HELICAL PATH ELECTROPHORESIS IN VERTICAL FLUIDSHEATHS*

BY ALEXANDER KOLIN

DEPARTMENT OF BIOPHYSICS AND NUCLEAR MEDICINE,

UNIVERSITY OF CALIFORNIA (LJOS ANGELES)

Communicated by D. J. Cram, July 18, 1966

The general principle underlying the method described below is that of deviationelectrophoresis. The mixture of ions to be spearated from each other enters anelectric field in form of a thin streak carried by a buffer flow transversely to theelectric field. The streak is affected by the electric field similarly to a zone in zoneelectrophoresis. The different ions are moved by the electric field transversely tothe direction of flow of the surrounding buffer solution with velocities determinedby their ionic mobilities. As a result, the streaks are deviated from the course theywould have followed in the absence of the electric field. Since the slopes of thedeviated streaks depend on the ratio of the electrophoretic velocities of the ions tothe buffer flow velocity perpendicular to the electric field, one obtains a series ofstreaks deviated from the course of the reference streak corresponding to an ion ofzero charge by angles depending on the ionic mobilities, the electric field strength,and the rate of buffer flow. This is the well-known arrangement used in filter papercurtain electrophoresis.1The resolving power of filter paper electrophoresis as applied to macromolecular

ions is greatly impaired by interaction between the ions and the filter paper. As arule, suspensions of particles cannot be separated by this method due to adsorptionby the curtain matrix.To eliminate the troublesome adsorption, Barrolier et al.2 replaced the filter

paper curtain by a nonvertical thin sheath of buffer solution about 0.5 mm in thick-ness. This arrangement has, however, the disadvantage that small particles tendto precipitate on the bottom plate of the inclined sandwich containing the buffersheath between two glass plates measuring about 50 X 50 cm.This drawback was eliminated by Hanning by mounting the fluid curtain in the

vertical plane.' His plates measured 50 X 50 cm and were 0.5 mm apart. Thisorientation of the fluid curtain eliminated the problem of sedimentation of theparticles on the bottom plate and made separation of cells and subcellular particlespossible. The small distance between the plates and an elaborate thermoelectriccooling system serve in this apparatus to suppress thermal convection.Two different approaches were used by the author to suppress thermal convection

and particle sedimentation. In one of them, the liquid sheath follows a serpentinepath.4' 5 Figure la shows how particles issuing from injector IN and carried by thebuffer flow following the serpentine path in the direction of the arrow are fallingtoward the bottom wall of the first horizontal leg of the serpentine path. However,as the particles enter the upper horizontal leg, the wall which previously was thebottom wall is now the top wall and the particles begin to recede from it due tosedimentation. Thus, the particles oscillate between the walls without depositingon them, provided the speed of the buffer flow exceeds a certain minimum valuewhich depends upon the rate of particle sedimentation.

105

1052 BJOCHEAMISRY: A. KOLIN PROC. N. A. S.

MUTT 2 : Y mT

MB I~~~~~~

IN.... ..... ;.

MS

(a)FIG. 1.-Principles, of stabilization against thermal convection / - 1

and of suppression of particle sedimentation by meandering and A Xrotational flows.

(a) Scheme of serpentine continuous-flow electrophoresis. Thedashed line represents the path of dense sedimenting particleswhich fluctuates between the two walls of the serpentine flow bed.g, Acceleration of gravity vector; IN, injector; M, manifold;C, collector; t, collector exit tube; TT, test tube; MB, Mariottebottle. m

(b) Cross section of an annular horizontal buffer columnmaintained in rotational motion (indicated by arrow) by inter-action between a radial magnetic field (emanating from ironcore m) and an axial electric current (perpendicular to the planeof the paper). IN, injector; C1, C2, the inner and outerboundaries, respectively, of the rotating annular buffer column.Dashed line: path of a dense particle emerging from IN andperforming a motion which combines sedimentation with rotation :about the center of cylinder m.

(c) Configuration similar to the scheme of Fig. lb except that {an and the shape of the rotating fluid ribbon are no longer circular.IN is the injector, and the dashed line represents again the path of a dense particle. Sedimentatiolnis no longer noticeable because of the shortness of the horizontal component of the particle motionas compared to the total path length. C1 and C2, inner and outer boundaries of the noncircularannular horizontal fluid column.

