,archive_/,american ,libraries47 ,a ,,study ,,of ,,splashes ,,by ,,the ,,same ,,author4 99 99 99 99 99 ,a ,,first ,,course ,,of ,,physical ,,laboratory ,,practice4 ,,containing #bfd ,,experiments4 ,with ,illustrations4 ,crown #hvo1 #ds4 #f;d4 99 99 99 99 99 ,,dynamics ,,of ,,rotation4 ,,an ,,elementary ,,introduction ,,to ,,rigid ,,dynamics4 ,crown #hvo1 #ds4 #f;d4 99 99 99 99 99 ,,longmans1 ,,green1 ,,and ,,co4 ,,london1 ,,new ,,york1 ,,bombay1 ,,and ,,calcutta4 ,illustration3 ,permanent ,splashes left where a ,projectile has entered an ,armour-plate4 ,see page #abj4 ,a ,,study ,,of ,,splashes ,,by ,a4 ,m4 ,,worthington ,c4,b41 ,m4,a41 ,f4,r4,s4 ,,headmaster ,,and ,,professor ,,of ,,physics ,,at ,,the ,,royal ,,naval ,,engineering ,,college1 ,,devonport ,,with #aig ,,illustrations ,,from ,,instantaneous ,,photographs ,,longmans1 ,,green1 ,,and ,,co4 #ci ,,paternoster ,,row1 ,,london ,,new ,,york1 ,,bombay1 ,,and ,,calcutta #aijh ,all rights reserved ,,dedicated ,,to ,,the ,,natural ,,history ,,society ,,of ,,rugby ,,school ,,and ,,its ,,former ,,president ,,arthur ,,sidgwick ,,in ,,remembrance ,,of ,,the ,,encouragement ,,given ,,to ,,the ,,early ,,observations ,,made ,,in ,,boyhood ,,by ,,my ,,old ,,school-,,friend ,h4 ,f4 ,,newall ,,from ,,which ,,this ,,study ,,sprang4 ,,preface ,this publication is an attempt to present in a form acceptable to the general reader the outcome of an inquiry conducted by the aid of instantaneous photography1 which was begun about fourteen years ago4 ,the author1 in #ahid1 had occasion to lecture at the ,royal ,institution on the ,splash of a ,drop1 of which he had already made a somewhat prolonged study4 ,that lecture1 which was subsequently reprinted in the ,romance of ,science series by the ,society for ,promoting ,christian ,knowledge1 dealt largely with the splash of a drop falling on a solid plate1 with which the present volume is not concerned4 ,at the close of the lecture were exhibited for the first time a few photographs of some of the phenomena now dealt with1 which the author had just succeeded in taking with the help of his friend ,mr4 ,r4 ,s4 ,cole4 ,the success of the photographs and the additional information they afforded led to a long photographic investigation1 which formed the subject of two papers,a in the ,transactions of the ,royal ,society4 ,except for two magazine articles1,b the results of this work have not been presented to the general public4 ,moreover1 in the illustrations printed by the ,royal ,society much of the beauty of the original photographs was lost in the reproduction1 or was sacrificed in a selection of which the only object was the elucidation of points of technical scientific interest4 ,if the present volume is so fortunate as to find many readers among the general public1 as the author hopes it may1 especially among the young whose eyes are still quick to observe1 and whose minds are eager1 it will be on account of admiration for the exquisite beauty of some of the forms assumed1 of surprise at the revelation of so much where so little was expected1 and because of the peculiar fascination that is always felt in following any gradually changing natural phenomenon1 in which the sequence of events can1 partly at any rate1 be anticipated and understood4 ,for the sake of serious students of ,physics who may be interested in unexpected phenomena of fluid motion1 all references that seem necessary have been given in footnotes1 and it may be mentioned that the later photographs of ,series ,i and those of ,series ,i-a and ,,iii1 have not been previously published1 and afford new information on certain points4 ,in taking these photographs the author has been much helped by his friends ,dr4 ,g4 ,b4 ,bryan and ,mr4 ,g4 ,f4 ,page4 ,a4 ,m4 ,w4 ,,tavistock1 ,sept4 #ah1 #aijg4 ,added ,march #a1 #aijh4 ,a slight delay in the publication of this book has afforded the opportunity of obtaining the new and quite unexpected information given in the supplementary chapter4 ,,contents ,,page ,,chapter ,i ,,preliminary--,,methods ,,of ,,observation ,,and ,,apparatus #a ,,chapter ,,ii ,,the ,,splash ,,of ,a ,,drop--,,low ,,fall #ae ,,chapter ,,iii ,,principles ,,involved #cb ,,chapter ,,iv ,,the ,,splash ,,continued #da ,,chapter ,v ,,higher ,,falls--,,bubble-,,building #ec ,,chapter ,,vi ,,below ,,the ,,surface #fi ,,chapter ,,vii ,,the ,,two ,,kinds ,,of ,,splashes ,,of ,,solid ,,spheres #gc ,,chapter ,,viii ,,the ,,transition ,,from ,,the ,,smooth ,,or ,,sheath ,,splash ,,to ,,the ,,rough ,,or ,,basket ,,splash #ie ,,chapter ,,ix ,,the ,,explanation ,,of ,,the ,,cause ,,of ,,difference ,,between ,,the ,,two ,,splashes #ajh ,,chapter ,x ,,conclusion #aah ,,chapter ,,xi 7,,supplementary7 ,a ,,new ,,phenomenon ,,that ,,appears ,,with ,,an ,,increase ,,in ,,the ,,velocity ,,of ,,entry ,,of ,a ,,rough ,,sphere #aba ,,footnotes3 ,a ,impact with a ,liquid ,surface1 by ,worthington and ,cole4 ,phil4 ,trans4 ,roy4 ,soc41 ,a #aic1 #ahig1 and ,a #bee1 #aijj4 ,b ,pearson's ,magazine1 ,july and ,august1 #ahih4 ,a ,,study ,,of ,,splashes ,,chapter ,i ,,preliminary--,,methods ,,of ,,observation ,,and ,,apparatus ,there will be but few of my readers who have not1 in some heavy shower of rain1 beguiled the tedium of enforced waiting by watching1 perhaps half-unconsciously1 the thousand little crystal fountains that start up from the surface of pool or river2 noting now and then a surrounding coronet of lesser jets1 or here and there a bubble that floats for a moment and then vanishes4 ,it is to this apparently insignificant transaction1 which always has been and always will be so familiar1 and to others of a like nature1 that ,i desire to call the attention of those who are interested in natural phenomena2 hoping to share with them some of the delight that ,i have myself felt1 in contemplating the exquisite forms that the camera has revealed1 and in watching the progress of a multitude of events1 compressed indeed within the limits of a few hundredths of a second1 but none the less orderly and inevitable1 and of which the sequence is in part easy to anticipate and understand1 while in part it taxes the highest mathematical powers to elucidate4 ,in these modern days of kinematographs and snapshot cameras it might seem an easy matter to follow1 by the aid of photography1 even a splashing drop4 ,but in reality the task is not so simple1 for the changes of form that take place in a splash are far too rapid to come within reach of any ordinary kinematograph1 and even the quickest photographic shutter is also much too slow1 so that it is necessary to have recourse to the far shorter exposure of a suitable electric spark4 ,the originals of the photographs which illustrate this book were taken by means of a spark1 whose duration was certainly less than three-millionths of a second1 an interval of time which bears to a whole second about the same proportion as a day to a thousand years4 ,in order to obtain the photographs1 advantage was taken of the fact that whatever be the sequence of events in any particular splash1 this sequence will be exactly repeated every time that a falling drop strikes the surface under exactly the same conditions1 and the problem to be solved was1 therefore1 as follows3--,to cause a drop of definite size to fall from a definite height in absolute darkness so as to strike the surface of the liquid into which it falls at a spot towards which is directed a photographic camera with uncovered lens1 and armed with an exceptionally sensitive plate1 and to illuminate the drop at the instant that it just touches the surface by a flash of such excessively short duration that no appreciable change of form can take place while the drop is illuminated4 ,this gives us a photograph of the earliest stage4 ,the plate must then be removed and a fresh one substituted2 a second drop1 of exactly the same size1 must be let fall from exactly the same place1 and photographed in just the same way1 but the flash must now be so timed as to take place at a slightly later stage of the splash1 say1 one-thousandth of a second later4 ,the photographic plate must be then again removed and a third substituted1 on which a still later stage is to be depicted1 and in this way the phenomenon can be followed step by step4 ,by adopting this process1 and not attempting to follow the same individual splash throughout1 we avoid two great difficulties3 7#a7 the necessity of shifting our photographic plate or film through a distance equal to the breadth of the whole picture every five hundredth or thousandth of a second 7if we wish to obtain pictures of stages so near together as this72 and 7#b7 the difficulty of obtaining brilliant flashes of light of sufficiently short duration at these very short intervals4 ,for these we substitute two other difficulties3 7#a7 that of delivering the drops exactly as required2 and 7#b7 that of timing the flash on each occasion within one or two thousandths of a second1 so as to pick out the exact stage we wish to photograph4 ,i will now describe how these two problems have been solved4 ,it is easy enough to arrange for the production of small drops of almost exactly equal size4 ,they may be allowed to fall one by one at a steady rate from the end of a fine glass tube connected to a vessel in which the liquid is maintained at a constant level1 as in ,fig4 #a1 or they may be squeezed out slowly as required by means of a syringe held in a clip as in ,fig4 #b4 ,any required number of these small drops can be caught1 and allowed to run together if a larger drop is to be experimented with4 ,illustration3 ,,fig4 #a ,illustration3 ,,fig4 #b ,if the liquid used is mercury1 the drops may be caught in any little glass cup such as a deeply concave watch-glass2 but other liquids1 such as water or milk1 would wet the glass and stick to it4 ,if1 however1 the inside surface of the watch-glass be first carefully smoked in the flame of a candle1 then even water or milk will roll over it without sticking1 and the drop thus made up will retain a spheroidal form1 and can be conveyed to the place of observation in the dark room1 where it is transferred to the dropping cup4 ,this consists of a similar1 deep1 smoked watch-glass 7,w7--see ,plate ,i--supported on the end of a small horizontal lever1 a light cylindrical rod of about the dimensions of an ordinary uncut lead pencil1 pivoted about a horizontal axle near the end to which the watch-glass is attached4 ,the other end is armed with a small light piece of iron 7,i7 and is held in position by means of an electro-magnet 7,m71 against the action of a spring4 ,on cutting off the current from the electro-magnet the spring1 acting as a catapult1 tosses up the longer arm of the lever and thus removes the watch-glass from below the drop 7,d71 which is left unsupported in mid-air1 so that it falls from a definite fixed distance into a bowl of water placed below it1 towards the surface of which the camera 7,c7 is directed4 ,this solves problem number one4 ,of course1 if we wish to observe the splash of a solid sphere1 there is no need to smoke the surface of the watch-glass4 ,indeed1 the sphere may be more conveniently supported on a small ring4 ,now for the production and timing of the flash4 ,two large ,leyden jars 7,,jj7 are provided1 and charged by an electrical machine on their inner coats1 one positively and one negatively4 ,stout wires lead from the outer coats to the dark room1 and terminate in a spark-gap 7,s7 between magnesium terminals close over the surface of the water in the bowl just mentioned4 ,if the inner coats are now connected together1 the positive and negative charges unite with a dazzling flash and a simultaneous discharge and flash takes place between the two outer coats across the spark-gap in the dark room4 ,this latter is the illuminating spark2 we have now to time it correctly4 ,for this purpose it is arranged that the discharge shall be effected by means of a falling metal sphere 7,t7 which ,i shall call the timing sphere1 which passes between two terminals ,s and ,s connected one to the inside of one jar and one to the inside of the other4 ,these terminals are just too far apart for a spark to leap across1 till the timing sphere passes between them and thus shortens the gap2 then the discharge takes place1 with its accompanying flash in the dark room4 ,the release of the timing sphere is effected by an arrangement of lever and spring controlled by an electro-magnet exactly similar to that which releases the drop in the dark room1 and the two electro-magnets are on the same electric circuit1 so that the drop and timing sphere are released simultaneously4 ,but while the drop always falls the same distance1 the height through which the timing sphere has to fall before producing discharge can be adjusted at will1 and to great nicety1 by moving its releasing-lever up or down a vertical support with a scale attached4 ,if1 for example1 a particular stage of the splash is photographed when the timing sphere falls just four feet to the gap1 then by raising its releasing-lever about two-fifths of an inch1 the laws of falling bodies tell us that we shall postpone the flash by just one-thousandth of a second1 and the next photograph will accordingly reveal a stage just so much later4 ,illustration3 ,,plate ,i ,arrangement of apparatus for photographing splashes4 ,,laboratory ,e is the electrical machine4 ,j ,j are the ,leyden jars whose inner coats are connected to the sparking knobs ,s ,s4 ,l is the lever for releasing the timing sphere ,t4 ,c is the catapult4 ,i is the