigid. 720 72-8 •0073 Rigid. 734 •0191 .. 30-3 •0186 tl . 72-9 •0136 Slender. M -0139 M The capillary coirection for a rigid frame 10 centim. wide, whose vertical sides are half a miHimetre thick, does not exceed 1 jiart in 1000. -' ost wholly e frame be eacli other " .v will he the course ?Cote«. Frsiines nearly rigid. Rigid. Slender. tini. wide, , does not Measuring the Surface-Tension of Liijuids. 11 The weight required to balance a film of soap solution increased slightly for some time after its formation. The apparent tension of films of glycerine and of strong sulphuric acid decreased, at first rapidly, then more and more slowly for several minutes, finally becoming sensibly constant. The whole amount of inci-ease or decrease after the first few seconds was generally about -02 per cent, of the tension. The ai)parent tension of a film of water was in all cases sensibly constant as long as the film lasted. This seems remarkable when it is remembered that the water-film must have been growing thinner by evaporation, and also that the water under the bar m and along the sides ii n was gradually flowing down into the licjuid. The first process tended to decrease the weight very little and to increase the surface- ' ^nsion by lowering the temperature ; the second to decrease the weight. A change of one part in ten thousand could be readily detected. The second weight — the weight of the frame plus adherent water after the film is broken — is variable. If the film is broken two or three seconds after its formation, the weight of the frame may be two or three milligrams greater than it is when the film lasts ten seconds. But the differences when the film has lasted more than five or six seconds are very small , amounting to only one or two tenths of a milligram for a frame 10 centim. wide. This variability in the second weighing marks the limit of accuracy of the method as about one part in 5000, or -02 i)or cent., though a change in the tension amounting to less than •01 per cent, may be readily measured. It will be shown later that the bar m must bo raised from five to ten millimetres above the liquid surface before a true film is formed, and that the tension is not correctly found at a less height. It follows that the tension of alcohol, ether, chloroform, and similar liquids, in which the film breaks almost instantly at such a height, cannot be found by this method. B. In order to find the surface-tension of such liquids I adopted a modification of Wilhelmy's method. When the edge of a thin vertical plate is touched to a liquid surface, the liquid usually ri.'ses along the line of contact, and the weight of the plate is increased by w = 2(a + /j)Tcos^, where a is the length and b the thickness of the plate in centimetres, T the surface-tension in grams per centimetre. ,./ nl! » • # l# Mr. T. Proctor Hall on Neto Methods of and d the contact-angle. When the plate is wet by the liquid, ^ = and to = 2(a + i)T. When the lower edge of the jilate is kc])t at the general level of the surface, as in fig. 4, the thickness of the plate Fig. 4. is of uo consequence ; but if it be placed h centimetre too high or too low there will be an error introduced equal to the weight of the liquid supported under the plate or dis- placed by it. That is to say, if p be the density of the liquid and h positive when the plate is too high, an error of ahhp gram is introduced. This error becomes very small without material alteration in to when the plate is made very thin. In practice I found that for a plate 10 centim. long h rarely exceeded +-01 centim., and that the amount of this error of setting for a plate -005 millim. thick was not more than gifj milligram ; or, for alcohol, about "Ol per cent, of the surface-tension. Thin plates were placed in a holder (I'lg. 5) made of glass Fig. 5. n/ / K "^f l)=4 rods 1 millim. thick. Before inserting a plate the Jiolder was balanced so that the stem hung vertically. The spring- clips c (also of glass) were then wedged with little bits of wood, the plate inserted under them, two of the clips released, and the piate adjusted by trial over a liquid until the whole . • « wet by the tho gonenil of the plate [itimetre too !ed equal to late or dis- isitj- of the , an error of i very small s made very :entim. long loiint of this IS not more ler cent, of ade of fflass the holder The spring ittle bits of ps released, I the whole Measuring the Surface-Tension of Lujuids. 