(d) Scheme of collection of separated fractions in the method shown in Fig. ic. WhereasFig. lc shows the path of a particle (dashed line) as it emerges from the injector near the buffercompartment B2, Fig. ld shows it as it approaches and enters the collector C located near thebuffer compartment B1. C1, C2, inner and outer boundaries of the rotating buffer belt; t, tubeconnected to the L-shaped channel in the collector; T, test tube; 0, point at which the nylon laceseparating the buffer compartment B1 from the electrophoretic column is provided with an openingto limit low hydraulic resistance communication between these two fluid compartments to thispoint.

The other approach6 utilizes rotational motion of the buffer solution to suppressthermal convection and particle sedimentation. Figure lb shows, in cross section,rotation of a circular, annular buffer column between two horizontal cylinders.The particles emerging from the injector IN begin to sediment at once and reach thepoint of closest approach to the inner cylinder at level b. From this point on, thesedimentation carries the particles away from the inner cylinder until level d is

VOL. 56, 1966 BIOCHEMISTRY: A. KOLIN 1053

reached with the particles at their point of closest approach to the outer cylinder.It is thus seen that the particles which do not coincide in density with the bufferdescribe an eccentric path in the annular rotational flow. If the rotational flow isslowed down, the particles will hit the inner cylinder at first at b, and at slowerflows closer to the injector IN. To avoid sedimentation, an adequate rate ofrotational flow must be maintained. Another consideration determining the rateof rotational velocity is the requirement that it be large as compared to fluid veloci-ties due to thermal convection.The present paper describes an apparatus which combines the latter principle of

stabilization by fluid rotation4 6with the most effective method of avoiding particleprecipitation based on utilization of a vertical fluid sheath. This is achieved bydeforming the circular path taken by the circulating fluid in Figure lb into the elon-gated, predominantly vertical closed path shown in Figure ic. The particle streakissuing from injector IN is seen to spend most of its course on a vertical path havingonly a small fraction of its cycle to sediment toward one of the walls in the smallcircular segments at the top and the bottom of its path. The sedimentation is notshown in the figure, being negligible. It is oscillatory in character since a deviationbelow the center line in the bottom curved section results in a deviation above thecenter line when the particle reaches the top curved section of its path.

Since the particle can complete many turns after its injection into the streambefore it is collected, the effective particle path length is many times as large as thelength of the separation cell. This great effective length is of particular importancesince it is desirable to make the velocity due to electromagnetic rotation (whichdetermines the length of a streak produced in a given time) large, as compared tofluid velocities due to thermal convection.

Principle of the Method.-In the apparatus on which the present modification is based, the rota-tion of the horizontal annular electrophoretic column was achieved by the interaction of the(axial) electrophoretic current with a radial magnetic field. The magnetic field with a radialcomponent was generated by sandwiching a soft-iron cylinder (m of Fig. lb) between two coaxialbar magnets facing each other with their north poles. The resulting electromagnetic force, beingperpendicular to the axial current and the radial magnetic field, moves the liquid tangentiallyin a circular path.

In the present instrument, the shape of the path of the circulating buffer is no longer circular,but rather elongated in the direction of the vertical axis as depicted in Figure ic. The height of thevertical path is 8.0 cm and the radius of curvature of the top and bottom edges of the soft-ironcore m is 1.3 cm. The iron core m is sandwiched between four bar magnets mi, m2, m3, and m4 showiin Figure 2a. The bar magnets are rectangular in cross section as shown in Figure 2b (mI, m2).They face each other with their north poles. In this configuration of magnets and iron, the normalcomponent of the magnetic field adjacent to the surfaces of the iron core m is adequate to cause thebuffer column surrounding m to revolve like an endless fluid belt around the inner core m. Themagnets used were Permag Pacific Corporation model #B-59-6. The normal component of themagnetic field 1/2 mm from the pole face varies from magnet to magnet, being in the neighborhoodof 1600 gauss. The normal component 1/2 mm from the center of the flat surface of the innercore m is 260 gauss.A particle emerging from the injector IN of Figure lc (cf. Fig. 2a) spends most of the duration

of the cycle of revolution in a vertical path scarcely having an opportunity to settle on the instru-ment walls. (It is recommended that the instrument be leveled carefully so as to ensure precisevertical orientation of the side walls.) When passing around the lower curvature of its path, whichis well-centered in the annulus, it tends to sediment slightly downward so that it would shift off thecenter line on its way up in the left leg of its path if it was well-centered on its way down. Whenpassing over the upper curvature of its path, the particle will tend to move back toward the center