light strip of iron held down by the electro-magnet ,m4 ,,dark ,,room ,d is the drop resting on the smoked watch-glass ,w4 ,m is the electro-magnet holding down the lever against the action of the catapult1 by means of the thin strip of iron ,i4 ,c is the camera directed towards the liquid ,l into which the drop will fall4 ,s is the spark-gap between magnesium terminals connected to the outer coats of the ,leyden jars4 ,r is the concave mirror4 ,it ought still to be mentioned that to make the utmost use of the illuminating power of the spark1 it is necessary to place close behind it a little concave mirror 7,r71 by means of which a compact beam of rays1 which would otherwise have been wasted1 is directed to the required spot4 ,by this addition we imitate1 in miniature1 the search-light of a man-of-war4 99 99 99 99 99 ,as with all experimental devices1 the precision attainable with this arrangement is limited by several circumstances4 ,in the first place1 the demagnetization of the iron cores of the electro-magnets1 when the current is cut off1 is not truly instantaneous1 and the time required depends on the strength of the magnetizing current and on the temperature of the iron1 which in turn will depend on the length of time for which the current has been running4 ,this variation would be of no importance if the two magnets were exactly alike and the springs of exactly equal strength1 conditions which can be nearly but not perfectly fulfilled4 ,illustration3 ,,plate ,,ii ,photographs taken to test the accuracy of the timing4 #a #b #c #d #e ,a more important source of uncertainty arises from the fact that the time at which the spark takes place depends partly on the magnitude of the and - charges which have been allowed to accumulate on the discharging knobs connected to the two ,leyden jars1 for when these charges are larger1 then the spark will be longer and will take place earlier and before the timing sphere has reached the mid-position4 ,the charging has therefore to be carefully watched by means of the indications of a suitable electrometer1 and the timing sphere must on each occasion be released when the charges have just reached the right value4 ,but even this does not entirely suffice1 for the passage of the spark depends also partly on the state of the surface of the knobs1 which cannot be kept at any high degree of polish4 ,still1 when care is taken to keep the conditions as nearly as possible constant1 neither of these sources of error is serious1 and the reader can judge for himself of the accuracy of the timing from the photographs given on ,plate ,,ii1 in which a solid sphere was let fall in the dark room past a metre scale4 ,the timing sphere was arranged1 in the first four photographs1 to illuminate it at the same stage in its fall1 after a descent of thirty centimetres2 if the timing had been perfect the sphere would appear on each occasion at the same mark on the scale4 ,it will be observed that in the first1 second1 and fourth photographs the falling sphere is almost accurately bisected by the long line of the three-inch mark on the right-hand edge of the scale4 ,the greatest difference of position being just about one millimetre 7as read off the left-hand scale71 which would correspond to an error of about #a_/bgjj of a second4 ,but the third photograph is earlier1 showing the sphere #d4e millimetres higher up1 a distance which implies an error of just #a_/fjj of a second4 ,a fifth photograph was then taken1 with the timing arranged so as to illuminate the sphere one centimetre higher up1 and it will be seen that if we compare this with ,no4 #c1 the error is again only one millimetre4 ,thus ,nos4 #c and #e agree very closely1 but disagree with ,nos4 #a1 #b1 and #d by about #a_/fjj of a second4 ,the photographs themselves supply the reason4 ,for there happens to be visible on each an 7out-of-focus7 image of the spark1 and this image is very much the same in #a1 #b and #d1 but much larger and brighter in #c and #e1 showing that the knobs were then more highly charged1 which would account for the spark occurring a little too early4 ,but when we are watching the splash made by the fall of a liquid drop1 instead of a solid sphere1 there is a new and more serious source of difficulty4 ,for the drop as it lies on the smoked glass cup is not perfectly spherical1 but is flattened by its own weight1 as shown in ,fig4 #c1 and on the sudden removal of the supporting cup it oscillates between an oval form1 elongated vertically1 and a flattened form 7see ,fig4 #d74 ,these oscillations are unavoidable1 and their extent will depend partly on the amount of adhesion between the smoked surface and the drop1 and as this adhesion is never entirely absent and is variable1 depending partly on the length of time that the drop has been lying in the cup1 it follows that the drop will always receive a slight tug downwards at starting1 which will be greater on some occasions than on others4 ,on this account not only will the time taken to reach the water vary slightly1 but the drop will strike it sometimes when elongated and sometimes when flattened1 and the resulting splash will be affected by this circumstance4 ,illustration3 ,,fig4 #c ,illustration3 ,,fig4 #d ,the four photographs on the next page were taken in succession in order to afford the reader an opportunity of judging for himself the sort of accuracy attainable when a liquid drop was concerned4 ,the fall was #cj centim41 and the greatest discrepancy is #d4h millimetres1 corresponding to #a_/efj of a second4 ,thus even here the error does not amount to two-thousandths of a second4 ,illustration3 ,photographs taken to test the timing of a falling drop4 #a #b #c #d ,with higher falls the timing sphere is moving more quickly past the discharging knobs1 and the error due to a longer or shorter spark is correspondingly less1 so that it appears safe to say that the accuracy of the timing was such that1 when all precautions were taken1 any desired stage could be picked out within two-thousandths of a second4 ,it is not however pretended that the precautions necessary for the most accurate timing were always taken1 especially in the earlier ,series of ,photographs1 for the main object of the experiments was to find out what happened1 and only incidentally to ascertain exactly how long it took to happen1 and there is no doubt that on some occasions1 through the smoke-film being allowed to wear away1 adhesions to the dropping cup occurred1 with a corresponding disturbance of the timing1 before the defect was noticed and remedied4 ,illustration3 ,,fig4 #e ,photograph of the edge of a rapidly whirling disc4 ,it remains to mention1 for the sake of those interested in photography1 that notwithstanding the sensitiveness of the plates and the brilliance of the illuminating spark1 its duration was so short that the negatives were always under-exposed4,c ,i have mentioned that the effective duration of the spark was less than three-millionths of a second4 ,the evidence for this is the accompanying photograph 7,fig4 #e71 taken of a cardboard disc when rotating at a rate of fifty-three turns per second2 the disc was #bb cm4 in diameter1 and had been roughly graduated round the edge with pen and ink4 ,the photograph of the part that was in focus shows no perceptible blurring of the edge of the marks1 and with a lens1 a blurring of one-tenth of a millimetre would be easily detectable4 ,since the edge was moving at a rate of #cf4e metres per second 7about #gh miles per hour71 the time taken to traverse one-tenth of a millimetre would be rather less than three-millionths of a second4 ,hence we may conclude that the illumination did not last so long as this4 ,the weakness of the negatives was met by a prolonged development of about forty minutes in a saturated solution of eikonogen4 ,this forbade the use of any artificial light1 and all the photographic processes had to be conducted in absolute darkness4 ,to avoid the tedium of long waiting in the dark room1 a light-tight tray was constructed1 in which several developing dishes could be placed1 and the whole brought out into the daylight and suitably rocked4 ,in this way ten or twelve photographs could be developed simultaneously4 ,it may be worth while to mention here that the bright spark given by breaking the primary circuit of an induction coil at the surface of mercury was found to be of much too long duration to be useful for the purposes of splash-photography4 ,,footnotes3 ,c ,the plates which ,i have mostly used have been ,thomas's ,a #a ordinary4 ,,chapter ,,ii ,,the ,,splash ,,of ,a ,,drop--,,low ,,fall ,we will now turn to the photographic record itself4 ,the first series shows the splash of a drop of water weighing 4#b of a gram1 and therefore #g4cf millimetres 7or rather less than one-third of an inch7 in diameter1 falling #dj cm4 7about #af inches7 into milk mixed with water4 ,the object of adding milk to the water was to make it more visible4 ,the addition of milk makes1 as we shall see1 a little but not much difference in the general character of the splash4 ,the scale of the figures is three-quarters of the actual size4 ,the number written against any figure gives1 on the assumption that no unobserved error has crept in1 the time in decimal parts of a second that has elapsed since the stage marked ,t #j1 which is nearest to the first instant of contact4 ,the reader will understand from what has been said that the error in any of these times may be as much as two-thousandths of a second1 but is not likely to be more than that1 when all precautions were taken4 ,it will be observed that as the drop descends into the liquid the upper portion is at first not appreciably distorted1 but that a little cup or crater of liquid is thrown up round it4 ,as the drop descends further1 this crater grows wider and higher and thicker in the wall1 and jets are shot out from its edge or rim4 ,these jets are visible even in the second figure4 ,the black marks on the inside wall of the crater are due to the lamp-black carried down with the drop from the smoked surface of the supporting cup3 though in one sense a disfigurement1 they serve to show by their presence that the interior of the crater is lined by the original liquid which formed the drop1 and thus afford useful information as to the nature of the flow4 ,the crater rises with great rapidity up to ,fig4 #d4 ,in ,fig4 #e the walls are beginning to grow thicker1 while the next three figures show the crater subsiding and widening1 till in ,fig4 #i it lies as a mere ring of lobes on the surface1 surrounding a central hollow4 ,illustration3 ,,series ,i ,milk into water 7#dj cm474 ,scale #c_/d4 #a #b ,t #j #c #j4jjb sec4 #d #j4jjg sec4 #e #j4jah sec4 #f #j4jca sec4 #g #j4jdj sec4 #h #j4jej sec4 #i #j4jef sec4 ,fig4 #aj shows the beginning of the rebound1 in the rising of a central column4 ,it will be seen that the lamp-black is now all swept to the middle1 indicating that the liquid of the original drop emerges at the head of the central column4 ,full confirmation of this is obtained from ,fig4 #ab1 which represents the emergent column obtained when the circumstances are all the same1 except that we have a drop of milk falling into water instead of water falling into milk4 ,it will be observed that the upper part only of the column is visible1 precisely because it contains nearly all the milk of the drop1 while the lower part1 consisting chiefly of transparent water1 remains invisible4 ,illustration3 ,,series ,i--7continued7 #aj #j4jfd sec4 #aa #j4jgc sec4 #ab #ac #j4jic sec4 ,no4 #ae shows the column at its greatest height1 and it should be noticed that ,figs4 #af and #ag show a tendency on the part of the head of this column to split off as a separate drop4 ,illustration3 ,,series ,i--7continued7 #ad #j4ajc sec4 #ae #j4aaf sec4 #af #j4abi sec4 ,the column in subsiding forms a cake of liquid round the base4 ,the edge of this circular cake 7see ,figs4 #ag1 #ah1 and #ai7 is the first well-marked ripple spreading outwards in an ever-widening circle4 ,illustration3 ,,series ,i--7continued7 #ag #j4aec sec4 #ah #j4aig sec4 #ai #j4bag sec4 ,if ,fig4 #ai is reached without the top of the column having separated1 then the splash follows the course shown in ,figs4 #bj-;a to #bc-;a1 in which it will be observed that the disappearance of the first column is very quickly followed by the rise of a secondary column very different in shape1 which itself subsides again1 but has not yet 7in #bc-;a7 formed1 as it ultimately will1 a second cake on the top of the first4 ,thus the second ripple follows late after the first4 ,illustration3 ,,series ,i--7continued7 ,alternative 7a74 #bj-;a #j4bdj sec4 #ba-;a #j4bdb sec4 #bb-;a #j4bdh sec4 #bc-;a #j4bec sec4 ,if1 however1 the summit of the primary column succeeds in breaking off 7as in ,fig4 #ah-;b71 or even in very nearly breaking off1 then the impact of this newly-formed drop forms a second slight crater on the top of the first cake1 and we have the series 7#ah-;b to #bd-;b71 in which it will be observed that the rim of the secondary crater spreads rapidly outwards1 so that a second well-marked circular ripple in this case quickly follows the first4 ,the secondary column that is thrown up in ,fig4 #bc-;b is very like that which emerged at a much earlier stage in the 7a7 series4 ,the photographs of this 7b7 series show very beautifully the manner in which the advancing edge of the ripple degenerates into smaller ripples travelling with greater speed4 ,illustration3 ,,series ,i--7continued7 ,alternative 7b74 #ah-;b #j4bad sec4 #ai-;b #j4bcg sec4 #bj-;b #j4bdb sec4 #ba-;b #j4bdd sec4 ,illustration3 ,,series ,i--7continued7 ,alternative 7b74 #bb-;b #j4bfa sec4 #bc-;b #j4beg sec4 #bd-;b #j4caa sec4 ,it will be readily understood that if the splitting off of the head of the primary column happens to take place a little earlier1 or on the other hand is nearly1 but not quite1 complete when it descends below the surface1 then subsequent configurations will differ somewhat from either of the sub-series here shown4 ,since any figure photographed might belong to either sequence1 the disentanglement of the two series required careful consideration and long experimenting4 ,the reappearance of the original drop at the head of the rebounding column1 of which the explanation has been given in this chapter1 is easily verified by naked-eye observation4 ,let the reader when he next receives a cup of tea or coffee to which no milk has yet been added1 make the simple experiment of dropping into it from a spoon1 at the height of fifteen or sixteen inches above the surface1 a single drop of milk4 ,he will have no difficulty in recognizing that the column which emerges carries the white milk-drop at the top only slightly stained by the liquid into which it has fallen4 ,in the same way naked-eye observation reveals the crater thrown up by the entry of a big rain-drop into a pool of water4 ,in either case what we are able to glimpse is a stationary stage4 ,the rebounding column reaches a maximum height1 remains poised for an instant1 and then descends4 ,the same is true of the crater4 ,it is the relatively long duration of the moment of poise that produces on the eye a clear impression where all else is blurred by rapid change4 ,but there is frequently a curious illusion4 ,we often seem to see the crater with the column standing erect in the middle of it4 ,we know now that in reality the crater has vanished before the column appears4 ,but the image of the crater has not time to fade before that of the column is superposed on it4 ,those who are accustomed to believe nothing that they hear and only half of what they see may be glad to find at least the latter part of their maxim so completely justified4 ,,chapter ,,iii ,,principles ,,involved ,the reader's attention has now been directed to various features which1 with certain modifications1 will be found in many of the splashes that we shall examine2 but so far the language used has been simply descriptive and in no way explanatory4 ,instead of going on to describe other splashes in the same way1 and thus to accumulate a great mass of uncooerdinated descriptive detail1 it will be better to pause for a moment in order to become acquainted with certain principles connected with the behaviour of liquids1 the application of which will go a long way towards explaining what we see going on in any splash4 ,the first principle to be understood is that the surface layers of any liquid behave like a uniformly stretched skin or membrane1 which is always endeavouring to contract and to diminish its area4 ,if the surface is flat1 like the surface of still liquid in a bowl1 this surface-tension has only the effect of exerting a small inward pull on the walls of the bowl4 ,but if the surface is curved1 with a convexity outwards1 then the surface layers1 on account of their tension1 press the interior liquid back1 and thus tend to check the growth of any protuberance2 while1 on the other hand1 if the surface is concave outwards1 then the surface-tension tends to pull the interior liquid forward1 and so to diminish the concavity4 ,direct evidence of this surface-tension is easy to cite4 ,we have it in any pendent drop1 such as any of those shown in the accompanying figures4 ,illustration3 ,,water4 ,,turpentine4 ,pendent drops 7magnified #b-a_/d times74 ,if we ask ourselves how it is that the liquid in the interior of one of these drops does not flow out1 pressed as it is by the liquid above it1 the answer is that everywhere the stretched skin presses it back4 ,a soap-bubble too presses on the air in its interior1 both the outside layers and the inside layers of the thin film being curved over the interior space4 ,this is the reason that a soap-bubble blown on the bowl of a pipe will slowly collapse again if we remove the stem of the pipe from our mouth4 ,the bubble drives the interior air back through the pipe4 ,and it is easy to show that if two soap-bubbles be blown on the ends of two tubes which can be connected together by opening a tap between them1 then the smaller will collapse and blow out the larger4 ,the reason of this is that in the bubble of smaller radius the surface layers are more sharply curved1 and therefore exert a greater pressure on the air within4 ,thus if a strap be pulled at each end with a total tension ,t and bent over a solid cylinder of small radius1 as in ,fig4 #f1 it is easy to see that the pressure on the surface of the part of the cylinder touched by the strap is less than if the strap be bent over an equal area on a cylinder of larger radius 7,fig4 #g74 ,the tension of the surface layers of a liquid causes them to act on the liquid within1 exactly as does the stretched strap on the solid in these figures4 ,if at any place the liquid presents1 as it generally does1 not a cylindrical surface1 but one with curvature in two directions1 then the pressure corresponds to what would be produced by two straps crossing at right angles1 laid one over the other1 each with the curvature of the surface in its direction 7,fig4 #h74 ,illustration3 ,,fig4 #f ,illustration3 ,,fig4 #g ,illustration3 ,,fig4 #h ,illustration3 ,,fig4 #i ,we can now understand why the drop that has been lying on the watch-glass should oscillate in its descent4 ,the sharp curvature of the edge ,,aa of the drop 7see ,fig4 #i7 tells us that the liquid there is pushed back by the pressure of the stretched surface layers1 and when the supporting glass is removed the sides of the drop move inwards1 driving the liquid into the lower part1 the tendency being to make the drop spherical1 and so to equalize the pressure of the surface at all points4 ,but in the process the liquid overshoots the mark1 and the drop becomes elongated vertically and flattened at the sides4 ,this causes the curvature at top and bottom to be sharper than at the sides1 and on this account the back-pressure of the ends soon checks the elongation and finally reverses the flow of liquid1 and the drop flattens again4 ,as an example of the way in which a concavity of the surface is pulled out by the surface-tension may be cited the dimples made by the weight of an aquatic insect1 where its feet rest on the surface without penetrating it4 ,this same surface-tension checks the rise of the crater1 and would cause it to subside again even without the action of gravity4 ,thus the pressures of the sharply curved crater-edge on the liquid between the crater walls are indicated by the dotted arrows in ,fig4 #aj1 and arise from the surface-tension indicated by the full arrows4 ,during the early part of the splash the surface-tension is more important than gravity in checking the rise of the walls4 ,for1 as the numbers show1 the crater of ,series ,i is already at about its maximum height in ,no4 #d1 i4e4 about seven-thousandths of a second after first contact4 ,in this time the fall due to gravity would be only about #a_/ajj of an inch4 ,thus if gravity had not acted the crater would only have risen about #a_/ajj of an inch higher4 ,the same reasoning applies to the rise of the central column1 but here the curvature at the summit is much less sharp4 ,the numbers show that the column reaches its maximum height in about #e_/ajj of a second after its start in ,no4 #aj1 and in this time the fall due to gravity is about half an inch1 so that gravity has reduced the height by this amount4 ,illustration3 ,,fig4 #aj ,the second principle which ,i will now mention enables us to explain the occurrence of the jets and rays at the edge of the crater and their splitting into drops4 ,it was shown in #ahgc by the blind ,belgian philosopher1 ,plateau1,d that a cylinder of liquid is not a figure of stable equilibrium if its length exceeds about #c-a_/g times its diameter4 ,thus a long cylindrical rod of liquid1 such as ,fig4 #aa1 if it could be obtained and left for a moment to itself1 would at once topple into a row of sensibly equal1 equidistant drops1 the number of which is expressed by a very simple law1 viz4 that for every #c-a_/g times the diameter there is a drop1 or that the distance between the centres of the drops is equal to the circumference of the cylinder4 ,illustration3 ,,fig4 #aa ,the cause of this instability is the action of the same skin-tension that we have already spoken of4 ,calculation shows1 and ,plateau was able to confirm the calculation by experiment1 that if through chance agitations lobes are formed at a nearer distance apart than #c-a_/g times the radius1 with hollows between as in the accompanying ,fig4 #ab1 then the curvatures will be such as to make the skin-tension push the protuberances back and pull the hollows out4 ,but if the protuberances occur at any greater distances apart than the length of the perimeter1 then the sharper curvature of the narrower parts will drive the liquid there into the parts already wider1 thus any such an initial accidental inequality of diameter will go on increasing1 or the whole will topple into drops4 ,illustration3 ,,fig4 #ab ,at the last moment the drops are joined by narrow necks of liquid 7,fig4 #ac71 which themselves split up into secondary droplets 7,fig4 #ad74 ,illustration3 ,,fig4 #ac ,illustration3 ,,fig4 #ad ,what we have said of a straight liquid cylinder applies also to an annulus of liquid made by bending such a cylinder into a ring4 ,this also will spontaneously segment or topple into drops according to the same law4,e ,now the edge of the crater is practically such a ring1 and it topples into a more or less regular set of protuberances1 the liquid being driven from the parts between into the protuberances4 ,now while the crater is rising the liquid is flowing up from below towards the rim1 and the spontaneous segmentation of the rim means that channels of easier flow are created1 whereby the liquid is driven into the protuberances1 which thus become a series of jets4 ,these are the jets or arms which we see at the edge of the crater4 ,examination with a lens of some of the craters will show that the lines of easier flow leading to a jet are often marked by streaks of lamp-black in ,series ,i1 or by streaks of milk in ,series ,,ii4 ,this explanation of the formation of the jets applies also to a similar phenomenon on a much larger scale1 with which the reader will be already familiar4 ,if he has ever watched on a still day1 on a straight1 slightly shelving sandy shore1 the waves that have just impetus enough to curl over and break1 he will have noticed that up to a certain moment the wave presents a long1 smooth1 horizontal cylindrical edge 7see ,fig4 #ae-;a7 from which1 at a given instant1 are shot out an immense array of little jets which speedily break into foam1 and at the same moment the back of the wave1 hitherto smooth1 is seen to be furrowed or combed 7see ,fig4 #ae-;b74 ,the jets are due to the segmentation of the cylindrical rim according to ,plateau's law1 and the ridges between the furrows mark the lines of easier flow determined by the position of the jets4 ,illustration3 ,,fig4 #ae-;b ,,fig4 #ae-;a ,diagrams of a breaking wave4 ,the tendency of the central column of ,series ,i to separate into two parts is only another illustration of the same instability of a liquid cylinder4 ,the column1 however1 is much thicker than the jets1 and its surface is therefore less sharply curved1 and consequently the inward pressure of the stretched curved surface is relatively slight and the segmentation proceeds only slowly4 ,since this segmentation must originate in some accidental tremor1 we see how it is that the summit of the column may succeed in separating off on some occasions and not on others4 ,as a matter of fact1 the height of fall for this particular splash was purposely selected1 so that the column thrown up should just not succeed in dividing in order that the formation of the subsequent ripples might not be disturbed by the falling in of the drops split off4 ,but1 as the reader will have perceived1 the margin allowed was not quite sufficient4 ,the two principles that ,i have now explained1 viz4 the principle of the skin-tension1 and the principle of the instability and spontaneous segmentation of a liquid cylinder1 jet1 or annulus1 will go far to explain much that we shall see in any splash1 but it is well that the reader should realize how much has been left unexplained4 ,why1 for example1 should the crater rise so suddenly and vertically immediately round the drop as it enters8 ,why should the drop spread itself out as a lining over the inside of the crater1 turning itself inside out1 as it were1 and making an inverted umbrella of itself8 ,why when the crater subsides should it flow inwards rather than outwards1 so as to throw up such a remarkable central column8 ,these questions1 which demand that we should trace the motion of every particle of the water back to the original impulse given by the impact of the drop1 are much more difficult to answer1 and can only be satisfactorily dealt with by a complicated mathematical analysis4 ,something1 however1 in the way of a general explanation will be given in a later chapter4 ,,footnotes3 ,d ,statique ,experimentale et ,theorique des ,liquides4 ,e ,see ,worthington on the ,segmentation of a ,liquid ,annulus1 ,proc4 ,roy4 ,soc41 ,no4 #bjj1 #ahgi4 ,,chapter ,,iv ,,the ,,splash ,,continued ,i have stated that the addition of the milk to the water made but little difference in the character of the resulting splash4 ,it does1 however1 make certain differences in detail1 as will be gathered from an examination of the next ,series ,i-a1 which shows the effect of letting the water-drop fall from the same height into water instead of into milk4 ,such a splash is difficult to photograph unless the illumination is from behind4 ,as shown in this way1 the early figures of the crater might be unintelligible to the reader had he not already studied the same crater lighted up from the side4 ,sometimes1 though the front of the crater is hardly visible directly1 yet every lobe on it can be clearly traced in the inverted image seen by reflection4 ,the most noticeable difference between the two splashes is perhaps the very much greater number of ripples seen with the splash in pure water4 ,this is partly because1 with the illumination behind1 such ripples are more easily visible1 but arises chiefly from the fact that ripples are not so readily propagated over the surface of milk on account both of its smaller surface-tension and its greater viscosity4 ,the first appearance of outward-spreading ripples is in ,no4 #f1 just round the subsiding crater4 ,illustration3 ,,series ,i-a ,water into water 7#dj cm4 fall74 ,scale #i_/aj4 #a ,t #j #b #j4jjd sec4 #c #j4jac sec4 #d #j4jah sec4 ,illustration3 ,,series ,i-a--7continued7 #e #j4jbf sec4 #f #j4jdb sec4 #g #j4jeh sec4 #h #j4jgc sec4 ,since the origination of these ripples is an interesting phenomenon from a physical point of view1 as throwing light on the dispersion of waves travelling with different velocities1 special precautions were taken to secure the most favourable conditions1 and in order to clean the surface after the arrival of each drop1 which inevitably brings down a little adherent lamp-black1 a continuous slow stream of fresh water was maintained which swept the contaminated surface-liquid away over the edge of the vessel4 ,the effect of this precaution is seen by a comparison of the photographs ,no4 #aa and ,no4 #aa-;a4 ,in the first the surface was kept quite clean in the way described2 in the second it had only been cleaned by skimming it with a fine wire-gauze dish4 ,the beginning of the descent of the first central column seems to be marked by the appearance of a slight depression round its base1 which has just not begun in ,no4 #aa-;a1 and has just begun in ,no4 #aa1 and goes on increasing in ,figs4 #ab and #ac4 ,illustration3 ,,series ,i-a--7continued7 ,running water4 ,scale reduced to #f_/aj4 #i #j4jhg sec4 #aj #j4jad sec4 #aa #j4aci sec4 #aa-;a #j4aci sec4 ,illustration3 ,,series ,i-a--7continued7 ,running water4 ,scale #f_/aj4 #ab #j4afc sec4 #ac #j4ahe sec4 #ad #j4bjg sec4 #ae #j4bbg sec4 ,the same feature marks the beginning of the descent of the secondary central column1 which is still rising in ,fig4 #ag1 is just poised in ,fig4 #ah1 and thence onwards shows a gradually increasing central depression4 ,these last four figures carry us to a rather later stage than was reached in ,series ,i4 ,it should be noticed that in this ,series the water-drop used was of smaller diameter than that of ,series ,i1 weighing 4#ac grams as against 4#b grams4 ,by employing the smaller drop1 we diminish irregularities due to oscillations of form set up on release1 for the smaller drop is more spherical when lying on the dropping cup than the larger2 a few photographs taken for comparison with the full-sized drop showed1 however1 extremely little difference in the splashes at this height of fall4 ,illustration3 ,,series ,i-a--7continued7 ,still water4 ,scale #i_/aj4 #af #j4bdg sec4 #ag #j4bff sec4 #ah #j4bid sec4 ,illustration3 ,,series ,i-a--7continued7 ,still water4 ,scale #i_/aj4 #ai #j4bhe sec4 #bj #j4caa sec4 #ba #j4cba sec4 ,,chapter ,v ,,higher ,,falls--,,bubble-,,building ,it might well be expected that the effect of increasing the height of fall of our drop to #ajj cm4 would be simply to emphasize the phenomena already observed1 and to obtain a higher crater and a taller rebounding column4 ,such an expectation would be mistaken4 ,a new phenomenon makes its appearance4 ,the crater does indeed rise to a greater height1 but its mouth closes so as to form a bubble on the surface of the liquid4 ,if the height be not too great the closing is either incomplete or at any rate only temporary1 and the bubble reopens at the top to make way for the column which rises as before from the base1 but is now much thicker and hardly so high as before4 ,in the ,series ,,ii1 which is now given1 the drop was of milk1 #g4cf mm4 in diameter1 and fell #ajj cm4 into water4 ,photographs #a and #b--to which is added #b-;a1 though taken under slightly different conditions--show that the drop on entering punches a sheer-walled hole1 for the fine line of light seen above the level of the top of the drop in ,figs4 #b and #b-;a marks the circular cliff-like edge of the as yet undisturbed liquid4 ,up the vertical sides of this circular pit the liquid of the drop is streaming4 ,this cliff is highest and perhaps clearest in ,fig4 #b-;a4 ,the closing of the mouth of the crater1 which is just beginning in ,fig4 #e1 is to be explained as follows4 ,if the crater were a simple thin-walled cylinder of liquid1 it would contract under the influence of the surface-tension just as does a soap-bubble1 but not so fast1 since the walls have only a horizontal curvature4 ,if the wall is thinner above than below1 then the upper part will contract faster than the lower1 through there being less liquid to accelerate4 ,now the supply of liquid is from below1 and will thicken the lower part of the walls first1 and thus account for the faster closing of the mouth4 ,on the other hand1 the uppermost edge of the crater is the place where the checking influence of the surface-tension on the upward flow is first felt1 with the result that the edge of the rim is thickened by the influx from below1 so that a more or less regular rope-like annulus is formed round the edge4 ,now calculation shows that such an annulus1 so long as its thickness is not more than #a4fa times the thickness of the wall below1 will contract quicker than the wall1 and this will tend to close the crater1 somewhat as a bag would be closed by the contraction of an elastic cord round the mouth4 ,this rope-like thickening of the edge is to be seen in ,figs4 #e and #g1 and especially in ,figs4 #c and #d of ,series ,,iii on page #fc4 ,illustration3 ,,series ,,ii ,milk into water 7#ajj cm4 fall74 #a #j4jjb sec4 #b-;a #b #j4jjb sec4 #c #j4jjb sec4 #d #j4jji sec4 #e #j4jah sec4 #f #j4jah sec4 #g #j4jci sec4 ,the photographs #i1 #aj1 and #aa 7obtained after adding a little milk to the water in order to render it more visible7 were at first very puzzling4 ,what happens is that the bubble sometimes reopens very soon 7or perhaps does not quite close7 as in ,fig4 #i1 and makes way for the column which rises from the base exactly as in the previous series4 ,this column may be dimly seen through the walls of the bubble in ,fig4 #i1 and ,no4 #aj shows the column alone1 the bubble having opened early and receded with great velocity1 a few drops round the base being all that is left of it4 ,nos4 #aj-;a and #aj-;b illustrate this reopening4 ,in #aj-;a the milk-drop was allowed to fall again into quite pure water1 and the photograph shows very beautifully the summit of the column1 with the original milk-drop at the top1 emerging through the reopening mouth of the bubble2 and ,fig4 #aj-;b shows the same at a very slightly later stage when the bubble has completely retreated4 ,illustration3 ,,series ,,ii--7continued7 #h #j4jed sec4 #i #j4jhe sec4 #aj #j4aje sec4 #aj-;a #j4ajc sec4 #aj-;b #j4aaa sec4 ,in ,fig4 #aa the bubble has been too firmly closed to reopen1 and the summit has been struck by the column within4 ,the next figure 7,no4 #ab7 shows how in such a case the emergent column becomes entangled in the liquid of the bubble when it bursts4 ,under the influence1 however1 of the surface-tension1 which pushes back the protuberances and pulls out the hollows1 regularity of form is soon regained4 ,thus ,fig4 #ac shows the emergent columns at a later stage after such an encounter1 already much more symmetrical2 and the subsequent photographs 7for which a good deal of milk was added for the sake of greater visibility7 show a column of uniformly sedate and respectable rotundity1 betraying no traces of any youthful irregularities4 ,illustration3 ,,series ,,ii--7continued7 #aa #j4aje sec4 #ab #j4jie sec4 #ac #j4aac sec4 #ad #j4acb sec4 #ae #j4aid sec4 ,illustration3 ,,series ,,ii--7continued7 #af #j4bag sec4 #ag #j4bdj sec4 #ah #j4bgb sec4 #ai #j4caa sec4 ,series ,,iii shows the effect of still further increasing the height of fall of the water-drop 7to #acg cm41 or about #d ft4 #f in471 and at the same time doubling its volume so that it now weighs 4#d gram4 ,the crater now closes in about #ah_/ajjj of a second1 and forms a comparatively permanent bubble4 ,the rope-like thickening of the edge1 already alluded to1 is well seen in ,figs4 #c and #d4 ,in its earlier stages the bubble is thick-walled1 rough1 and furrowed1 but becomes smoother and thinner the longer it lasts1 both because the liquid drains down the sides and because it becomes more uniformly distributed under the equalizing influence of the surface-tension4 ,illustration3 ,,series ,,iii ,water-drop weighing #j4d grams falling #acg cm4 7#d-a_/b feet7 into milk mixed with water4 ,scale #a_/b4 #a ,t #j #b #j4jje sec4 #c #j4jaf sec4 #d #j4jai sec4 ,such a bubble may remain long closed1 as in ,fig4 #h1 becoming every moment more delicate and exquisite1 or it may open at an even earlier stage1 as in ,fig4 #i4 ,there is a characteristic difference between the arms of a closing and of an opening bubble4 ,it will be noticed that up to the moment of closing the arms slope outwards4 ,the upper portions have been projected at an earlier stage when the mouth of the crater was wider open and the flow was either actually outwards or more nearly vertical2 then as the mouth contracts the arms are left behind in the upper parts4 ,illustration3 ,,series ,,iii--7continued7 #e #j4jag sec4 #f #j4jbj sec4 #g #j4jcf sec4 #h #j4jec sec4 ,in an opening bubble1 on the other hand1 the arms are at first vertical1 and later have the very characteristic inward slope of the last figure1 which is also well seen in ,fig4 #aj-;a of the last series4 ,here the edge of the opened bubble retreats outwards and downwards1 leaving the arms behind4 ,such is the origin of the bubbles raised by the big drops of a thunder shower on the surface of a pool4 ,the building of each fairy dome is accomplished in less than two-hundredths of a second1 and before one-tenth of a second has elapsed the whole construction may have vanished4 ,one can almost regret that so beautiful a process should have been so long unwatched4 ,to build these bubbles a large drop is essential4 ,with a drop weighing only #j4d of a gram1 even though it fall from a height of #agg cm41 there is no bubble1 and the splash is almost exactly that of ,series ,i-a4 ,the exact time required for the closing of the bubble probably depends a good deal on the phase of oscillation of the drop at the moment of entry1 and1 as already observed1 a big drop1 which lies very flat in the dropping cup1 is set vibrating more strongly on liberation than a small one4 ,we shall see in ,chapter ,,vii that the impact of a rough solid sphere1 if falling from a sufficient height1 produces a very exquisite bubble2 in this case irregularities due to oscillation are absent1 and the closing can be timed with greater precision4 ,illustration3 ,,series ,,iii--7continued7 #i #j4jdj sec4 #aj #j4jdf sec4 #aa #j4jgj sec4 ,illustration3 ,,fig4 #af ,arrangement for taking photographs below the surface of the liquid4 ,,chapter ,,vi ,,below ,,the ,,surface,f ,our investigation has so far been limited to what we can see from above the surface of the liquid2 nor perhaps would it occur to any one acquainted only with so much as we have yet examined that it might be worth while to look below the general level of the surface4 ,the discovery1 however1 that when the splash is made by a solid sphere very remarkable phenomena1 which will be described in the next chapter1 take place below the surface1 led at a much later date to a similar examination in the case of a liquid drop4 ,a suitable arrangement of the apparatus in the dark room is shown in the accompanying diagram 7,fig4 #af74 ,the water into which the drop is to fall is placed in a thin glass vessel ,,ab1 with parallel sides4 7,an inverted clock-shade makes a very convenient vessel47 ,the water fills the vessel to the brim1 and is allowed to overflow it in a steady stream1 thus presenting a surface which1 being perpetually renewed1 is maintained perfectly clean4 ,close behind the vessel is a plate ,p of finely roughened glass1 on which the light from the spark-gap ,f1 in front of its concave reflector ,m1 is thrown by means of the condenser lens ,l taken from an optical lantern4 ,this provides a very uniformly illuminated background against which the splash is viewed by means of the camera ,c1 whose optic axis is horizontal1 either a little below the level of the liquid surface or at that level4 ,by having it just at the level