13 edge seemed to enter the liquid at once when loweced, and when raised slowly parted from the liquid first at the two ends and lastly in the middle of the lower edge. After adjustmeut the' holder and plate were washed, dried over a Bunsen flame, attached to the balance in the same way as the frame (flg. 2), left hanging over the liquid to l)e examined until the temperatures were nearly the same, then weighed. The index of the balance was next "set exactly at zero, taking care that the beam was not lifted, and the liquid slowly raised by turning the screw-handle s until it touched the plate. The weight was again adjusted to bring the index exactly to zero. For a second determination the plate was lifted out of the liquid by tipping the balance-beam, the liquid lowered a little, and after all visible disturbance of the surface had ceased the operation of setting was repeated. The surface-area of the liquid must be so great that the measurement is not sensibly increased by the lowering of level due to the capillary elevi'.tion; or else this must be taken account of in the calculation. It was necessary to ascertain, in the first place, whether the contact-angle can be considered zero to the limit of accuracy attainable by this method, and if so under what conditions. I proceeded to try plates of various materials in some liquids whose tension could be found by Michelson's method. (1) Glass Plate in glycerine. A microscope cover-glai!s, 5-044 centim. long and -026 centim. thick, was cleaned, dried, and touched to the glycerine surface without being allowed to sink even momentarily deeper. The first three weighings were made rapidly ; the last three after an hour's contact. w (grain). TcosS (dynes). Temp. C. ■ o 1. •6405 61-92 16-6 2. •6391 61-79 1) a. •6420 620() 11 4. •6550 63-32 169 5. •6538 (5307 »» 0. •6534 63^12 " The tension, as found by Michelson's method immediately afterwards, was 63-14dvnesat 17°C. ' !I 14 Ml'. T. Proctor Hull on Neto Methods of The prror ofaotting Ciilculated for this plato is +"13 dyne. Tlie anglo of contact may therefore be considered zero for glycerine and glass if time is allowed for attaining equi- librium. (2) Plaftnnm in (jlycerine. In the same liquid a platinum plate, 6*375 contim. long, •0045 centim. thick, was toucl ed to the surface and let stand a few min-ates. The "rror of setting is + "02 dyne (3) Glass Plate in taji-ivater. The same plate as in (1). w. •7585 •758] •7683 TcosO. 73-33 73-20 73-31 Tonip. 0. O 14.52 14-55 14-68 T, by frama, =73-32 at 14°-41. (4) Platinum in tap-water. The plate used in (2) in the liquid of (3). w. TeosO. Teiiip.C. -8018 -05-11 ■'J535 • -0538 7330 73-26 73-28 O 14-8 »> The first weight was taken with the same precautions as before to prevent dipping below the water-level. In the other three cases th.e plate was dipped I millim. into the water, to wet it. The correction for — 0°*4 is + "06 dyne, which makes the mean of the last three results 73'34 dynes at 14°-4. P15r?S^fS3!W»*" JO/ is +*13 dyne, ered zero for staining oqui- centim. long, and let stand 0. 0. irecautions as i\v\. In tlie llim. into the is + "06 dyno, s 73'34 dynes MeasHi'ing the Surface-Tension cf lAijuids. (5) PUitinum in distilled lonter. Plate the same as in (2), dipped I nr'lini. 15 MI. T c(»n e. Temp. C. ■',),-)44 7;ia2 O liV28 1510 The mean of these coiTes])onds to 73'31 dynes at 15""04, at which tlh' tension was found by a frame to bo 73*3() dynes. Another trial with water freshly boiled gave with the i)late T cos ^=72-10, and with a frame T = 72-7(;, bothatl!)°-9C. In all these cases the platinum j)late was washed with a caustic soda solution, well rinsed either in distilled water or at the ta]), and made red-hot in a Bunsen flame before touching the licjuid. 