1054 BIOCHEMISTRY: A. KOLIN - PROC. N. A. S.

PAB

BT

MF

NV

i SL .SL

FIG v. (a) =ceai view 0fte2etohrtcsprto.M:Mrot ote

Stw P p CTc

0 0

IVI~~~ ~ ~ ~FIG2.a Sceai ie fteeecrpoei Seato.M: artebtl;les

water flowing through the hollow soft-iron core m. CT2, CT4: tubes conveying coolant flowingthrough the cooling jacket CC which surrounds the electrophoretic column, which, in turn, sur-rounds the soft-iron core m. 01, 02: overflow tubes draining buffer from electrode compartmentsE,, E2. d5, d2: Bundlers of thin plastic tubes delivering buffer to the buffer compartments (inactual practice these tubes are submerged into the buffer solution). MF, manifold; E+, E,electrodes; V, air outlet valve; N, S, north and south poles of magnets; inl, n2 in3, m4, barmagnets of rectangular cross section; C, collector; t,t . . . , collector tubes; e, e. .., collector tubeexits. T. T... ., test tubes; SL, nylon laces closing the annular space surrounding mn on both sidesso as to provide a path of increased hydrodynamic resistance between the electrophoretic sheathand the buffer compartments. 0, opening in the left nylon lace SL establishing a low hydraulic-resistance communication between the buffer compartment B5 and the electrophoretic sheathsurrounding the soft-iron core mn; E,, E2, electrode compartments; B1, B2, buffer compart-ments; M5, M2, dialyzing membranes separating the buffer compartments from the electrodecompartments; A, annular space surrounding mn which is filled with a buffer solution which rotatesin the fashion of an endless belt. The solid and the dashed lines emanating from the injector rep-resent a slow and a fast electrophoretic component which form noncircular helices in the rotatingendless fluid belt. Only the front sides of the turns of the helix are shown until the pointswhere the helical streaks enter the collector C. J, Lucite jacket corresponding to the outerboundary C2 of Figs. ic and id.

(b) Side view of electrophoretic separator onl the side of the anode. E5 +, E2 t electrodes;E51, Ed', electrode compartments; Ct. tube connecting the electrode compartments; BT, buffersupply tube; 01, exit tubes draining the electrode compartments; inl, in2, bar magnets; 8, southpoles of the magnets; CT3, tube draining coolant from the hollow soft-iron core (in of Fig. 2a);V,, vent to allow air to escape from the hollow core in as it is filled with coolant,

Voi,. 56, 1966 BIOCHEMISTRY: A. KOLIN 1055

line. To achieve symmetrical conditions, one can adjust the injector IN slightly to the left of thecenter line so that the particle will be above the center line as it enters the lower curvature of itspath. With proper adjustment, it will sink below the center line before it reaches the straightupward path in the left leg and will continue upward, deviating to the left of the center line by thesame amount as it did on its way down in the right leg. When moving over the upper curvatureof the path, the particle will be returned to the original path in the right leg.The lateral adjustment of the injector IN can be accomplished very simply. Instead of using a

perfectly straight hypodermic tubing to serve as injector, the tubing is slightly curved. If thetubing is rotated about its axis, its exit opening at the bottom sweeps from wall to wall. In prac-tice, the optimal position of the injector exit is found empirically by rotating the injector tubeuntil the sharpest streaks are observed at the collector.

It is very important to secure perfect electrical insulation of the injector to avoid its pluggingby electrolytic evolution of gas. This is achieved by slipping the hypodermic tubing into a Teflontube. In our experiments, a #29 gauge hypodermic tube was used with a tightly fitting Teflontube (Shabman and Co.) slipped over it. A short piece of #23 gauge hypodermic tubing wassoldered to the top end of the #29 gauge tube to connect it via a PE20 "Intramedic" polyethylenetube to the reservoir Res (Fig. 2a), delivering the particle mixture to be separated.As a charged particle issuing from IN revolves about the inner core m, it advances to the left