of the surface we secure simultaneous pictures of what is going on both above and below the surface4 ,there is1 to be sure1 a narrow band or region of confusion stretching across the photographs in which the images obtained by reflection1 both external and internal1 overlap the direct images1 and it should also be mentioned that the two pictures will not be quite in focus together1 for the optical effect of the water1 through which the part below the surface is viewed1 is to bring the image forward4 ,the photographs of ,series ,,iv were obtained in this way from the splash of a drop of water weighing #j4agf grams falling #dj cm4 into water4 7,the same splash as that of ,series ,i-a47 ,the perfectly spherical form presented by the cavity below the surface is very remarkable4 ,in the present case1 this spherical cavity when at its deepest1 as in ,fig4 #e1 would contain about fifty of the original drops1 and in other cases--e4g4 with a drop of #a_/d the volume1 falling from #agg cm4--the cavity would contain as many as #cfj of the original drops4 ,in ,figs4 #e1 #f1 and #g the depth of the cavity is nearly constant1 but the diameter is steadily increasing4 ,the spherical form1 however1 is still maintained4 ,the last figure shows the central column just beginning to rise4 ,illustration3 ,,series ,,iv ,the splash of ,series ,i-a viewed below the surface4 #a #b ,t #j #c #j4jji sec4 #d #j4jab sec4 #e #j4jaf sec4 #f #j4jbc sec4 #g #j4jci sec4 #h #j4jee sec4 #i #j4jgj sec4 ,there can be no doubt that the liquid of the original drop is spread out in an excessively thin lining over the interior of this sphere4 ,the reader has seen for himself part of the evidence in the streaks of milk that are carried up the inner walls of the crater when a milk-drop falls into water 7,series ,,ii72 in the streaks of lamp-black that are carried there when the drop is of milk1 and it may here be mentioned that other photographs that cannot be reproduced here have enabled me to trace the gradual deformation of the drop into this thin layer and show that it passes through configurations like ,figs4 #ag1 #ah1 and #ai4 ,illustration3 ,,fig4 #ag ,illustration3 ,,fig4 #ah ,illustration3 ,,fig4 #ai ,it appears possible that the study of this remarkable spherical excavation may afford a clue that will lead to a solution of the very difficult hydro-dynamical questions involved1 and the matter is still being investigated4 ,,footnotes3 ,f ,the information conveyed in this chapter was first published in a communication to the ,mathematical and ,physical ,section of the ,british ,association at ,leicester in #aijg4 ,,chapter ,,vii ,,the ,,two ,,kinds ,,of ,,splashes ,,of ,,solid ,,spheres ,in the present chapter will be described the splash that follows the entry of a solid sphere falling vertically into a liquid from a small height1 and ,i should like to persuade the reader1 if possible before he begins to read1 or at any rate afterwards1 to make a very simple experiment4 ,let a few child's marbles be taken--not glass marbles1 for these are seldom round enough or smooth enough1 but what are sold in the toy-shops as stone marbles--and let one of these be well rubbed and polished with a dry handkerchief1 and then dropped from a height of about #cj cm41 or1 say1 #a foot1 into a deep bowl or basin of water1 the bottom of which may be conveniently protected from breakage by a few folds of fine copper gauze4 ,if the polishing has been good1 and the surface of the sphere has not been dimmed by subsequent handling with hot or greasy fingers1 it will be observed that the splash is singularly insignificant1 the sphere slipping noiselessly into the liquid with very little disturbance of the surface4 ,but if the same sphere be fished out of the water1 and again let fall from the same height without being first dried1 or1 better still1 if another marble be taken1 which has been previously roughened with sand-paper1 the resulting splash is totally different4 ,there is now a noise of bubbles1 which may be seen rising through the liquid1 and a tall jet is seen to be tossed into the air4 7#a7 ,,the ,,splash ,,of ,a ,,rough ,,sphere4 ,to understand the cause of this really surprising difference we must turn to the photographic record1 and we will take first the case of a rough sphere falling into water to which milk has been added for the sake of clearness in the photographs4 ,the diameter of the sphere was #a4e cm4 7or #c_/e inch71 and the height of fall #ae cm41 or just about #f inches4 ,the sphere on each occasion was fished out1 redried1 and re-roughened with sand- or emery-paper4 ,examination of the first photographs of ,series ,v shows that the liquid1 instead of flowing over and wetting the surface of the sphere1 is driven violently away1 so that as far as can be seen from above the upper portion is1 at first at any rate1 unwetted by the liquid4 ,the crater that is subsequently formed is very similar to that which was thrown by the liquid drop in ,series ,i1 the main difference being that in the present-case the crater is thinner in the wall and more regular4 ,this greater regularity is chiefly to be attributed to the fact that the solid sphere enters the liquid with a true spherical form1 and is not distorted by the oscillations and tremors which disturb a falling drop4 ,the gradual thickening of the wall and the corresponding reduction in the number of lobes as the subsidence proceeds is beautifully shown in ,figs4 #g1 #h1 #i1 and #aj1 the last-mentioned figure being hardly distinguishable from the corresponding ,fig4 #i of ,series ,i1 p4 #ag4 ,this stage is in each case reached in about #eh_/ajjj of a second4 ,illustration3 ,,series ,v ,rough sphere4 ,basket splash4 ,diameter of sphere1 #a4e centim4 ,height of fall1 #ae centim4 #a ,t #j #b #j4jjc sec4 #c #j4jjf sec4 #d #e #f ,illustration3 ,,series ,v ,rough sphere--7continued74 #g #j4jbd sec4 #h #j4jcb sec4 #i #j4jdb sec4 #aj #j4jfj sec4 ,now from the depths of the crater there rises with surprising velocity the exquisite jet of ,fig4 #aa1 which in obedience to the law of segmentation at once splits up in its upper portion into little drops1 while at the same time it gathers volume from below1 and rises ultimately as a tall1 graceful column to a height which may be even greater than that from which the sphere fell4 ,this is the emergent jet which one sees with the naked eye whenever a sufficiently rough sphere is dropped from a small height into water1 but if we are to ascertain how this column originates1 we must follow the sphere below the surface of the liquid4 ,the arrangement already described on p4 #fi enables this to be done4 ,we let the sphere fall into clear water contained in a narrow1 flat-sided1 inverted clock-shade and illuminate this from behind while the camera stands straight in front4 ,illustration3 ,,series ,v ,rough sphere--7continued74 #aa #j4jfh sec4 #ab #j4jgf sec4 #ac #j4jhh sec4 #ad #j4ajj sec4 ,in this manner were obtained the photographs of ,series ,,vi1 which require a little explanation4 ,in the first figure we see the sphere just entering the liquid4 ,the faint horizontal line shows the level of the surface4 ,above this line we see the internally reflected image of the part that has already entered1 while still higher in the figure may be discerned the summit of the sphere itself4 ,the slight lateral displacement of the part below the surface is due to refraction consequent on the camera having been set with its optic axis not quite perpendicular to the face of the vessel4 ,in the subsequent figures it will be observed that the sphere1 as it descends1 drags with it the surface of the liquid in the form of a gradually deepening pocket or bag1 the upper part of the sphere being for a long time quite unwetted by the liquid4 ,the sides of this pocket or bag of air not being quite smooth1 give a somewhat distorted appearance to the sphere within4 ,also1 since the sides are sloping1 their reflected image in the level surface slopes in the opposite direction and produces an angle where the two meet4 ,this angle marks very clearly the level of the surface4 ,above the surface-line in ,figs4 #b to #e is seen the beaded lip of the crater which we have already viewed from above1 but this is somewhat out of focus1 for the camera had to be focused on the sphere as seen under water1 and the effect of the water is to bring the sphere optically nearer4 ,hence only the nearer part of the crater1 i4e4 the middle part of the front edge1 is distinctly shown4 ,illustration3 ,,series ,,vi ,the splash of a rough sphere as seen below the surface4 ,diameter1 #a4e centim4 ,height of fall1 #ae centim4 #a ,t #j #b #j4jaj sec4 #c #j4jah sec4 #d #j4jbc sec4 #e #j4jcb sec4 ,coming now to ,fig4 #f1 we perceive that the long cylindrical hollow has begun to divide4 ,in this spontaneous division we have another illustration of the law of instability which regulated the sub-division of the jets and columns of earlier series4 ,this law is the same whether the cylinder be of air surrounded by liquid or of liquid surrounded by air4 ,hitherto we have only seen it operating in jets of liquid in air2 now we have a jet of air in a liquid4 ,the lower part of the long cylinder of air splits off into a bubble just behind the sphere1 and follows in its wake to the bottom of the vessel1 and is only detached and rises to the surface when the sphere strikes the bottom4 ,many years ago1 through the kindness of the curator of the ,brighton ,aquarium1 ,i was enabled to watch this bubble of air following in the wake of the sphere to the bottom of the deepest tank4 ,figs4 #g1 #h1 and #i show the two parts gradually separating4 ,illustration3 ,,series ,,vi--7continued7 ,scale reduced to about #g_/aj4 #f #j4jde sec4 #g #h #j4jej sec4 #i #j4jed sec4 ,fig4 #aj shows specially well the ripples on the surface of the descending bubble4 ,these undulations sometimes become so accentuated that the upper part of this descending bubble is detached1 and then the curious phenomenon may be seen of this detached part still following the rest downwards through the liquid with an unsteady1 lurching motion4 ,meanwhile the upper half of the divided air-column is seen in ,fig4 #i to resemble a deep basin which now rapidly fills up by the influx of liquid from all sides4 ,it is from the confluence of this inflowing liquid into channels which necessarily narrow as the centre is approached that the great velocity with which the liquid spirts upwards is obtained4 ,in ,fig4 #aa the jet is just discernible above the surface1 and in ,fig4 #ac it is well-established4 ,illustration3 ,,series ,,vi--7continued7 #aj #j4jfb sec4 #aa #ab #j4jfb sec4 #ac #j4jgj sec4 ,on increasing the height of fall of a rough sphere to #fj cm41 we obtain a higher crater which closes and forms a bubble1 exactly as when we increased the height of fall of a liquid drop4 ,the process as viewed from above the surface is shown in ,series ,,vii4 ,the first figure of this series shows very well how completely the liquid is driven away from the surface of the sphere the first moment of contact4 ,the subsequent crater and bubble are of exquisite delicacy4 ,this bubble1 though it closes completely as in the last figure1 is doomed to almost immediate destruction4 ,for we see1 on looking below the surface1 that the proceedings there are of the same kind as in the case of the lower fall already described1 and result in the formation of an upward-directed jet4 ,illustration3 ,,series ,,vii ,rough sphere falling #fj cm4 ,scale #c_/d4 #a ,t #j #b #j4jjc sec4 #c #j4jag sec4 #d #j4jag sec4 #e #j4jcc sec4 ,thus the first three figures of ,series ,,viii show the last moments of a bubble which has burst1 spontaneously1 and so has made way for the jet of ,fig4 #c4 7,these are taken from a splash into petroleum with #bd4e cm4 fall47 ,but the last two figures1 #d and #e 7taken with a #cb cm4 fall71 show how a bubble which might otherwise have been permanent1 is stabbed by the rising jet and destroyed4 ,with water and #fj cm4 fall the jet appears sometimes to rise quite unimpeded1 and sometimes to be checked by the still closed bubble4 ,before leaving the splash of a rough sphere1 ,i desire to call the reader's attention to another point4 ,such figures as #g1 #i1 and #aj of ,series ,v1 p4 #gg1 show that the surface of the liquid beyond the walls of the crater is still flat and undisturbed2 yet we now know from the corresponding ,figs4 #e1 #f1 and #g of ,series ,,vi1 p4 #hc1 that a large volume of liquid has been displaced1 much larger than the quantity required to form the crater wall4 ,the inference is that the level of the surface has been slightly raised even at a great distance from the place of the splash4 ,figs4 #g1 #h1 and #i of ,series ,,vi themselves confirm the impression of the undisturbed flatness of the surface at even a small distance from the splash4 7#b7 ,,the ,,splash ,,of ,a ,,smooth ,,sphere4 ,the reader who has been sufficiently interested to make for himself the simple experiment suggested at the beginning of this chapter1 will have already realized that the splash of a smooth sphere is totally different from that of a rough one4 ,the photographs of ,series ,,ix show that the difference is quite pronounced from the first instant of contact4 ,in this series the sphere was of polished stone #c4b cm4 in diameter and fell #ad cm4 ,the scale of magnification is #c_/d4 ,the second figure shows that the liquid1 instead of being driven away from the surface as was the case with a rough sphere1 now rises up in a thin1 closely-fitting sheath