1 found that if the plate touched the liquid surface before it had time to cool after leaving the flame, the contact- angle would remain (sensibly) zero for a few minutes, without dipping the plate at all. It seems probable that condensation of air upon the ])late may be one cause of the failure to get a zero angle. When the plate was washed without alkali, ■with or without acids, I failed to make the contact-angle even approximate to zero. (G) Platinum in a dilute solution of caustic soda. Plate the same as in (2). to. •9023 TcosO. Temp. C. 09-32 10-24 •9t)19 69--'0 10-24 •9019 (19-29 10-22 •9019 69-29 16-20 By a frame, T= 69-36 dynes at 16°-17. (7) Silver plate in distilled xoatcr. This plate was 7'625 centim. long, •00''5 centlm. thick. It was washed in caustic soda solution, then in water, and dipped 1 niillim. into the liqiud before each weighing. T^r^sm* 1, :. TiiV I I li < I: >■ u Mr. T. Troctor Hall on Nexo Methods of w. TcobO. 6427 Temp. C. lOlOO 17°7() looao (14'4G It l(X»3f) IM4» »' I'OO.'iO 70-37 1800 1(1853 C9-7H 1770 108:) » (Jit -;] n 1. 2. 3. 4. 6. fi. Bv a frame, T= 72-84 dynos at 18°-37. Boforo the fourth woigliincr the plate was warmed over a Bunsen flame., touched iinmodiately to the water surface, aud allowed to remain in contact ten minutei. 5 and were tjiken after two hours of contact. (8) These results, along with soin& others of the same kind, show that the contact-ijngle can be considered zero for • 1 1 • Glass and water, sulphuric a>nd, glycerine, Mica and water, Zinc and water, when the surfaces are clean, and, in the case of zinc, freshly shaved ; and that the angle for Platinui.i and water, Silver and water, can he made zero, or nearly zero, with certain precautions. In every case it is easy" to see by a glance along the lino of contact in a good Hght whether the angle of contact is zero or not. (9) Though there could be no reasonable doubt that the angle of contact for alcohol and similaf liquids would be zero in nearly all cases, as some observers have supposed otherwise I thought it worth while to measure the surface- tension of alcohol by several diflFerent plates. If there is a finite contact-angle for each plate, the values found for T cos will be different. If these values are all alike, it is reason- ably certain that the contact-angle is zero. The following table gives the results. In no case was any difFoi..ice found in the weight atier dipping the plate one or two millimetres into the alcohol, provided the plate was then allowed to stand two or three minutes in the normal position. During the operations the surface-tension probably increased a little by absorption of water-vapour from the air. "./ p.C. o •70 00 70 irnipil ovor a surface, and ) and (J were of the same isidered zero pine, zinc, freshly )recaiitions. ilong the line of contact is oubt that the lids would be lave supposed 3 the surface- If there is a ind for T cos I, it is reason- The following [Foi..ice found vo millimetres iti allowed to tion. During jreased a little Measuring tlu Jurface-Tension of Liquids. Common Alcohol. 17 Plate. Length (ccntitu.) Thick- ness (centira.) ToosP (dynes). Temp. C. TcosO at 16° C. Variation from mean of(l) aud (2). Error of setting, calcu- lated. Platinum (1) 0375 •0045 23-38 23-38 15-80 It 23-36 2a-36 -02 -•02 -02 dyne. Zinc 12-3005 •0105 23-52 23-53 16-00 16-y2 23-51 23-52 + 13 + 14 •05 „ Silver 7-025 -0025 23-56 23-67 1600 It 23-66 23-67 +•18 + 19 -01 „ Tin 11-480 -004 23-34 2334 10-20 10-24 23 30 23 30 -02 --02 •02 „ Qlagg 5-044 •026 23-40 23-41 10-30 23-43 23-44 -^-o6 +-06 •10 „ Platinum (a) 13-481 -002 23-37 2337 16-43 If 23 40 23-40 + 02 + 02 •01 „ The zinc plate was slightly wedge-shaped and not very regular on the edge. There was no such irregularity in the silver plate ; but on watching closely I could see that the alcohol crept rapidly up the plate, wetting it to a height of several mi' ilmttres above the normal line of contact. Several other trials v tl. a silver plute showed the same peculiarity. There may have been something similar happening on the zinc plate, but if so I failed to detec^ lu Mica plates give the same