in the arrangement shown in Figure 2a due to electrophoresis. As a result, its path is a non-circular helix. The pitch of the helix is determined by the electrophoretic velocity, the velocity oftangential fluid flow, and by the circumference of the fluid path, since the latter determines theelectrophoretic migration time during one cycle. Components differing but slightly in their elec-trophoretic mobilities can be resolved by allowing them to complete several helical turns beforereaching the collector C (Fig. 2a). In the present instrument, the height of the flat section of theinner core m is 8.0 cm, its thickness is 2.6 cm, its length is 7.5 cm, and the distance between INand the right edge of C is 5.0 cm. One could thus place about ten turns of a 5-mm pitch into thisspace, achieving a streak length corresponding approximately to a 2.3-m-long column in an equiva-lent curtain electrophoresis setup. Longer streak lengths can be achieved with more closely woundhelical paths.The mode of action of collector C is shown in Figure id depicting a 2.2-cm wide Lucite block

with 20 L-shaped drilled channels. (An alternative type of collector consists of 20 channels 0.02 in.wide milled into the Lucite block.) Buffer enters these channels in the direction of rotation ofthe fluid and leaves the collector via the plastic tubes tt ... to be collected in the test tubes TT....The level of the exit holes of the tubes tt ... below the buffer surface in the apparatus determinesthe rate of buffer outflow from the collector. This efflux rate is adjusted approximately so as tobe nearly equal to the volume flow of buffer which would have passed through the collector areadue to electromagnetic rotation if there were no collector. The achievement of this condition canbe judged visually as follows, using two dyes. If the rate of collector outflow is zero, the twodye streaks bend around the collector which acts as an obstacle to flow. When the outflow is tooslow, the streaks become wider and enter the collector diverging widely as they approach it.If the outflow is too fast, the streaks become thinner and converge as they enter the collector.With proper adjustment, the streaks diverge slightly due to electrophoretic separation as theyenter the collector without noticeably changing their width.

The apparatus: Figures 2a and b show the scheme of the instrument. The inner core (m) ismade of cold rolled steel (1020). Its dimensions as viewed in Figure 2a are 7.5 cm (length) X10.6 cm (height), and its thickness as viewed in Figure 2b is 2.6 cm. It is hollow so that coolingwater can be supplied through tube CT, from the pump P which is immersed in the ice-waterreservoir to circulate through the core m leaving it through tube CTs to be returned to the reser-voir. V is a vent allowing the air to escape from the interior of m as it is filled with water (Fig. 2a).

It is most important to insulate m very well against electrical contact with the surroundingbuffer solution in which a high-potential gradient is maintained. This is accomplished by mold-ing m into a crust of epoxy ("Hysol" #2038 resin with #3490 hardener), which is subsequentlymilled off to leave a layer ten thousandths of an inch adhering to the iron over the entire surfaceof m. To facilitate visualization of colored components, part of the epoxy surface is paintedwith a layer of white enamel 0.003-in. thick and, to facilitate visualization of particle streaks bylight-scattering, the remaining surface area of m is painted with a black enamel of equal thickness.8

1056 BIOCHEMISTRY: A. KOLIN PROC. N. A. S.

A_.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..

FIG. 3.-(a) A s5treak of Scripps ff62 black ink (made unusually thick to improve photographicreproduction) issues from injector IN and splits into two visible components, a red one (of highermobility) and a blue one. A third component (yellow) directly behind the red one can be seenonly after collection in the test tubes. C, collector, SL, nylon lace. (b) Photograph of the rearof the separation pattern shown in (a) in front view.