which 7see ,fig4 #c7 completely envelops the sphere even before its summit has reached the water-level4 ,figs4 #d and #e show the comparatively insignificant column that remains to mark the spot where the sphere has entered4 ,fig4 #f was the result of a lucky accident1 which left the sphere rough on the right-hand side1 smooth on the left4 ,nothing could show better than this photograph the essential difference between the two splashes4 ,illustration3 ,,series ,,viii ,rough sphere4 ,splashes viewed below the surface4 ,the bursting of the bubble4 #a #j4jee sec4 ,from a splash into ,petroleum #bd4e cm4 fall4 #b #j4jfj sec4 #c #j4jfd sec4 ,from a splash into ,petroleum #cb cm4 fall4 #d #j4jgj sec4 #e #j4jhb sec4 ,the reader's attention is directed to the remarkably deep furrows which characterize the whole sheath in ,fig4 #c and the left-hand 7smooth splash7 part in ,fig4 #e4 ,about these furrows we shall have something to say later4 ,a better idea of the extreme thinness of the enveloping sheath is obtained when the illumination is from behind as in ,series ,x1 in which the sphere was of highly polished serpentine stone #b4eg cm4 7or just over #a inch7 in diameter1 the fall being #ad cm4 7or not quite #f inches74 ,illustration3 ,,series ,,ix ,the sheath splash of a smooth sphere4 #a ,t #j #b #j4jjb sec4 #c #j4jac sec4 #d #j4jbd sec4 #e #j4jci sec4 #f ,examination of either ,series ,,ix or ,series ,x shows that with the smooth sphere as with the rough the amount of water lifted above the surface in the immediate neighbourhood of the splash is much less than the whole volume displaced1 so that we are again driven to the conclusion that the surface at even a considerable distance must be bodily lifted without its flatness being sensibly disturbed4 ,this conclusion was confirmed by a direct experiment4 ,the not very wide vessel of ,fig4 ,a was taken and filled brimful with milk1 and the lower edge of a card millimetre scale was placed just in contact with the liquid surface at one side4 ,the reader should notice that the liquid is not quite up to the level of the spout on the right-hand side of this figure4 ,then the sphere was dropped in and the photograph of ,fig4 ,b was taken when the sphere was about two-thirds immersed4 ,the rise at the edge of the scale is about #c millimetres1 and there is an apparently equal rise at the spout1 where1 however1 the surface appears quite flat4 ,illustration3 ,,fig4 ,a ,illustration3 ,,fig4 ,b ,it seems probable1 then1 that whenever a stone is thrown into a lake the impulse accompanying its entry travels with the velocity of a compressional wave 7i4e4 with the velocity of sound7 through the liquid1 and is therefore almost instantly felt and produces a minute rise of level even in remote parts of the lake long before the arrival of any ripple or surface disturbance4 ,illustration3 ,,series ,x ,polished serpentine sphere falling #ad cm4 into water4 #a #j4jjc sec4 #b #j4jjf sec4 #c #j4jjh sec4 #d #j4jaa sec4 #e #j4jac sec4 #f #j4jad sec4 ,it may here be observed that whether the sphere be rough or smooth1 its size makes little or no difference in the character of the splash1 within a range of diameter from #ab to #cb millimetres--i4e4 from about #a_/b inch to about #a-a_/c inches4 ,no doubt with a very large sphere1 taking a long time to enter1 the splash would be controlled more by gravity than by surface-tension1 but so long as the sphere is within the limits mentioned this is not the case unless the height of fall be made very small indeed4 ,,chapter ,,viii ,,the ,,transition ,,from ,,the ,,smooth ,,or ,,sheath ,,splash ,,to ,,the ,,rough ,,or ,,basket ,,splash ,,the ,,influence ,,of ,,velocity4 ,if we gradually increase the velocity with which a well-polished sphere enters the liquid we find that there is a gradual transition from the silent smooth or sheath splash taking down no air and giving rise to only an insignificant column1 to the noisy1 rough1 basket splash taking down much air and throwing up a tall and conspicuous jet4 ,thus in the fourth figure of ,series ,,xi1 in which the height of fall has been increased from #ae to #fj cm4 7i4e4 from #f inches to #b feet71 the sphere being of polished ivory1 we see that the enveloping sheath has in many places broken away from the surface before the summit has been covered4 ,it is well known that a sphere moving through a liquid pushes away the liquid in front of it1 which flowing round closes in at the back of the sphere4 ,although the surface round the column of ,fig4 #f is still very flat1 the liquid just below it must be streaming inwards1,g as is indicated by the radial striae4 ,to the meeting of these converging streams we must attribute the large access of liquid that is forced up into the column1 whose subsequent toppling into drops is accompanied by the curious1 characteristic1 lop-sided curvature of the later figures4 ,illustration3 ,,series ,,xi ,polished ivory sphere1 #a4i centim4 in diameter1 falling #fj cm4 into water mixed with milk4 #a #b ,t #j #c #d #j4jjb sec4 #e #f #j4jjd sec4 #g #j4jca sec4 #h #j4jde sec4 #i #j4jfb sec4 ,series ,,xii shows how even with a very highly polished metal sphere falling into water from the still greater height of #ajj cm4 the characteristic sheath of the smooth splash is no longer so closely fitting even at an early stage1 but is beginning to resemble the earlier stages of the basket-shaped crater of the rough splash2 yet no air was taken down at this height4 ,the transition was also watched by means of photographs taken below the water-line4 ,it may be well here to guard the reader against a possible misconception4 ,the curved outline of the liquid in these photographs does not represent the path followed by the particles4 ,each particle must have travelled in a nearly straight line from the moment it left the surface of the sphere1 and must still be moving upwards and outwards4 ,gravity has not had time to produce any sensible displacement4 ,this applies also to the curved outlines in many other early figures4 ,,influence ,,of ,,the ,,condition ,,of ,,the ,,surface4 ,by very careful rubbing of such a polished1 steel sphere1 it was found possible to increase the height of fall to #afb4e cm4 7well over #e feet7 and yet to secure a perfectly airless1 smooth splash4 ,but the equilibrium of the splash1 if ,i may use the phrase1 is1 at this high velocity of entry 7#efd cm4 per sec41 or about #ah feet per sec471 very unstable1 and was found to depend on minute differences in the condition of the surface4 ,how minute this difference may be1 which yet makes the whole difference in the character of the splash1 may be gathered from the following extract from the original paper3-- ,a polished steel sphere #ae4i cm4 in diameter was found 7by naked-eye observation7 to give an airless splash when falling into water from a height of #acb4e cm42 at #acg4e cm41 there was much air taken down4 ,this observation at #acg4e cm4 was repeated three times1 observer ,c4 doing the polishing4 ,then observer ,w4 polished1 and the splash was first nearly airless and then quite airless4 ,then1 by persevering in the rubbing1 the height of fall was gradually raised to #afb4e cm41 and a perfectly airless splash was secured1 and even at #agb4e cm4 the record was 'very little air indeed4' ,again1 a polished marble sphere #b4eg cm4 in diameter falling into water from a height of #aab cm4 was found to take down 'much air' when rubbed with a certain clean handkerchief ,a1 and 'none at all1 or only very little1' when rubbed with clean handkerchief ,b4 ,this result was confirmed four times with ,b and five with ,a4 ,these handkerchiefs were subsequently examined under the microscope1 but were found to be extremely similar1 and the cause of the difference remained for the time beyond conjecture4 ,on another occasion1 of two similar nickel-plated steel spheres1 each #ai millimetres in diameter1 and each treated in exactly the same way1 falling #bb cm4 into paraffin oil1 one would always take down much air and the other little or none1 and again microscopic examination showed only a very slight difference in the surfaces4 ,illustration3 ,,series ,,xii ,smooth sphere of polished serpentine falling #ajj centim4 into water4 ,scale #c_/d4 #a ,t #j #b #j4jja sec4 #c #j4jjb sec4 ,by wetting the surface of a smooth sphere we can always convert a smooth or sheath splash into a rough or basket splash4 ,thus when the ivory sphere 7which when dry and well-polished gave1 with a fall of #fj cm41 the splash of ,series ,,xi1 p4 #ig71 was allowed to fall wet into the liquid1 all other circumstances remaining the same1 the splash of ,series ,,xiii1 p4 #ajc1 was obtained1 which is entirely different from the first4 ,the wetting was effected by dipping the sphere into the bowl of milky water into which it was to fall1 and then shaking off as much as possible of the adherent liquid1 but in all cases the splash quickly became unsymmetrical1 probably through the liquid1 during the fall1 drifting to one side of the sphere4 ,,influence ,,of ,,the ,,nature ,,of ,,the ,,liquid4 ,the nature of the liquid employed has a great influence in determining whether at a given height the splash shall be rough or smooth4 ,thus with paraffin oil the maximum height that could be reached with an airless splash with highly polished nickel-plated spheres1 well rubbed on a selvyt cloth1 was found to be only #bd4g cm4 7about #aj inches71 but1 with water1 a fall of #afj cm4 7over #e feet7 could be reached4 ,the paraffin oil used in these experiments had1 at a temperature of #ab deg44#e centigrade1 a specific gravity 4#hdj and a surface-tension about 4#ci of that of water4 ,since only a small increase of height was required with this liquid to make a smooth sphere give the same splash as a rough one1 this liquid was found much more convenient than water in investigating the transition4 ,when water is made more viscid by the gradual addition of glycerine1,h the surface-tension and the specific gravity are but little altered though the viscosity is steadily and sensibly increased4 ,an admixture of two parts of glycerine to fifty-one of water produced no perceptible change in the splashes observed4 ,when the glycerine was increased to six volumes in fifty-one of water1 though this made the viscosity half as great again1 the change was noticeable but still slight1 the chief difference being1 with a smooth sphere1 the greater salience of the ribs or flutings in some of the earlier stages of the glycerine splash1 and the much greater reluctance of the subsequent jets to topple into droplets4 ,this latter feature is well seen in the first figure on page #aje1 showing the entry of a smooth sphere of polished serpentine stone into this glycerine mixture from a height of #ej cm4 ,illustration3 ,,series ,,xiii ,splash of a smooth wet sphere4 #a ,t #j #b #j4jjc sec4 #c #j4jae sec4 #d #j4jcg sec4 ,with pure glycerine1 which is much more viscous1 the splash of the same polished serpentine sphere falling from #ge cm4 7about #b-a_/b feet71 is shown in ,series ,,xiv4 ,in the original photographs the radial furrows on the right-hand side of ,fig4 #b are very pronounced1 and even in ,fig4 #a the fluting of the film is seen to be already well developed on the left-hand side2 but these details have proved rather too delicate for reproduction in the plate4 ,two photographs taken of stage #b had each of them an isolated jet1 owing probably to the fact that when working with so sticky a liquid it was difficult to avoid contaminating the cloth on which the sphere was each time repolished after washing in water1 with the result that the spheres behaved as if locally rough4 ,the relatively great length and height of this jet brings out well the part played by viscosity1 both in delaying segmentation into droplets and also in hindering the flow of the rest of the liquid sheath which has remained in contact with the sphere4 ,with a rough sphere falling into pure glycerine from the same height of #ge cm41 except for an occasional jet that may escape as in ,fig4 #d of ,series ,,xv1 the proceedings are uneventful1 as a glance at the series will show4 ,with the same height of fall into water we should have had an exquisite crater fringed with a multitude of fine jets1 and ultimately closing to form a bubble4 ,we thus see how little play is given to the action of the surface-tension in a very viscous liquid4 ,illustration3 ,polished stone sphere falling #ae centim4 into water mixed with glycerine4 ,illustration3 ,,series ,,xiv ,polished stone sphere falling #ge centim4 into pure glycerine4 ,scale #i_/aj4 #a #b #c ,illustration3 ,,series ,,xv ,rough sphere falling #ge centim4 into pure glycerine4 ,scale #a_/a4 #a ,t #j #b #j4jja sec4 #c #j4jjb sec4 #d #j4jjc sec4 ,,the ,,influence ,,of ,,temperature4 ,it was found that if a polished sphere was heated in boiling water1 quickly rubbed dry1 and let fall while still hot1 a very marked difference was produced4 ,with the sphere hot1 the height of fall can be much increased before the splash becomes rough4 ,thus with paraffin oil1 the height with a nickel-plated sphere rose from #bb4b cm4 to #bi4c cm41 and with water from #aeg cm4 to #bcd cm4 ,,the ,,remarkable ,,influence ,,of ,a ,,flame ,,held ,,near ,,the ,,liquid1 ,,and ,,traversed ,,by ,,the ,,sphere ,,in ,,its ,,fall4 ,in our search for the explanation of the difference between the rough and the smooth splash1 it occurred to us to let the smooth sphere drop through a flame held near the liquid1 and the result was very remarkable4 ,with paraffin oil 7and