result as plates of platinum and glass. A platinum plate, if it can be obtained of the right thick- ness, is most satisfactory for liquids like alcohol. But mica makes a very good substitute. Mica can be split into sheets 10 or 15 centim. square and less than one hundredth of a millimetre thick by a thin paper-knife under water. The thin sheets may be floated upon sheets of paper, taken out and left to dry. They are easily cut with the point of a sharp knife when lying under a sharp-edged rule upon a glass plate; but they requi ^ rather delicate handling at every stage. One of the difficulties of this method is caused hy the ten- dency of minute specks, if there be any on the liquid surface, to gradually collect upon the plate aud aflfect the measure- ment more than they affect the tension of the whole surface. A platinum plate should therefore be occasionalljr heated in the Bunsen flame, and for this reason it is convenient to have the plate in a metal holder. On a mica plate the effects of b . • . 18 Mr. T. Troctor Hall on New ^fethods of dust &c. are more easily soon, but i oa careful wasliinK with a soft brush. Under favourable conditions — a fresh clean surface, con- stant tem|)eratiiro, no dust, no disturbing vapours — a hi^^h degree of accuracy is attJiinablo by this method. The fol- lowing are selected from my results when these conditions were most nearly fulfilled. 1. Platinum plate, 13-495 centim. lonfj, '0045 contim. thick, in i)9'8 per cent, alcohol. Error ot setting, calculated, •02 dyne. w. T (dynes). Temp. -6210 •62095 •6209 •6209 22-5'18 22 543 2S537 22.')37 18-22 18-25 1829 18-31 The temperature-correction for 0°'l is —•008 dyne. 2. Mica plate, 11'3180 centim. long, '0007 centim. thick, in common alcohol at 17°'20 C. Calculated error of setting, •003 dyne. w. T (dynes). •55304 •55307 •55306 23-949 23950 23-960 3. Mica plate, 11*42285 centim. long, "0004 centim. thick, in common alcohol. Calculated error of setting, '002 dyne. w. T (dyne.). Temp. •56360 •56363 •66.363 24-183 24-184 24-184 1620 1624 16-26 0. It has been already stated that, in order to form a true film between the liquid and the bar m of the frame (fig. 1), this bar must be from five to ten millimetres above the level surface. Even when the bar is excessively thirj a distinct f fill washing 11 r face, con- irs — ii hi^h I. Tho fol- 3 conditions mtim. thick, calculated, yne. mtim. thick, r of setting, mtim. thick, •002 dyne. n a true film (fig. 1), this ive the level a a distinct Menmring the Surfacc-Tension of LiiiHiih, ID miixiinnin of weight is notio<>al)lo uh tho frnnio is rnisod, just hoforotlic true (l()iil)lo-fihii is formtMl. TImh miixiniiini fnii he found vory oxuctiv, and is mad*, tho l)a»is of a third inutiiod of inoasiiring surfaco-tcn.sion. An ('(Illation to th(* r'ajiillary cnrvo is found in tho cxprcs- eion oftiuv tiu^t, that tho vertical eoin|)()nent of tho Hurface- tension at any point is equal to tho weight of liquid raised ahove the levtd surface, hy the curved surface, from the lov(d up to a perpendicular through that jioint. That is to say, taking a section of the capillary elevation of unit thickness T8ina=y/3l ydjtt, (1) wl lore = the angle made hy the tangent with axis of x (the level surface) ; T = the surface-tension, in dynes per centim. ; p = tho li(|uid density; g = the constant of gravitation. lf6-''' = 4%/), then dx And since tan u=di//dx, -J- = -f- C08«. da iy Integrating, di/ da = T sm a. 4y cos«= — -„-^-; (2) .♦. / = tanaoi ^ dx Integrating again. ±y^- cos^ _ ±2y\/c^-!i^ co8« ~ -''p//ac — r'py m\ » coh «, " l2 where .ry ia a point of contact of the cylinder and the Hurfaco film. FJg. e. or i + 2r_y Hin« + r''«— r'»in«cos« r, . (4) We have also (fig. G) /t=y + y— r COS*, .... ••• ^^^y-^-iy' • • • • from (2), (5) (6) .'. y=x- (v/c''' + 8r/t— c) Equations (4), (5), and (6) are sufficient to determine to when /j, r, p, and T are given. The condition that v} snail be a maximum is that dtPldh = 0. Now dw _ dw ^ d» dh ~ da dh 'J* fc' . o I o • o' sin « , 3 , . 2 1 s!-j7/3< ^cos« + 2rycosa + 2rsma -J f-2?'