The layers of enamel are sprayed with a layer of a clear varnish ("Sealux" #474) which adds0.004 in. to the thickness of the insulating layer. The surface of m corresponds to the contourC1 of Figures 1c and d. The core m is slipped into a Lucite jacket J of Figure 2a whose inner sur-face corresponds to the contour C2 of Figures 1c and d. The noncircular annular space betweencontours C1 and C2 is 1.5-mm wide. To ensure proper centering of m within the jacket J, smallcylindrical spacers 1.5 mm in thickness are placed around the rim of core m so as to achieve auniform separation from Lucite jacket J, or, to put it differently, so as to center contour C1 ofFigure 1c within contour C2. The buffer compartments B1 and B2 communicate electrically andhydraulically with each other through the annular space A which is sandwiched between thecontours C1 and C2 within the jacket J. This annular space is the electrophoretic column. Thebuffer compartments B1 and B2 also communicate electrically with the two outer electrode cham-bers E1 and E2 which are hydraulically isolated from B1 and B2 by membranes Ml and M2 madeof dialyzing tubing material. The jacket J is surrounded by Lucite walls so that cooling watercan be circulated around this jacket entering through tube CT2 and leaving through tube CT4.A Lucite stack ST allows the injector tube IN to be introduced centrally into the annular space Abetween the contours C1 and C2 of Figure 1c. The reservoir Res feeds the suspension or solutionto be subjected to electrophoretic analysis to the injector IN. There are four electrode compart-ments, as apparent from Figure 2b, each buffer compartment being in contact with two electrodecompartments. The two lateral electrode compartments are placed on either side of the cell,sandwiching the magnet bars in1, ini between them, as shown in Figure 2b. The electrode com-partments are in communication via the tubing Ct. Each of them is separated by a dialyzingmembrane (MI, M2 of Fig. 2a) from the adjacent buffer compartment behind it (not shown inFig. 2b) and is provided with a platinum electrode (E' and E'). The outlets 01 allow buffersolution to escape as fresh buffer is constantly supplied via tube BT from the main buffer reservoirMB (Mariotte bottle).

X'OL. 56, 1966 BIOCHEMISTRY: A. KOLIN 1057

The buffer compartments B1 and B2 also derive TABLE 1a constant buffer supply from the reservoir MB. TemperatureThis buffer influx replenishes the buffer escaping Current (ma) (20Cthrough the collector as previously explained. 75 75After a brief interval of equilibration, the buffer 100 10.0level in the compartments B1 and B2 adjusts 150 16.2itself so as to make the rate of buffer escape from 200 22.8the collector equal to the rate of influx from MB. Temperature at the center of annular

space as a function of cell current.The buffer supply to the compartments B1 and Room temperature: 25.50C; coolantB2 is guided through 20 tubes of the same gauge reservoir temperature: 0'C; diameter

of thermistor probe: 0.5 mm; bufferas the 20 tubes tt... attached to the collector. resistivity = 1740 ohm-cm at 16'C.By changing the distribution of these tubesamong the compartments B1 and B2 (see tubes di and d2 of Fig.2 a), one can alter the rate andeven the direction of the axial buffer flow through the annular space A without altering thetotal rate of buffer inflow from MB.The mixture of molecules and particles entering the annular space A splits into individual streaks

as shown for two components in Figure 2a (indicated by a solid and a dashed line). Collector Chas 20 openings, oriented as shown in Figure 1d, through which the separated components areguided to different test tubes TT... via the thin plastic tubes tt....

If no special precautions are taken to suppress thermal convection, the performance of the in-strument is very poor. The convection problem is most severe along the edges of the annularspace A which border on the buffer compartments B1 and B2 . The emerging streak is severelycurved tending to get out of the annular space into the buffer compartment B2. If the streakdoes not get lost in compartment B2 after leaving the injector, it may be swept by thermal con-vection into compartment B1 before reaching the collector. This problem can be solved veryeffectively by simple means. Both buffer compartments can be, to a sufficient extent, isolatedhydraulically from the annular space A without impairing the electrical communication. Anundyed nylon shoe lace SL (indicated by a pattern of coarse dots), approximately 4.5 mm indiameter, was fitted tightly into a 3-mm-wide groove shown in Figure 2a adjacent to the entranceto the annular space A. To allow unimpeded replenishment of fluid leaving via the collector,a small opening 0 was cut into the shoe lace just below the collector C on the left side of the core m,providing a path of low hydrodynamic resistance between buffer compartment B1 and the electro-phoretic column just below the collector. This simple device eliminates the convective disturb-ance to the extent illustrated in Figure 3. Figure 3a shows a front-view photograph of the separa-tion pattern obtained with Scripps black ink #62 using a pH 10 buffer ("Hydrion" buffer obtainedby dissolving 1 pH 10 buffer tablet in 1 liter of water). Figure 3b shows the same separationpattern as photographed from the rear of the cell. (To avoid obstruction of vision by condensa-tion of water on the cell windows which are cooled by ice-water circulating through the coolingcompartment CC, compressed air is constantly blown against the windows). The black inkseparates into a fast red component and an electrophoretically slower green dye. Actually, afaint yellow component (not seen in the photograph), slightly slower than the red one, is col-lected in the adjacent test tube.Under typical operating conditions, utilizing "Hydrion" buffer solutions of pH 10 (1 tablet/1.5