the sphere hot7 the airless height now rose from #bi4c cm4 to #de4c cm41 and with water and a cold sphere1 it rose from #aeg cm4 to over #beh cm41 which was the greatest height that the laboratory would permit4 ,either the luminous flame of a bat's-wing burner or the flame of a ,bunsen burner held nearly horizontal produces the effect1 provided the flame is held near enough to the surface of the liquid1 and it is a very striking experiment to let the polished sphere fall several times from a height which gives a large volume of bubbles rising with much noise to the surface1 and then to let it fall through the flame1 and to observe the complete change in the phenomenon4 ,on a sphere already roughened the flame has no observable effect4 ,,the ,,supposition ,,of ,,electrification ,,tested ,,and ,,rejected4 ,the behaviour with a flame led at first to the supposition that we had to deal with an electrical phenomenon1 for a flame would certainly discharge completely any electrified sphere passing through it1 and it appeared reasonable to suppose that the sphere might become electrified by friction with the air through which it fell4 ,it required a long series of experiments1 into the details of which ,i need not now ask my readers to enter1 to prove that this tempting explanation was untenable1 and that there was no reason to believe that electrification had anything to do with the matter4 ,,experiments ,,in ,,vacuo4 ,it remained to examine what part was played by the air in the whole transaction4 ,this could only be settled by removing the air and letting the spheres1 whether rough or smooth1 fall through a vacuum into the liquid1 or rather through a space occupied only by the vapour of the liquid in use4 ,instantaneous photographs obtained under these conditions showed that the presence of the air has no material influence on the early course of the splash1 and that a sphere which gives a smooth splash in air will give a smooth splash in vacuo1 while if the splash is rough in air1 it will also be rough in vacuo4 ,,footnotes3 ,g ,some useful information about the internal flow of the liquid was obtained by the device of letting the sphere descend between two slowly ascending streams of very minute bubbles liberated by electrolysis at two electrodes placed in the liquid4 ,these streams1 initially straight and vertical1 were displaced and distorted as the sphere passed near them and afforded a measure of the displacement of the fluid at different points4 ,for details see ,phil4 ,trans4 ,roy4 ,soc41 ,vol4 #aid1 p4 #agh 7#aijj74 ,h ,glycerine was found to be a rather treacherous liquid1 requiring special precautions for which the reader who desires details is referred to the original memoir4 ,phil4 ,trans4 ,roy4 ,soc41 ,series ,a1 #aijj4 ,vol4 #aid1 p4 #aih4 ,,chapter ,,ix ,,the ,,explanation ,,of ,,the ,,cause ,,of ,,difference ,,between ,,the ,,two ,,splashes ,i have some hope that1 by the enumeration of the many surprising and puzzling facts mentioned in the last chapter1 ,i may have succeeded in producing in the mind of my reader some sympathy with the state of perplexity of ,mr4 ,cole and myself when1 after four years of experimenting1 we found ourselves still unable to answer the question1 ,why does the rough sphere make one kind of splash1 the smooth sphere another kind8 ,by reflecting1 however1 on all the facts at our disposal1 we were at last led to what seems to be an entirely satisfactory explanation1 and one moreover which we were able to test by further experiment4 ,this explanation may be stated as follows3-- ,when a sphere1 either rough or smooth1 first strikes the liquid1 there is an impulsive pressure between the two1 and the column of liquid lying vertically below the elementary area of first contact is compressed4 ,for very rapid displacements the liquid on account of its viscosity behaves like a solid4 ,in the case of a solid rod we know that the head would be somewhat flattened out by a similar blow1 and a wave of compression would travel down it2 to this flattening or broadening out of the head of the column corresponds the great outward radial velocity1 tangential to the surface1 initiated in the liquid1 of which we have abundant evidence in many of the photographs4 7,see pp4 #ge1 #hg1 and #ii47 ,into this outward-flowing sheath the sphere descends1 and since each successive zone of surface which enters is more nearly parallel to the direction of motion of the sphere1 the displacement of liquid is most rapid at the lowest point1 from the neighbourhood of which fresh liquid is supplied to flow along the surface4 ,whether the rising sheath shall leave the surface of the sphere1 or shall follow it1 depends upon the efficiency of the adhesion to the sphere4 ,if the sphere is smooth and clean1 the molecular forces of cohesion will guide the nearest layers of the advancing edge of the sheath1 and will thus cause the initial flow to be along the surface of the sphere4 ,to pull any portion of the advancing liquid out of its rectilinear path the sphere must have rigidity4 ,if the advancing liquid meets loosely attached particles1 e4g4 of dust1 these will constitute places of departure from the surface of the sphere2 the dust will be swept away by the momentum of the liquid which1 being no longer in contact with the sphere1 perseveres in its rectilinear motion4 ,if the dust particles are few and far between1 the cohesion of the neighbouring liquid will bring back the deserting parts1 but if the places of departure are many1 then the momentum of the deserters will prevail4 ,thus at every instant there is a struggle between the momentum of the advancing edge of the sheath and the cohesion of the sphere2 the greater the height of fall the greater will be the momentum of the rising liquid1 and the less likely is the cohesion to prevail1 and the presence or absence of dust particles may determine the issue of the struggle4 ,roughness of the surface will be equally efficient in causing the liquid to leave the sphere4 ,for the momentum will readily carry the liquid past the mouth of any cavities 7see ,fig4 #bj71 into which it can only enter with a very sharp curvature of its path4 ,it is to be observed that the surface-tension of the air-liquid surface of the sheath will act at all times in favour of the cohesion of the sphere1 and even if the film has left the sphere the surface-tension will tend to make it close in again1 but we should not be right in attributing much importance to this capillary pressure which1 with finite curvatures1 is a force of a lower order of magnitude than the cohesion1 and1 as the photographs now to be shown will clearly show1 is incompetent to produce the effects observed4 ,illustration3 ,,fig4 #bj ,having arrived at this general explanation1 we proceeded to test it4 ,,experiments ,,on ,,the ,,influence ,,of ,,dust4 ,in the first place1 to test the influence of dust1 the experiment was made of deliberately dusting the surface of the sphere4 ,for this purpose a highly polished nickelled sphere was held in a pair of crucible tongs by an electrified person standing on an insulating stool1 and by him presented to any dusty object that stood or could be brought within reach4 ,particles of dust soon settled on the electrified sphere1 which was then carefully placed on the dropping ring with the dusty side lowest4 ,the liquid used was paraffin oil1 and the height of fall was #ca4g cm41 at which this sphere when not dusted gave always a quite airless splash4 ,when dusted an enormous bubble of air was carried down on each occasion4 ,although the sphere when laid on the dropping ring must have completely lost the electrical charge1 yet it seemed worth while to go through the same electrifying process without dusting4 ,the result showed that no change was produced4 ,in order to see how far the influence of dust would go1 the height of fall was now reduced1 and it was found that with sphere 7#a7 a fall of #ag4a cm4 gave a perfectly rough splash when the surface was visibly dimmed with fine dust1 and with a second similar sphere a fall of #af4g cm4 availed4 ,if the surface was only slightly dusty1 then at these low heights the splash remained smooth4 ,it then occurred to us to try the effect of partial or local dusting1 for we had already found by experimenting with a marked sphere that the method of dropping did not impart any appreciable rotation to the sphere1 which reached the liquid in the attitude with which it started from the dropping ring4 ,accordingly1 after dusting the sphere in the manner already described1 the dust was carefully rubbed away from all but certain parts whose position was recorded4 ,the experiments were very successful1 and the results are shown on page #aac4 ,the liquid used was water1 and the sphere was of polished serpentine1 #b4eg centim4 in diameter1 falling #ad centim4 ,in ,fig4 #a of ,series ,,xvi the sphere was dusted on the right-hand side1 and a sound of splash was recorded4 ,on the left side we see that there is no disturbance of the smooth splash2 on the right is a pocket of air such as was obtained by accident in ,series ,,ix1 ,fig4 #f 7see p4 #ia74 ,the point of departure at which the liquid left the sphere is well marked1 and a tangent from this point passes through the outermost conspicuous droplets that must have been projected from it4 ,in ,fig4 #b the sphere was dusted at the top and on the right-hand side1 but not much more than half-way down1 and the configuration corresponds entirely to the facts4 ,here again a tangent from the well-marked drops on the right-hand side leads very nearly to the place of departure from the surface of the sphere4 ,in ,fig4 #c the sphere was dusted near the bottom only4 ,the appearance on the left-hand side seems to show that the liquid has1 after leaving the sphere1 again been brought within reach4 ,this recovery at an early stage is explained by reference to photographs of ,series ,,vi 7p4 #ha7 of the splash of a rough sphere1 which show that even the rough sphere is soon wetted for some distance up the sides1 by the gradual passage of the sphere into the divergently flowing cone of liquid which surrounds the lower part4 ,when the liquid again touches a polished part the film will be again guided up it in the manner already explained4 ,illustration3 ,,series ,,xvi ,spheres dusted at one side4 #a #b #c ,we observe that in ,figs4 #a and #b 7as also in ,fig4 #f of page #ia7 the continuous film or shell of liquid no longer reaches the outermost droplets that once have been at its edge4 ,it must evidently have been pulled in by its own surface-tension1 which of course will cease to exercise any inward pull on a drop that has once separated4 ,the influence of dust1 thus incontestably proved1 seems also to afford a satisfactory explanation of-- 7#a7 ,the effect of a flame4 7#b7 ,the effect of heating4 7#c7 ,the variable and uncertain effects of electrification4 ,for1 7#a71 we may suppose that the flame burns off minute particles of dust2 7#b71 we know from ,aitken's experiments,i that dust from the atmosphere will not settle on a surface hotter than the air2 7#c7 an electrified sphere descending through the air would attract dust to its surface unless it happened1 as well might happen1 that the air round about it1 with its contained dust1 had become itself similarly charged through the working of the electrical machine4 ,in further confirmation of our view that the leading clue to the explanation of the motion is the struggle between the adhesion of the rigid sphere and the tangential momentum of the liquid1 we may cite the following points3-- ,a liquid sphere makes a rough splash1 and the photographs obtained show that the lower part of the in-falling drop is swept away by the tangential flow1 while the upper part is still undistorted4 ,here we have cohesion but no rigidity4 ,also we find that the rough splash is obtained by any process which gives a non-rigid surface to the sphere4 ,thus the splash made by a marble freshly roughened by sand-papering1 or by grinding between two files and let fall from the very small height of #g4e cm41 can be practically controlled by attending to the condition of the surface4 ,if the surface is quite dry and still covered with the fine powder resulting from the process of roughening1 the splash is rough1 and a great bubble of air is taken down4 ,but if this coat of powder1 which has neither cohesion nor shearing strength1 be removed by rubbing1 the splash 7under this low velocity7 is smooth4 ,again1 a marble freshly sand-papered and covered with the resulting powder1 if let fall from #ab or #ae cm41 gives a rough splash4 ,the same marble picked out of the liquid and very quickly dropped in again from the same height1 will give again a rough splash4 ,here the liquid film is thick and shearable4 ,but if the same sphere be allowed to drain or be lightly wiped1 the splash will be smooth4 ,we may conjecture that in this case enough fluid is left to fill up the interstices1 but that the coat is not thick enough to shear easily4 ,if1 however1 the sphere be thoroughly dried1 the splash becomes rough again4 ,this gives us the explanation of the facts already recorded in respect of the splash of a wet sphere4 ,this splash was always irregular2 the liquid drifted to one side where it would shear1 while it disappeared from the other or became there too thin to shear1 though sufficient to fill up crevices4 ,,explanation ,,of ,,the ,,ribs ,,or ,,flutings ,,in ,,the ,,splash ,,of ,a ,,smooth ,,sphere4 ,the fact thus established experimentally1 that the