^sm''« y, liiidcr and I' nuliiis of rums, tlien Met, \, . . (4) the surfaco . . (5) . . (6) itcrmine w t dic/dh = 0. 2?-' sin in2«|, Measuring the Surface- Tenn'um of Lvjuida. 21 and puttinir lor cosm and sin« tlu'ir vuluuH t'rum (2), thu condition tiuit ro hIuiII ho a niaxiniuni is 16r»/ + 1 ichy + '2v\c'' - 8r»).v - 8cV// - c* = 0. . (7 ) Tho numerical value of y may be foimd in any particular cuHO by a8SUiniu/4 tbak when to in a maximum «= ^ , and finding for c" from (l) an approximate valiu) to use in (7). /'» i: :i maximum wlien ilhjdw^O, in which ca.s»« a = 7r and tc=i7rr''p, Hut before this condition is attained the liijuid surfaces meet below the cylinder and form (in some casus) a film. This occurs when (tig. tJ) + *=+rsinfc, c = ^ log <^±^^^ -y' _ \^c'-y'+ -51572 c, from (3), ,„/^v^?! = (Ij.? + ?)v'-3:^._ 1.03144, (»> from which y may be found approximately in terms of c anJ r by trial. The required value of i/ is greiter than c/v'2 and less than c, hence the selection of signs in (8). As soon as a true film is formed having planci surfaces, tho qiuintity 2»v/ sin a in (4) is reduced to 2»'sin a(^— c/v/i!), because tho column of liquid below the film no longer acta directly to jjroduce a (negative) pressure uj)on the bottom of the cylinder; and w is reduced to 2T j)lus tho weight of the cylinder and of the small quantity of liquid suspended under the cylinder and above the film. Up to this point the ends of the cylinder, which in practice must be turned down, have been disregarded. Their effect may be eliminated by the use of a long and a short cylinder having tho same thickness and their ends alike ; but if the bend is like an elbow, or is made by a rectangular prism abutting squan.'ly on the end of the cylinder, the effect of the ends nuiy be calculated. Taking the former case, let / (fig. 7) be tho whole length of the cylinder along the dotted line, r its radius, h as before the height of the top of the horizontal cylinder above the general level of the licjuid, and k the length of each vertical end-piece, measured from the top. Equation (4) may be applied over the length Z— 2r— 7rr/2. And if we subtract ^ {ti) Vi~'""^"M ' ''T^" ' »r" '.i*'^?*^a ''''>\i i|i >ri i >«i:/M-T-» i n i ri-'» i n!ir i iiij' i 22 Mr. T. Proctor Hall on Neio Methods of the weight of liquid displaced by the cylinder, the increase in Fiff. 7. weight over the weight of the frame in air is, for this central part, (l — 2r—'jTrl^)p< {-- +2j7jsina4-r^(«— tt)— r^sina cos « I. To this is to bo added the surface-tension around the viMtical ends, and also the weight of liquid supported under tliem above the level of the surface ; making as a very close ap- proximation the whole increase of weight to be W, where W//3= (/-2?— 7rj-/2){ (c«/2 -f- iry) sin « + rXu-nr) — »'^sin«cos«}+7r;-c* + 27r/'2(/t— A), . . (9) In the following table are given the observed weights with a somewhat irregular glass frame, along with the calcu- lated values of the four terms on the right of equation (4) for the same height h, in grams {)er centim. The liquid was water, whose density is assumed as unity. r=*0375 (mean); Z = 9*76; T = "07395 gram per centim. A{mm.). w, obs. a. 2T sin a. 2 ry sin a. r'ci. — r'^ sin a cos «. w, calc. J •0109 13° 47' •0352 •U012 0003 -0003 ■0364 2 •1042 41° 4' •0972 ■0149 ■0010 -0007 •1124 H •1547 69° Ki' •1383 •0217 ■0017 -0005 •1(!12 4 •1724 84° 29' •1472 •0273 ■0021 -•0001 •1765 44 •175ii 92° 49' •1477 ■0298 ■00-23 + 0001 •1799 44 •17fi3 97° 9' •14B8 ■0304 •0024 + 0002 ■1798 t # 99° 42' •1458 •0307 ■0025 + 0003 •1793 41 •1755 4| •1739 5 •1722 54 •1579 6} 6 •1547 •1520 •1520 ... •1468 2r8iii »{y—cl >J2) ■0025 +•0003 •1509 •0023 \ » During tlio next five weighings the balnnce was in unstable equilibrium. t The numbers in this row are calculated from the value of y I'ound from equation (8), and are for the poiut at which tlio two liquid surfaces meet below the bar. I See the paragraph following equation (8). « » / > increase in this central )• m « cos « the vci-tical under tliem iry close ap- V, where ot—7r) . . (9) ved weights ;h the calcu- equation (4) le Uquid was er centim. r* sin a cos «. w, calc. -0003 •0364 — 0007 •1124 _ 0005 •1(!12 _ 0001 •17(55 + 0001 •171)9 + 0002 •1798 + 0003 •1793 +•0003 •1509 equilibrium. 