liters of water), a current of 150 ma is maintained in the separation cell. The potential gradientin the electrophoretic sheath can be computed from the dimensions of this sheath, the current,and the buffer resistivity (1,740 ohm-cm at 16'C). Its value under above conditions is dV/dx =72.4 v/cm (assuming a temperature of 16.20C in the annulus according to Table 1).To assure stable performance of the separator, a constant-current power supply is recom-

mended. The constant-current supply used in our experiments (Electronic Measurements Co.,model C 636) was incapable of supplying 150 ma at 770 v across the cell. The necessary powerwas obtained by connecting it in series with a second power supply (Hewlett Packard model#712A) which need not be a constant-current device since fluctuations in its output are auto-mnatically compensated by the constant-current supply.Under the above conditions, which include circulation of cooling water derived from the ice-

water reservoir, the temperature at the center of the annular space as determined by a thermis-tor probe (Scientific Products Co.) remained well below the room temperature even at the high-est current which the power supply could deliver, as shown in Table 1.

1058 BIOCHEMISTRY: A. KOLIN PROC. N. A. S.

The magnetic field intensity normal to the surface at the center of the flat surface of m, 1/2mm from the surface, was 260 gauss. The linear velocity within the streak due to electromagneticconvection was approximately 5 mm/sec. The rate of total buffer outflow from the collector was0.13 cc/sec.

Resolution.-Two components can be considered as resolved if they arrive at thecollector as adjacent nonoverlapping streaks. Diffusion will tend to reduce theresolving power by causing exchange of ions between adjacent streaks. But evenin the case of large molecules or microscopic particles for which diffusion is negligible,a broadening of each streak with consequent loss of resolution occurs, due to thefact that the velocity of electromagnetic convection is not uniform( approximatelyparabolic) throughout the cross section of the electrophoretic column C, while theelectrophoretic migration velocity is uniform. We shall refer to this cause of streakbroadening as "parabolic divergence."'On the assumption of a parabolic velocity distribution as an approximation, aln

equation for the resolving power has been derived.7 This equation provides anestimate of the minimum difference in electrophoretic mobility AU = U2 -U1,which two components of mobilities Ui and U2> U1 may have and still be margin-ally resolved as adjacent nonoverlapping streaks when issuing from the injector as astreak of diameter d into an annular gap of depth h. The resolving power R isdefined as the reciprocal ratio of the resolved mobility difference to the higher of thetwo ionic mobilities and is found to be:

R= U2 = ( 2)2 (1)

For instance, with an initial streak diameter of 0.2 mm and an annular gap of 1..5mm, we obtain: R = (1.5/0.2)2 56 approximately. This means that two com-ponents differing about 2 per cent in electrophoretic mobility could be resolvedunder the assumed conditions which approximate normal practice. A finer initialstreak would lead to higher resolution.Summary.-A modification of electrophoresis stabilized by electromagnetic

rotation is presented which yields higher resolution, and permits processing ofmaterials at higher concentration (higher-streak density). It is particularly suit-able for separation of microscopic particles. The improvement is achieved by de-forming the previously used circular path into a tall vertically oriented "endlessfluid belt." High potential gradients in the order of 70 v/cm can be used withoutundue heating of the materials and without causing thermal convection.

* This work was supported by a grant from the Office of Naval Research.'Grassmann, W., and K. Hannig, Naturwissenschaften, 37, 93 (1950).2 Barrolier, J., E. Watzke, and H. Gibian, Z. Naturforsch., 136, 754 (1958).3Hannig, K., Z. Physiol. Chem., 338, 211 (1964).4Kolin, A., these PROCEEDINGS, 51, 1110 (1964).1 Kolin, A., and P. Cox, these PROCEEDINGS, 52, 19 (1964).6 Kolin, A., these PROCEEDINGS, 46, 509 (1960).7 Kolin, A., J. Chromatog., in press.8 The blisters in the paint layer seen in Fig. 3 are accentuated by oblique illumination. They

do not disturb the performance of the apparatus, and streaks passing over them remain unper-turbed.