surface of a smooth sphere must be rigid if the film is to envelop it closely1 suggests also a satisfactory explanation of the flutings4 ,for we know from other researches on the motion of liquids1,j that a layer of liquid actually in contact with a solid can have no motion relative to the solid1 but must move with it4 ,thus in the film or sheath which rises over and envelops the sphere1 the layer of liquid next to the solid must be moving downwards with it1 while the outermost layers at least are moving upwards2 thus there must be a strong viscous shear in the film impeding its rise4 ,if by any fortuitous oscillation a radial rib arises1 this will be a channel in which the liquid1 being farther from the surface1 will be less affected by the viscous drag2 it will therefore be a channel of more rapid flow and diminished pressure1 into which1 therefore1 the neighbouring liquid will be forced from either side4 ,thus a rib once formed is in stable equilibrium1 and will correspond to a jet at the edge of the rim4 ,this explains the persistence of the ribs when once established1 and we may attribute their regular distribution to the fact that they first originate in the spontaneous segmentation of the annular rim at the edge of the advancing sheath4 ,this explanation quite accords with the appearance of such figures as ,fig4 #f of page #ia and ,figs4 #a and #b of page #aac1 in which1 firstly1 we see that the flutings are absent from that part of the sheath which has left the sphere1 and1 secondly1 we see how much higher in every case the continuous film has risen in that part which has left the sphere than in the part which has clung to it1 and has been hindered by the viscous drag4 ,especially is this the case in ,fig4 #b1 ,series ,,xiv 7p4 #aje71 where the liquid was pure glycerine4 ,the effect of the viscous drag is1 in fact1 most marked in the most viscous liquid1 and it is also in the viscous liquid that the ribs are most strongly marked4 ,,influence ,,of ,,the ,,nature ,,of ,,the ,,liquid ,,explained4 ,finally1 in confirmation of our explanation1 we have the fact that with a liquid of small density and surface-tension1 such as paraffin oil1 a much smaller velocity of impact with a highly polished sphere suffices to give a rough splash than with water1 a liquid of greater density and surface-tension1 the reason being without doubt that the tangential velocity given by the impact is greater with the lighter liquid1 as1 indeed1 is proved to be the case by the greater height to which the surrounding sheath is thrown up4 ,the surface-tension also being smaller1 the less is the abatement of velocity on account of work done in extending the surface4 ,,footnotes3 ,i ,see ,nature1 vol4 xxix41 ,january #ca1 #ahhd4 ,j ,see ,whetham on ,the ,alleged ,slipping at the ,boundary of a ,liquid in ,motion4 ,phil4 ,trans4 ,roy4 ,soc41 ,vol4 #aha 7#ahij74 ,,chapter ,x ,,conclusion ,we have now reached the end of the story1 as far at least as ,i am able to tell it4 ,but there is certainly more to be found out4 ,no one has yet examined what happens when a rough sphere enters a liquid with a very high velocity4 ,that the motion set up must differ from that at a low velocity is apparent to any one who has thrown stones from a low bridge into deep water below4 ,the stone that is thrown with a great velocity makes neither quite the same sound nor the same kind of splash as a slow-falling stone1 and though in the light of our present knowledge we may conjecture the kind of difference to be expected1 yet experience has taught me that the subject is so full of unexpected turns that it is better to wait for the photographic record than to speculate without it4 ,it would be an immense convenience1 as was suggested in the first chapter1 if we could use a kinematograph and watch such a splash in broad daylight1 without the troublesome necessity of providing darkness and an electric spark4 ,but the difficulties of contriving an exposure of the whole lens short enough to prevent blurring1 either from the motion of the object1 or from that of the rapidly-shifting sensitive film1 are very great1 and any one who may be able to overcome them satisfactorily1 will find a multitude of applications awaiting his invention4 ,but even were the photographic record complete1 what does it amount to8 ,all that we have done has been merely to follow the rapid changes of form that take place in the bounding surface of the liquid4 ,the interior particles of the liquid itself have remained invisible to us4 ,but it is precisely the motion of these particles that the student of hydrodynamics desires to be able to trace4 ,his study is so difficult that even in the apparently simple case of the gently-undulating surface of deep water1 the reasoning necessary to discover the real path of any particle can at present only be followed by the highly-trained mathematician4 ,in other and more complicated cases such as are exemplified by the sudden disturbances that we have studied1 any definite information that can be obtained1 even as to the motion of the surface1 may afford a clue to the solution of important questions2 and ,i have been encouraged to hope that the observations here recorded may serve as a useful basis of experimental fact in a confessedly difficult subject4 ,to take a single illustration of a possible application in an unexpected quarter1 ,i would invite the attention of the reader to the two photographs in the frontispiece1 which exhibit the splash of a projectile on striking the steel armour-plate of a battleship4 ,these are ordinary photographs taken after the plate had been used as a target4 ,they represent the side on which the projectile has entered4 ,in one picture the projectile is still seen embedded in the plate4 ,no one looking at these photographs can fail to be struck with the close resemblance to some of the splashes that we have studied4 ,there is the same slight upheaval of the neighbouring surface1 the same crater1 with the same curled lip1 leading to the inference that under the immense and suddenly applied pressure1 the steel has behaved like a liquid4 ,such flow of metals under great pressure is familiar enough to mechanical engineers1 but what ,i desire to suggest is1 that from a study of the motions set up in a liquid in an analogous case1 it may be possible to deduce information about the distribution of internal stress1 which may apply also to a solid1 and may thus lead to improvements in the construction of a plate that is intended to resist penetration4 ,,chapter ,,xi 7,,supplementary7 ,a ,,new ,,phenomenon ,,that ,,appears ,,with ,,an ,,increase ,,in ,,the ,,velocity ,,of ,,entry ,,of ,a ,,rough ,,sphere ,a slight delay in the passage of this book through the press has enabled me to obtain some of the missing information referred to in the opening paragraph of the last chapter4 ,if any reader who may have been persuaded to try for himself the simple experiment mentioned at the beginning of ,chapter ,,vii1 will extend his observations by increasing the height of fall of the roughened marble to #d or #e feet 7say to #adj centim471 he will find that while1 as before1 much air is still carried down1 there is nevertheless1 now1 no rebounding jet projected high into the air1 such as is invariably seen with the lower fall of #b feet 7#fj centim471 and he will notice a curious seething appearance at the surface4,k ,thinking that this appearance which the naked eye detects must be due to an entanglement of the rising jet with the bubble1 which entanglement was likely to produce confused motions that could not be profitably studied1 ,i had not till now been sufficiently curious to examine what really happened4 ,but certain recent observations of the persistence with which the seething motion again and again recurred when a stone was dropped or thrown into a river1 led me to suspect that something required investigation4 ,i was1 however1 quite unprepared to find the remarkable change of procedure that is revealed by the following series of photographs 7,series ,,xvii71 in the taking of which ,i owe much to the kind and skilful assistance of ,dr4 ,bryan4 ,the earlier figures show the very rapid rise of the crater and its closing as a bubble much before the entrapped column of air divides4 ,before the division takes place1 the liquid now flowing in from all sides closes over the upper end of the long air-tube1 separates it from the air outside1 and forms a downward jet which shoots down the middle of the air-tube in pursuit of the sphere4 ,the first formation of this jet is not easy to observe1 because the view is obscured by much splashing and turbulent vortical motion resulting apparently from the collision of the streams that converge from all sides on the axis of the air-tube at its upper end4 ,thus in ,fig4 #e the jet is not yet well established1 or at least not easily discerned2 but in ,fig4 #f the turbulence has cleared away from the upper part1 and from this stage onwards the jet is well seen in all the figures1 and it persists long after the segmentation of the air column has taken place4 ,the reader must not suppose that this jet is a mere falling of the water under the action of gravity1 for the rapidity with which it advances is far greater than could be accounted for in this way2 indeed1 as the times show1 the effect of gravity during the establishment of the jet is insignificant4 ,illustration3 ,,series ,,xvii ,rough sphere falling #adj cm4 into water4 ,scale #b_/c4 #a #j4jjf sec4 #b #j4jjh sec4 #c #j4jae sec4 #d #j4jba sec4 #e #j4jch sec4 ,the segmentation of the air column appears to be independent of the jet2 but some photographs1 such as ,fig4 #g1 show the jet striking the side and breaking into the surrounding liquid with a great accompaniment of air-dust4 ,illustration3 ,,series ,,xvii--7continued7 #f #j4jdc sec4 #g #j4jeb sec4 ,n4,b4--,each of these figures is made up from two photographs2 one of the upper and one of the lower portion taken from different splashes1 but with the same timing4 ,the reader will observe that after division of the air-tube has taken place1 say from ,fig4 #i onwards1 the water entering the jet at the top and coming out again at the bottom must circulate as in a vortex ring1 part of the core of which is filled with the air surrounding the jet4 ,it is also to be observed that after the establishment of the jet1 there is a steady increase in the size of the heap above the surface2 but it is not easy in any given photograph to say how much of this protuberance is air and how much is water4 ,an examination of ,figs4 #g1 #h1 and #i shows that the place of origin of the jet is gradually lifted above the level of the free surface4 ,that the jet we now see should be directed downwards rather than upwards may1 ,i think1 be explained in a general way as follows3--,the great initial momentum of the sphere causes it to continue in rapid motion after the bubble has closed1 thus the sphere acts as a sort of piston1 which by increasing the length of the air-tube diminishes the pressure in it and so sucks in the bubble1 which is driven down by the greater atmospheric pressure above4 ,the converging horizontal inflow near the mouth of the air-tube cannot1 of course1 produce the downward-directed jet without an equal and opposite generation of momentum upwards2 but this is now expended1 not in producing a similar upward jet1 but in balancing the excess of atmospheric pressure4 ,the reaction1 in fact1 to the projection of the jet downwards1 is the force which holds up and slowly raises the roof of the long air-shaft4 ,illustration3 ,,series ,,xvii--7continued7 #h #j4jeg sec4 #i #j4jfc sec4 #aj #j4jgc sec4 #aa #j4jhi sec4 ,when1 as in the last figure of ,series ,,vi1 p4 #he1 we saw the upward-directed jet1 then also there must have been an equal and opposite generation of downward momentum distributed in some way through the liquid below the basin1 of which1 however1 there could be no visible sign4 ,hence we see that the present downward jet is1 in a sense1 not a new phenomenon1 but one which1 having existed unnoticed before1 is now rendered visible to us by reason of its being produced in air instead of in water4 ,by means of a hole bored through the ceiling of the dark room1 the fall was then increased to #bha centim4 7just over #i feet74 ,the very beautiful earlier stages of the splash at this height are shown in ,series ,,xviii4 ,fig4 #d shows very well the internal splashing at the top of the air-column which accompanies the initiation of the jet4 ,some later photographs taken at this height 7not yet quite presentable7 show the jet passing right down the narrow neck of air-tube and probably striking the top of the sphere1 the descent of which must thus be liable to a curious irregularity4 ,a further increase of the height of fall to #fhf centim4 7#bb-a_/b feet7 was found to produce but little change in the phenomena4 ,illustration3 ,,series ,,xviii ,early stages of the splash of a rough sphere 7diam4 #a4e centim47 falling #bha centim4 7about #i feet7 into water4 #a ,t #j #b #j4jjc sec4 #c #j4jje sec4 #d ,,footnotes3 ,k ,i can recommend any reader who is not afraid of being late for breakfast to keep a bag of marbles in his bath-room4 ,,printed ,,by ,,william ,,brendon ,,and ,,son1 ,,ltd ,,plymouth ,transcriber's ,note3 ,the following changes have been made to the original text4 ,page #aj3 the same in #a1 #c and #d changed to the same in #a1 #b and #d ,page #ff3 4#jd of a gram changed to #j4d of a gram ,page #gg3 ,added full stop to image caption #i #j4jdb sec4