1/ I'ouiid from ces meet below Measuring the Surface-Tension of Liquids. 23 To the last calculated value of w is to be added "0005 for the displacement of the two end-pieces of the frame, leaving + "0006 per centim. to account for the surface-tension about the (irregular) ends. In fig. 8 the curves a and b represent the calculated and observed values of to given in the table. The calculated li=0. . . . (11) These equations are almost unmanageable, however, and time will bo saved in most cases by disregarding them and plotting a curve of experimental values to show the relation between T and W/p for a given frame. The convenience of this method in practice will repay the trouble of finding such a relation. While Michelson's method has the merit of directness and simplicity, its use is limited to such liquids as form a fairly stable film in air. The method of thin, plates is constantly open to suspicion as to the ge of surface- the frame ia ^ho liquid was ;ht was found l^) due to the I values of T ill exactness as calculated to values of the lethods before [ise, the values frame, so that jr liquids with f=a/2. Then + 4cr sin /3 //)=0. . (10) -8r/ic sin yS • . . (11) however, and ling them and w the relation will repay the elson's method use is limited in air. The licion as to the Measuring the Sur/ace-Tenston of Liquids. 25 maximum -weight existence of a finite contact-angle. The method is free from both these objections, and can be used for almost any liquid. If the specific gravity of the liquid is not accurately known, a thin frame should be used, so that an error in the specific gravity will have small influence on the final result. For accurate results great care must be taken to prevent any oscillation of the balance as the weight approaches the maximum ''"-" — •'-^' '— -,„„„.,t;„i Zero weighings are also essential. III. Surface-Tension of Water. In spite of the labours of a laige number of investigators, the surface-tension of water is still more or less uncertain. Apart from experimental errors, M'hich are seldom less than one half of one per cent., there is very great difficulty in retaining a pure water surface throughout the measurement. Using the methods of measurement described in Part II. of this paper, it became evident at once that the problem of find- ing the surface-tension of water accurately, to one tenth of one per cent, or less, was practically reduced to that of securing a clean surface and a constant temperature for pure water. The weights used were found consistent with each other, and therefore presumably correct, to one tenth of a milligram, with two or three exceptions which were taken note of. The arms of the balance were sensibly equal, and the riders accurate. One of the mercury thermometers was graduated in half degrees. Centigrade, from —10° to -1-100° ; the other in fifths of a degree, from —4° to -1-30°. The latter could be easily read to fiftieths. The zeros of both were correct. Sone water that had been distilled repeatedly by Dr. Loeb in such a manner as to remove carbon dioxide and organic matter and ammonia, was kindly furnished by him for measurement of the surface-tension. I preserved it in a large well-washed glass bottle whose stopper and neck were covered by an inverted beaker to keep off dust. The deep evaporating-dish already mentioned, its cover, the thermometer, and the glass frames (fig. 1) were well washed in a dilute solution of caustic soda and thoroughly rinsed, first in ordinary distilled water and secondly in some of the ■water that was to be examined. The ground-glass cover remained on the dish except while frames were being put in or taken out ; and before each measurement the temperature of the whole was kept nearly constant for half an hour or more. The observations extended over two days, partly because of the difficulty there was in getting a film to last long enough to be weighed. Ou the third day the surface-tension was so >M«iMUt«ki6« ws B b^*fe iA Jtt a!»Wti t JM ^a8^